Class Matrix
- java.lang.Object
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- jhplot.math.kalman.jama.Matrix
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- All Implemented Interfaces:
- java.io.Serializable, java.lang.Cloneable
public class Matrix extends java.lang.Object implements java.lang.Cloneable, java.io.Serializable
Jama = Java Matrix class.The Java Matrix Class provides the fundamental operations of numerical linear algebra. Various constructors create Matrices from two dimensional arrays of double precision floating point numbers. Various "gets" and "sets" provide access to submatrices and matrix elements. Several methods implement basic matrix arithmetic, including matrix addition and multiplication, matrix norms, and element-by-element array operations. Methods for reading and printing matrices are also included. All the operations in this version of the Matrix Class involve real matrices. Complex matrices may be handled in a future version.
Five fundamental matrix decompositions, which consist of pairs or triples of matrices, permutation vectors, and the like, produce results in five decomposition classes. These decompositions are accessed by the Matrix class to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions. The five decompositions are:
- Cholesky Decomposition of symmetric, positive definite matrices.
- LU Decomposition of rectangular matrices.
- QR Decomposition of rectangular matrices.
- Singular Value Decomposition of rectangular matrices.
- Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.
- Example of use:
- Solve a linear system A x = b and compute the residual norm, ||b - A x||.
double[][] vals = {{1.,2.,3},{4.,5.,6.},{7.,8.,10.}}; Matrix A = new Matrix(vals); Matrix b = Matrix.random(3,1); Matrix x = A.solve(b); Matrix r = A.times(x).minus(b); double rnorm = r.normInf();
- See Also:
- Serialized Form
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Constructor Summary
Constructors Constructor and Description Matrix(double[][] A)
Construct a matrix from a 2-D array.Matrix(double[][] A, int m, int n)
Construct a matrix quickly without checking arguments.Matrix(double[] vals, int m)
Construct a matrix from a one-dimensional packed arrayMatrix(int m, int n)
Construct an m-by-n matrix of zeros.Matrix(int m, int n, double s)
Construct an m-by-n constant matrix.
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method and Description Matrix
arrayLeftDivide(Matrix B)
Element-by-element left division, C = A.\BMatrix
arrayLeftDivideEquals(Matrix B)
Element-by-element left division in place, A = A.\BMatrix
arrayRightDivide(Matrix B)
Element-by-element right division, C = A./BMatrix
arrayRightDivideEquals(Matrix B)
Element-by-element right division in place, A = A./BMatrix
arrayTimes(Matrix B)
Element-by-element multiplication, C = A.*BMatrix
arrayTimesEquals(Matrix B)
Element-by-element multiplication in place, A = A.*Bjava.lang.Object
clone()
Clone the Matrix object.static Matrix
constructWithCopy(double[][] A)
Construct a matrix from a copy of a 2-D array.Matrix
copy()
Make a deep copy of a matrixdouble
det()
Matrix determinantMatrix
gemm(Matrix B, Matrix C, double alpha, double beta)
Generalized linear algebraic matrix-matrix multiplication (of A); C = alpha*A x B + beta*C.double
get(int i, int j)
Get a single element.double[][]
getArray()
Access the internal two-dimensional array.double[][]
getArrayCopy()
Copy the internal two-dimensional array.int
getColumnDimension()
Get column dimension.double[]
getColumnPackedCopy()
Make a one-dimensional column packed copy of the internal array.Matrix
getMatrix(int[] r, int[] c)
Get a submatrix.Matrix
getMatrix(int[] r, int j0, int j1)
Get a submatrix.Matrix
getMatrix(int i0, int i1, int[] c)
Get a submatrix.Matrix
getMatrix(int i0, int i1, int j0, int j1)
Get a submatrix.int
getRowDimension()
Get row dimension.double[]
getRowPackedCopy()
Make a one-dimensional row packed copy of the internal array.Matrix
identity()
Generate identity matrixstatic Matrix
identity(int m, int n)
Generate identity matrixstatic Matrix
identity(int m, int n, double value)
Generate identity matrixMatrix
inverse()
Matrix inverse or pseudoinverseMatrix
minus(Matrix B)
C = A - BMatrix
minusEquals(Matrix B)
A = A - Bdouble
norm1()
One normdouble
normF()
Frobenius normdouble
normInf()
Infinity normMatrix
plus(Matrix B)
C = A + BMatrix
plusEquals(Matrix B)
A = A + Bvoid
print(int w, int d)
Print the matrix to stdout.void
print(java.text.NumberFormat format, int width)
Print the matrix to stdout.void
print(java.io.PrintWriter output, int w, int d)
Print the matrix to the output stream.void
print(java.io.PrintWriter output, java.text.NumberFormat format, int width)
Print the matrix to the output stream.QRDecomposition
qr()
QR Decompositionstatic Matrix
random(int m, int n)
Generate matrix with random elementsstatic Matrix
read(java.io.BufferedReader input)
Read a matrix from a stream.void
set(int i, int j, double s)
Set a single element.void
setMatrix(int[] r, int[] c, Matrix X)
Set a submatrix.void
setMatrix(int[] r, int j0, int j1, Matrix X)
Set a submatrix.void
setMatrix(int i0, int i1, int[] c, Matrix X)
Set a submatrix.void
setMatrix(int i0, int i1, int j0, int j1, Matrix X)
Set a submatrix.Matrix
solve(Matrix B)
Solve A*X = BMatrix
solveTranspose(Matrix B)
Solve X*A = B, which is also A'*X' = B'Matrix
times(double s)
Multiply a matrix by a scalar, C = s*AMatrix
times(Matrix B)
Linear algebraic matrix multiplication, A * BMatrix
timesEquals(double s)
Multiply a matrix by a scalar in place, A = s*Ajava.lang.String
toString()
Overrides the ObjecttoString()
method.java.lang.String
toString(int w, int d)
Hybrid toString.double
trace()
Matrix trace.Matrix
transpose()
Matrix transpose.Matrix
uminus()
Unary minus
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Constructor Detail
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Matrix
public Matrix(int m, int n)
Construct an m-by-n matrix of zeros.- Parameters:
m
- Number of rows.n
- Number of colums.
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Matrix
public Matrix(int m, int n, double s)
Construct an m-by-n constant matrix.- Parameters:
m
- Number of rows.n
- Number of colums.s
- Fill the matrix with this scalar value.
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Matrix
public Matrix(double[][] A)
Construct a matrix from a 2-D array.- Parameters:
A
- Two-dimensional array of doubles.- Throws:
java.lang.IllegalArgumentException
- All rows must have the same length- See Also:
constructWithCopy(double[][])
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Matrix
public Matrix(double[][] A, int m, int n)
Construct a matrix quickly without checking arguments.- Parameters:
A
- Two-dimensional array of doubles.m
- Number of rows.n
- Number of colums.
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Matrix
public Matrix(double[] vals, int m)
Construct a matrix from a one-dimensional packed array- Parameters:
vals
- One-dimensional array of doubles, packed by columns (ala Fortran).m
- Number of rows.- Throws:
java.lang.IllegalArgumentException
- Array length must be a multiple of m.
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Method Detail
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constructWithCopy
public static Matrix constructWithCopy(double[][] A)
Construct a matrix from a copy of a 2-D array.- Parameters:
A
- Two-dimensional array of doubles.- Throws:
java.lang.IllegalArgumentException
- All rows must have the same length
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copy
public Matrix copy()
Make a deep copy of a matrix
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clone
public java.lang.Object clone()
Clone the Matrix object.- Overrides:
clone
in classjava.lang.Object
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getArray
public double[][] getArray()
Access the internal two-dimensional array.- Returns:
- Pointer to the two-dimensional array of matrix elements.
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getArrayCopy
public double[][] getArrayCopy()
Copy the internal two-dimensional array.- Returns:
- Two-dimensional array copy of matrix elements.
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getColumnPackedCopy
public double[] getColumnPackedCopy()
Make a one-dimensional column packed copy of the internal array.- Returns:
- Matrix elements packed in a one-dimensional array by columns.
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getRowPackedCopy
public double[] getRowPackedCopy()
Make a one-dimensional row packed copy of the internal array.- Returns:
- Matrix elements packed in a one-dimensional array by rows.
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getRowDimension
public int getRowDimension()
Get row dimension.- Returns:
- m, the number of rows.
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getColumnDimension
public int getColumnDimension()
Get column dimension.- Returns:
- n, the number of columns.
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get
public double get(int i, int j)
Get a single element.- Parameters:
i
- Row index.j
- Column index.- Returns:
- A(i,j)
- Throws:
java.lang.ArrayIndexOutOfBoundsException
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getMatrix
public Matrix getMatrix(int i0, int i1, int j0, int j1)
Get a submatrix.- Parameters:
i0
- Initial row indexi1
- Final row indexj0
- Initial column indexj1
- Final column index- Returns:
- A(i0:i1,j0:j1)
- Throws:
java.lang.ArrayIndexOutOfBoundsException
- Submatrix indices
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getMatrix
public Matrix getMatrix(int[] r, int[] c)
Get a submatrix.- Parameters:
r
- Array of row indices.c
- Array of column indices.- Returns:
- A(r(:),c(:))
- Throws:
java.lang.ArrayIndexOutOfBoundsException
- Submatrix indices
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getMatrix
public Matrix getMatrix(int i0, int i1, int[] c)
Get a submatrix.- Parameters:
i0
- Initial row indexi1
- Final row indexc
- Array of column indices.- Returns:
- A(i0:i1,c(:))
- Throws:
java.lang.ArrayIndexOutOfBoundsException
- Submatrix indices
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getMatrix
public Matrix getMatrix(int[] r, int j0, int j1)
Get a submatrix.- Parameters:
r
- Array of row indices.i0
- Initial column indexi1
- Final column index- Returns:
- A(r(:),j0:j1)
- Throws:
java.lang.ArrayIndexOutOfBoundsException
- Submatrix indices
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set
public void set(int i, int j, double s)
Set a single element.- Parameters:
i
- Row index.j
- Column index.s
- A(i,j).- Throws:
java.lang.ArrayIndexOutOfBoundsException
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setMatrix
public void setMatrix(int i0, int i1, int j0, int j1, Matrix X)
Set a submatrix.- Parameters:
i0
- Initial row indexi1
- Final row indexj0
- Initial column indexj1
- Final column indexX
- A(i0:i1,j0:j1)- Throws:
java.lang.ArrayIndexOutOfBoundsException
- Submatrix indices
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setMatrix
public void setMatrix(int[] r, int[] c, Matrix X)
Set a submatrix.- Parameters:
r
- Array of row indices.c
- Array of column indices.X
- A(r(:),c(:))- Throws:
java.lang.ArrayIndexOutOfBoundsException
- Submatrix indices
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setMatrix
public void setMatrix(int[] r, int j0, int j1, Matrix X)
Set a submatrix.- Parameters:
r
- Array of row indices.j0
- Initial column indexj1
- Final column indexX
- A(r(:),j0:j1)- Throws:
java.lang.ArrayIndexOutOfBoundsException
- Submatrix indices
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setMatrix
public void setMatrix(int i0, int i1, int[] c, Matrix X)
Set a submatrix.- Parameters:
i0
- Initial row indexi1
- Final row indexc
- Array of column indices.X
- A(i0:i1,c(:))- Throws:
java.lang.ArrayIndexOutOfBoundsException
- Submatrix indices
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transpose
public Matrix transpose()
Matrix transpose.- Returns:
- A'
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norm1
public double norm1()
One norm- Returns:
- maximum column sum.
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normInf
public double normInf()
Infinity norm- Returns:
- maximum row sum.
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normF
public double normF()
Frobenius norm- Returns:
- sqrt of sum of squares of all elements.
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uminus
public Matrix uminus()
Unary minus- Returns:
- -A
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plusEquals
public Matrix plusEquals(Matrix B)
A = A + B- Parameters:
B
- another matrix- Returns:
- A + B
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minusEquals
public Matrix minusEquals(Matrix B)
A = A - B- Parameters:
B
- another matrix- Returns:
- A - B
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arrayTimes
public Matrix arrayTimes(Matrix B)
Element-by-element multiplication, C = A.*B- Parameters:
B
- another matrix- Returns:
- A.*B
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arrayTimesEquals
public Matrix arrayTimesEquals(Matrix B)
Element-by-element multiplication in place, A = A.*B- Parameters:
B
- another matrix- Returns:
- A.*B
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arrayRightDivide
public Matrix arrayRightDivide(Matrix B)
Element-by-element right division, C = A./B- Parameters:
B
- another matrix- Returns:
- A./B
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arrayRightDivideEquals
public Matrix arrayRightDivideEquals(Matrix B)
Element-by-element right division in place, A = A./B- Parameters:
B
- another matrix- Returns:
- A./B
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arrayLeftDivide
public Matrix arrayLeftDivide(Matrix B)
Element-by-element left division, C = A.\B- Parameters:
B
- another matrix- Returns:
- A.\B
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arrayLeftDivideEquals
public Matrix arrayLeftDivideEquals(Matrix B)
Element-by-element left division in place, A = A.\B- Parameters:
B
- another matrix- Returns:
- A.\B
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times
public Matrix times(double s)
Multiply a matrix by a scalar, C = s*A- Parameters:
s
- scalar- Returns:
- s*A
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timesEquals
public Matrix timesEquals(double s)
Multiply a matrix by a scalar in place, A = s*A- Parameters:
s
- scalar- Returns:
- replace A by s*A
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times
public Matrix times(Matrix B)
Linear algebraic matrix multiplication, A * B- Parameters:
B
- another matrix- Returns:
- Matrix product, A * B
- Throws:
java.lang.IllegalArgumentException
- Matrix inner dimensions must agree.
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qr
public QRDecomposition qr()
QR Decomposition- Returns:
- QRDecomposition
- See Also:
QRDecomposition
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solve
public Matrix solve(Matrix B)
Solve A*X = B- Parameters:
B
- right hand side- Returns:
- solution if A is square, least squares solution otherwise
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solveTranspose
public Matrix solveTranspose(Matrix B)
Solve X*A = B, which is also A'*X' = B'- Parameters:
B
- right hand side- Returns:
- solution if A is square, least squares solution otherwise.
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inverse
public Matrix inverse()
Matrix inverse or pseudoinverse- Returns:
- inverse(A) if A is square, pseudoinverse otherwise.
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det
public double det()
Matrix determinant- Returns:
- determinant
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trace
public double trace()
Matrix trace.- Returns:
- sum of the diagonal elements.
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random
public static Matrix random(int m, int n)
Generate matrix with random elements- Parameters:
m
- Number of rows.n
- Number of colums.- Returns:
- An m-by-n matrix with uniformly distributed random elements.
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identity
public static Matrix identity(int m, int n)
Generate identity matrix- Parameters:
m
- Number of rows.n
- Number of colums.- Returns:
- An m-by-n matrix with ones on the diagonal and zeros elsewhere.
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print
public void print(int w, int d)
Print the matrix to stdout. Line the elements up in columns with a Fortran-like 'Fw.d' style format.- Parameters:
w
- Column width.d
- Number of digits after the decimal.
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print
public void print(java.io.PrintWriter output, int w, int d)
Print the matrix to the output stream. Line the elements up in columns with a Fortran-like 'Fw.d' style format.- Parameters:
output
- Output stream.w
- Column width.d
- Number of digits after the decimal.
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print
public void print(java.text.NumberFormat format, int width)
Print the matrix to stdout. Line the elements up in columns. Use the format object, and right justify within columns of width characters. Note that is the matrix is to be read back in, you probably will want to use a NumberFormat that is set to US Locale.- Parameters:
format
- A Formatting object for individual elements.width
- Field width for each column.- See Also:
DecimalFormat.setDecimalFormatSymbols(java.text.DecimalFormatSymbols)
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print
public void print(java.io.PrintWriter output, java.text.NumberFormat format, int width)
Print the matrix to the output stream. Line the elements up in columns. Use the format object, and right justify within columns of width characters. Note that is the matrix is to be read back in, you probably will want to use a NumberFormat that is set to US Locale.- Parameters:
output
- the output stream.format
- A formatting object to format the matrix elementswidth
- Column width.- See Also:
DecimalFormat.setDecimalFormatSymbols(java.text.DecimalFormatSymbols)
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read
public static Matrix read(java.io.BufferedReader input) throws java.io.IOException
Read a matrix from a stream. The format is the same the print method, so printed matrices can be read back in (provided they were printed using US Locale). Elements are separated by whitespace, all the elements for each row appear on a single line, the last row is followed by a blank line.- Parameters:
input
- the input stream.- Throws:
java.io.IOException
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gemm
public Matrix gemm(Matrix B, Matrix C, double alpha, double beta)
Generalized linear algebraic matrix-matrix multiplication (of A); C = alpha*A x B + beta*C.Matrix shapes: A(m x n), B(n x p), C(m x p).
After potential transpositions and shape conformance check; C[i,j] = alpha*Sum(A[i,k] * B[k,j]) + beta*C[i,j], k=0..n-1.
Use:
C = A.gemm(B, null, 1, 1); // similar to A.times(B);
C = A.transpose().gemm(B.transpose(), C, 1, -1);
- Parameters:
B
- the second source matrix.C
- the matrix where results are to be stored. Set this parameter to null to indicate that a new result matrix shall be constructed.alpha
- a scale factor.beta
- a result scale factor.- Returns:
- C product matrix (for convenience only).
- Throws:
java.lang.IllegalArgumentException
- if B.rows() != A.columns().java.lang.IllegalArgumentException
- if C.rows() != A.rows() || C.columns() != B.columns().java.lang.IllegalArgumentException
- if A == C || B == C.
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toString
public java.lang.String toString(int w, int d)
Hybrid toString.- See Also:
print(int w, int d)
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toString
public java.lang.String toString()
Overrides the ObjecttoString()
method.- Overrides:
toString
in classjava.lang.Object
- Returns:
- String tab-separated rows on separate lines
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identity
public Matrix identity()
Generate identity matrix- Returns:
- An m-by-n matrix with ones on the diagonal and zeros elsewhere.
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identity
public static Matrix identity(int m, int n, double value)
Generate identity matrix- Parameters:
m
- Number of rows.n
- Number of colums.- Returns:
- An m-by-n matrix with ones on the diagonal and zeros elsewhere.
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