Documentation of 'org.netlib.blas.BLAS' Java class
BLAS
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org.netlib.blas

Class BLAS


  • public abstract class BLAS
extends java.lang.Object
    BLAS provider which will attempt to access a native implementation and falling back to use F2J if none is available.
    See Also:
    http://sourceforge.net/projects/f2j, http://www.netlib.org/blas/

    • Constructor Summary

      Constructors 
      Constructor and Description
      BLAS() 

    • Method Summary

      All Methods Static Methods Instance Methods Abstract Methods Concrete Methods 
      Modifier and Type Method and Description
      abstract double dasum(int n, double[] dx, int incx)
      ..
      abstract void daxpy(int n, double da, double[] dx, int incx, double[] dy, int incy)
      ..
      abstract void dcopy(int n, double[] dx, int incx, double[] dy, int incy)
      ..
      abstract double ddot(int n, double[] dx, int incx, double[] dy, int incy)
      ..
      abstract void dgbmv(java.lang.String trans, int m, int n, int kl, int ku, double alpha, double[] a, int lda, double[] x, int incx, double beta, double[] y, int incy)
      ..
      abstract void dgemm(java.lang.String transa, java.lang.String transb, int m, int n, int k, double alpha, double[] a, int lda, double[] b, int ldb, double beta, double[] c, int Ldc)
      ..
      abstract void dgemv(java.lang.String trans, int m, int n, double alpha, double[] a, int lda, double[] x, int incx, double beta, double[] y, int incy)
      ..
      abstract void dger(int m, int n, double alpha, double[] x, int incx, double[] y, int incy, double[] a, int lda)
      ..
      abstract double dnrm2(int n, double[] x, int incx)
      ..
      abstract void drot(int n, double[] dx, int incx, double[] dy, int incy, double c, double s)
      ..
      abstract void drotg(org.netlib.util.doubleW da, org.netlib.util.doubleW db, org.netlib.util.doubleW c, org.netlib.util.doubleW s)
      ..
      abstract void drotm(int n, double[] dx, int incx, double[] dy, int incy, double[] dparam)
      ..
      abstract void drotmg(org.netlib.util.doubleW dd1, org.netlib.util.doubleW dd2, org.netlib.util.doubleW dx1, double dy1, double[] dparam)
      ..
      abstract void dsbmv(java.lang.String uplo, int n, int k, double alpha, double[] a, int lda, double[] x, int incx, double beta, double[] y, int incy)
      ..
      abstract void dscal(int n, double da, double[] dx, int incx)
      ..
      abstract void dspmv(java.lang.String uplo, int n, double alpha, double[] ap, double[] x, int incx, double beta, double[] y, int incy)
      ..
      abstract void dspr(java.lang.String uplo, int n, double alpha, double[] x, int incx, double[] ap)
      ..
      abstract void dspr2(java.lang.String uplo, int n, double alpha, double[] x, int incx, double[] y, int incy, double[] ap)
      ..
      abstract void dswap(int n, double[] dx, int incx, double[] dy, int incy)
      ..
      abstract void dsymm(java.lang.String side, java.lang.String uplo, int m, int n, double alpha, double[] a, int lda, double[] b, int ldb, double beta, double[] c, int Ldc)
      ..
      abstract void dsymv(java.lang.String uplo, int n, double alpha, double[] a, int lda, double[] x, int incx, double beta, double[] y, int incy)
      ..
      abstract void dsyr(java.lang.String uplo, int n, double alpha, double[] x, int incx, double[] a, int lda)
      ..
      abstract void dsyr2(java.lang.String uplo, int n, double alpha, double[] x, int incx, double[] y, int incy, double[] a, int lda)
      ..
      abstract void dsyr2k(java.lang.String uplo, java.lang.String trans, int n, int k, double alpha, double[] a, int lda, double[] b, int ldb, double beta, double[] c, int Ldc)
      ..
      abstract void dsyrk(java.lang.String uplo, java.lang.String trans, int n, int k, double alpha, double[] a, int lda, double beta, double[] c, int Ldc)
      ..
      abstract void dtbmv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, int k, double[] a, int lda, double[] x, int incx)
      ..
      abstract void dtbsv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, int k, double[] a, int lda, double[] x, int incx)
      ..
      abstract void dtpmv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, double[] ap, double[] x, int incx)
      ..
      abstract void dtpsv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, double[] ap, double[] x, int incx)
      ..
      abstract void dtrmm(java.lang.String side, java.lang.String uplo, java.lang.String transa, java.lang.String diag, int m, int n, double alpha, double[] a, int lda, double[] b, int ldb)
      ..
      abstract void dtrmv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, double[] a, int lda, double[] x, int incx)
      ..
      abstract void dtrsm(java.lang.String side, java.lang.String uplo, java.lang.String transa, java.lang.String diag, int m, int n, double alpha, double[] a, int lda, double[] b, int ldb)
      ..
      abstract void dtrsv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, double[] a, int lda, double[] x, int incx)
      ..
      static BLAS getInstance() 
      abstract int idamax(int n, double[] dx, int incx)
      ..
      abstract int isamax(int n, float[] sx, int incx)
      ..
      boolean lsame(java.lang.String ca, java.lang.String cb)
      ..
      abstract float sasum(int n, float[] sx, int incx)
      ..
      abstract void saxpy(int n, float sa, float[] sx, int incx, float[] sy, int incy)
      ..
      abstract void scopy(int n, float[] sx, int incx, float[] sy, int incy)
      ..
      abstract float sdot(int n, float[] sx, int incx, float[] sy, int incy)
      ..
      abstract float sdsdot(int n, float sb, float[] sx, int incx, float[] sy, int incy)
      ..
      abstract void sgbmv(java.lang.String trans, int m, int n, int kl, int ku, float alpha, float[] a, int lda, float[] x, int incx, float beta, float[] y, int incy)
      ..
      abstract void sgemm(java.lang.String transa, java.lang.String transb, int m, int n, int k, float alpha, float[] a, int lda, float[] b, int ldb, float beta, float[] c, int Ldc)
      ..
      abstract void sgemv(java.lang.String trans, int m, int n, float alpha, float[] a, int lda, float[] x, int incx, float beta, float[] y, int incy)
      ..
      abstract void sger(int m, int n, float alpha, float[] x, int incx, float[] y, int incy, float[] a, int lda)
      ..
      abstract float snrm2(int n, float[] x, int incx)
      ..
      abstract void srot(int n, float[] sx, int incx, float[] sy, int incy, float c, float s)
      ..
      abstract void srotg(org.netlib.util.floatW sa, org.netlib.util.floatW sb, org.netlib.util.floatW c, org.netlib.util.floatW s)
      ..
      abstract void srotm(int n, float[] sx, int incx, float[] sy, int incy, float[] sparam)
      ..
      abstract void srotmg(org.netlib.util.floatW sd1, org.netlib.util.floatW sd2, org.netlib.util.floatW sx1, float sy1, float[] sparam)
      ..
      abstract void ssbmv(java.lang.String uplo, int n, int k, float alpha, float[] a, int lda, float[] x, int incx, float beta, float[] y, int incy)
      ..
      abstract void sscal(int n, float sa, float[] sx, int incx)
      ..
      abstract void sspmv(java.lang.String uplo, int n, float alpha, float[] ap, float[] x, int incx, float beta, float[] y, int incy)
      ..
      abstract void sspr(java.lang.String uplo, int n, float alpha, float[] x, int incx, float[] ap)
      ..
      abstract void sspr2(java.lang.String uplo, int n, float alpha, float[] x, int incx, float[] y, int incy, float[] ap)
      ..
      abstract void sswap(int n, float[] sx, int incx, float[] sy, int incy)
      ..
      abstract void ssymm(java.lang.String side, java.lang.String uplo, int m, int n, float alpha, float[] a, int lda, float[] b, int ldb, float beta, float[] c, int Ldc)
      ..
      abstract void ssymv(java.lang.String uplo, int n, float alpha, float[] a, int lda, float[] x, int incx, float beta, float[] y, int incy)
      ..
      abstract void ssyr(java.lang.String uplo, int n, float alpha, float[] x, int incx, float[] a, int lda)
      ..
      abstract void ssyr2(java.lang.String uplo, int n, float alpha, float[] x, int incx, float[] y, int incy, float[] a, int lda)
      ..
      abstract void ssyr2k(java.lang.String uplo, java.lang.String trans, int n, int k, float alpha, float[] a, int lda, float[] b, int ldb, float beta, float[] c, int Ldc)
      ..
      abstract void ssyrk(java.lang.String uplo, java.lang.String trans, int n, int k, float alpha, float[] a, int lda, float beta, float[] c, int Ldc)
      ..
      abstract void stbmv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, int k, float[] a, int lda, float[] x, int incx)
      ..
      abstract void stbsv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, int k, float[] a, int lda, float[] x, int incx)
      ..
      abstract void stpmv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, float[] ap, float[] x, int incx)
      ..
      abstract void stpsv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, float[] ap, float[] x, int incx)
      ..
      abstract void strmm(java.lang.String side, java.lang.String uplo, java.lang.String transa, java.lang.String diag, int m, int n, float alpha, float[] a, int lda, float[] b, int ldb)
      ..
      abstract void strmv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, float[] a, int lda, float[] x, int incx)
      ..
      abstract void strsm(java.lang.String side, java.lang.String uplo, java.lang.String transa, java.lang.String diag, int m, int n, float alpha, float[] a, int lda, float[] b, int ldb)
      ..
      abstract void strsv(java.lang.String uplo, java.lang.String trans, java.lang.String diag, int n, float[] a, int lda, float[] x, int incx)
      ..

      • Methods inherited from class java.lang.Object

        equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Constructor Detail

      • BLAS

        public BLAS()

    • Method Detail

      • getInstance

        public static BLAS getInstance()

      • dasum

        public abstract double dasum(int n,
                             double[] dx,
                             int incx)
        
     ..

  Purpose
  =======

     takes the sum of the absolute values.
     jack dongarra, linpack, 3/11/78.
     modified 3/93 to return if incx .le. 0.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        dx -
        incx -

      • daxpy

        public abstract void daxpy(int n,
                           double da,
                           double[] dx,
                           int incx,
                           double[] dy,
                           int incy)
        
     ..

  Purpose
  =======

     constant times a vector plus a vector.
     uses unrolled loops for increments equal to one.
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        da -
        dx -
        incx -
        dy -
        incy -

      • dcopy

        public abstract void dcopy(int n,
                           double[] dx,
                           int incx,
                           double[] dy,
                           int incy)
        
     ..

  Purpose
  =======

     copies a vector, x, to a vector, y.
     uses unrolled loops for increments equal to one.
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        dx -
        incx -
        dy -
        incy -

      • ddot

        public abstract double ddot(int n,
                            double[] dx,
                            int incx,
                            double[] dy,
                            int incy)
        
     ..

  Purpose
  =======

     forms the dot product of two vectors.
     uses unrolled loops for increments equal to one.
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        dx -
        incx -
        dy -
        incy -

      • dgbmv

        public abstract void dgbmv(java.lang.String trans,
                           int m,
                           int n,
                           int kl,
                           int ku,
                           double alpha,
                           double[] a,
                           int lda,
                           double[] x,
                           int incx,
                           double beta,
                           double[] y,
                           int incy)
        
     ..

  Purpose
  =======

  DGBMV  performs one of the matrix-vector operations

     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,

  where alpha and beta are scalars, x and y are vectors and A is an
  m by n band matrix, with kl sub-diagonals and ku super-diagonals.

  Arguments
  ==========

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.

              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.

              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.

           Unchanged on exit.

  M      - INTEGER.
           On entry, M specifies the number of rows of the matrix A.
           M must be at least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  KL     - INTEGER.
           On entry, KL specifies the number of sub-diagonals of the
           matrix A. KL must satisfy  0 .le. KL.
           Unchanged on exit.

  KU     - INTEGER.
           On entry, KU specifies the number of super-diagonals of the

           matrix A. KU must satisfy  0 .le. KU.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
           Before entry, the leading ( kl + ku + 1 ) by n part of the
           array A must contain the matrix of coefficients, supplied
           column by column, with the leading diagonal of the matrix in
           row ( ku + 1 ) of the array, the first super-diagonal
           starting at position 2 in row ku, the first sub-diagonal
           starting at position 1 in row ( ku + 2 ), and so on.
           Elements in the array A that do not correspond to elements
           in the band matrix (such as the top left ku by ku triangle)

           are not referenced.
           The following program segment will transfer a band matrix
           from conventional full matrix storage to band storage:

                 DO 20, J = 1, N
                    K = KU + 1 - J
                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
                       A( K + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           ( kl + ku + 1 ).
           Unchanged on exit.

  X      - DOUBLE PRECISION array of DIMENSION at least
           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
           Before entry, the incremented array X must contain the
           vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  BETA   - DOUBLE PRECISION.
           On entry, BETA specifies the scalar beta. When BETA is
           supplied as zero then Y need not be set on input.
           Unchanged on exit.

  Y      - DOUBLE PRECISION array of DIMENSION at least
           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
           Before entry, the incremented array Y must contain the
           vector y. On exit, Y is overwritten by the updated vector y.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.

     .. Parameters ..
        Parameters:
        trans -
        m -
        n -
        kl -
        ku -
        alpha -
        a -
        lda -
        x -
        incx -
        beta -
        y -
        incy -

      • dgemm

        public abstract void dgemm(java.lang.String transa,
                           java.lang.String transb,
                           int m,
                           int n,
                           int k,
                           double alpha,
                           double[] a,
                           int lda,
                           double[] b,
                           int ldb,
                           double beta,
                           double[] c,
                           int Ldc)
        
     ..

  Purpose
  =======

  DGEMM  performs one of the matrix-matrix operations

     C := alpha*op( A )*op( B ) + beta*C,

  where  op( X ) is one of

     op( X ) = X   or   op( X ) = X',

  alpha and beta are scalars, and A, B and C are matrices, with op( A )
  an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.

  Arguments
  ==========

  TRANSA - CHARACTER*1.
           On entry, TRANSA specifies the form of op( A ) to be used in
           the matrix multiplication as follows:

              TRANSA = 'N' or 'n',  op( A ) = A.

              TRANSA = 'T' or 't',  op( A ) = A'.

              TRANSA = 'C' or 'c',  op( A ) = A'.

           Unchanged on exit.

  TRANSB - CHARACTER*1.
           On entry, TRANSB specifies the form of op( B ) to be used in
           the matrix multiplication as follows:

              TRANSB = 'N' or 'n',  op( B ) = B.

              TRANSB = 'T' or 't',  op( B ) = B'.

              TRANSB = 'C' or 'c',  op( B ) = B'.

           Unchanged on exit.

  M      - INTEGER.
           On entry,  M  specifies  the number  of rows  of the  matrix
           op( A )  and of the  matrix  C.  M  must  be at least  zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry,  N  specifies the number  of columns of the matrix
           op( B ) and the number of columns of the matrix C. N must be
           at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry,  K  specifies  the number of columns of the matrix
           op( A ) and the number of rows of the matrix op( B ). K must
           be at least  zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
           part of the array  A  must contain the matrix  A,  otherwise
           the leading  k by m  part of the array  A  must contain  the
           matrix A.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
           LDA must be at least  max( 1, m ), otherwise  LDA must be at
           least  max( 1, k ).
           Unchanged on exit.

  B      - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
           part of the array  B  must contain the matrix  B,  otherwise
           the leading  n by k  part of the array  B  must contain  the
           matrix B.
           Unchanged on exit.

  LDB    - INTEGER.
           On entry, LDB specifies the first dimension of B as declared
           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
           LDB must be at least  max( 1, k ), otherwise  LDB must be at
           least  max( 1, n ).
           Unchanged on exit.

  BETA   - DOUBLE PRECISION.
           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
           supplied as zero then C need not be set on input.
           Unchanged on exit.

  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
           Before entry, the leading  m by n  part of the array  C must
           contain the matrix  C,  except when  beta  is zero, in which
           case C need not be set on entry.
           On exit, the array  C  is overwritten by the  m by n  matrix
           ( alpha*op( A )*op( B ) + beta*C ).

  LDC    - INTEGER.
           On entry, LDC specifies the first dimension of C as declared
           in  the  calling  (sub)  program.   LDC  must  be  at  least
           max( 1, m ).
           Unchanged on exit.


  Level 3 Blas routine.

  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        transa -
        transb -
        m -
        n -
        k -
        alpha -
        a -
        lda -
        b -
        ldb -
        beta -
        c -
        Ldc -

      • dgemv

        public abstract void dgemv(java.lang.String trans,
                           int m,
                           int n,
                           double alpha,
                           double[] a,
                           int lda,
                           double[] x,
                           int incx,
                           double beta,
                           double[] y,
                           int incy)
        
     ..

  Purpose
  =======

  DGEMV  performs one of the matrix-vector operations

     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,

  where alpha and beta are scalars, x and y are vectors and A is an
  m by n matrix.

  Arguments
  ==========

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.

              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.

              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.

           Unchanged on exit.

  M      - INTEGER.
           On entry, M specifies the number of rows of the matrix A.
           M must be at least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
           Before entry, the leading m by n part of the array A must
           contain the matrix of coefficients.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, m ).
           Unchanged on exit.

  X      - DOUBLE PRECISION array of DIMENSION at least
           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
           Before entry, the incremented array X must contain the
           vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  BETA   - DOUBLE PRECISION.
           On entry, BETA specifies the scalar beta. When BETA is
           supplied as zero then Y need not be set on input.
           Unchanged on exit.

  Y      - DOUBLE PRECISION array of DIMENSION at least
           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
           Before entry with BETA non-zero, the incremented array Y
           must contain the vector y. On exit, Y is overwritten by the

           updated vector y.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        trans -
        m -
        n -
        alpha -
        a -
        lda -
        x -
        incx -
        beta -
        y -
        incy -

      • dger

        public abstract void dger(int m,
                          int n,
                          double alpha,
                          double[] x,
                          int incx,
                          double[] y,
                          int incy,
                          double[] a,
                          int lda)
        
     ..

  Purpose
  =======

  DGER   performs the rank 1 operation

     A := alpha*x*y' + A,

  where alpha is a scalar, x is an m element vector, y is an n element

  vector and A is an m by n matrix.

  Arguments
  ==========

  M      - INTEGER.
           On entry, M specifies the number of rows of the matrix A.
           M must be at least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( m - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the m
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  Y      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the n
           element vector y.
           Unchanged on exit.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
           Before entry, the leading m by n part of the array A must
           contain the matrix of coefficients. On exit, A is
           overwritten by the updated matrix.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, m ).
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        m -
        n -
        alpha -
        x -
        incx -
        y -
        incy -
        a -
        lda -

      • dnrm2

        public abstract double dnrm2(int n,
                             double[] x,
                             int incx)
        
     ..

  Purpose
  =======

  DNRM2 returns the euclidean norm of a vector via the function
  name, so that

     DNRM2 := sqrt( x'*x )


  -- This version written on 25-October-1982.
     Modified on 14-October-1993 to inline the call to DLASSQ.
     Sven Hammarling, Nag Ltd.


     .. Parameters ..
        Parameters:
        n -
        x -
        incx -

      • drot

        public abstract void drot(int n,
                          double[] dx,
                          int incx,
                          double[] dy,
                          int incy,
                          double c,
                          double s)
        
     ..

  Purpose
  =======

     applies a plane rotation.
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        dx -
        incx -
        dy -
        incy -
        c -
        s -

      • drotg

        public abstract void drotg(org.netlib.util.doubleW da,
                           org.netlib.util.doubleW db,
                           org.netlib.util.doubleW c,
                           org.netlib.util.doubleW s)
        
     ..

  Purpose
  =======

     construct givens plane rotation.
     jack dongarra, linpack, 3/11/78.


     .. Local Scalars ..
        Parameters:
        da -
        db -
        c -
        s -

      • drotm

        public abstract void drotm(int n,
                           double[] dx,
                           int incx,
                           double[] dy,
                           int incy,
                           double[] dparam)
        
     ..

  Purpose
  =======

     APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX


     (DX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN
     (DY**T)

     DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE
     LX = (-INCX)*N, AND SIMILARLY FOR SY USING LY AND INCY.
     WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS..

     DFLAG=-1.D0     DFLAG=0.D0        DFLAG=1.D0     DFLAG=-2.D0

       (DH11  DH12)    (1.D0  DH12)    (DH11  1.D0)    (1.D0  0.D0)
     H=(          )    (          )    (          )    (          )
       (DH21  DH22),   (DH21  1.D0),   (-1.D0 DH22),   (0.D0  1.D0).
     SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM.

  Arguments
  =========

  N      (input) INTEGER
         number of elements in input vector(s)

  DX     (input/output) DOUBLE PRECISION array, dimension N
         double precision vector with 5 elements

  INCX   (input) INTEGER
         storage spacing between elements of DX

  DY     (input/output) DOUBLE PRECISION array, dimension N
         double precision vector with N elements

  INCY   (input) INTEGER
         storage spacing between elements of DY

  DPARAM (input/output)  DOUBLE PRECISION array, dimension 5 
     DPARAM(1)=DFLAG
     DPARAM(2)=DH11
     DPARAM(3)=DH21
     DPARAM(4)=DH12
     DPARAM(5)=DH22

  =====================================================================

     .. Local Scalars ..
        Parameters:
        n -
        dx -
        incx -
        dy -
        incy -
        dparam -

      • drotmg

        public abstract void drotmg(org.netlib.util.doubleW dd1,
                            org.netlib.util.doubleW dd2,
                            org.netlib.util.doubleW dx1,
                            double dy1,
                            double[] dparam)
        
     ..

  Purpose
  =======

     CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS

     THE SECOND COMPONENT OF THE 2-VECTOR  (DSQRT(DD1)*DX1,DSQRT(DD2)*

     DY2)**T.
     WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS..

     DFLAG=-1.D0     DFLAG=0.D0        DFLAG=1.D0     DFLAG=-2.D0

       (DH11  DH12)    (1.D0  DH12)    (DH11  1.D0)    (1.D0  0.D0)
     H=(          )    (          )    (          )    (          )
       (DH21  DH22),   (DH21  1.D0),   (-1.D0 DH22),   (0.D0  1.D0).
     LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22
     RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE
     VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.)

     THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE
     INEXACT.  THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE
     OF DD1 AND DD2.  ALL ACTUAL SCALING OF DATA IS DONE USING GAM.


  Arguments
  =========

  DD1    (input/output) DOUBLE PRECISION

  DD2    (input/output) DOUBLE PRECISION 

  DX1    (input/output) DOUBLE PRECISION 

  DY1    (input) DOUBLE PRECISION

  DPARAM (input/output)  DOUBLE PRECISION array, dimension 5
     DPARAM(1)=DFLAG
     DPARAM(2)=DH11
     DPARAM(3)=DH21
     DPARAM(4)=DH12
     DPARAM(5)=DH22

  =====================================================================

     .. Local Scalars ..
        Parameters:
        dd1 -
        dd2 -
        dx1 -
        dy1 -
        dparam -

      • dsbmv

        public abstract void dsbmv(java.lang.String uplo,
                           int n,
                           int k,
                           double alpha,
                           double[] a,
                           int lda,
                           double[] x,
                           int incx,
                           double beta,
                           double[] y,
                           int incy)
        
     ..

  Purpose
  =======

  DSBMV  performs the matrix-vector  operation

     y := alpha*A*x + beta*y,

  where alpha and beta are scalars, x and y are n element vectors and
  A is an n by n symmetric band matrix, with k super-diagonals.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the band matrix A is being supplied as
           follows:

              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  being supplied.

              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  being supplied.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry, K specifies the number of super-diagonals of the
           matrix A. K must satisfy  0 .le. K.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
           by n part of the array A must contain the upper triangular
           band part of the symmetric matrix, supplied column by
           column, with the leading diagonal of the matrix in row
           ( k + 1 ) of the array, the first super-diagonal starting at
           position 2 in row k, and so on. The top left k by k triangle
           of the array A is not referenced.
           The following program segment will transfer the upper
           triangular part of a symmetric band matrix from conventional
           full matrix storage to band storage:

                 DO 20, J = 1, N
                    M = K + 1 - J
                    DO 10, I = MAX( 1, J - K ), J
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
           by n part of the array A must contain the lower triangular
           band part of the symmetric matrix, supplied column by
           column, with the leading diagonal of the matrix in row 1 of

           the array, the first sub-diagonal starting at position 1 in

           row 2, and so on. The bottom right k by k triangle of the
           array A is not referenced.
           The following program segment will transfer the lower
           triangular part of a symmetric band matrix from conventional
           full matrix storage to band storage:

                 DO 20, J = 1, N
                    M = 1 - J
                    DO 10, I = J, MIN( N, J + K )
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           ( k + 1 ).
           Unchanged on exit.

  X      - DOUBLE PRECISION array of DIMENSION at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the
           vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  BETA   - DOUBLE PRECISION.
           On entry, BETA specifies the scalar beta.
           Unchanged on exit.

  Y      - DOUBLE PRECISION array of DIMENSION at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the
           vector y. On exit, Y is overwritten by the updated vector y.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        k -
        alpha -
        a -
        lda -
        x -
        incx -
        beta -
        y -
        incy -

      • dscal

        public abstract void dscal(int n,
                           double da,
                           double[] dx,
                           int incx)
        
     ..

  Purpose
  =======

     scales a vector by a constant.
     uses unrolled loops for increment equal to one.
     jack dongarra, linpack, 3/11/78.
     modified 3/93 to return if incx .le. 0.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        da -
        dx -
        incx -

      • dspmv

        public abstract void dspmv(java.lang.String uplo,
                           int n,
                           double alpha,
                           double[] ap,
                           double[] x,
                           int incx,
                           double beta,
                           double[] y,
                           int incy)
        
     ..

  Purpose
  =======

  DSPMV  performs the matrix-vector operation

     y := alpha*A*x + beta*y,

  where alpha and beta are scalars, x and y are n element vectors and
  A is an n by n symmetric matrix, supplied in packed form.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:

              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.

              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  AP     - DOUBLE PRECISION array of DIMENSION at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on.
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  BETA   - DOUBLE PRECISION.
           On entry, BETA specifies the scalar beta. When BETA is
           supplied as zero then Y need not be set on input.
           Unchanged on exit.

  Y      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the n
           element vector y. On exit, Y is overwritten by the updated
           vector y.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        ap -
        x -
        incx -
        beta -
        y -
        incy -

      • dspr

        public abstract void dspr(java.lang.String uplo,
                          int n,
                          double alpha,
                          double[] x,
                          int incx,
                          double[] ap)
        
     ..

  Purpose
  =======

  DSPR    performs the symmetric rank 1 operation

     A := alpha*x*x' + A,

  where alpha is a real scalar, x is an n element vector and A is an
  n by n symmetric matrix, supplied in packed form.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:

              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.

              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  AP     - DOUBLE PRECISION array of DIMENSION at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on. On exit, the array
           AP is overwritten by the upper triangular part of the
           updated matrix.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on. On exit, the array
           AP is overwritten by the lower triangular part of the
           updated matrix.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        x -
        incx -
        ap -

      • dspr2

        public abstract void dspr2(java.lang.String uplo,
                           int n,
                           double alpha,
                           double[] x,
                           int incx,
                           double[] y,
                           int incy,
                           double[] ap)
        
     ..

  Purpose
  =======

  DSPR2  performs the symmetric rank 2 operation

     A := alpha*x*y' + alpha*y*x' + A,

  where alpha is a scalar, x and y are n element vectors and A is an
  n by n symmetric matrix, supplied in packed form.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:

              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.

              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  Y      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the n
           element vector y.
           Unchanged on exit.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.

  AP     - DOUBLE PRECISION array of DIMENSION at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on. On exit, the array
           AP is overwritten by the upper triangular part of the
           updated matrix.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on. On exit, the array
           AP is overwritten by the lower triangular part of the
           updated matrix.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        x -
        incx -
        y -
        incy -
        ap -

      • dswap

        public abstract void dswap(int n,
                           double[] dx,
                           int incx,
                           double[] dy,
                           int incy)
        
     ..

  Purpose
  =======

     interchanges two vectors.
     uses unrolled loops for increments equal one.
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        dx -
        incx -
        dy -
        incy -

      • dsymm

        public abstract void dsymm(java.lang.String side,
                           java.lang.String uplo,
                           int m,
                           int n,
                           double alpha,
                           double[] a,
                           int lda,
                           double[] b,
                           int ldb,
                           double beta,
                           double[] c,
                           int Ldc)
        
     ..

  Purpose
  =======

  DSYMM  performs one of the matrix-matrix operations

     C := alpha*A*B + beta*C,

  or

     C := alpha*B*A + beta*C,

  where alpha and beta are scalars,  A is a symmetric matrix and  B and
  C are  m by n matrices.

  Arguments
  ==========

  SIDE   - CHARACTER*1.
           On entry,  SIDE  specifies whether  the  symmetric matrix  A
           appears on the  left or right  in the  operation as follows:

              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,

              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,

           Unchanged on exit.

  UPLO   - CHARACTER*1.
           On  entry,   UPLO  specifies  whether  the  upper  or  lower
           triangular  part  of  the  symmetric  matrix   A  is  to  be
           referenced as follows:

              UPLO = 'U' or 'u'   Only the upper triangular part of the
                                  symmetric matrix is to be referenced.

              UPLO = 'L' or 'l'   Only the lower triangular part of the
                                  symmetric matrix is to be referenced.

           Unchanged on exit.

  M      - INTEGER.
           On entry,  M  specifies the number of rows of the matrix  C.
           M  must be at least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of the matrix C.
           N  must be at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
           m  when  SIDE = 'L' or 'l'  and is  n otherwise.
           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
           the array  A  must contain the  symmetric matrix,  such that
           when  UPLO = 'U' or 'u', the leading m by m upper triangular
           part of the array  A  must contain the upper triangular part
           of the  symmetric matrix and the  strictly  lower triangular
           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
           the leading  m by m  lower triangular part  of the  array  A
           must  contain  the  lower triangular part  of the  symmetric
           matrix and the  strictly upper triangular part of  A  is not
           referenced.
           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
           the array  A  must contain the  symmetric matrix,  such that
           when  UPLO = 'U' or 'u', the leading n by n upper triangular
           part of the array  A  must contain the upper triangular part
           of the  symmetric matrix and the  strictly  lower triangular
           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
           the leading  n by n  lower triangular part  of the  array  A
           must  contain  the  lower triangular part  of the  symmetric
           matrix and the  strictly upper triangular part of  A  is not
           referenced.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
           LDA must be at least  max( 1, m ), otherwise  LDA must be at
           least  max( 1, n ).
           Unchanged on exit.

  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
           Before entry, the leading  m by n part of the array  B  must
           contain the matrix B.
           Unchanged on exit.

  LDB    - INTEGER.
           On entry, LDB specifies the first dimension of B as declared
           in  the  calling  (sub)  program.   LDB  must  be  at  least
           max( 1, m ).
           Unchanged on exit.

  BETA   - DOUBLE PRECISION.
           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
           supplied as zero then C need not be set on input.
           Unchanged on exit.

  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
           Before entry, the leading  m by n  part of the array  C must
           contain the matrix  C,  except when  beta  is zero, in which
           case C need not be set on entry.
           On exit, the array  C  is overwritten by the  m by n updated
           matrix.

  LDC    - INTEGER.
           On entry, LDC specifies the first dimension of C as declared
           in  the  calling  (sub)  program.   LDC  must  be  at  least
           max( 1, m ).
           Unchanged on exit.


  Level 3 Blas routine.

  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        side -
        uplo -
        m -
        n -
        alpha -
        a -
        lda -
        b -
        ldb -
        beta -
        c -
        Ldc -

      • dsymv

        public abstract void dsymv(java.lang.String uplo,
                           int n,
                           double alpha,
                           double[] a,
                           int lda,
                           double[] x,
                           int incx,
                           double beta,
                           double[] y,
                           int incy)
        
     ..

  Purpose
  =======

  DSYMV  performs the matrix-vector  operation

     y := alpha*A*x + beta*y,

  where alpha and beta are scalars, x and y are n element vectors and
  A is an n by n symmetric matrix.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the array A is to be referenced as
           follows:

              UPLO = 'U' or 'u'   Only the upper triangular part of A
                                  is to be referenced.

              UPLO = 'L' or 'l'   Only the lower triangular part of A
                                  is to be referenced.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
           Before entry with  UPLO = 'U' or 'u', the leading n by n
           upper triangular part of the array A must contain the upper

           triangular part of the symmetric matrix and the strictly
           lower triangular part of A is not referenced.
           Before entry with UPLO = 'L' or 'l', the leading n by n
           lower triangular part of the array A must contain the lower

           triangular part of the symmetric matrix and the strictly
           upper triangular part of A is not referenced.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, n ).
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  BETA   - DOUBLE PRECISION.
           On entry, BETA specifies the scalar beta. When BETA is
           supplied as zero then Y need not be set on input.
           Unchanged on exit.

  Y      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the n
           element vector y. On exit, Y is overwritten by the updated
           vector y.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        a -
        lda -
        x -
        incx -
        beta -
        y -
        incy -

      • dsyr

        public abstract void dsyr(java.lang.String uplo,
                          int n,
                          double alpha,
                          double[] x,
                          int incx,
                          double[] a,
                          int lda)
        
     ..

  Purpose
  =======

  DSYR   performs the symmetric rank 1 operation

     A := alpha*x*x' + A,

  where alpha is a real scalar, x is an n element vector and A is an
  n by n symmetric matrix.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the array A is to be referenced as
           follows:

              UPLO = 'U' or 'u'   Only the upper triangular part of A
                                  is to be referenced.

              UPLO = 'L' or 'l'   Only the lower triangular part of A
                                  is to be referenced.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
           Before entry with  UPLO = 'U' or 'u', the leading n by n
           upper triangular part of the array A must contain the upper

           triangular part of the symmetric matrix and the strictly
           lower triangular part of A is not referenced. On exit, the
           upper triangular part of the array A is overwritten by the
           upper triangular part of the updated matrix.
           Before entry with UPLO = 'L' or 'l', the leading n by n
           lower triangular part of the array A must contain the lower

           triangular part of the symmetric matrix and the strictly
           upper triangular part of A is not referenced. On exit, the
           lower triangular part of the array A is overwritten by the
           lower triangular part of the updated matrix.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, n ).
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        x -
        incx -
        a -
        lda -

      • dsyr2

        public abstract void dsyr2(java.lang.String uplo,
                           int n,
                           double alpha,
                           double[] x,
                           int incx,
                           double[] y,
                           int incy,
                           double[] a,
                           int lda)
        
     ..

  Purpose
  =======

  DSYR2  performs the symmetric rank 2 operation

     A := alpha*x*y' + alpha*y*x' + A,

  where alpha is a scalar, x and y are n element vectors and A is an n

  by n symmetric matrix.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the array A is to be referenced as
           follows:

              UPLO = 'U' or 'u'   Only the upper triangular part of A
                                  is to be referenced.

              UPLO = 'L' or 'l'   Only the lower triangular part of A
                                  is to be referenced.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  Y      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the n
           element vector y.
           Unchanged on exit.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
           Before entry with  UPLO = 'U' or 'u', the leading n by n
           upper triangular part of the array A must contain the upper

           triangular part of the symmetric matrix and the strictly
           lower triangular part of A is not referenced. On exit, the
           upper triangular part of the array A is overwritten by the
           upper triangular part of the updated matrix.
           Before entry with UPLO = 'L' or 'l', the leading n by n
           lower triangular part of the array A must contain the lower

           triangular part of the symmetric matrix and the strictly
           upper triangular part of A is not referenced. On exit, the
           lower triangular part of the array A is overwritten by the
           lower triangular part of the updated matrix.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, n ).
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        x -
        incx -
        y -
        incy -
        a -
        lda -

      • dsyr2k

        public abstract void dsyr2k(java.lang.String uplo,
                            java.lang.String trans,
                            int n,
                            int k,
                            double alpha,
                            double[] a,
                            int lda,
                            double[] b,
                            int ldb,
                            double beta,
                            double[] c,
                            int Ldc)
        
     ..

  Purpose
  =======

  DSYR2K  performs one of the symmetric rank 2k operations

     C := alpha*A*B' + alpha*B*A' + beta*C,

  or

     C := alpha*A'*B + alpha*B'*A + beta*C,

  where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
  and  A and B  are  n by k  matrices  in the  first  case  and  k by n
  matrices in the second case.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On  entry,   UPLO  specifies  whether  the  upper  or  lower
           triangular  part  of the  array  C  is to be  referenced  as
           follows:

              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                  is to be referenced.

              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                  is to be referenced.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry,  TRANS  specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   C := alpha*A*B' + alpha*B*A' +
                                        beta*C.

              TRANS = 'T' or 't'   C := alpha*A'*B + alpha*B'*A +
                                        beta*C.

              TRANS = 'C' or 'c'   C := alpha*A'*B + alpha*B'*A +
                                        beta*C.

           Unchanged on exit.

  N      - INTEGER.
           On entry,  N specifies the order of the matrix C.  N must be
           at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
           of  columns  of the  matrices  A and B,  and on  entry  with
           TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
           of rows of the matrices  A and B.  K must be at least  zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
           part of the array  A  must contain the matrix  A,  otherwise
           the leading  k by n  part of the array  A  must contain  the
           matrix A.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
           then  LDA must be at least  max( 1, n ), otherwise  LDA must
           be at least  max( 1, k ).
           Unchanged on exit.

  B      - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
           part of the array  B  must contain the matrix  B,  otherwise
           the leading  k by n  part of the array  B  must contain  the
           matrix B.
           Unchanged on exit.

  LDB    - INTEGER.
           On entry, LDB specifies the first dimension of B as declared
           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
           then  LDB must be at least  max( 1, n ), otherwise  LDB must
           be at least  max( 1, k ).
           Unchanged on exit.

  BETA   - DOUBLE PRECISION.
           On entry, BETA specifies the scalar beta.
           Unchanged on exit.

  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n

           upper triangular part of the array C must contain the upper

           triangular part  of the  symmetric matrix  and the strictly

           lower triangular part of C is not referenced.  On exit, the

           upper triangular part of the array  C is overwritten by the

           upper triangular part of the updated matrix.
           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n

           lower triangular part of the array C must contain the lower

           triangular part  of the  symmetric matrix  and the strictly

           upper triangular part of C is not referenced.  On exit, the

           lower triangular part of the array  C is overwritten by the

           lower triangular part of the updated matrix.

  LDC    - INTEGER.
           On entry, LDC specifies the first dimension of C as declared
           in  the  calling  (sub)  program.   LDC  must  be  at  least
           max( 1, n ).
           Unchanged on exit.


  Level 3 Blas routine.


  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        uplo -
        trans -
        n -
        k -
        alpha -
        a -
        lda -
        b -
        ldb -
        beta -
        c -
        Ldc -

      • dsyrk

        public abstract void dsyrk(java.lang.String uplo,
                           java.lang.String trans,
                           int n,
                           int k,
                           double alpha,
                           double[] a,
                           int lda,
                           double beta,
                           double[] c,
                           int Ldc)
        
     ..

  Purpose
  =======

  DSYRK  performs one of the symmetric rank k operations

     C := alpha*A*A' + beta*C,

  or

     C := alpha*A'*A + beta*C,

  where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
  and  A  is an  n by k  matrix in the first case and a  k by n  matrix
  in the second case.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On  entry,   UPLO  specifies  whether  the  upper  or  lower
           triangular  part  of the  array  C  is to be  referenced  as
           follows:

              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                  is to be referenced.

              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                  is to be referenced.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry,  TRANS  specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   C := alpha*A*A' + beta*C.

              TRANS = 'T' or 't'   C := alpha*A'*A + beta*C.

              TRANS = 'C' or 'c'   C := alpha*A'*A + beta*C.

           Unchanged on exit.

  N      - INTEGER.
           On entry,  N specifies the order of the matrix C.  N must be
           at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
           of  columns   of  the   matrix   A,   and  on   entry   with
           TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
           of rows of the matrix  A.  K must be at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
           part of the array  A  must contain the matrix  A,  otherwise
           the leading  k by n  part of the array  A  must contain  the
           matrix A.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
           then  LDA must be at least  max( 1, n ), otherwise  LDA must
           be at least  max( 1, k ).
           Unchanged on exit.

  BETA   - DOUBLE PRECISION.
           On entry, BETA specifies the scalar beta.
           Unchanged on exit.

  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n

           upper triangular part of the array C must contain the upper

           triangular part  of the  symmetric matrix  and the strictly

           lower triangular part of C is not referenced.  On exit, the

           upper triangular part of the array  C is overwritten by the

           upper triangular part of the updated matrix.
           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n

           lower triangular part of the array C must contain the lower

           triangular part  of the  symmetric matrix  and the strictly

           upper triangular part of C is not referenced.  On exit, the

           lower triangular part of the array  C is overwritten by the

           lower triangular part of the updated matrix.

  LDC    - INTEGER.
           On entry, LDC specifies the first dimension of C as declared
           in  the  calling  (sub)  program.   LDC  must  be  at  least
           max( 1, n ).
           Unchanged on exit.


  Level 3 Blas routine.

  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        uplo -
        trans -
        n -
        k -
        alpha -
        a -
        lda -
        beta -
        c -
        Ldc -

      • dtbmv

        public abstract void dtbmv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           int k,
                           double[] a,
                           int lda,
                           double[] x,
                           int incx)
        
     ..

  Purpose
  =======

  DTBMV  performs one of the matrix-vector operations

     x := A*x,   or   x := A'*x,

  where x is an n element vector and  A is an n by n unit, or non-unit,
  upper or lower triangular band matrix, with ( k + 1 ) diagonals.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   x := A*x.

              TRANS = 'T' or 't'   x := A'*x.

              TRANS = 'C' or 'c'   x := A'*x.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry with UPLO = 'U' or 'u', K specifies the number of
           super-diagonals of the matrix A.
           On entry with UPLO = 'L' or 'l', K specifies the number of
           sub-diagonals of the matrix A.
           K must satisfy  0 .le. K.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
           by n part of the array A must contain the upper triangular
           band part of the matrix of coefficients, supplied column by

           column, with the leading diagonal of the matrix in row
           ( k + 1 ) of the array, the first super-diagonal starting at
           position 2 in row k, and so on. The top left k by k triangle
           of the array A is not referenced.
           The following program segment will transfer an upper
           triangular band matrix from conventional full matrix storage
           to band storage:

                 DO 20, J = 1, N
                    M = K + 1 - J
                    DO 10, I = MAX( 1, J - K ), J
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
           by n part of the array A must contain the lower triangular
           band part of the matrix of coefficients, supplied column by

           column, with the leading diagonal of the matrix in row 1 of

           the array, the first sub-diagonal starting at position 1 in

           row 2, and so on. The bottom right k by k triangle of the
           array A is not referenced.
           The following program segment will transfer a lower
           triangular band matrix from conventional full matrix storage
           to band storage:

                 DO 20, J = 1, N
                    M = 1 - J
                    DO 10, I = J, MIN( N, J + K )
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Note that when DIAG = 'U' or 'u' the elements of the array A
           corresponding to the diagonal elements of the matrix are not
           referenced, but are assumed to be unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           ( k + 1 ).
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x. On exit, X is overwritten with the
           tranformed vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        k -
        a -
        lda -
        x -
        incx -

      • dtbsv

        public abstract void dtbsv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           int k,
                           double[] a,
                           int lda,
                           double[] x,
                           int incx)
        
     ..

  Purpose
  =======

  DTBSV  solves one of the systems of equations

     A*x = b,   or   A'*x = b,

  where b and x are n element vectors and A is an n by n unit, or
  non-unit, upper or lower triangular band matrix, with ( k + 1 )
  diagonals.

  No test for singularity or near-singularity is included in this
  routine. Such tests must be performed before calling this routine.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the equations to be solved as
           follows:

              TRANS = 'N' or 'n'   A*x = b.

              TRANS = 'T' or 't'   A'*x = b.

              TRANS = 'C' or 'c'   A'*x = b.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry with UPLO = 'U' or 'u', K specifies the number of
           super-diagonals of the matrix A.
           On entry with UPLO = 'L' or 'l', K specifies the number of
           sub-diagonals of the matrix A.
           K must satisfy  0 .le. K.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
           by n part of the array A must contain the upper triangular
           band part of the matrix of coefficients, supplied column by

           column, with the leading diagonal of the matrix in row
           ( k + 1 ) of the array, the first super-diagonal starting at
           position 2 in row k, and so on. The top left k by k triangle
           of the array A is not referenced.
           The following program segment will transfer an upper
           triangular band matrix from conventional full matrix storage
           to band storage:

                 DO 20, J = 1, N
                    M = K + 1 - J
                    DO 10, I = MAX( 1, J - K ), J
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
           by n part of the array A must contain the lower triangular
           band part of the matrix of coefficients, supplied column by

           column, with the leading diagonal of the matrix in row 1 of

           the array, the first sub-diagonal starting at position 1 in

           row 2, and so on. The bottom right k by k triangle of the
           array A is not referenced.
           The following program segment will transfer a lower
           triangular band matrix from conventional full matrix storage
           to band storage:

                 DO 20, J = 1, N
                    M = 1 - J
                    DO 10, I = J, MIN( N, J + K )
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Note that when DIAG = 'U' or 'u' the elements of the array A
           corresponding to the diagonal elements of the matrix are not
           referenced, but are assumed to be unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           ( k + 1 ).
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element right-hand side vector b. On exit, X is overwritten

           with the solution vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        k -
        a -
        lda -
        x -
        incx -

      • dtpmv

        public abstract void dtpmv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           double[] ap,
                           double[] x,
                           int incx)
        
     ..

  Purpose
  =======

  DTPMV  performs one of the matrix-vector operations

     x := A*x,   or   x := A'*x,

  where x is an n element vector and  A is an n by n unit, or non-unit,
  upper or lower triangular matrix, supplied in packed form.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   x := A*x.

              TRANS = 'T' or 't'   x := A'*x.

              TRANS = 'C' or 'c'   x := A'*x.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  AP     - DOUBLE PRECISION array of DIMENSION at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular matrix packed sequentially,
           column by column, so that AP( 1 ) contains a( 1, 1 ),
           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
           respectively, and so on.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular matrix packed sequentially,
           column by column, so that AP( 1 ) contains a( 1, 1 ),
           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
           respectively, and so on.
           Note that when  DIAG = 'U' or 'u', the diagonal elements of

           A are not referenced, but are assumed to be unity.
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x. On exit, X is overwritten with the
           tranformed vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        ap -
        x -
        incx -

      • dtpsv

        public abstract void dtpsv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           double[] ap,
                           double[] x,
                           int incx)
        
     ..

  Purpose
  =======

  DTPSV  solves one of the systems of equations

     A*x = b,   or   A'*x = b,

  where b and x are n element vectors and A is an n by n unit, or
  non-unit, upper or lower triangular matrix, supplied in packed form.


  No test for singularity or near-singularity is included in this
  routine. Such tests must be performed before calling this routine.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the equations to be solved as
           follows:

              TRANS = 'N' or 'n'   A*x = b.

              TRANS = 'T' or 't'   A'*x = b.

              TRANS = 'C' or 'c'   A'*x = b.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  AP     - DOUBLE PRECISION array of DIMENSION at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular matrix packed sequentially,
           column by column, so that AP( 1 ) contains a( 1, 1 ),
           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
           respectively, and so on.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular matrix packed sequentially,
           column by column, so that AP( 1 ) contains a( 1, 1 ),
           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
           respectively, and so on.
           Note that when  DIAG = 'U' or 'u', the diagonal elements of

           A are not referenced, but are assumed to be unity.
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element right-hand side vector b. On exit, X is overwritten

           with the solution vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        ap -
        x -
        incx -

      • dtrmm

        public abstract void dtrmm(java.lang.String side,
                           java.lang.String uplo,
                           java.lang.String transa,
                           java.lang.String diag,
                           int m,
                           int n,
                           double alpha,
                           double[] a,
                           int lda,
                           double[] b,
                           int ldb)
        
     ..

  Purpose
  =======

  DTRMM  performs one of the matrix-matrix operations

     B := alpha*op( A )*B,   or   B := alpha*B*op( A ),

  where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

     op( A ) = A   or   op( A ) = A'.

  Arguments
  ==========

  SIDE   - CHARACTER*1.
           On entry,  SIDE specifies whether  op( A ) multiplies B from
           the left or right as follows:

              SIDE = 'L' or 'l'   B := alpha*op( A )*B.

              SIDE = 'R' or 'r'   B := alpha*B*op( A ).

           Unchanged on exit.

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix A is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANSA - CHARACTER*1.
           On entry, TRANSA specifies the form of op( A ) to be used in
           the matrix multiplication as follows:

              TRANSA = 'N' or 'n'   op( A ) = A.

              TRANSA = 'T' or 't'   op( A ) = A'.

              TRANSA = 'C' or 'c'   op( A ) = A'.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit triangular
           as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  M      - INTEGER.
           On entry, M specifies the number of rows of B. M must be at

           least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of B.  N must be
           at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
           zero then  A is not referenced and  B need not be set before
           entry.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
           upper triangular part of the array  A must contain the upper
           triangular matrix  and the strictly lower triangular part of
           A is not referenced.
           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
           lower triangular part of the array  A must contain the lower
           triangular matrix  and the strictly upper triangular part of
           A is not referenced.
           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
           A  are not referenced either,  but are assumed to be  unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
           then LDA must be at least max( 1, n ).
           Unchanged on exit.

  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
           Before entry,  the leading  m by n part of the array  B must
           contain the matrix  B,  and  on exit  is overwritten  by the
           transformed matrix.

  LDB    - INTEGER.
           On entry, LDB specifies the first dimension of B as declared
           in  the  calling  (sub)  program.   LDB  must  be  at  least
           max( 1, m ).
           Unchanged on exit.


  Level 3 Blas routine.

  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        side -
        uplo -
        transa -
        diag -
        m -
        n -
        alpha -
        a -
        lda -
        b -
        ldb -

      • dtrmv

        public abstract void dtrmv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           double[] a,
                           int lda,
                           double[] x,
                           int incx)
        
     ..

  Purpose
  =======

  DTRMV  performs one of the matrix-vector operations

     x := A*x,   or   x := A'*x,

  where x is an n element vector and  A is an n by n unit, or non-unit,
  upper or lower triangular matrix.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   x := A*x.

              TRANS = 'T' or 't'   x := A'*x.

              TRANS = 'C' or 'c'   x := A'*x.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
           Before entry with  UPLO = 'U' or 'u', the leading n by n
           upper triangular part of the array A must contain the upper

           triangular matrix and the strictly lower triangular part of

           A is not referenced.
           Before entry with UPLO = 'L' or 'l', the leading n by n
           lower triangular part of the array A must contain the lower

           triangular matrix and the strictly upper triangular part of

           A is not referenced.
           Note that when  DIAG = 'U' or 'u', the diagonal elements of

           A are not referenced either, but are assumed to be unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, n ).
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x. On exit, X is overwritten with the
           tranformed vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        a -
        lda -
        x -
        incx -

      • dtrsm

        public abstract void dtrsm(java.lang.String side,
                           java.lang.String uplo,
                           java.lang.String transa,
                           java.lang.String diag,
                           int m,
                           int n,
                           double alpha,
                           double[] a,
                           int lda,
                           double[] b,
                           int ldb)
        
     ..

  Purpose
  =======

  DTRSM  solves one of the matrix equations

     op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,

  where alpha is a scalar, X and B are m by n matrices, A is a unit, or
  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

     op( A ) = A   or   op( A ) = A'.

  The matrix X is overwritten on B.

  Arguments
  ==========

  SIDE   - CHARACTER*1.
           On entry, SIDE specifies whether op( A ) appears on the left
           or right of X as follows:

              SIDE = 'L' or 'l'   op( A )*X = alpha*B.

              SIDE = 'R' or 'r'   X*op( A ) = alpha*B.

           Unchanged on exit.

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix A is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANSA - CHARACTER*1.
           On entry, TRANSA specifies the form of op( A ) to be used in
           the matrix multiplication as follows:

              TRANSA = 'N' or 'n'   op( A ) = A.

              TRANSA = 'T' or 't'   op( A ) = A'.

              TRANSA = 'C' or 'c'   op( A ) = A'.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit triangular
           as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  M      - INTEGER.
           On entry, M specifies the number of rows of B. M must be at

           least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of B.  N must be
           at least zero.
           Unchanged on exit.

  ALPHA  - DOUBLE PRECISION.
           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
           zero then  A is not referenced and  B need not be set before
           entry.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
           upper triangular part of the array  A must contain the upper
           triangular matrix  and the strictly lower triangular part of
           A is not referenced.
           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
           lower triangular part of the array  A must contain the lower
           triangular matrix  and the strictly upper triangular part of
           A is not referenced.
           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
           A  are not referenced either,  but are assumed to be  unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
           then LDA must be at least max( 1, n ).
           Unchanged on exit.

  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
           Before entry,  the leading  m by n part of the array  B must
           contain  the  right-hand  side  matrix  B,  and  on exit  is
           overwritten by the solution matrix  X.

  LDB    - INTEGER.
           On entry, LDB specifies the first dimension of B as declared
           in  the  calling  (sub)  program.   LDB  must  be  at  least
           max( 1, m ).
           Unchanged on exit.


  Level 3 Blas routine.


  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        side -
        uplo -
        transa -
        diag -
        m -
        n -
        alpha -
        a -
        lda -
        b -
        ldb -

      • dtrsv

        public abstract void dtrsv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           double[] a,
                           int lda,
                           double[] x,
                           int incx)
        
     ..

  Purpose
  =======

  DTRSV  solves one of the systems of equations

     A*x = b,   or   A'*x = b,

  where b and x are n element vectors and A is an n by n unit, or
  non-unit, upper or lower triangular matrix.

  No test for singularity or near-singularity is included in this
  routine. Such tests must be performed before calling this routine.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the equations to be solved as
           follows:

              TRANS = 'N' or 'n'   A*x = b.

              TRANS = 'T' or 't'   A'*x = b.

              TRANS = 'C' or 'c'   A'*x = b.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
           Before entry with  UPLO = 'U' or 'u', the leading n by n
           upper triangular part of the array A must contain the upper

           triangular matrix and the strictly lower triangular part of

           A is not referenced.
           Before entry with UPLO = 'L' or 'l', the leading n by n
           lower triangular part of the array A must contain the lower

           triangular matrix and the strictly upper triangular part of

           A is not referenced.
           Note that when  DIAG = 'U' or 'u', the diagonal elements of

           A are not referenced either, but are assumed to be unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, n ).
           Unchanged on exit.

  X      - DOUBLE PRECISION array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element right-hand side vector b. On exit, X is overwritten

           with the solution vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        a -
        lda -
        x -
        incx -

      • idamax

        public abstract int idamax(int n,
                           double[] dx,
                           int incx)
        
     ..

  Purpose
  =======

     finds the index of element having max. absolute value.
     jack dongarra, linpack, 3/11/78.
     modified 3/93 to return if incx .le. 0.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        dx -
        incx -

      • isamax

        public abstract int isamax(int n,
                           float[] sx,
                           int incx)
        
     ..

  Purpose
  =======

     finds the index of element having max. absolute value.
     jack dongarra, linpack, 3/11/78.
     modified 3/93 to return if incx .le. 0.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        sx -
        incx -

      • lsame

        public boolean lsame(java.lang.String ca,
                     java.lang.String cb)
        
     ..

  Purpose
  =======

  LSAME returns .TRUE. if CA is the same letter as CB regardless of
  case.

  Arguments
  =========

  CA      (input) CHARACTER*1

  CB      (input) CHARACTER*1
          CA and CB specify the single characters to be compared.

 =====================================================================


     .. Intrinsic Functions ..
        Parameters:
        ca -
        cb -

      • sasum

        public abstract float sasum(int n,
                            float[] sx,
                            int incx)
        
     ..

  Purpose
  =======

     takes the sum of the absolute values.
     uses unrolled loops for increment equal to one.
     jack dongarra, linpack, 3/11/78.
     modified 3/93 to return if incx .le. 0.
     modified 12/3/93, array(1) declarations changed to array(*)


 
     .. Local Scalars ..
        Parameters:
        n -
        sx -
        incx -

      • saxpy

        public abstract void saxpy(int n,
                           float sa,
                           float[] sx,
                           int incx,
                           float[] sy,
                           int incy)
        
     ..

  Purpose
  =======

     SAXPY constant times a vector plus a vector.
     uses unrolled loop for increments equal to one.
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        sa -
        sx -
        incx -
        sy -
        incy -

      • scopy

        public abstract void scopy(int n,
                           float[] sx,
                           int incx,
                           float[] sy,
                           int incy)
        
     ..

  Purpose
  =======

     copies a vector, x, to a vector, y.
     uses unrolled loops for increments equal to 1.
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        sx -
        incx -
        sy -
        incy -

      • sdot

        public abstract float sdot(int n,
                           float[] sx,
                           int incx,
                           float[] sy,
                           int incy)
        
     ..

  Purpose
  =======

     forms the dot product of two vectors.
     uses unrolled loops for increments equal to one.
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)


 
     .. Local Scalars ..
        Parameters:
        n -
        sx -
        incx -
        sy -
        incy -

      • sdsdot

        public abstract float sdsdot(int n,
                             float sb,
                             float[] sx,
                             int incx,
                             float[] sy,
                             int incy)
        
     ..

  PURPOSE
  =======

  Compute the inner product of two vectors with extended
  precision accumulation.

  Returns S.P. result with dot product accumulated in D.P.
  SDSDOT = SB + sum for I = 0 to N-1 of SX(LX+I*INCX)*SY(LY+I*INCY),
  where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is
  defined in a similar way using INCY.

  AUTHOR
  ======
  Lawson, C. L., (JPL), Hanson, R. J., (SNLA),
  Kincaid, D. R., (U. of Texas), Krogh, F. T., (JPL)

  ARGUMENTS 
  =========

  N      (input) INTEGER
         number of elements in input vector(s)

  SB     (input) REAL
         single precision scalar to be added to inner product

  SX     (input) REAL array, dimension (N)
         single precision vector with N elements

  INCX   (input) INTEGER
         storage spacing between elements of SX

  SY     (input) REAL array, dimension (N)
         single precision vector with N elements

  INCY   (input) INTEGER
         storage spacing between elements of SY

  SDSDOT (output) REAL
         single precision dot product (SB if N .LE. 0)

  REFERENCES
  ==========

  C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T.
  Krogh, Basic linear algebra subprograms for Fortran
  usage, Algorithm No. 539, Transactions on Mathematical
  Software 5, 3 (September 1979), pp. 308-323.

  REVISION HISTORY  (YYMMDD)
  ==========================
      
  791001  DATE WRITTEN
  890531  Changed all specific intrinsics to generic.  (WRB)
  890831  Modified array declarations.  (WRB)
  890831  REVISION DATE from Version 3.2
  891214  Prologue converted to Version 4.0 format.  (BAB)
  920310  Corrected definition of LX in DESCRIPTION.  (WRB)
  920501  Reformatted the REFERENCES section.  (WRB)
  070118  Reformat to LAPACK coding style

  =====================================================================

     .. Local Scalars ..
        Parameters:
        n -
        sb -
        sx -
        incx -
        sy -
        incy -

      • sgbmv

        public abstract void sgbmv(java.lang.String trans,
                           int m,
                           int n,
                           int kl,
                           int ku,
                           float alpha,
                           float[] a,
                           int lda,
                           float[] x,
                           int incx,
                           float beta,
                           float[] y,
                           int incy)
        
     ..

  Purpose
  =======

  SGBMV  performs one of the matrix-vector operations

     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,

  where alpha and beta are scalars, x and y are vectors and A is an
  m by n band matrix, with kl sub-diagonals and ku super-diagonals.

  Arguments
  ==========

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.

              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.

              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.

           Unchanged on exit.

  M      - INTEGER.
           On entry, M specifies the number of rows of the matrix A.
           M must be at least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  KL     - INTEGER.
           On entry, KL specifies the number of sub-diagonals of the
           matrix A. KL must satisfy  0 .le. KL.
           Unchanged on exit.

  KU     - INTEGER.
           On entry, KU specifies the number of super-diagonals of the

           matrix A. KU must satisfy  0 .le. KU.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, n ).
           Before entry, the leading ( kl + ku + 1 ) by n part of the
           array A must contain the matrix of coefficients, supplied
           column by column, with the leading diagonal of the matrix in
           row ( ku + 1 ) of the array, the first super-diagonal
           starting at position 2 in row ku, the first sub-diagonal
           starting at position 1 in row ( ku + 2 ), and so on.
           Elements in the array A that do not correspond to elements
           in the band matrix (such as the top left ku by ku triangle)

           are not referenced.
           The following program segment will transfer a band matrix
           from conventional full matrix storage to band storage:

                 DO 20, J = 1, N
                    K = KU + 1 - J
                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
                       A( K + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           ( kl + ku + 1 ).
           Unchanged on exit.

  X      - REAL             array of DIMENSION at least
           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
           Before entry, the incremented array X must contain the
           vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  BETA   - REAL            .
           On entry, BETA specifies the scalar beta. When BETA is
           supplied as zero then Y need not be set on input.
           Unchanged on exit.

  Y      - REAL             array of DIMENSION at least
           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
           Before entry, the incremented array Y must contain the
           vector y. On exit, Y is overwritten by the updated vector y.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.

     .. Parameters ..
        Parameters:
        trans -
        m -
        n -
        kl -
        ku -
        alpha -
        a -
        lda -
        x -
        incx -
        beta -
        y -
        incy -

      • sgemm

        public abstract void sgemm(java.lang.String transa,
                           java.lang.String transb,
                           int m,
                           int n,
                           int k,
                           float alpha,
                           float[] a,
                           int lda,
                           float[] b,
                           int ldb,
                           float beta,
                           float[] c,
                           int Ldc)
        
     ..

  Purpose
  =======

  SGEMM  performs one of the matrix-matrix operations

     C := alpha*op( A )*op( B ) + beta*C,

  where  op( X ) is one of

     op( X ) = X   or   op( X ) = X',

  alpha and beta are scalars, and A, B and C are matrices, with op( A )
  an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.

  Arguments
  ==========

  TRANSA - CHARACTER*1.
           On entry, TRANSA specifies the form of op( A ) to be used in
           the matrix multiplication as follows:

              TRANSA = 'N' or 'n',  op( A ) = A.

              TRANSA = 'T' or 't',  op( A ) = A'.

              TRANSA = 'C' or 'c',  op( A ) = A'.

           Unchanged on exit.

  TRANSB - CHARACTER*1.
           On entry, TRANSB specifies the form of op( B ) to be used in
           the matrix multiplication as follows:

              TRANSB = 'N' or 'n',  op( B ) = B.

              TRANSB = 'T' or 't',  op( B ) = B'.

              TRANSB = 'C' or 'c',  op( B ) = B'.

           Unchanged on exit.

  M      - INTEGER.
           On entry,  M  specifies  the number  of rows  of the  matrix
           op( A )  and of the  matrix  C.  M  must  be at least  zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry,  N  specifies the number  of columns of the matrix
           op( B ) and the number of columns of the matrix C. N must be
           at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry,  K  specifies  the number of columns of the matrix
           op( A ) and the number of rows of the matrix op( B ). K must
           be at least  zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, ka ), where ka is
           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
           part of the array  A  must contain the matrix  A,  otherwise
           the leading  k by m  part of the array  A  must contain  the
           matrix A.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
           LDA must be at least  max( 1, m ), otherwise  LDA must be at
           least  max( 1, k ).
           Unchanged on exit.

  B      - REAL             array of DIMENSION ( LDB, kb ), where kb is
           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
           part of the array  B  must contain the matrix  B,  otherwise
           the leading  n by k  part of the array  B  must contain  the
           matrix B.
           Unchanged on exit.

  LDB    - INTEGER.
           On entry, LDB specifies the first dimension of B as declared
           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
           LDB must be at least  max( 1, k ), otherwise  LDB must be at
           least  max( 1, n ).
           Unchanged on exit.

  BETA   - REAL            .
           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
           supplied as zero then C need not be set on input.
           Unchanged on exit.

  C      - REAL             array of DIMENSION ( LDC, n ).
           Before entry, the leading  m by n  part of the array  C must
           contain the matrix  C,  except when  beta  is zero, in which
           case C need not be set on entry.
           On exit, the array  C  is overwritten by the  m by n  matrix
           ( alpha*op( A )*op( B ) + beta*C ).

  LDC    - INTEGER.
           On entry, LDC specifies the first dimension of C as declared
           in  the  calling  (sub)  program.   LDC  must  be  at  least
           max( 1, m ).
           Unchanged on exit.


  Level 3 Blas routine.

  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        transa -
        transb -
        m -
        n -
        k -
        alpha -
        a -
        lda -
        b -
        ldb -
        beta -
        c -
        Ldc -

      • sgemv

        public abstract void sgemv(java.lang.String trans,
                           int m,
                           int n,
                           float alpha,
                           float[] a,
                           int lda,
                           float[] x,
                           int incx,
                           float beta,
                           float[] y,
                           int incy)
        
     ..

  Purpose
  =======

  SGEMV  performs one of the matrix-vector operations

     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,

  where alpha and beta are scalars, x and y are vectors and A is an
  m by n matrix.

  Arguments
  ==========

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.

              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.

              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.

           Unchanged on exit.

  M      - INTEGER.
           On entry, M specifies the number of rows of the matrix A.
           M must be at least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, n ).
           Before entry, the leading m by n part of the array A must
           contain the matrix of coefficients.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, m ).
           Unchanged on exit.

  X      - REAL             array of DIMENSION at least
           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
           Before entry, the incremented array X must contain the
           vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  BETA   - REAL            .
           On entry, BETA specifies the scalar beta. When BETA is
           supplied as zero then Y need not be set on input.
           Unchanged on exit.

  Y      - REAL             array of DIMENSION at least
           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
           Before entry with BETA non-zero, the incremented array Y
           must contain the vector y. On exit, Y is overwritten by the

           updated vector y.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        trans -
        m -
        n -
        alpha -
        a -
        lda -
        x -
        incx -
        beta -
        y -
        incy -

      • sger

        public abstract void sger(int m,
                          int n,
                          float alpha,
                          float[] x,
                          int incx,
                          float[] y,
                          int incy,
                          float[] a,
                          int lda)
        
     ..

  Purpose
  =======

  SGER   performs the rank 1 operation

     A := alpha*x*y' + A,

  where alpha is a scalar, x is an m element vector, y is an n element

  vector and A is an m by n matrix.

  Arguments
  ==========

  M      - INTEGER.
           On entry, M specifies the number of rows of the matrix A.
           M must be at least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( m - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the m
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  Y      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the n
           element vector y.
           Unchanged on exit.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, n ).
           Before entry, the leading m by n part of the array A must
           contain the matrix of coefficients. On exit, A is
           overwritten by the updated matrix.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, m ).
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        m -
        n -
        alpha -
        x -
        incx -
        y -
        incy -
        a -
        lda -

      • snrm2

        public abstract float snrm2(int n,
                            float[] x,
                            int incx)
        
     ..

  Purpose
  =======

  SNRM2 returns the euclidean norm of a vector via the function
  name, so that

     SNRM2 := sqrt( x'*x ).

  Further Details
  ===============

  -- This version written on 25-October-1982.
     Modified on 14-October-1993 to inline the call to SLASSQ.
     Sven Hammarling, Nag Ltd.


     .. Parameters ..
        Parameters:
        n -
        x -
        incx -

      • srot

        public abstract void srot(int n,
                          float[] sx,
                          int incx,
                          float[] sy,
                          int incy,
                          float c,
                          float s)
        
     ..

  Purpose
  =======

     applies a plane rotation.

  Further Details
  ===============

     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)


 
     .. Local Scalars ..
        Parameters:
        n -
        sx -
        incx -
        sy -
        incy -
        c -
        s -

      • srotg

        public abstract void srotg(org.netlib.util.floatW sa,
                           org.netlib.util.floatW sb,
                           org.netlib.util.floatW c,
                           org.netlib.util.floatW s)
        
     ..

  Purpose
  =======

     construct givens plane rotation.
     jack dongarra, linpack, 3/11/78.


     .. Local Scalars ..
        Parameters:
        sa -
        sb -
        c -
        s -

      • srotm

        public abstract void srotm(int n,
                           float[] sx,
                           int incx,
                           float[] sy,
                           int incy,
                           float[] sparam)
        
     ..

  Purpose
  =======

     APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX


     (SX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF SX ARE IN
     (DX**T)

     SX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE
     LX = (-INCX)*N, AND SIMILARLY FOR SY USING USING LY AND INCY.
     WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS..

     SFLAG=-1.E0     SFLAG=0.E0        SFLAG=1.E0     SFLAG=-2.E0

       (SH11  SH12)    (1.E0  SH12)    (SH11  1.E0)    (1.E0  0.E0)
     H=(          )    (          )    (          )    (          )
       (SH21  SH22),   (SH21  1.E0),   (-1.E0 SH22),   (0.E0  1.E0).
     SEE  SROTMG FOR A DESCRIPTION OF DATA STORAGE IN SPARAM.


  Arguments
  =========

  N      (input) INTEGER
         number of elements in input vector(s)

  SX     (input/output) REAL array, dimension N
         double precision vector with 5 elements

  INCX   (input) INTEGER
         storage spacing between elements of SX

  SY     (input/output) REAL array, dimension N
         double precision vector with N elements

  INCY   (input) INTEGER
         storage spacing between elements of SY

  SPARAM (input/output)  REAL array, dimension 5
     SPARAM(1)=SFLAG
     SPARAM(2)=SH11
     SPARAM(3)=SH21
     SPARAM(4)=SH12
     SPARAM(5)=SH22

  =====================================================================

     .. Local Scalars ..
        Parameters:
        n -
        sx -
        incx -
        sy -
        incy -
        sparam -

      • srotmg

        public abstract void srotmg(org.netlib.util.floatW sd1,
                            org.netlib.util.floatW sd2,
                            org.netlib.util.floatW sx1,
                            float sy1,
                            float[] sparam)
        
     ..

  Purpose
  =======

     CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS

     THE SECOND COMPONENT OF THE 2-VECTOR  (SQRT(SD1)*SX1,SQRT(SD2)*
     SY2)**T.
     WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS..

     SFLAG=-1.E0     SFLAG=0.E0        SFLAG=1.E0     SFLAG=-2.E0

       (SH11  SH12)    (1.E0  SH12)    (SH11  1.E0)    (1.E0  0.E0)
     H=(          )    (          )    (          )    (          )
       (SH21  SH22),   (SH21  1.E0),   (-1.E0 SH22),   (0.E0  1.E0).
     LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22
     RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE
     VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.)

     THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE
     INEXACT.  THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE
     OF SD1 AND SD2.  ALL ACTUAL SCALING OF DATA IS DONE USING GAM.


  Arguments
  =========


  SD1    (input/output) REAL

  SD2    (input/output) REAL

  SX1    (input/output) REAL

  SY1    (input) REAL


  SPARAM (input/output)  REAL array, dimension 5
     SPARAM(1)=SFLAG
     SPARAM(2)=SH11
     SPARAM(3)=SH21
     SPARAM(4)=SH12
     SPARAM(5)=SH22

  =====================================================================

     .. Local Scalars ..
        Parameters:
        sd1 -
        sd2 -
        sx1 -
        sy1 -
        sparam -

      • ssbmv

        public abstract void ssbmv(java.lang.String uplo,
                           int n,
                           int k,
                           float alpha,
                           float[] a,
                           int lda,
                           float[] x,
                           int incx,
                           float beta,
                           float[] y,
                           int incy)
        
     ..

  Purpose
  =======

  SSBMV  performs the matrix-vector  operation

     y := alpha*A*x + beta*y,

  where alpha and beta are scalars, x and y are n element vectors and
  A is an n by n symmetric band matrix, with k super-diagonals.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the band matrix A is being supplied as
           follows:

              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  being supplied.

              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  being supplied.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry, K specifies the number of super-diagonals of the
           matrix A. K must satisfy  0 .le. K.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, n ).
           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
           by n part of the array A must contain the upper triangular
           band part of the symmetric matrix, supplied column by
           column, with the leading diagonal of the matrix in row
           ( k + 1 ) of the array, the first super-diagonal starting at
           position 2 in row k, and so on. The top left k by k triangle
           of the array A is not referenced.
           The following program segment will transfer the upper
           triangular part of a symmetric band matrix from conventional
           full matrix storage to band storage:

                 DO 20, J = 1, N
                    M = K + 1 - J
                    DO 10, I = MAX( 1, J - K ), J
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
           by n part of the array A must contain the lower triangular
           band part of the symmetric matrix, supplied column by
           column, with the leading diagonal of the matrix in row 1 of

           the array, the first sub-diagonal starting at position 1 in

           row 2, and so on. The bottom right k by k triangle of the
           array A is not referenced.
           The following program segment will transfer the lower
           triangular part of a symmetric band matrix from conventional
           full matrix storage to band storage:

                 DO 20, J = 1, N
                    M = 1 - J
                    DO 10, I = J, MIN( N, J + K )
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           ( k + 1 ).
           Unchanged on exit.

  X      - REAL             array of DIMENSION at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the
           vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  BETA   - REAL            .
           On entry, BETA specifies the scalar beta.
           Unchanged on exit.

  Y      - REAL             array of DIMENSION at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the
           vector y. On exit, Y is overwritten by the updated vector y.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        k -
        alpha -
        a -
        lda -
        x -
        incx -
        beta -
        y -
        incy -

      • sscal

        public abstract void sscal(int n,
                           float sa,
                           float[] sx,
                           int incx)
        
     ..

  Purpose
  =======

     scales a vector by a constant.
     uses unrolled loops for increment equal to 1.
     jack dongarra, linpack, 3/11/78.
     modified 3/93 to return if incx .le. 0.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        sa -
        sx -
        incx -

      • sspmv

        public abstract void sspmv(java.lang.String uplo,
                           int n,
                           float alpha,
                           float[] ap,
                           float[] x,
                           int incx,
                           float beta,
                           float[] y,
                           int incy)
        
     ..

  Purpose
  =======

  SSPMV  performs the matrix-vector operation

     y := alpha*A*x + beta*y,

  where alpha and beta are scalars, x and y are n element vectors and
  A is an n by n symmetric matrix, supplied in packed form.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:

              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.

              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  AP     - REAL             array of DIMENSION at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on.
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  BETA   - REAL            .
           On entry, BETA specifies the scalar beta. When BETA is
           supplied as zero then Y need not be set on input.
           Unchanged on exit.

  Y      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the n
           element vector y. On exit, Y is overwritten by the updated
           vector y.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        ap -
        x -
        incx -
        beta -
        y -
        incy -

      • sspr

        public abstract void sspr(java.lang.String uplo,
                          int n,
                          float alpha,
                          float[] x,
                          int incx,
                          float[] ap)
        
     ..

  Purpose
  =======

  SSPR    performs the symmetric rank 1 operation

     A := alpha*x*x' + A,

  where alpha is a real scalar, x is an n element vector and A is an
  n by n symmetric matrix, supplied in packed form.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:

              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.

              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  AP     - REAL             array of DIMENSION at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on. On exit, the array
           AP is overwritten by the upper triangular part of the
           updated matrix.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on. On exit, the array
           AP is overwritten by the lower triangular part of the
           updated matrix.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        x -
        incx -
        ap -

      • sspr2

        public abstract void sspr2(java.lang.String uplo,
                           int n,
                           float alpha,
                           float[] x,
                           int incx,
                           float[] y,
                           int incy,
                           float[] ap)
        
     ..

  Purpose
  =======

  SSPR2  performs the symmetric rank 2 operation

     A := alpha*x*y' + alpha*y*x' + A,

  where alpha is a scalar, x and y are n element vectors and A is an
  n by n symmetric matrix, supplied in packed form.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:

              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.

              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  Y      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the n
           element vector y.
           Unchanged on exit.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.

  AP     - REAL             array of DIMENSION at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on. On exit, the array
           AP is overwritten by the upper triangular part of the
           updated matrix.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on. On exit, the array
           AP is overwritten by the lower triangular part of the
           updated matrix.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        x -
        incx -
        y -
        incy -
        ap -

      • sswap

        public abstract void sswap(int n,
                           float[] sx,
                           int incx,
                           float[] sy,
                           int incy)
        
     ..

  Purpose
  =======

     interchanges two vectors.
     uses unrolled loops for increments equal to 1.
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)


     .. Local Scalars ..
        Parameters:
        n -
        sx -
        incx -
        sy -
        incy -

      • ssymm

        public abstract void ssymm(java.lang.String side,
                           java.lang.String uplo,
                           int m,
                           int n,
                           float alpha,
                           float[] a,
                           int lda,
                           float[] b,
                           int ldb,
                           float beta,
                           float[] c,
                           int Ldc)
        
     ..

  Purpose
  =======

  SSYMM  performs one of the matrix-matrix operations

     C := alpha*A*B + beta*C,

  or

     C := alpha*B*A + beta*C,

  where alpha and beta are scalars,  A is a symmetric matrix and  B and
  C are  m by n matrices.

  Arguments
  ==========

  SIDE   - CHARACTER*1.
           On entry,  SIDE  specifies whether  the  symmetric matrix  A
           appears on the  left or right  in the  operation as follows:

              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,

              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,

           Unchanged on exit.

  UPLO   - CHARACTER*1.
           On  entry,   UPLO  specifies  whether  the  upper  or  lower
           triangular  part  of  the  symmetric  matrix   A  is  to  be
           referenced as follows:

              UPLO = 'U' or 'u'   Only the upper triangular part of the
                                  symmetric matrix is to be referenced.

              UPLO = 'L' or 'l'   Only the lower triangular part of the
                                  symmetric matrix is to be referenced.

           Unchanged on exit.

  M      - INTEGER.
           On entry,  M  specifies the number of rows of the matrix  C.
           M  must be at least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of the matrix C.
           N  must be at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, ka ), where ka is
           m  when  SIDE = 'L' or 'l'  and is  n otherwise.
           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
           the array  A  must contain the  symmetric matrix,  such that
           when  UPLO = 'U' or 'u', the leading m by m upper triangular
           part of the array  A  must contain the upper triangular part
           of the  symmetric matrix and the  strictly  lower triangular
           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
           the leading  m by m  lower triangular part  of the  array  A
           must  contain  the  lower triangular part  of the  symmetric
           matrix and the  strictly upper triangular part of  A  is not
           referenced.
           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
           the array  A  must contain the  symmetric matrix,  such that
           when  UPLO = 'U' or 'u', the leading n by n upper triangular
           part of the array  A  must contain the upper triangular part
           of the  symmetric matrix and the  strictly  lower triangular
           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
           the leading  n by n  lower triangular part  of the  array  A
           must  contain  the  lower triangular part  of the  symmetric
           matrix and the  strictly upper triangular part of  A  is not
           referenced.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
           LDA must be at least  max( 1, m ), otherwise  LDA must be at
           least  max( 1, n ).
           Unchanged on exit.

  B      - REAL             array of DIMENSION ( LDB, n ).
           Before entry, the leading  m by n part of the array  B  must
           contain the matrix B.
           Unchanged on exit.

  LDB    - INTEGER.
           On entry, LDB specifies the first dimension of B as declared
           in  the  calling  (sub)  program.   LDB  must  be  at  least
           max( 1, m ).
           Unchanged on exit.

  BETA   - REAL            .
           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
           supplied as zero then C need not be set on input.
           Unchanged on exit.

  C      - REAL             array of DIMENSION ( LDC, n ).
           Before entry, the leading  m by n  part of the array  C must
           contain the matrix  C,  except when  beta  is zero, in which
           case C need not be set on entry.
           On exit, the array  C  is overwritten by the  m by n updated
           matrix.

  LDC    - INTEGER.
           On entry, LDC specifies the first dimension of C as declared
           in  the  calling  (sub)  program.   LDC  must  be  at  least
           max( 1, m ).
           Unchanged on exit.


  Level 3 Blas routine.

  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        side -
        uplo -
        m -
        n -
        alpha -
        a -
        lda -
        b -
        ldb -
        beta -
        c -
        Ldc -

      • ssymv

        public abstract void ssymv(java.lang.String uplo,
                           int n,
                           float alpha,
                           float[] a,
                           int lda,
                           float[] x,
                           int incx,
                           float beta,
                           float[] y,
                           int incy)
        
     ..

  Purpose
  =======

  SSYMV  performs the matrix-vector  operation

     y := alpha*A*x + beta*y,

  where alpha and beta are scalars, x and y are n element vectors and
  A is an n by n symmetric matrix.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the array A is to be referenced as
           follows:

              UPLO = 'U' or 'u'   Only the upper triangular part of A
                                  is to be referenced.

              UPLO = 'L' or 'l'   Only the lower triangular part of A
                                  is to be referenced.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, n ).
           Before entry with  UPLO = 'U' or 'u', the leading n by n
           upper triangular part of the array A must contain the upper

           triangular part of the symmetric matrix and the strictly
           lower triangular part of A is not referenced.
           Before entry with UPLO = 'L' or 'l', the leading n by n
           lower triangular part of the array A must contain the lower

           triangular part of the symmetric matrix and the strictly
           upper triangular part of A is not referenced.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, n ).
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  BETA   - REAL            .
           On entry, BETA specifies the scalar beta. When BETA is
           supplied as zero then Y need not be set on input.
           Unchanged on exit.

  Y      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the n
           element vector y. On exit, Y is overwritten by the updated
           vector y.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        a -
        lda -
        x -
        incx -
        beta -
        y -
        incy -

      • ssyr

        public abstract void ssyr(java.lang.String uplo,
                          int n,
                          float alpha,
                          float[] x,
                          int incx,
                          float[] a,
                          int lda)
        
     ..

  Purpose
  =======

  SSYR   performs the symmetric rank 1 operation

     A := alpha*x*x' + A,

  where alpha is a real scalar, x is an n element vector and A is an
  n by n symmetric matrix.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the array A is to be referenced as
           follows:

              UPLO = 'U' or 'u'   Only the upper triangular part of A
                                  is to be referenced.

              UPLO = 'L' or 'l'   Only the lower triangular part of A
                                  is to be referenced.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, n ).
           Before entry with  UPLO = 'U' or 'u', the leading n by n
           upper triangular part of the array A must contain the upper

           triangular part of the symmetric matrix and the strictly
           lower triangular part of A is not referenced. On exit, the
           upper triangular part of the array A is overwritten by the
           upper triangular part of the updated matrix.
           Before entry with UPLO = 'L' or 'l', the leading n by n
           lower triangular part of the array A must contain the lower

           triangular part of the symmetric matrix and the strictly
           upper triangular part of A is not referenced. On exit, the
           lower triangular part of the array A is overwritten by the
           lower triangular part of the updated matrix.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, n ).
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        x -
        incx -
        a -
        lda -

      • ssyr2

        public abstract void ssyr2(java.lang.String uplo,
                           int n,
                           float alpha,
                           float[] x,
                           int incx,
                           float[] y,
                           int incy,
                           float[] a,
                           int lda)
        
     ..

  Purpose
  =======

  SSYR2  performs the symmetric rank 2 operation

     A := alpha*x*y' + alpha*y*x' + A,

  where alpha is a scalar, x and y are n element vectors and A is an n

  by n symmetric matrix.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the upper or lower
           triangular part of the array A is to be referenced as
           follows:

              UPLO = 'U' or 'u'   Only the upper triangular part of A
                                  is to be referenced.

              UPLO = 'L' or 'l'   Only the lower triangular part of A
                                  is to be referenced.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.
           Unchanged on exit.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  Y      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the n
           element vector y.
           Unchanged on exit.

  INCY   - INTEGER.
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, n ).
           Before entry with  UPLO = 'U' or 'u', the leading n by n
           upper triangular part of the array A must contain the upper

           triangular part of the symmetric matrix and the strictly
           lower triangular part of A is not referenced. On exit, the
           upper triangular part of the array A is overwritten by the
           upper triangular part of the updated matrix.
           Before entry with UPLO = 'L' or 'l', the leading n by n
           lower triangular part of the array A must contain the lower

           triangular part of the symmetric matrix and the strictly
           upper triangular part of A is not referenced. On exit, the
           lower triangular part of the array A is overwritten by the
           lower triangular part of the updated matrix.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, n ).
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        n -
        alpha -
        x -
        incx -
        y -
        incy -
        a -
        lda -

      • ssyr2k

        public abstract void ssyr2k(java.lang.String uplo,
                            java.lang.String trans,
                            int n,
                            int k,
                            float alpha,
                            float[] a,
                            int lda,
                            float[] b,
                            int ldb,
                            float beta,
                            float[] c,
                            int Ldc)
        
     ..

  Purpose
  =======

  SSYR2K  performs one of the symmetric rank 2k operations

     C := alpha*A*B' + alpha*B*A' + beta*C,

  or

     C := alpha*A'*B + alpha*B'*A + beta*C,

  where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
  and  A and B  are  n by k  matrices  in the  first  case  and  k by n
  matrices in the second case.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On  entry,   UPLO  specifies  whether  the  upper  or  lower
           triangular  part  of the  array  C  is to be  referenced  as
           follows:

              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                  is to be referenced.

              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                  is to be referenced.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry,  TRANS  specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   C := alpha*A*B' + alpha*B*A' +
                                        beta*C.

              TRANS = 'T' or 't'   C := alpha*A'*B + alpha*B'*A +
                                        beta*C.

              TRANS = 'C' or 'c'   C := alpha*A'*B + alpha*B'*A +
                                        beta*C.

           Unchanged on exit.

  N      - INTEGER.
           On entry,  N specifies the order of the matrix C.  N must be
           at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
           of  columns  of the  matrices  A and B,  and on  entry  with
           TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
           of rows of the matrices  A and B.  K must be at least  zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, ka ), where ka is
           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
           part of the array  A  must contain the matrix  A,  otherwise
           the leading  k by n  part of the array  A  must contain  the
           matrix A.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
           then  LDA must be at least  max( 1, n ), otherwise  LDA must
           be at least  max( 1, k ).
           Unchanged on exit.

  B      - REAL             array of DIMENSION ( LDB, kb ), where kb is
           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
           part of the array  B  must contain the matrix  B,  otherwise
           the leading  k by n  part of the array  B  must contain  the
           matrix B.
           Unchanged on exit.

  LDB    - INTEGER.
           On entry, LDB specifies the first dimension of B as declared
           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
           then  LDB must be at least  max( 1, n ), otherwise  LDB must
           be at least  max( 1, k ).
           Unchanged on exit.

  BETA   - REAL            .
           On entry, BETA specifies the scalar beta.
           Unchanged on exit.

  C      - REAL             array of DIMENSION ( LDC, n ).
           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n

           upper triangular part of the array C must contain the upper

           triangular part  of the  symmetric matrix  and the strictly

           lower triangular part of C is not referenced.  On exit, the

           upper triangular part of the array  C is overwritten by the

           upper triangular part of the updated matrix.
           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n

           lower triangular part of the array C must contain the lower

           triangular part  of the  symmetric matrix  and the strictly

           upper triangular part of C is not referenced.  On exit, the

           lower triangular part of the array  C is overwritten by the

           lower triangular part of the updated matrix.

  LDC    - INTEGER.
           On entry, LDC specifies the first dimension of C as declared
           in  the  calling  (sub)  program.   LDC  must  be  at  least
           max( 1, n ).
           Unchanged on exit.


  Level 3 Blas routine.


  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        uplo -
        trans -
        n -
        k -
        alpha -
        a -
        lda -
        b -
        ldb -
        beta -
        c -
        Ldc -

      • ssyrk

        public abstract void ssyrk(java.lang.String uplo,
                           java.lang.String trans,
                           int n,
                           int k,
                           float alpha,
                           float[] a,
                           int lda,
                           float beta,
                           float[] c,
                           int Ldc)
        
     ..

  Purpose
  =======

  SSYRK  performs one of the symmetric rank k operations

     C := alpha*A*A' + beta*C,

  or

     C := alpha*A'*A + beta*C,

  where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
  and  A  is an  n by k  matrix in the first case and a  k by n  matrix
  in the second case.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On  entry,   UPLO  specifies  whether  the  upper  or  lower
           triangular  part  of the  array  C  is to be  referenced  as
           follows:

              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                  is to be referenced.

              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                  is to be referenced.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry,  TRANS  specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   C := alpha*A*A' + beta*C.

              TRANS = 'T' or 't'   C := alpha*A'*A + beta*C.

              TRANS = 'C' or 'c'   C := alpha*A'*A + beta*C.

           Unchanged on exit.

  N      - INTEGER.
           On entry,  N specifies the order of the matrix C.  N must be
           at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
           of  columns   of  the   matrix   A,   and  on   entry   with
           TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
           of rows of the matrix  A.  K must be at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, ka ), where ka is
           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
           part of the array  A  must contain the matrix  A,  otherwise
           the leading  k by n  part of the array  A  must contain  the
           matrix A.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
           then  LDA must be at least  max( 1, n ), otherwise  LDA must
           be at least  max( 1, k ).
           Unchanged on exit.

  BETA   - REAL            .
           On entry, BETA specifies the scalar beta.
           Unchanged on exit.

  C      - REAL             array of DIMENSION ( LDC, n ).
           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n

           upper triangular part of the array C must contain the upper

           triangular part  of the  symmetric matrix  and the strictly

           lower triangular part of C is not referenced.  On exit, the

           upper triangular part of the array  C is overwritten by the

           upper triangular part of the updated matrix.
           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n

           lower triangular part of the array C must contain the lower

           triangular part  of the  symmetric matrix  and the strictly

           upper triangular part of C is not referenced.  On exit, the

           lower triangular part of the array  C is overwritten by the

           lower triangular part of the updated matrix.

  LDC    - INTEGER.
           On entry, LDC specifies the first dimension of C as declared
           in  the  calling  (sub)  program.   LDC  must  be  at  least
           max( 1, n ).
           Unchanged on exit.


  Level 3 Blas routine.

  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        uplo -
        trans -
        n -
        k -
        alpha -
        a -
        lda -
        beta -
        c -
        Ldc -

      • stbmv

        public abstract void stbmv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           int k,
                           float[] a,
                           int lda,
                           float[] x,
                           int incx)
        
     ..

  Purpose
  =======

  STBMV  performs one of the matrix-vector operations

     x := A*x,   or   x := A'*x,

  where x is an n element vector and  A is an n by n unit, or non-unit,
  upper or lower triangular band matrix, with ( k + 1 ) diagonals.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   x := A*x.

              TRANS = 'T' or 't'   x := A'*x.

              TRANS = 'C' or 'c'   x := A'*x.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry with UPLO = 'U' or 'u', K specifies the number of
           super-diagonals of the matrix A.
           On entry with UPLO = 'L' or 'l', K specifies the number of
           sub-diagonals of the matrix A.
           K must satisfy  0 .le. K.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, n ).
           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
           by n part of the array A must contain the upper triangular
           band part of the matrix of coefficients, supplied column by

           column, with the leading diagonal of the matrix in row
           ( k + 1 ) of the array, the first super-diagonal starting at
           position 2 in row k, and so on. The top left k by k triangle
           of the array A is not referenced.
           The following program segment will transfer an upper
           triangular band matrix from conventional full matrix storage
           to band storage:

                 DO 20, J = 1, N
                    M = K + 1 - J
                    DO 10, I = MAX( 1, J - K ), J
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
           by n part of the array A must contain the lower triangular
           band part of the matrix of coefficients, supplied column by

           column, with the leading diagonal of the matrix in row 1 of

           the array, the first sub-diagonal starting at position 1 in

           row 2, and so on. The bottom right k by k triangle of the
           array A is not referenced.
           The following program segment will transfer a lower
           triangular band matrix from conventional full matrix storage
           to band storage:

                 DO 20, J = 1, N
                    M = 1 - J
                    DO 10, I = J, MIN( N, J + K )
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Note that when DIAG = 'U' or 'u' the elements of the array A
           corresponding to the diagonal elements of the matrix are not
           referenced, but are assumed to be unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           ( k + 1 ).
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x. On exit, X is overwritten with the
           tranformed vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        k -
        a -
        lda -
        x -
        incx -

      • stbsv

        public abstract void stbsv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           int k,
                           float[] a,
                           int lda,
                           float[] x,
                           int incx)
        
     ..

  Purpose
  =======

  STBSV  solves one of the systems of equations

     A*x = b,   or   A'*x = b,

  where b and x are n element vectors and A is an n by n unit, or
  non-unit, upper or lower triangular band matrix, with ( k + 1 )
  diagonals.

  No test for singularity or near-singularity is included in this
  routine. Such tests must be performed before calling this routine.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the equations to be solved as
           follows:

              TRANS = 'N' or 'n'   A*x = b.

              TRANS = 'T' or 't'   A'*x = b.

              TRANS = 'C' or 'c'   A'*x = b.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  K      - INTEGER.
           On entry with UPLO = 'U' or 'u', K specifies the number of
           super-diagonals of the matrix A.
           On entry with UPLO = 'L' or 'l', K specifies the number of
           sub-diagonals of the matrix A.
           K must satisfy  0 .le. K.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, n ).
           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
           by n part of the array A must contain the upper triangular
           band part of the matrix of coefficients, supplied column by

           column, with the leading diagonal of the matrix in row
           ( k + 1 ) of the array, the first super-diagonal starting at
           position 2 in row k, and so on. The top left k by k triangle
           of the array A is not referenced.
           The following program segment will transfer an upper
           triangular band matrix from conventional full matrix storage
           to band storage:

                 DO 20, J = 1, N
                    M = K + 1 - J
                    DO 10, I = MAX( 1, J - K ), J
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
           by n part of the array A must contain the lower triangular
           band part of the matrix of coefficients, supplied column by

           column, with the leading diagonal of the matrix in row 1 of

           the array, the first sub-diagonal starting at position 1 in

           row 2, and so on. The bottom right k by k triangle of the
           array A is not referenced.
           The following program segment will transfer a lower
           triangular band matrix from conventional full matrix storage
           to band storage:

                 DO 20, J = 1, N
                    M = 1 - J
                    DO 10, I = J, MIN( N, J + K )
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Note that when DIAG = 'U' or 'u' the elements of the array A
           corresponding to the diagonal elements of the matrix are not
           referenced, but are assumed to be unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           ( k + 1 ).
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element right-hand side vector b. On exit, X is overwritten

           with the solution vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        k -
        a -
        lda -
        x -
        incx -

      • stpmv

        public abstract void stpmv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           float[] ap,
                           float[] x,
                           int incx)
        
     ..

  Purpose
  =======

  STPMV  performs one of the matrix-vector operations

     x := A*x,   or   x := A'*x,

  where x is an n element vector and  A is an n by n unit, or non-unit,
  upper or lower triangular matrix, supplied in packed form.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   x := A*x.

              TRANS = 'T' or 't'   x := A'*x.

              TRANS = 'C' or 'c'   x := A'*x.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  AP     - REAL             array of DIMENSION at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular matrix packed sequentially,
           column by column, so that AP( 1 ) contains a( 1, 1 ),
           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
           respectively, and so on.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular matrix packed sequentially,
           column by column, so that AP( 1 ) contains a( 1, 1 ),
           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
           respectively, and so on.
           Note that when  DIAG = 'U' or 'u', the diagonal elements of

           A are not referenced, but are assumed to be unity.
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x. On exit, X is overwritten with the
           tranformed vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        ap -
        x -
        incx -

      • stpsv

        public abstract void stpsv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           float[] ap,
                           float[] x,
                           int incx)
        
     ..

  Purpose
  =======

  STPSV  solves one of the systems of equations

     A*x = b,   or   A'*x = b,

  where b and x are n element vectors and A is an n by n unit, or
  non-unit, upper or lower triangular matrix, supplied in packed form.


  No test for singularity or near-singularity is included in this
  routine. Such tests must be performed before calling this routine.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the equations to be solved as
           follows:

              TRANS = 'N' or 'n'   A*x = b.

              TRANS = 'T' or 't'   A'*x = b.

              TRANS = 'C' or 'c'   A'*x = b.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  AP     - REAL             array of DIMENSION at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular matrix packed sequentially,
           column by column, so that AP( 1 ) contains a( 1, 1 ),
           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
           respectively, and so on.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular matrix packed sequentially,
           column by column, so that AP( 1 ) contains a( 1, 1 ),
           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
           respectively, and so on.
           Note that when  DIAG = 'U' or 'u', the diagonal elements of

           A are not referenced, but are assumed to be unity.
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element right-hand side vector b. On exit, X is overwritten

           with the solution vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        ap -
        x -
        incx -

      • strmm

        public abstract void strmm(java.lang.String side,
                           java.lang.String uplo,
                           java.lang.String transa,
                           java.lang.String diag,
                           int m,
                           int n,
                           float alpha,
                           float[] a,
                           int lda,
                           float[] b,
                           int ldb)
        
     ..

  Purpose
  =======

  STRMM  performs one of the matrix-matrix operations

     B := alpha*op( A )*B,   or   B := alpha*B*op( A ),

  where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

     op( A ) = A   or   op( A ) = A'.

  Arguments
  ==========

  SIDE   - CHARACTER*1.
           On entry,  SIDE specifies whether  op( A ) multiplies B from
           the left or right as follows:

              SIDE = 'L' or 'l'   B := alpha*op( A )*B.

              SIDE = 'R' or 'r'   B := alpha*B*op( A ).

           Unchanged on exit.

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix A is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANSA - CHARACTER*1.
           On entry, TRANSA specifies the form of op( A ) to be used in
           the matrix multiplication as follows:

              TRANSA = 'N' or 'n'   op( A ) = A.

              TRANSA = 'T' or 't'   op( A ) = A'.

              TRANSA = 'C' or 'c'   op( A ) = A'.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit triangular
           as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  M      - INTEGER.
           On entry, M specifies the number of rows of B. M must be at

           least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of B.  N must be
           at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
           zero then  A is not referenced and  B need not be set before
           entry.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, k ), where k is m
           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
           upper triangular part of the array  A must contain the upper
           triangular matrix  and the strictly lower triangular part of
           A is not referenced.
           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
           lower triangular part of the array  A must contain the lower
           triangular matrix  and the strictly upper triangular part of
           A is not referenced.
           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
           A  are not referenced either,  but are assumed to be  unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
           then LDA must be at least max( 1, n ).
           Unchanged on exit.

  B      - REAL             array of DIMENSION ( LDB, n ).
           Before entry,  the leading  m by n part of the array  B must
           contain the matrix  B,  and  on exit  is overwritten  by the
           transformed matrix.

  LDB    - INTEGER.
           On entry, LDB specifies the first dimension of B as declared
           in  the  calling  (sub)  program.   LDB  must  be  at  least
           max( 1, m ).
           Unchanged on exit.


  Level 3 Blas routine.

  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        side -
        uplo -
        transa -
        diag -
        m -
        n -
        alpha -
        a -
        lda -
        b -
        ldb -

      • strmv

        public abstract void strmv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           float[] a,
                           int lda,
                           float[] x,
                           int incx)
        
     ..

  Purpose
  =======

  STRMV  performs one of the matrix-vector operations

     x := A*x,   or   x := A'*x,

  where x is an n element vector and  A is an n by n unit, or non-unit,
  upper or lower triangular matrix.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   x := A*x.

              TRANS = 'T' or 't'   x := A'*x.

              TRANS = 'C' or 'c'   x := A'*x.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, n ).
           Before entry with  UPLO = 'U' or 'u', the leading n by n
           upper triangular part of the array A must contain the upper

           triangular matrix and the strictly lower triangular part of

           A is not referenced.
           Before entry with UPLO = 'L' or 'l', the leading n by n
           lower triangular part of the array A must contain the lower

           triangular matrix and the strictly upper triangular part of

           A is not referenced.
           Note that when  DIAG = 'U' or 'u', the diagonal elements of

           A are not referenced either, but are assumed to be unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, n ).
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x. On exit, X is overwritten with the
           tranformed vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        a -
        lda -
        x -
        incx -

      • strsm

        public abstract void strsm(java.lang.String side,
                           java.lang.String uplo,
                           java.lang.String transa,
                           java.lang.String diag,
                           int m,
                           int n,
                           float alpha,
                           float[] a,
                           int lda,
                           float[] b,
                           int ldb)
        
     ..

  Purpose
  =======

  STRSM  solves one of the matrix equations

     op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,

  where alpha is a scalar, X and B are m by n matrices, A is a unit, or
  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

     op( A ) = A   or   op( A ) = A'.

  The matrix X is overwritten on B.

  Arguments
  ==========

  SIDE   - CHARACTER*1.
           On entry, SIDE specifies whether op( A ) appears on the left
           or right of X as follows:

              SIDE = 'L' or 'l'   op( A )*X = alpha*B.

              SIDE = 'R' or 'r'   X*op( A ) = alpha*B.

           Unchanged on exit.

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix A is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANSA - CHARACTER*1.
           On entry, TRANSA specifies the form of op( A ) to be used in
           the matrix multiplication as follows:

              TRANSA = 'N' or 'n'   op( A ) = A.

              TRANSA = 'T' or 't'   op( A ) = A'.

              TRANSA = 'C' or 'c'   op( A ) = A'.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit triangular
           as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  M      - INTEGER.
           On entry, M specifies the number of rows of B. M must be at

           least zero.
           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the number of columns of B.  N must be
           at least zero.
           Unchanged on exit.

  ALPHA  - REAL            .
           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
           zero then  A is not referenced and  B need not be set before
           entry.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, k ), where k is m
           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
           upper triangular part of the array  A must contain the upper
           triangular matrix  and the strictly lower triangular part of
           A is not referenced.
           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
           lower triangular part of the array  A must contain the lower
           triangular matrix  and the strictly upper triangular part of
           A is not referenced.
           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
           A  are not referenced either,  but are assumed to be  unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
           then LDA must be at least max( 1, n ).
           Unchanged on exit.

  B      - REAL             array of DIMENSION ( LDB, n ).
           Before entry,  the leading  m by n part of the array  B must
           contain  the  right-hand  side  matrix  B,  and  on exit  is
           overwritten by the solution matrix  X.

  LDB    - INTEGER.
           On entry, LDB specifies the first dimension of B as declared
           in  the  calling  (sub)  program.   LDB  must  be  at  least
           max( 1, m ).
           Unchanged on exit.


  Level 3 Blas routine.


  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.


     .. External Functions ..
        Parameters:
        side -
        uplo -
        transa -
        diag -
        m -
        n -
        alpha -
        a -
        lda -
        b -
        ldb -

      • strsv

        public abstract void strsv(java.lang.String uplo,
                           java.lang.String trans,
                           java.lang.String diag,
                           int n,
                           float[] a,
                           int lda,
                           float[] x,
                           int incx)
        
     ..

  Purpose
  =======

  STRSV  solves one of the systems of equations

     A*x = b,   or   A'*x = b,

  where b and x are n element vectors and A is an n by n unit, or
  non-unit, upper or lower triangular matrix.

  No test for singularity or near-singularity is included in this
  routine. Such tests must be performed before calling this routine.

  Arguments
  ==========

  UPLO   - CHARACTER*1.
           On entry, UPLO specifies whether the matrix is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

           Unchanged on exit.

  TRANS  - CHARACTER*1.
           On entry, TRANS specifies the equations to be solved as
           follows:

              TRANS = 'N' or 'n'   A*x = b.

              TRANS = 'T' or 't'   A'*x = b.

              TRANS = 'C' or 'c'   A'*x = b.

           Unchanged on exit.

  DIAG   - CHARACTER*1.
           On entry, DIAG specifies whether or not A is unit
           triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.

           Unchanged on exit.

  N      - INTEGER.
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  A      - REAL             array of DIMENSION ( LDA, n ).
           Before entry with  UPLO = 'U' or 'u', the leading n by n
           upper triangular part of the array A must contain the upper

           triangular matrix and the strictly lower triangular part of

           A is not referenced.
           Before entry with UPLO = 'L' or 'l', the leading n by n
           lower triangular part of the array A must contain the lower

           triangular matrix and the strictly upper triangular part of

           A is not referenced.
           Note that when  DIAG = 'U' or 'u', the diagonal elements of

           A are not referenced either, but are assumed to be unity.
           Unchanged on exit.

  LDA    - INTEGER.
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, n ).
           Unchanged on exit.

  X      - REAL             array of dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element right-hand side vector b. On exit, X is overwritten

           with the solution vector x.

  INCX   - INTEGER.
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.


  Level 2 Blas routine.

  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.


     .. Parameters ..
        Parameters:
        uplo -
        trans -
        diag -
        n -
        a -
        lda -
        x -
        incx -
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