PdMatrix

Documentation of 'jv.vecmath.PdMatrix' Java class PdMatrix ("JavaView Reference Manual")

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"JavaView^? v5.03.003"

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java.lang.Object
- jv.vecmath.PdMatrix

All Implemented Interfaces:

java.io.Serializable, PdMatrixIf
```
public class PdMatrix
extends java.lang.Object
implements java.io.Serializable, PdMatrixIf
```
Linear algebra class for small matrices of doubles. For methods on large matrices see jvx.numeric.PnMatrix.

See Also:

Serialized Form

Author:

Konrad Polthier

Version:

28.12.03, 1.40 revised (kp) New methods getRow() and getColumn().
12.03.02, 1.30 revised (kp) Two new method leftMult and rightMult for partial multiplication.
08.11.00, 1.20 revised (kp) Replace string formatting routines of Fmt with PuString.
07.09.99, 1.10 revised (kp) Some new methods added.
00.00.97, 1.00 created (kp)

Field Summary

Fields
Modifier and Type Field and Description

double[][] m_data
Data array containing the components of the vector.

Fields
Modifier and Type	Field and Description
`double[][]`	`m_data` Data array containing the components of the vector.

Constructor Summary

Constructors
Constructor and Description
`PdMatrix()` Create a new matrix of zero size.
`PdMatrix(double[][] x)` Constructs a matrix having same size and given initial data as given array.
`PdMatrix(int aSize)` Create a square matrix with given dimension.
`PdMatrix(int iSize, int jSize)` Create a non-square matrix with given dimensions.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`add(PdMatrix m)` Add given matrix to this, this = this+m.
`void`	`add(PdMatrix m1, PdMatrix m2)` Add two matrices and assign to this, this = m1+m2.
`void`	`addEntry(int i, int j, double value)` Add value to component of matrix, and possibly enlarge matrix if too small.
`boolean`	`adjoint(PdVector v)` Compute `this = v * v^t` using adjoint(v, v).
`boolean`	`adjoint(PdVector v, PdVector w)` Compute `this = v * w^t`.
`void`	`blend(double a, PdMatrix u, double b, PdMatrix v, double c, PdMatrix w)` Interpolate between three matrices with given weights, i.e.
`void`	`blend(PdBary bary, PdMatrix u, PdMatrix v, PdMatrix w)` Interpolate between three matrices with given barycentric weights.
`void`	`clear()` Set all entries to zero.
`java.lang.Object`	`clone()` Duplicate matrix and data array.
`void`	`copy(PdMatrix m)` Copy given matrix to this, this = m.
`static boolean`	`copy(PdMatrix[] dataDest, int destInd, PdMatrix[] dataSrc, int srcInd, int size)` Copy PdMatrix array.
`static PdMatrix`	`copyNew(PdMatrix mat)` Create a new matrix as clone of argument matrix.
`static PdMatrix[]`	`copyNew(PdMatrix[] data)` Duplicate PdMatrix array.
`static PdMatrix[]`	`copyNew(PdMatrix[] data, int size)` Duplicate data PdMatrix array to new PdMatrix array of given size.
`double`	`det()` Compute determinant square matrix with dimensions less or equal four.
`double`	`det33()` Compute determinant of (3*3) left upper block of matrix.
`static PdMatrix`	`expandComponents(PdMatrix mat, int dim)` Create a bigger matrix such that each original entry expands to a (dim, dim)-diagonal matrix.
`PdVector`	`getColumn(int aColumn)` Get column vector of matrix.
`double[][]`	`getEntries()` Return a copy of content of matrix as array of arrays of doubles.
`double`	`getEntry(int i, int j)` Get the component of matrix at (i-th row, j-th column).
`int`	`getISize()` Get number of rows of matrix.
`int`	`getJSize()` Get number of columns of matrix.
`int`	`getNumCols()` Get number of columns of matrix.
`int`	`getNumRows()` Get number of rows of matrix.
`PdVector`	`getRow(int aRow)` Get row vector of matrix.
`int`	`getSize()` Get dimension of square matrix, return -1 for non-square matrices.
`boolean`	`invert()` Invert a square matrix of dimension less than five by `this = inverse(this)`.
`boolean`	`invert(PdMatrix m)` Invert a square matrix of dimension less than five by `this = inverse(m)`.
`boolean`	`invert34(PdMatrix m)` Invert the top-left 3x4 square of a matrix44 in place.
`boolean`	`invertTopLeft(PdMatrix m, int aSubSize)` Invert the top-left subSize x subSize square of a matrix m in place and assign full matrix m to this matrix.
`boolean`	`isSquare()` Check if matrix is square.
`void`	`leftMult(PdMatrix m)` Multiply with square matrix from left of same sizes using `this = m*this`.
`void`	`leftMult(PdMatrix m, int size)` Multiply a submatrix of this matrix with a submatrix of the parameter matrix.
`PdVector`	`leftMultMatrix(PdVector out, PdVector in)` Multiply this matrix with vector and fill output vector, `out = this*in.`
`void`	`mult(PdMatrix mat1, PdMatrix mat2)` Multiply two matrices of possibly different sizes using `this = mat1*mat2`.
`double`	`multQuadratic(PdVector left, PdVector right)` Compute `left^Tthisright`.
`void`	`multScalar(double scalar)` Multiply all matrix components with scalar.
`void`	`multScalar(PdMatrix m, double scalar)` Multiply all matrix components of m with scalar s, this = m*s.
`static PdMatrix[]`	`realloc(PdMatrix[] data, int arraySize)` Allocate array of PdMatrix.
`static PdMatrix[]`	`realloc(PdMatrix[] data, int arraySize, int iSize, int jSize)` Allocate an array of PdMatrix with given length and matrix dimensions.
`void`	`rightMult(PdMatrix m)` Multiply with square matrix from right of same sizes using `this = this*m`.
`void`	`rightMult(PdMatrix m, int size)` Multiply a submatrix of this matrix with a submatrix of the parameter matrix..
`PdVector`	`rightMultMatrix(PdVector out, PdVector in)` Multiply this matrix with vector and fill output vector, `out = in*this.`
`void`	`set(double[] x)` Assign values of array assuming length of argument array is equal or bigger than available matrix entries.
`void`	`set(double[][] x)` Assign values of array, and adjust length of matrix if different from length of array.
`void`	`setColumn(int aColumn, PdVector aVector)` Set column vector of matrix.
`void`	`setColumns(PdVector[] aVector)` Fill matrix with array of column vectors.
`void`	`setConstant(double aValue)` Set all matrix entries to a constant value.
`void`	`setDiagonal(double diag)` Set diagonal entries of a square matrix to given double value.
`void`	`setDiagonal(PdVector diag)` Set diagonal entries of a square matrix to components of a given vector.
`void`	`setEntry(int i, int j, double value)` Assign value to component of matrix, and possibly enlarge matrix if too small.
`void`	`setIdentity()` Initialize square matrix to be identity matrix.
`void`	`setRow(int aRow, PdVector aVector)` Set row vector of matrix.
`void`	`setRows(PdVector[] aVector)` Fill matrix with array of row vectors.
`void`	`setSize(int size)` Resize square matrix with new dimension (size, size).
`void`	`setSize(int iSize, int jSize)` Resize matrix to new dimension (iSize, jSize) with iSize rows and jSize columns.
`void`	`sub(PdMatrix m)` Subtract given matrix from this, this = this-m.
`void`	`sub(PdMatrix m1, PdMatrix m2)` Subtract two matrices and assign to this, this = m1-m2.
`java.lang.String`	`toShortString()` Create a short string representation of matrix with all instance variables.
`java.lang.String`	`toString()` Create a multi-line string representation with detailed information about all instance variables.
`void`	`transpose()` Transpose a square matrix by `this = transpose(this)`.
`void`	`transpose(PdMatrix m)` Transpose a matrix by `this = transpose(m)`.

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Field Detail
  - m_data
```
public double[][] m_data
```
    Data array containing the components of the vector. Array has public access for efficiency reasons in numerical computations, although method access should be preferred. Do not modify length of array directly.
- Constructor Detail
  - PdMatrix
```
public PdMatrix()
```
    Create a new matrix of zero size.
    
    Version:
    
    27.12.01, 1.10 revised (kp) Now allocate arrays with zero length.
  - PdMatrix
```
public PdMatrix(int aSize)
```
    Create a square matrix with given dimension.
  - PdMatrix
```
public PdMatrix(int iSize,
                int jSize)
```
    Create a non-square matrix with given dimensions.
  - PdMatrix
```
public PdMatrix(double[][] x)
```
    Constructs a matrix having same size and given initial data as given array.
    
    Version:
    
    20.07.00, 1.00 created (kp).
- Method Detail
  - realloc
```
public static PdMatrix[] realloc(PdMatrix[] data,
                                 int arraySize,
                                 int iSize,
                                 int jSize)
```
    Allocate an array of PdMatrix with given length and matrix dimensions. If existing data is given then method tries to reused existing data, otherwise missing data is newly allocated.
    
    Parameters:
    
    data - null or existing array of matrices
    
    arraySize - length of array to be allocated
    
    iSize - number of rows
    
    jSize - number of columns
  - realloc
```
public static PdMatrix[] realloc(PdMatrix[] data,
                                 int arraySize)
```
    Allocate array of PdMatrix.
  - clone
```
public java.lang.Object clone()
```
    Duplicate matrix and data array. Method just returns result of copyNew(PdMatrix).
    
    Overrides:
    
    clone in class java.lang.Object
    
    See Also:
    
    copyNew(PdMatrix)
    
    Version:
    
    05.07.00, 1.00 created (kp)
  - copyNew
```
public static PdMatrix[] copyNew(PdMatrix[] data)
```
    Duplicate PdMatrix array.
  - copyNew
```
public static PdMatrix[] copyNew(PdMatrix[] data,
                                 int size)
```
    Duplicate data PdMatrix array to new PdMatrix array of given size.
  - copyNew
```
public static PdMatrix copyNew(PdMatrix mat)
```
    Create a new matrix as clone of argument matrix.
    
    Version:
    
    29.04.01, 1.10 revised (kp) Do not break if source matrix is empty.
  - copy
```
public static boolean copy(PdMatrix[] dataDest,
                           int destInd,
                           PdMatrix[] dataSrc,
                           int srcInd,
                           int size)
```
    Copy PdMatrix array.
  - set
```
public void set(double[][] x)
```
    Assign values of array, and adjust length of matrix if different from length of array.
    
    Version:
    
    20.07.00 created (kp)
  - set
```
public void set(double[] x)
```
    Assign values of array assuming length of argument array is equal or bigger than available matrix entries. That means, the first entries of the vector are used to completely fill the matrix. Size of matrix is not changed.
    
    Since:
    
    JavaView v4.00.009
    
    Version:
    
    26.11.12 created (kp)
  - getNumRows
```
public int getNumRows()
```
    Get number of rows of matrix.
    
    Specified by:
    
    getNumRows in interface PdMatrixIf
  - getNumCols
```
public int getNumCols()
```
    Get number of columns of matrix.
    
    Specified by:
    
    getNumCols in interface PdMatrixIf
  - getISize
```
public int getISize()
```
    Get number of rows of matrix.
  - getJSize
```
public int getJSize()
```
    Get number of columns of matrix.
  - getSize
```
public int getSize()
```
    Get dimension of square matrix, return -1 for non-square matrices.
  - setSize
```
public void setSize(int size)
```
    Resize square matrix with new dimension (size, size). Existing content of matrix is kept as much as possible.
  - setSize
```
public void setSize(int iSize,
                    int jSize)
```
    Resize matrix to new dimension (iSize, jSize) with iSize rows and jSize columns. Existing content of matrix is kept as much as possible.
    
    Version:
    
    11.12.02, 2.00 revised (kp) Matrix now keeps original content.
  - getEntries
```
public double[][] getEntries()
```
    Return a copy of content of matrix as array of arrays of doubles.
  - getEntry
```
public double getEntry(int i,
                       int j)
```
    Get the component of matrix at (i-th row, j-th column).
    
    Specified by:
    
    getEntry in interface PdMatrixIf
  - setEntry
```
public void setEntry(int i,
                     int j,
                     double value)
```
    Assign value to component of matrix, and possibly enlarge matrix if too small.
    
    Specified by:
    
    setEntry in interface PdMatrixIf
    
    Version:
    
    09.08.10, 1.10 revised (ur) Enlarge matrix size for i and j separately. 17.07.00, 1.00 revised (kp) . 17.07.00, 1.00 created (kp)
  - addEntry
```
public void addEntry(int i,
                     int j,
                     double value)
```
    Add value to component of matrix, and possibly enlarge matrix if too small.
    
    Specified by:
    
    addEntry in interface PdMatrixIf
    
    Version:
    
    20.03.10, 1.00 revised (kp) . 20.03.10, 1.00 created (kp)
  - isSquare
```
public boolean isSquare()
```
    Check if matrix is square.
    
    Specified by:
    
    isSquare in interface PdMatrixIf
  - setIdentity
```
public void setIdentity()
```
    Initialize square matrix to be identity matrix.
    
    Version:
    
    12.07.13, 1.10 revised (kp) Use methods setConstant and setDiagonal.
  - setConstant
```
public void setConstant(double aValue)
```
    Set all matrix entries to a constant value.
  - clear
```
public void clear()
```
    Set all entries to zero.
    
    Specified by:
    
    clear in interface PdMatrixIf
  - setDiagonal
```
public void setDiagonal(double diag)
```
    Set diagonal entries of a square matrix to given double value. No other values of matrix are modified, i.e. used in conjunction e.g. with setConstant().
    
    Parameters:
    
    diag - Value of diagonal components
    
    Since:
    
    JavaView 4.04.009
    
    Version:
    
    12.07.13, 1.00 created (kp).
  - setDiagonal
```
public void setDiagonal(PdVector diag)
```
    Set diagonal entries of a square matrix to components of a given vector. No other values of matrix are modified, i.e. used in conjunction e.g. with setConstant(). Size of vector must be equal or larger than size of square matrix.
    
    Parameters:
    
    diag - Vector with diagonal components
  - getRow
```
public PdVector getRow(int aRow)
```
    Get row vector of matrix. Method returns null if row index out of bounds.
    
    Version:
    
    28.12.03, 1.00 created (kp)
  - setRow
```
public void setRow(int aRow,
                   PdVector aVector)
```
    Set row vector of matrix. Length of vector must be equal or greater than number of columns. Dimension of matrix is not modified.
  - getColumn
```
public PdVector getColumn(int aColumn)
```
    Get column vector of matrix. Method returns null if column index out of bounds.
    
    Version:
    
    28.12.03, 1.00 created (kp)
  - setColumn
```
public void setColumn(int aColumn,
                      PdVector aVector)
```
    Set column vector of matrix. Length of vector must be equal or greater than number of rows. Dimension of matrix is not modified.
  - setRows
```
public void setRows(PdVector[] aVector)
```
    Fill matrix with array of row vectors. Number of vectors and length of each vector must be equal or greater than corresponding sizes of matrix. Dimension of matrix is not modified.
  - setColumns
```
public void setColumns(PdVector[] aVector)
```
    Fill matrix with array of column vectors. Number of vectors and length of each vector must be equal or greater than corresponding sizes of matrix. Dimension of matrix is not modified.
  - add
```
public void add(PdMatrix m)
```
    Add given matrix to this, this = this+m. Dimensions of argument matrix must be equal or larger than of this.
  - add
```
public void add(PdMatrix m1,
                PdMatrix m2)
```
    Add two matrices and assign to this, this = m1+m2. Dimensions of argument matrices must be equal or larger than of this.
  - sub
```
public void sub(PdMatrix m)
```
    Subtract given matrix from this, this = this-m. Dimensions of argument matrix must be equal or larger than of this.
  - sub
```
public void sub(PdMatrix m1,
                PdMatrix m2)
```
    Subtract two matrices and assign to this, this = m1-m2. Dimensions of argument matrices must be equal or larger than of this.
  - copy
```
public void copy(PdMatrix m)
```
    Copy given matrix to this, this = m. Dimensions of argument matrix must be equal or larger than of this.
  - multScalar
```
public void multScalar(double scalar)
```
    Multiply all matrix components with scalar.
    
    Specified by:
    
    multScalar in interface PdMatrixIf
  - multScalar
```
public void multScalar(PdMatrix m,
                       double scalar)
```
    Multiply all matrix components of m with scalar s, this = m*s. Dimensions of argument matrix must be equal or larger than of this.
  - det
```
public double det()
```
    Compute determinant square matrix with dimensions less or equal four.
    
    Version:
    
    24.01.05, 1.10 revised (kp) Determinant of 4*4 matrix implemented.
  - det33
```
public double det33()
```
    Compute determinant of (3*3) left upper block of matrix.
  - leftMult
```
public void leftMult(PdMatrix m,
                     int size)
```
    Multiply a submatrix of this matrix with a submatrix of the parameter matrix. Size of 'this' does not change. Matrices must be larger than size of submatrix.
    
    Parameters:
    
    m - parameter matrix
    
    size - size of square sub matrix affected within this.
    
    Version:
    
    15.08.03, 1.10 revised (kp) Reduce memory allocation to single row from full matrix.
  - leftMult
```
public void leftMult(PdMatrix m)
```
    Multiply with square matrix from left of same sizes using this = m*this. Size of 'this' does not change.
    
    Version:
    
    10.08.10, 1.20 revised (ur) Bugfix - always use the correct dimensions.
    15.08.03, 1.10 revised (kp) Reduce memory allocation to single row from full matrix.
  - rightMult
```
public void rightMult(PdMatrix m,
                      int size)
```
    Multiply a submatrix of this matrix with a submatrix of the parameter matrix.. Size of 'this' does not change. Matrices must be larger than size of submatrix.
    
    Parameters:
    
    m - parameter matrix
    
    size - size of square sub matrix affected within this.
    
    Version:
    
    15.08.03, 1.10 revised (kp) Reduce memory allocation to single row from full matrix.
  - rightMult
```
public void rightMult(PdMatrix m)
```
    Multiply with square matrix from right of same sizes using this = this*m. Size of 'this' does not change.
    
    Version:
    
    10.08.10, 1.20 revised (ur) Always use the correct matrix dimensions.
    15.08.03, 1.10 revised (kp) Reduce memory allocation to single row from full matrix.
  - mult
```
public void mult(PdMatrix mat1,
                 PdMatrix mat2)
```
    Multiply two matrices of possibly different sizes using this = mat1*mat2. Size of 'this' is adjusted to have number of rows equal to first factor and number of columns equal to second factor.
    
    Version:
    
    10.08.10, 1.60 revised (ur) Added security check for compatible matrix dimensions.
    21.07.02, 1.50 revised (kp) Optimized if first argument matrix is sparse.
  - leftMultMatrix
```
public PdVector leftMultMatrix(PdVector out,
                               PdVector in)
```
    Multiply this matrix with vector and fill output vector, out = this*in.. Matrix need not be square. Input vector must have same size as number of columns of this matrix. Method modifies size of output vector to number of rows of this matrix. If output vector is null then it is created.
    Method calls PdVector.leftMultMatrix(PdMatrix, PdVector).
    
    Specified by:
    
    leftMultMatrix in interface PdMatrixIf
    
    Version:
    
    20.03.10, 1.00 created (kp) Created to sync with PnMatrixIf and PnSparseMatrix.
  - rightMultMatrix
```
public PdVector rightMultMatrix(PdVector out,
                                PdVector in)
```
    Multiply this matrix with vector and fill output vector, out = in*this.. Matrix need not be square. Input vector must have same size as number of rows of this matrix. Method modifies size of output vector to number of columns of this matrix. If output vector is null then it is created.
    Method calls PdVector.rightMultMatrix(PdVector, PdMatrix).
    
    Specified by:
    
    rightMultMatrix in interface PdMatrixIf
    
    Version:
    
    20.03.10, 1.00 created (kp) Created to sync with PnMatrixIf and PnSparseMatrix.
  - transpose
```
public void transpose()
```
    Transpose a square matrix by this = transpose(this).
    
    Specified by:
    
    transpose in interface PdMatrixIf
  - transpose
```
public void transpose(PdMatrix m)
```
    Transpose a matrix by this = transpose(m).
    
    Version:
    
    23.12.05, 1.10 revised (kp) Allow non-square matrices.
  - invert
```
public boolean invert()
```
    Invert a square matrix of dimension less than five by this = inverse(this).
  - invert
```
public boolean invert(PdMatrix m)
```
    Invert a square matrix of dimension less than five by this = inverse(m).
    
    Returns:
    
    false if error occurred, and if arg is singular call this.setIdentity().
    
    Version:
    
    14.03.06, 1.31 revised (kp) Bug in 4*4 inversion corrected which led to return of id matrix.
    27.01.05, 1.30 revised (ep) Removed warning that was thrown when matrix is not invertible.
    24.01.05, 1.20 revised (kp) Check size of this and argument, if arg is singular call this.setIdentity().
    02.06.04, 1.10 revised (kp) Check det against EPS instead of ZERO.
  - invertTopLeft
```
public boolean invertTopLeft(PdMatrix m,
                             int aSubSize)
```
    Invert the top-left subSize x subSize square of a matrix m in place and assign full matrix m to this matrix.
    In case of error set this to identity.
    
    Version:
    
    2019-10-07, 1.10 revised (kp) Initialize with original matrix only of submatrix is smaller.
  - invert34
```
public boolean invert34(PdMatrix m)
```
    Invert the top-left 3x4 square of a matrix44 in place.
  - adjoint
```
public boolean adjoint(PdVector v)
```
    Compute this = v * v^t using adjoint(v, v).
    
    Version:
    
    02.06.04, 1.10 revised (kp) Use adjoint(v,v).
  - adjoint
```
public boolean adjoint(PdVector v,
                       PdVector w)
```
    Compute this = v * w^t.
    
    Version:
    
    02.06.04, 1.10 revised (kp) Better check of sizes.
  - toString
```
public java.lang.String toString()
```
    Create a multi-line string representation with detailed information about all instance variables.
    
    Overrides:
    
    toString in class java.lang.Object
  - toShortString
```
public java.lang.String toShortString()
```
    Create a short string representation of matrix with all instance variables.
  - expandComponents
```
public static PdMatrix expandComponents(PdMatrix mat,
                                        int dim)
```
    Create a bigger matrix such that each original entry expands to a (dim, dim)-diagonal matrix.
  - blend
```
public void blend(double a,
                  PdMatrix u,
                  double b,
                  PdMatrix v,
                  double c,
                  PdMatrix w)
```
    Interpolate between three matrices with given weights, i.e. this = u*a + v*b + w*c. If the matrix 'this' is empty, the size of this is adjusted equal to the size of the matrix u. Otherwise interpolation is done up to length of result vector.
    
    Parameters:
    
    a - weight of first matrix
    
    u - first matrix
    
    b - weight of second matrix
    
    v - second matrix
    
    c - weight of third matrix
    
    w - third matrix
    
    Author:
    
    Klaus Hildebrandt
    
    Version:
    
    02.12.07, 1.00 created (kh)
  - blend
```
public void blend(PdBary bary,
                  PdMatrix u,
                  PdMatrix v,
                  PdMatrix w)
```
    Interpolate between three matrices with given barycentric weights. Uses this = u*bary.getEntry(0) + v*bary.getEntry(1) + w*bary.getEntry(2). If the matrix 'this' is empty, the size of this is adjusted equal to the size of the matrix u. Otherwise interpolation is done up to length of result vector.
    
    Parameters:
    
    bary - barycentric weights of three matrices
    
    u - first matrix
    
    v - second matrix
    
    w - third matrix
    
    Author:
    
    Klaus Hildebrandt
    
    Version:
    
    13.01.08, 1.01 revised (kp) Doc corrected.
    02.12.07, 1.00 created (kh)
  - multQuadratic
```
public double multQuadratic(PdVector left,
                            PdVector right)
```
    Compute left^T*this*right. The matrix is interpreted as a quadratic form.
    
    Specified by:
    
    multQuadratic in interface PdMatrixIf
    
    Parameters:
    
    left - The left argument.
    
    right - The right argument.
    
    Returns:
    
    left^T*this*right.

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Class PdMatrix

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

m_data

Constructor Detail

PdMatrix

PdMatrix

PdMatrix

PdMatrix

Method Detail

realloc

realloc

clone

copyNew

copyNew

copyNew

copy

set

set

getNumRows

getNumCols

getISize

getJSize

getSize

setSize

setSize

getEntries

getEntry

setEntry

addEntry

isSquare

setIdentity

setConstant

clear

setDiagonal

setDiagonal

getRow

setRow

getColumn

setColumn

setRows

setColumns

add

add

sub

sub

copy

multScalar

multScalar

det

det33

leftMult

leftMult

rightMult

rightMult

mult

leftMultMatrix

rightMultMatrix

transpose

transpose

invert

invert

invertTopLeft

invert34

adjoint

adjoint

toString

toShortString

expandComponents

blend

blend

multQuadratic