org.ejml.dense.row.CommonOps_ZDRM Maven / Gradle / Ivy
/*
* Copyright (c) 2020, Peter Abeles. All Rights Reserved.
*
* This file is part of Efficient Java Matrix Library (EJML).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.ejml.dense.row;
import org.ejml.EjmlParameters;
import org.ejml.LinearSolverSafe;
import org.ejml.UtilEjml;
import org.ejml.data.*;
import org.ejml.dense.row.decompose.lu.LUDecompositionAlt_ZDRM;
import org.ejml.dense.row.factory.LinearSolverFactory_ZDRM;
import org.ejml.dense.row.misc.TransposeAlgs_ZDRM;
import org.ejml.dense.row.mult.MatrixMatrixMult_ZDRM;
import org.ejml.interfaces.linsol.LinearSolverDense;
import org.jetbrains.annotations.Nullable;
import java.util.Arrays;
/**
* Common operations on complex numbers
*
* @author Peter Abeles
*/
public class CommonOps_ZDRM {
/**
*
* Creates an identity matrix of the specified size.
*
* aij = 0+0i if i ≠ j
* aij = 1+0i if i = j
*
*
* @param width The width and height of the identity matrix.
* @return A new instance of an identity matrix.
*/
public static ZMatrixRMaj identity( int width ) {
ZMatrixRMaj A = new ZMatrixRMaj(width, width);
for (int i = 0; i < width; i++) {
A.set(i, i, 1, 0);
}
return A;
}
/**
*
* Creates a matrix with diagonal elements set to 1 and the rest 0.
*
* aij = 0+0i if i ≠ j
* aij = 1+0i if i = j
*
*
* @param width The width of the identity matrix.
* @param height The height of the identity matrix.
* @return A new instance of an identity matrix.
*/
public static ZMatrixRMaj identity( int width, int height ) {
ZMatrixRMaj A = new ZMatrixRMaj(width, height);
int m = Math.min(width, height);
for (int i = 0; i < m; i++) {
A.set(i, i, 1, 0);
}
return A;
}
/**
*
* Creates a new square matrix whose diagonal elements are specified by data and all
* the other elements are zero.
*
* aij = 0 if i ≤ j
* aij = diag[i] if i = j
*
*
* @param data Contains the values of the diagonal elements of the resulting matrix.
* @return A new complex matrix.
*/
public static ZMatrixRMaj diag( double... data ) {
if (data.length%2 == 1)
throw new IllegalArgumentException("must be an even number of arguments");
return diag(new ZMatrixRMaj(1, 1), data.length/2, data);
}
public static ZMatrixRMaj diag( @Nullable ZMatrixRMaj output, int N, double... data ) {
output = UtilEjml.reshapeOrDeclare(output, N, N);
int index = 0;
for (int i = 0; i < N; i++) {
output.set(i, i, data[index++], data[index++]);
}
return output;
}
/**
*
* Extracts the diagonal elements 'src' write it to the 'dst' vector. 'dst'
* can either be a row or column vector.
*
*
* @param src Matrix whose diagonal elements are being extracted. Not modified.
* @param dst A vector the results will be written into. Modified.
*/
public static void extractDiag( ZMatrixRMaj src, ZMatrixRMaj dst ) {
int N = Math.min(src.numRows, src.numCols);
// reshape if it's not the right size
if (!MatrixFeatures_ZDRM.isVector(dst) || dst.numCols*dst.numCols != N) {
dst.reshape(N, 1);
}
for (int i = 0; i < N; i++) {
int index = src.getIndex(i, i);
dst.data[i*2] = src.data[index];
dst.data[i*2 + 1] = src.data[index + 1];
}
}
/**
* Converts the real matrix into a complex matrix.
*
* @param input Real matrix. Not modified.
* @param output Complex matrix. Modified.
*/
public static void convert( DMatrixD1 input, ZMatrixD1 output ) {
if (input.numCols != output.numCols || input.numRows != output.numRows) {
throw new IllegalArgumentException("The matrices are not all the same dimension.");
}
Arrays.fill(output.data, 0, output.getDataLength(), 0);
final int length = output.getDataLength();
for (int i = 0; i < length; i += 2) {
output.data[i] = input.data[i/2];
}
}
/**
* Places the real component of the input matrix into the output matrix.
*
* @param input Complex matrix. Not modified.
* @param output real matrix. Modified.
*/
public static DMatrixRMaj stripReal( ZMatrixD1 input, @Nullable DMatrixRMaj output ) {
output = UtilEjml.reshapeOrDeclare(output, input.numRows, input.numCols);
final int length = input.getDataLength();
for (int i = 0; i < length; i += 2) {
output.data[i/2] = input.data[i];
}
return output;
}
/**
* Places the imaginary component of the input matrix into the output matrix.
*
* @param input Complex matrix. Not modified.
* @param output real matrix. Modified.
*/
public static DMatrixRMaj stripImaginary( ZMatrixD1 input, @Nullable DMatrixRMaj output ) {
output = UtilEjml.reshapeOrDeclare(output, input.numRows, input.numCols);
final int length = input.getDataLength();
for (int i = 1; i < length; i += 2) {
output.data[i/2] = input.data[i];
}
return output;
}
/**
*
* Computes the magnitude of the complex number in the input matrix and stores the results in the output
* matrix.
*
*
* magnitude = sqrt(real^2 + imaginary^2)
*
* @param input Complex matrix. Not modified.
* @param output real matrix. Modified.
*/
public static void magnitude( ZMatrixD1 input, DMatrixD1 output ) {
output.reshape(input.numRows, input.numCols);
final int length = input.getDataLength();
for (int i = 0; i < length; i += 2) {
double real = input.data[i];
double imaginary = input.data[i + 1];
output.data[i/2] = Math.sqrt(real*real + imaginary*imaginary);
}
}
/**
*
* Computes the complex conjugate of the input matrix.
*
* reali,j = reali,j
* imaginaryi,j = -1*imaginaryi,j
*
*
* @param input Input matrix. Not modified.
* @param output The complex conjugate of the input matrix. Modified.
*/
public static ZMatrixD1 conjugate( ZMatrixD1 input, @Nullable ZMatrixRMaj output ) {
output = UtilEjml.reshapeOrDeclare(output, input.numRows, input.numCols);
final int length = input.getDataLength();
for (int i = 0; i < length; i += 2) {
output.data[i] = input.data[i];
output.data[i + 1] = -input.data[i + 1];
}
return output;
}
/**
*
* Sets every element in the matrix to the specified value.
*
* aij = value
*
*
* @param a A matrix whose elements are about to be set. Modified.
* @param real The real component
* @param imaginary The imaginary component
*/
public static void fill( ZMatrixD1 a, double real, double imaginary ) {
int N = a.getDataLength();
for (int i = 0; i < N; i += 2) {
a.data[i] = real;
a.data[i + 1] = imaginary;
}
}
/**
*
Performs the following operation:
*
* c = a + b
* cij = aij + bij
*
*
*
* Matrix C can be the same instance as Matrix A and/or B.
*
*
* @param a A Matrix. Not modified.
* @param b A Matrix. Not modified.
* @param c A Matrix where the results are stored. Modified.
*/
public static void add( ZMatrixD1 a, ZMatrixD1 b, ZMatrixD1 c ) {
UtilEjml.checkSameShape(a, b, true);
c.reshape(a.numRows, b.numCols);
final int length = a.getDataLength();
for (int i = 0; i < length; i++) {
c.data[i] = a.data[i] + b.data[i];
}
}
/**
* Performs the following operation:
*
* c = a - b
* cij = aij - bij
*
*
*
* Matrix C can be the same instance as Matrix A and/or B.
*
*
* @param a A Matrix. Not modified.
* @param b A Matrix. Not modified.
* @param c A Matrix where the results are stored. Modified.
*/
public static void subtract( ZMatrixD1 a, ZMatrixD1 b, ZMatrixD1 c ) {
UtilEjml.checkSameShape(a, b, true);
c.reshape(a.numRows, b.numCols);
final int length = a.getDataLength();
for (int i = 0; i < length; i++) {
c.data[i] = a.data[i] - b.data[i];
}
}
/**
*
* Performs an in-place element by element scalar multiplication.
*
* aij = α*aij
*
*
* @param a The matrix that is to be scaled. Modified.
* @param alphaReal real component of scale factor
* @param alphaImag imaginary component of scale factor
*/
public static void scale( double alphaReal, double alphaImag, ZMatrixD1 a ) {
// on very small matrices (2 by 2) the call to getNumElements() can slow it down
// slightly compared to other libraries since it involves an extra multiplication.
final int size = a.getNumElements()*2;
for (int i = 0; i < size; i += 2) {
double real = a.data[i];
double imag = a.data[i + 1];
a.data[i] = real*alphaReal - imag*alphaImag;
a.data[i + 1] = real*alphaImag + imag*alphaReal;
}
}
/**
* Performs the following operation:
*
* c = a * b
*
* cij = ∑k=1:n { * aik * bkj}
*
*
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void mult( ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
if (b.numCols >= EjmlParameters.CMULT_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.mult_reorder(a, b, c);
} else {
MatrixMatrixMult_ZDRM.mult_small(a, b, c);
}
}
/**
* Performs the following operation:
*
* c = α * a * b
*
* cij = α ∑k=1:n { * aik * bkj}
*
*
* @param realAlpha real component of scaling factor.
* @param imgAlpha imaginary component of scaling factor.
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void mult( double realAlpha, double imgAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
if (b.numCols >= EjmlParameters.CMULT_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.mult_reorder(realAlpha, imgAlpha, a, b, c);
} else {
MatrixMatrixMult_ZDRM.mult_small(realAlpha, imgAlpha, a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = c + a * b
* cij = cij + ∑k=1:n { aik * bkj}
*
*
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multAdd( ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
if (b.numCols >= EjmlParameters.MULT_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.multAdd_reorder(a, b, c);
} else {
MatrixMatrixMult_ZDRM.multAdd_small(a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = c + α * a * b
* cij = cij + α * ∑k=1:n { aik * bkj}
*
*
* @param realAlpha real component of scaling factor.
* @param imgAlpha imaginary component of scaling factor.
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multAdd( double realAlpha, double imgAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
if (b.numCols >= EjmlParameters.CMULT_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.multAdd_reorder(realAlpha, imgAlpha, a, b, c);
} else {
MatrixMatrixMult_ZDRM.multAdd_small(realAlpha, imgAlpha, a, b, c);
}
}
/**
* Performs the following operation:
*
* c = aH * b
*
* cij = ∑k=1:n { aki * bkj}
*
*
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multTransA( ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
if (a.numCols >= EjmlParameters.CMULT_COLUMN_SWITCH ||
b.numCols >= EjmlParameters.CMULT_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.multTransA_reorder(a, b, c);
} else {
MatrixMatrixMult_ZDRM.multTransA_small(a, b, c);
}
}
/**
* Performs the following operation:
*
* c = α * aH * b
*
* cij = α ∑k=1:n { aki * bkj}
*
*
* @param realAlpha Real component of scaling factor.
* @param imagAlpha Imaginary component of scaling factor.
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multTransA( double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
// TODO add a matrix vectory multiply here
if (a.numCols >= EjmlParameters.CMULT_COLUMN_SWITCH ||
b.numCols >= EjmlParameters.CMULT_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.multTransA_reorder(realAlpha, imagAlpha, a, b, c);
} else {
MatrixMatrixMult_ZDRM.multTransA_small(realAlpha, imagAlpha, a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = a * bH
* cij = ∑k=1:n { aik * bjk}
*
*
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multTransB( ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
MatrixMatrixMult_ZDRM.multTransB(a, b, c);
}
/**
*
* Performs the following operation:
*
* c = α * a * bH
* cij = α ∑k=1:n { aik * bjk}
*
*
* @param realAlpha Real component of scaling factor.
* @param imagAlpha Imaginary component of scaling factor.
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multTransB( double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
// TODO add a matrix vectory multiply here
MatrixMatrixMult_ZDRM.multTransB(realAlpha, imagAlpha, a, b, c);
}
/**
*
* Performs the following operation:
*
* c = aT * bT
* cij = ∑k=1:n { aki * bjk}
*
*
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multTransAB( ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
if (a.numCols >= EjmlParameters.CMULT_TRANAB_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.multTransAB_aux(a, b, c, null);
} else {
MatrixMatrixMult_ZDRM.multTransAB(a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = α * aH * bH
* cij = α ∑k=1:n { aki * bjk}
*
*
* @param realAlpha Real component of scaling factor.
* @param imagAlpha Imaginary component of scaling factor.
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multTransAB( double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
// TODO add a matrix vectory multiply here
if (a.numCols >= EjmlParameters.CMULT_TRANAB_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.multTransAB_aux(realAlpha, imagAlpha, a, b, c, null);
} else {
MatrixMatrixMult_ZDRM.multTransAB(realAlpha, imagAlpha, a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = c + aH * b
* cij = cij + ∑k=1:n { aki * bkj}
*
*
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multAddTransA( ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
if (a.numCols >= EjmlParameters.CMULT_COLUMN_SWITCH ||
b.numCols >= EjmlParameters.CMULT_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.multAddTransA_reorder(a, b, c);
} else {
MatrixMatrixMult_ZDRM.multAddTransA_small(a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = c + α * aH * b
* cij =cij + α * ∑k=1:n { aki * bkj}
*
*
* @param realAlpha Real component of scaling factor.
* @param imagAlpha Imaginary component of scaling factor.
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multAddTransA( double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
// TODO add a matrix vectory multiply here
if (a.numCols >= EjmlParameters.CMULT_COLUMN_SWITCH ||
b.numCols >= EjmlParameters.CMULT_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.multAddTransA_reorder(realAlpha, imagAlpha, a, b, c);
} else {
MatrixMatrixMult_ZDRM.multAddTransA_small(realAlpha, imagAlpha, a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = c + a * bH
* cij = cij + ∑k=1:n { aik * bjk}
*
*
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multAddTransB( ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
MatrixMatrixMult_ZDRM.multAddTransB(a, b, c);
}
/**
*
* Performs the following operation:
*
* c = c + α * a * bH
* cij = cij + α * ∑k=1:n { aik * bjk}
*
*
* @param realAlpha Real component of scaling factor.
* @param imagAlpha Imaginary component of scaling factor.
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multAddTransB( double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
// TODO add a matrix vectory multiply here
MatrixMatrixMult_ZDRM.multAddTransB(realAlpha, imagAlpha, a, b, c);
}
/**
*
* Performs the following operation:
*
* c = c + aH * bH
* cij = cij + ∑k=1:n { aki * bjk}
*
*
* @param a The left matrix in the multiplication operation. Not Modified.
* @param b The right matrix in the multiplication operation. Not Modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multAddTransAB( ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
if (a.numCols >= EjmlParameters.CMULT_TRANAB_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.multAddTransAB_aux(a, b, c, null);
} else {
MatrixMatrixMult_ZDRM.multAddTransAB(a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = c + α * aH * bH
* cij = cij + α * ∑k=1:n { aki * bjk}
*
*
* @param realAlpha Real component of scaling factor.
* @param imagAlpha Imaginary component of scaling factor.
* @param a The left matrix in the multiplication operation. Not Modified.
* @param b The right matrix in the multiplication operation. Not Modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multAddTransAB( double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c ) {
// TODO add a matrix vectory multiply here
if (a.numCols >= EjmlParameters.CMULT_TRANAB_COLUMN_SWITCH) {
MatrixMatrixMult_ZDRM.multAddTransAB_aux(realAlpha, imagAlpha, a, b, c, null);
} else {
MatrixMatrixMult_ZDRM.multAddTransAB(realAlpha, imagAlpha, a, b, c);
}
}
/**
* Performs an "in-place" transpose.
*
*
* For square matrices the transpose is truly in-place and does not require
* additional memory. For non-square matrices, internally a temporary matrix is declared and
* {@link #transpose(ZMatrixRMaj, ZMatrixRMaj)} is invoked.
*
*
* @param mat The matrix that is to be transposed. Modified.
*/
public static void transpose( ZMatrixRMaj mat ) {
if (mat.numCols == mat.numRows) {
TransposeAlgs_ZDRM.square(mat);
} else {
ZMatrixRMaj b = new ZMatrixRMaj(mat.numCols, mat.numRows);
transpose(mat, b);
mat.reshape(b.numRows, b.numCols);
mat.set(b);
}
}
/**
* Performs an "in-place" conjugate transpose.
*
* @param mat The matrix that is to be transposed. Modified.
* @see #transpose(ZMatrixRMaj)
*/
public static void transposeConjugate( ZMatrixRMaj mat ) {
if (mat.numCols == mat.numRows) {
TransposeAlgs_ZDRM.squareConjugate(mat);
} else {
ZMatrixRMaj b = new ZMatrixRMaj(mat.numCols, mat.numRows);
transposeConjugate(mat, b);
mat.reshape(b.numRows, b.numCols);
mat.set(b);
}
}
/**
*
* Transposes input matrix 'a' and stores the results in output matrix 'b':
*
* bij = aji
* where 'b' is the transpose of 'a'.
*
*
* @param input The original matrix. Not modified.
* @param output Where the transpose is stored. If null a new matrix is created. Modified.
* @return The transposed matrix.
*/
public static ZMatrixRMaj transpose( ZMatrixRMaj input, @Nullable ZMatrixRMaj output ) {
output = UtilEjml.reshapeOrDeclare(output, input.numCols, input.numRows);
TransposeAlgs_ZDRM.standard(input, output);
return output;
}
/**
*
* Conjugate transposes input matrix 'a' and stores the results in output matrix 'b':
*
* b-reali,j = a-realj,i
* b-imaginaryi,j = -1*a-imaginaryj,i
* where 'b' is the transpose of 'a'.
*
*
* @param input The original matrix. Not modified.
* @param output Where the transpose is stored. If null a new matrix is created. Modified.
* @return The transposed matrix.
*/
public static ZMatrixRMaj transposeConjugate( ZMatrixRMaj input, @Nullable ZMatrixRMaj output ) {
output = UtilEjml.reshapeOrDeclare(output, input.numCols, input.numRows);
TransposeAlgs_ZDRM.standardConjugate(input, output);
return output;
}
/**
*
* Performs a matrix inversion operation on the specified matrix and stores the results
* in the same matrix.
*
* a = a-1
*
*
*
* If the algorithm could not invert the matrix then false is returned. If it returns true
* that just means the algorithm finished. The results could still be bad
* because the matrix is singular or nearly singular.
*
*
* @param A The matrix that is to be inverted. Results are stored here. Modified.
* @return true if it could invert the matrix false if it could not.
*/
public static boolean invert( ZMatrixRMaj A ) {
LinearSolverDense solver = LinearSolverFactory_ZDRM.lu(A.numRows);
if (solver.setA(A)) {
solver.invert(A);
} else {
return false;
}
return true;
}
/**
*
* Performs a matrix inversion operation that does not modify the original
* and stores the results in another matrix. The two matrices must have the
* same dimension.
*
* b = a-1
*
*
*
* If the algorithm could not invert the matrix then false is returned. If it returns true
* that just means the algorithm finished. The results could still be bad
* because the matrix is singular or nearly singular.
*
*
*
* For medium to large matrices there might be a slight performance boost to using
* {@link LinearSolverFactory_ZDRM} instead.
*
*
* @param input The matrix that is to be inverted. Not modified.
* @param output Where the inverse matrix is stored. Modified.
* @return true if it could invert the matrix false if it could not.
*/
public static boolean invert( ZMatrixRMaj input, ZMatrixRMaj output ) {
LinearSolverDense solver = LinearSolverFactory_ZDRM.lu(input.numRows);
if (solver.modifiesA())
input = input.copy();
if (!solver.setA(input))
return false;
solver.invert(output);
return true;
}
/**
*
* Solves for x in the following equation:
*
* A*x = b
*
*
*
* If the system could not be solved then false is returned. If it returns true
* that just means the algorithm finished operating, but the results could still be bad
* because 'A' is singular or nearly singular.
*
*
*
* If repeat calls to solve are being made then one should consider using {@link LinearSolverFactory_ZDRM}
* instead.
*
*
*
* It is ok for 'b' and 'x' to be the same matrix.
*
*
* @param a A matrix that is m by n. Not modified.
* @param b A matrix that is n by k. Not modified.
* @param x A matrix that is m by k. Modified.
* @return true if it could invert the matrix false if it could not.
*/
public static boolean solve( ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj x ) {
LinearSolverDense solver;
if (a.numCols == a.numRows) {
solver = LinearSolverFactory_ZDRM.lu(a.numRows);
} else {
solver = LinearSolverFactory_ZDRM.qr(a.numRows, a.numCols);
}
// make sure the inputs 'a' and 'b' are not modified
solver = new LinearSolverSafe(solver);
if (!solver.setA(a))
return false;
solver.solve(b, x);
return true;
}
/**
* Returns the determinant of the matrix. If the inverse of the matrix is also
* needed, then using {@link LUDecompositionAlt_ZDRM} directly (or any
* similar algorithm) can be more efficient.
*
* @param mat The matrix whose determinant is to be computed. Not modified.
* @return The determinant.
*/
public static Complex_F64 det( ZMatrixRMaj mat ) {
LUDecompositionAlt_ZDRM alg = new LUDecompositionAlt_ZDRM();
if (alg.inputModified()) {
mat = mat.copy();
}
if (!alg.decompose(mat))
return new Complex_F64();
return alg.computeDeterminant();
}
/**
* Performs element by element multiplication operation with a complex numbert
*
* outputij = inputij * (real + imaginary*i)
*
*
* @param input The left matrix in the multiplication operation. Not modified.
* @param real Real component of the number it is multiplied by
* @param imaginary Imaginary component of the number it is multiplied by
* @param output Where the results of the operation are stored. Modified.
*/
public static ZMatrixRMaj elementMultiply( ZMatrixD1 input, double real, double imaginary, @Nullable ZMatrixRMaj output ) {
output = UtilEjml.reshapeOrDeclare(output, input.numRows, input.numCols);
int N = input.getDataLength();
for (int i = 0; i < N; i += 2) {
double inReal = input.data[i];
double intImag = input.data[i + 1];
output.data[i] = inReal*real - intImag*imaginary;
output.data[i + 1] = inReal*imaginary + intImag*real;
}
return output;
}
/**
* Performs element by element division operation with a complex number on the right
*
* outputij = inputij / (real + imaginary*i)
*
*
* @param input The left matrix in the multiplication operation. Not modified.
* @param real Real component of the number it is multiplied by
* @param imaginary Imaginary component of the number it is multiplied by
* @param output Where the results of the operation are stored. Modified.
*/
public static ZMatrixRMaj elementDivide( ZMatrixD1 input, double real, double imaginary, @Nullable ZMatrixRMaj output ) {
output = UtilEjml.reshapeOrDeclare(output, input.numRows, input.numCols);
double norm = real*real + imaginary*imaginary;
int N = input.getDataLength();
for (int i = 0; i < N; i += 2) {
double inReal = input.data[i];
double inImag = input.data[i + 1];
output.data[i] = (inReal*real + inImag*imaginary)/norm;
output.data[i + 1] = (inImag*real - inReal*imaginary)/norm;
}
return output;
}
/**
* Performs element by element division operation with a complex number on the right
*
* outputij = (real + imaginary*i) / inputij
*
*
* @param real Real component of the number it is multiplied by
* @param imaginary Imaginary component of the number it is multiplied by
* @param input The right matrix in the multiplication operation. Not modified.
* @param output Where the results of the operation are stored. Modified.
*/
public static ZMatrixRMaj elementDivide( double real, double imaginary, ZMatrixD1 input, @Nullable ZMatrixRMaj output ) {
output = UtilEjml.reshapeOrDeclare(output, input.numRows, input.numCols);
int N = input.getDataLength();
for (int i = 0; i < N; i += 2) {
double inReal = input.data[i];
double inImag = input.data[i + 1];
double norm = inReal*inReal + inImag*inImag;
output.data[i] = (real*inReal + imaginary*inImag)/norm;
output.data[i + 1] = (imaginary*inReal - real*inImag)/norm;
}
return output;
}
/**
*
* Returns the value of the real element in the matrix that has the minimum value.
*
* Min{ aij } for all i and j
*
*
* @param a A matrix. Not modified.
* @return The the minimum value out of all the real values.
*/
public static double elementMinReal( ZMatrixD1 a ) {
final int size = a.getDataLength();
double min = a.data[0];
for (int i = 2; i < size; i += 2) {
double val = a.data[i];
if (val < min) {
min = val;
}
}
return min;
}
/**
*
* Returns the value of the imaginary element in the matrix that has the minimum value.
*
* Min{ aij } for all i and j
*
*
* @param a A matrix. Not modified.
* @return The the minimum value out of all the real values.
*/
public static double elementMinImaginary( ZMatrixD1 a ) {
final int size = a.getDataLength();
double min = a.data[1];
for (int i = 3; i < size; i += 2) {
double val = a.data[i];
if (val < min) {
min = val;
}
}
return min;
}
/**
*
* Returns the value of the real element in the matrix that has the minimum value.
*
* Min{ aij } for all i and j
*
*
* @param a A matrix. Not modified.
* @return The the minimum value out of all the real values.
*/
public static double elementMaxReal( ZMatrixD1 a ) {
final int size = a.getDataLength();
double max = a.data[0];
for (int i = 2; i < size; i += 2) {
double val = a.data[i];
if (val > max) {
max = val;
}
}
return max;
}
/**
*
* Returns the value of the imaginary element in the matrix that has the minimum value.
*
* Min{ aij } for all i and j
*
*
* @param a A matrix. Not modified.
* @return The the minimum value out of all the real values.
*/
public static double elementMaxImaginary( ZMatrixD1 a ) {
final int size = a.getDataLength();
double max = a.data[1];
for (int i = 3; i < size; i += 2) {
double val = a.data[i];
if (val > max) {
max = val;
}
}
return max;
}
/**
*
* Returns the magnitude squared of the complex element with the largest magnitude
*
* Max{ |aij|^2 } for all i and j
*
*
* @param a A matrix. Not modified.
* @return The max magnitude squared
*/
public static double elementMaxMagnitude2( ZMatrixD1 a ) {
final int size = a.getDataLength();
double max = 0;
for (int i = 0; i < size; ) {
double real = a.data[i++];
double imaginary = a.data[i++];
double m = real*real + imaginary*imaginary;
if (m > max) {
max = m;
}
}
return max;
}
/**
* Sets all the diagonal elements equal to one and everything else equal to zero.
* If this is a square matrix then it will be an identity matrix.
*
* @param mat A square matrix.
*/
public static void setIdentity( ZMatrixRMaj mat ) {
int width = mat.numRows < mat.numCols ? mat.numRows : mat.numCols;
Arrays.fill(mat.data, 0, mat.getDataLength(), 0);
int index = 0;
int stride = mat.getRowStride();
for (int i = 0; i < width; i++, index += stride + 2) {
mat.data[index] = 1;
}
}
/**
*
* Creates a new matrix which is the specified submatrix of 'src'
*
*
* si-y0 , j-x0 = oij for all y0 ≤ i < y1 and x0 ≤ j < x1
*
* where 'sij' is an element in the submatrix and 'oij' is an element in the
* original matrix.
*
*
* @param src The original matrix which is to be copied. Not modified.
* @param srcX0 Start column.
* @param srcX1 Stop column+1.
* @param srcY0 Start row.
* @param srcY1 Stop row+1.
* @return Extracted submatrix.
*/
public static ZMatrixRMaj extract( ZMatrixRMaj src,
int srcY0, int srcY1,
int srcX0, int srcX1 ) {
if (srcY1 <= srcY0 || srcY0 < 0 || srcY1 > src.numRows)
throw new IllegalArgumentException("srcY1 <= srcY0 || srcY0 < 0 || srcY1 > src.numRows");
if (srcX1 <= srcX0 || srcX0 < 0 || srcX1 > src.numCols)
throw new IllegalArgumentException("srcX1 <= srcX0 || srcX0 < 0 || srcX1 > src.numCols");
int w = srcX1 - srcX0;
int h = srcY1 - srcY0;
ZMatrixRMaj dst = new ZMatrixRMaj(h, w);
extract(src, srcY0, srcY1, srcX0, srcX1, dst, 0, 0);
return dst;
}
/**
*
* Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.
*
*
* si-y0 , j-x0 = oij for all y0 ≤ i < y1 and x0 ≤ j < x1
*
* where 'sij' is an element in the submatrix and 'oij' is an element in the
* original matrix.
*
*
* @param src The original matrix which is to be copied. Not modified.
* @param srcX0 Start column.
* @param srcX1 Stop column+1.
* @param srcY0 Start row.
* @param srcY1 Stop row+1.
* @param dst Where the submatrix are stored. Modified.
* @param dstY0 Start row in dst.
* @param dstX0 start column in dst.
*/
public static void extract( ZMatrixRMaj src,
int srcY0, int srcY1,
int srcX0, int srcX1,
ZMatrixRMaj dst,
int dstY0, int dstX0 ) {
int numRows = srcY1 - srcY0;
int stride = (srcX1 - srcX0)*2;
for (int y = 0; y < numRows; y++) {
int indexSrc = src.getIndex(y + srcY0, srcX0);
int indexDst = dst.getIndex(y + dstY0, dstX0);
System.arraycopy(src.data, indexSrc, dst.data, indexDst, stride);
}
}
/**
* Converts the columns in a matrix into a set of vectors.
*
* @param A Matrix. Not modified.
* @param v Optional storage for columns.
* @return An array of vectors.
*/
public static ZMatrixRMaj[] columnsToVector( ZMatrixRMaj A, @Nullable ZMatrixRMaj[] v ) {
ZMatrixRMaj[] ret;
if (v == null || v.length < A.numCols) {
ret = new ZMatrixRMaj[A.numCols];
} else {
ret = v;
}
for (int i = 0; i < ret.length; i++) {
if (ret[i] == null) {
ret[i] = new ZMatrixRMaj(A.numRows, 1);
} else {
ret[i].reshape(A.numRows, 1);
}
ZMatrixRMaj u = ret[i];
int indexU = 0;
for (int j = 0; j < A.numRows; j++) {
int indexA = A.getIndex(j, i);
u.data[indexU++] = A.data[indexA++];
u.data[indexU++] = A.data[indexA];
}
}
return ret;
}
/**
*
* Returns the largest absolute value of any element in the matrix.
*
* Max{ |aij| } for all i and j
*
*
* @param a A matrix. Not modified.
* @return The max abs element value in the matrix.
*/
public static double elementMaxAbs( ZMatrixRMaj a ) {
final int size = a.getDataLength();
double max = 0;
for (int i = 0; i < size; i += 2) {
double real = a.data[i];
double imag = a.data[i + 1];
double val = real*real + imag*imag;
if (val > max) {
max = val;
}
}
return Math.sqrt(max);
}
/**
*
* Returns the smallest absolute value of any element in the matrix.
*
* Min{ |aij| } for all i and j
*
*
* @param a A matrix. Not modified.
* @return The min abs element value in the matrix.
*/
public static double elementMinAbs( ZMatrixRMaj a ) {
final int size = a.getDataLength();
double min = Double.MAX_VALUE;
for (int i = 0; i < size; i += 2) {
double real = a.data[i];
double imag = a.data[i + 1];
double val = real*real + imag*imag;
if (val < min) {
min = val;
}
}
return Math.sqrt(min);
}
}