fr.cnes.sirius.patrius.math.optim.joptimizer.algebra

Class AlgebraUtils

java.lang.Object

fr.cnes.sirius.patrius.math.optim.joptimizer.algebra.AlgebraUtils

public final class AlgebraUtils
extends Object

Algebraic utility operations.

Since:

4.6

Author:

alberto trivellato (alberto.trivellato@gmail.com)

Method Summary

Modifier and Type	Method and Description
static RealMatrix	add(RealMatrix a, RealMatrix b, double beta) Returns C = A + beta * B (linear combination).
static RealVector	add(RealVector v1, RealVector v2, double c) Returns v = v1 + c * v2 (linear combination).
static void	checkRectangularShape(RealMatrix[][] array) Checks whether the given array is rectangular, that is, whether all rows have the same number of columns.
static RealMatrix	composeMatrix(RealMatrix[][] parts) Constructs a block matrix made from the given parts.
static RealMatrix	diagonal(RealVector vector) Constructs a new diagonal matrix whose diagonal elements are the elements of vector.
static RealMatrix	diagonalMatrixMult(RealMatrix a, RealVector diagonalU) Return A.diagonalU with diagonalU diagonal.
static RealMatrix	diagonalMatrixMult(RealVector diagonalU, RealMatrix a) Return diagonalU.A with diagonalU diagonal.
static RealMatrix	diagonalMatrixMult(RealVector diagonalU, RealMatrix a, RealVector diagonalV) Return diagonalU.A.diagonalV with diagonalU and diagonalV diagonal.
static RealVector	diagonalMatrixMult(RealVector diagonalM, RealVector vector) Matrix-vector multiplication with diagonal matrix.
static RealMatrix	fillSubdiagonalSymmetricMatrix(RealMatrix s) Given a symm matrix S that stores just its subdiagonal elements, reconstructs the full symmetric matrix.
static double[]	getConditionNumberRange(RealMatrix a, int p) Returns a lower and an upper bound for the condition number kp(A) = Norm[A, p] / Norm[A^-1, p] where Norm[A, p] = sup ( Norm[A.x, p]/Norm[x, p] , x !
static RealVector	randomValuesVector(int dim, double min, double max, Long seed) Return a vector with random values
static RealVector	replaceValues(RealVector v, double oldValue, double newValue) Return a new array with all the occurrences of oldValue replaced by newValue.
static RealMatrix	subdiagonalMultiply(RealMatrix a, RealMatrix b) Return the sub-diagonal result of the multiplication.
static RealVector	zMult(RealMatrix matA, RealVector a, RealVector b, double beta) Returns v = A.a + beta*b.
static RealVector	zMultTranspose(RealMatrix matA, RealVector a, RealVector b, double beta) Returns v = A[T].a + beta*b.

Methods inherited from class java.lang.Object

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

Method Detail

diagonalMatrixMult

public static final RealVector diagonalMatrixMult(RealVector diagonalM,
                                                  RealVector vector)

Matrix-vector multiplication with diagonal matrix.

Parameters:

diagonalM - diagonal matrix M, in the form of a vector of its diagonal elements

vector - vector

Returns:

M.x

diagonalMatrixMult

public static final RealMatrix diagonalMatrixMult(RealVector diagonalU,
                                                  RealMatrix a)

Return diagonalU.A with diagonalU diagonal.

Parameters:

diagonalU - matrix U, in the form of a vector of its diagonal elements

a - matrix A

Returns:

U.A

diagonalMatrixMult

public static final RealMatrix diagonalMatrixMult(RealMatrix a,
                                                  RealVector diagonalU)

Return A.diagonalU with diagonalU diagonal.

Parameters:

a - matrix A

diagonalU - matrix U, in the form of a vector of its diagonal elements

Returns:

U.A

diagonalMatrixMult

public static final RealMatrix diagonalMatrixMult(RealVector diagonalU,
                                                  RealMatrix a,
                                                  RealVector diagonalV)

Return diagonalU.A.diagonalV with diagonalU and diagonalV diagonal.

Parameters:

diagonalU - diagonal matrix U, in the form of a vector of its diagonal elements

a - matrix A

diagonalV - diagonal matrix V, in the form of a vector of its diagonal elements

Returns:

U.A.V

subdiagonalMultiply

public static RealMatrix subdiagonalMultiply(RealMatrix a,
                                             RealMatrix b)

Return the sub-diagonal result of the multiplication. If A is sparse, returns a sparse matrix (even if, generally speaking, the multiplication of two sparse matrices is not sparse) because the result is at least 50% (aside the diagonal elements) sparse.

Parameters:

a - matrix

b - matrix

Returns:

sub-diagonal result of the multiplication

zMult

public static final RealVector zMult(RealMatrix matA,
                                     RealVector a,
                                     RealVector b,
                                     double beta)

Returns v = A.a + beta*b. Useful in avoiding the need of the copy() in the colt api.

Parameters:

matA - matrix A

a - vector

b - vector

beta - double

Returns:

v

zMultTranspose

public static final RealVector zMultTranspose(RealMatrix matA,
                                              RealVector a,
                                              RealVector b,
                                              double beta)

Returns v = A[T].a + beta*b. Useful in avoiding the need of the copy() in the colt api.

Parameters:

matA - matrix A

a - vector

b - vector

beta - constant

Returns:

v

add

public static final RealMatrix add(RealMatrix a,
                                   RealMatrix b,
                                   double beta)

Returns C = A + beta * B (linear combination). Useful in avoiding the need of the copy() in the colt api.

Parameters:

a - matrix

b - matrix

beta - constant

Returns:

C

add

public static final RealVector add(RealVector v1,
                                   RealVector v2,
                                   double c)

Returns v = v1 + c * v2 (linear combination). Useful in avoiding the need of the copy() in the colt api.

Parameters:

v1 - vector

v2 - vector

c - constant

Returns:

v

replaceValues

public static final RealVector replaceValues(RealVector v,
                                             double oldValue,
                                             double newValue)

Return a new array with all the occurrences of oldValue replaced by newValue.

Parameters:

v - vector

oldValue - value to be replaced

newValue - value to replace with

Returns:

new array

getConditionNumberRange

public static double[] getConditionNumberRange(RealMatrix a,
                                               int p)

Returns a lower and an upper bound for the condition number
kp(A) = Norm[A, p] / Norm[A^-1, p]
where
Norm[A, p] = sup ( Norm[A.x, p]/Norm[x, p] , x !=0 )
for a matrix and
Norm[x, 1] := Sum[MathLib.abs(x[i]), i]
Norm[x, 2] := MathLib.sqrt(Sum[MathLib.pow(x[i], 2), i])
Norm[x, 00] := Max[MathLib.abs(x[i]), i]
for a vector.

Parameters:

a - matrix you want the condition number of

p - norm order (2 or Integer.MAX_VALUE)

Returns:

an array with the two bounds (lower and upper bound) See Ravindra S. Gajulapalli, Leon S. Lasdon "Scaling Sparse Matrices for Optimization Algorithms"

fillSubdiagonalSymmetricMatrix

public static final RealMatrix fillSubdiagonalSymmetricMatrix(RealMatrix s)

Given a symm matrix S that stores just its subdiagonal elements, reconstructs the full symmetric matrix.

Parameters:

s - matrix

Returns:

full symmetric matrix

diagonal

public static RealMatrix diagonal(RealVector vector)

Constructs a new diagonal matrix whose diagonal elements are the elements of vector. Cells values are copied. The new matrix is not a view.

Parameters:

vector - with the diagonal values

Returns:

a new matrix.

randomValuesVector

public static RealVector randomValuesVector(int dim,
                                            double min,
                                            double max,
                                            Long seed)

Return a vector with random values

Parameters:

dim - dimension of the vector

min - minimum value

max - maximum value

seed - of the random number generator

Returns:

vector with random values

composeMatrix

public static RealMatrix composeMatrix(RealMatrix[][] parts)

Constructs a block matrix made from the given parts. All matrices of a given column within parts must have the same number of columns. All matrices of a given row within parts must have the same number of rows. Otherwise an IllegalArgumentException is thrown. Note that nulls within parts[row,col] are an exception to this rule: they are ignored. Cells are copied. From https://github.com/kzn/colt/blob/master/src/cern/colt/matrix/ DoubleFactory2D.java Extracted 17/11/2020

Parameters:

parts - matrices

Returns:

build matrix.

checkRectangularShape

public static void checkRectangularShape(RealMatrix[][] array)

Checks whether the given array is rectangular, that is, whether all rows have the same number of columns.

Parameters:

array - array

Throws:

IllegalArgumentException - if the array is not rectangular.