org.ejml.dense.row.CommonOps_DDRM Maven / Gradle / Ivy
/*
* Copyright (c) 2009-2020, 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.MatrixDimensionException;
import org.ejml.UtilEjml;
import org.ejml.data.*;
import org.ejml.dense.row.decomposition.TriangularSolver_DDRM;
import org.ejml.dense.row.decomposition.lu.LUDecompositionAlt_DDRM;
import org.ejml.dense.row.factory.LinearSolverFactory_DDRM;
import org.ejml.dense.row.linsol.chol.LinearSolverChol_DDRM;
import org.ejml.dense.row.linsol.lu.LinearSolverLu_DDRM;
import org.ejml.dense.row.linsol.svd.SolvePseudoInverseSvd_DDRM;
import org.ejml.dense.row.misc.*;
import org.ejml.dense.row.mult.MatrixMatrixMult_DDRM;
import org.ejml.dense.row.mult.MatrixMultProduct_DDRM;
import org.ejml.dense.row.mult.MatrixVectorMult_DDRM;
import org.ejml.dense.row.mult.VectorVectorMult_DDRM;
import org.ejml.interfaces.linsol.LinearSolverDense;
import org.ejml.interfaces.linsol.ReducedRowEchelonForm_F64;
import javax.annotation.Nullable;
import java.util.Arrays;
import static org.ejml.UtilEjml.stringShapes;
/**
*
* Common matrix operations are contained here. Which specific underlying algorithm is used
* is not specified just the out come of the operation. Nor should calls to these functions
* reply on the underlying implementation. Which algorithm is used can depend on the matrix
* being passed in.
*
*
* For more exotic and specialized generic operations see {@link SpecializedOps_DDRM}.
*
* @see MatrixMatrixMult_DDRM
* @see MatrixVectorMult_DDRM
* @see SpecializedOps_DDRM
* @see MatrixFeatures_DDRM
*
* @author Peter Abeles
*/
@SuppressWarnings({"ForLoopReplaceableByForEach"})
public class CommonOps_DDRM {
/**
* 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(DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
if( b.numCols == 1 ) {
MatrixVectorMult_DDRM.mult(a, b, c);
} else if( b.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.mult_reorder(a,b,c);
} else {
MatrixMatrixMult_DDRM.mult_small(a,b,c);
}
}
/**
* Performs the following operation:
*
* c = α * a * b
*
* cij = α ∑k=1:n { * aik * bkj}
*
*
* @param alpha 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 alpha , DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
// TODO add a matrix vectory multiply here
if( b.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.mult_reorder(alpha, a, b, c);
} else {
MatrixMatrixMult_DDRM.mult_small(alpha,a,b,c);
}
}
/**
* Performs the following operation:
*
* c = aT * 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(DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
if( b.numCols == 1 ) {
// todo check a.numCols == 1 and do inner product?
// there are significantly faster algorithms when dealing with vectors
if( a.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixVectorMult_DDRM.multTransA_reorder(a,b,c);
} else {
MatrixVectorMult_DDRM.multTransA_small(a,b,c);
}
} else if( a.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ||
b.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.multTransA_reorder(a, b, c);
} else {
MatrixMatrixMult_DDRM.multTransA_small(a, b, c);
}
}
/**
* Performs the following operation:
*
* c = α * aT * b
*
* cij = α ∑k=1:n { aki * bkj}
*
*
* @param alpha 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 alpha , DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
// TODO add a matrix vectory multiply here
if( a.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ||
b.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.multTransA_reorder(alpha, a, b, c);
} else {
MatrixMatrixMult_DDRM.multTransA_small(alpha, a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = a * bT
* 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(DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
if( b.numRows == 1 ) {
MatrixVectorMult_DDRM.mult(a, b, c);
} else {
MatrixMatrixMult_DDRM.multTransB(a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = α * a * bT
* cij = α ∑k=1:n { aik * bjk}
*
*
* @param alpha 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 alpha , DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
// TODO add a matrix vectory multiply here
MatrixMatrixMult_DDRM.multTransB(alpha,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(DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
if( b.numRows == 1) {
// there are significantly faster algorithms when dealing with vectors
if( a.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixVectorMult_DDRM.multTransA_reorder(a,b,c);
} else {
MatrixVectorMult_DDRM.multTransA_small(a,b,c);
}
} else if( a.numCols >= EjmlParameters.MULT_TRANAB_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.multTransAB_aux(a, b, c, null);
} else {
MatrixMatrixMult_DDRM.multTransAB(a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = α * aT * bT
* cij = α ∑k=1:n { aki * bjk}
*
*
* @param alpha 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 alpha , DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
// TODO add a matrix vectory multiply here
if( a.numCols >= EjmlParameters.MULT_TRANAB_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.multTransAB_aux(alpha, a, b, c, null);
} else {
MatrixMatrixMult_DDRM.multTransAB(alpha, a, b, c);
}
}
/**
*
* Computes the dot product or inner product between two vectors. If the two vectors are columns vectors
* then it is defined as:
* {@code dot(a,b) = aT * b}
* If the vectors are column or row or both is ignored by this function.
*
* @param a Vector
* @param b Vector
* @return Dot product of the two vectors
*/
public static double dot(DMatrixD1 a , DMatrixD1 b ) {
if( !MatrixFeatures_DDRM.isVector(a) || !MatrixFeatures_DDRM.isVector(b))
throw new RuntimeException("Both inputs must be vectors");
return VectorVectorMult_DDRM.innerProd(a,b);
}
/**
* Computes the matrix multiplication inner product:
*
* c = aT * a
*
* cij = ∑k=1:n { aki * akj}
*
*
*
* Is faster than using a generic matrix multiplication by taking advantage of symmetry. For
* vectors there is an even faster option, see {@link VectorVectorMult_DDRM#innerProd(DMatrixD1, DMatrixD1)}
*
*
* @param a The matrix being multiplied. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multInner(DMatrix1Row a , DMatrix1Row c )
{
c.reshape(a.numCols,a.numCols);
if( a.numCols >= EjmlParameters.MULT_INNER_SWITCH ) {
MatrixMultProduct_DDRM.inner_small(a, c);
} else {
MatrixMultProduct_DDRM.inner_reorder(a, c);
}
}
/**
* Computes the matrix multiplication outer product:
*
* c = a * aT
*
* cij = ∑k=1:m { aik * ajk}
*
*
*
* Is faster than using a generic matrix multiplication by taking advantage of symmetry.
*
*
* @param a The matrix being multiplied. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void multOuter(DMatrix1Row a , DMatrix1Row c )
{
c.reshape(a.numRows,a.numRows);
MatrixMultProduct_DDRM.outer(a, 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(DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
if( b.numCols == 1 ) {
MatrixVectorMult_DDRM.multAdd(a, b, c);
} else {
if( b.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.multAdd_reorder(a,b,c);
} else {
MatrixMatrixMult_DDRM.multAdd_small(a,b,c);
}
}
}
/**
*
* Performs the following operation:
*
* c = c + α * a * b
* cij = cij + α * ∑k=1:n { aik * bkj}
*
*
* @param alpha 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 alpha , DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
// TODO add a matrix vectory multiply here
if( b.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.multAdd_reorder(alpha, a, b, c);
} else {
MatrixMatrixMult_DDRM.multAdd_small(alpha,a,b,c);
}
}
/**
*
* Performs the following operation:
*
* c = c + aT * 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(DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
if( b.numCols == 1 ) {
if( a.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixVectorMult_DDRM.multAddTransA_reorder(a,b,c);
} else {
MatrixVectorMult_DDRM.multAddTransA_small(a,b,c);
}
} else {
if( a.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ||
b.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.multAddTransA_reorder(a, b, c);
} else {
MatrixMatrixMult_DDRM.multAddTransA_small(a, b, c);
}
}
}
/**
*
* Performs the following operation:
*
* c = c + α * aT * b
* cij =cij + α * ∑k=1:n { aki * bkj}
*
*
* @param alpha 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 alpha , DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
// TODO add a matrix vectory multiply here
if( a.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ||
b.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.multAddTransA_reorder(alpha, a, b, c);
} else {
MatrixMatrixMult_DDRM.multAddTransA_small(alpha, a, b, c);
}
}
/**
*
* Performs the following operation:
*
* c = c + a * bT
* 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(DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
MatrixMatrixMult_DDRM.multAddTransB(a,b,c);
}
/**
*
* Performs the following operation:
*
* c = c + α * a * bT
* cij = cij + α * ∑k=1:n { aik * bjk}
*
*
* @param alpha 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 alpha , DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
// TODO add a matrix vectory multiply here
MatrixMatrixMult_DDRM.multAddTransB(alpha,a,b,c);
}
/**
*
* Performs the following operation:
*
* c = c + aT * bT
* 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(DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
if( b.numRows == 1 ) {
// there are significantly faster algorithms when dealing with vectors
if( a.numCols >= EjmlParameters.MULT_COLUMN_SWITCH ) {
MatrixVectorMult_DDRM.multAddTransA_reorder(a,b,c);
} else {
MatrixVectorMult_DDRM.multAddTransA_small(a,b,c);
}
} else if( a.numCols >= EjmlParameters.MULT_TRANAB_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.multAddTransAB_aux(a,b,c,null);
} else {
MatrixMatrixMult_DDRM.multAddTransAB(a,b,c);
}
}
/**
*
* Performs the following operation:
*
* c = c + α * aT * bT
* cij = cij + α * ∑k=1:n { aki * bjk}
*
*
* @param alpha 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 alpha , DMatrix1Row a , DMatrix1Row b , DMatrix1Row c )
{
// TODO add a matrix vectory multiply here
if( a.numCols >= EjmlParameters.MULT_TRANAB_COLUMN_SWITCH ) {
MatrixMatrixMult_DDRM.multAddTransAB_aux(alpha, a, b, c, null);
} else {
MatrixMatrixMult_DDRM.multAddTransAB(alpha, a, b, c);
}
}
/**
*
* 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_DDRM}
* 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(DMatrixRMaj a , DMatrixRMaj b , DMatrixRMaj x )
{
x.reshape(a.numCols,b.numCols);
LinearSolverDense solver = LinearSolverFactory_DDRM.general(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;
}
/**
*
* Linear solver for systems which are symmetric positive definite.
* A*x = b
*
*
* @see UnrolledCholesky_DDRM
* @see LinearSolverFactory_DDRM
*
* @param A A matrix that is n by n and SPD. Not modified.
* @param b A matrix that is n by k. Not modified.
* @param x A matrix that is n by k. Modified.
* @return true if it could invert the matrix false if it could not.
*/
public static boolean solveSPD( DMatrixRMaj A , DMatrixRMaj b , DMatrixRMaj x )
{
if( A.numRows != A.numCols )
throw new IllegalArgumentException("Must be a square matrix");
x.reshape(A.numCols,b.numCols);
if( A.numRows <= UnrolledCholesky_DDRM.MAX ) {
DMatrixRMaj L = A.createLike();
// L*L' = A
if( !UnrolledCholesky_DDRM.lower(A,L) )
return false;
// if only one column then a faster method can be used
if( x.numCols == 1 ) {
x.set(b);
TriangularSolver_DDRM.solveL(L.data,x.data,L.numCols);
TriangularSolver_DDRM.solveTranL(L.data,x.data,L.numCols);
} else {
double vv[] = new double[A.numCols];
LinearSolverChol_DDRM.solveLower(L, b, x, vv);
}
} else {
LinearSolverDense solver = LinearSolverFactory_DDRM.chol(A.numCols);
solver = new LinearSolverSafe<>(solver);
if( !solver.setA(A) )
return false;
solver.solve(b, x);
return true;
}
return true;
}
/**
* 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(DMatrixRMaj, DMatrixRMaj)} is invoked.
*
*
* @param mat The matrix that is to be transposed. Modified.
*/
public static void transpose( DMatrixRMaj mat ) {
if( mat.numCols == mat.numRows ){
TransposeAlgs_DDRM.square(mat);
} else {
DMatrixRMaj b = new DMatrixRMaj(mat.numCols,mat.numRows);
transpose(mat,b);
mat.set(b);
}
}
/**
*
* Transposes matrix 'a' and stores the results in 'b':
*
* bij = aji
* where 'b' is the transpose of 'a'.
*
*
* @param A The original matrix. Not modified.
* @param A_tran Where the transpose is stored. If null a new matrix is created. Modified.
* @return The transposed matrix.
*/
public static DMatrixRMaj transpose(DMatrixRMaj A, DMatrixRMaj A_tran)
{
if( A_tran == null ) {
A_tran = new DMatrixRMaj(A.numCols,A.numRows);
} else {
if( A.numRows != A_tran.numCols || A.numCols != A_tran.numRows ) {
throw new MatrixDimensionException("Incompatible matrix dimensions");
}
}
if( A.numRows > EjmlParameters.TRANSPOSE_SWITCH &&
A.numCols > EjmlParameters.TRANSPOSE_SWITCH )
TransposeAlgs_DDRM.block(A,A_tran,EjmlParameters.BLOCK_WIDTH);
else
TransposeAlgs_DDRM.standard(A,A_tran);
return A_tran;
}
/**
*
* This computes the trace of the matrix:
*
* trace = ∑i=1:n { aii }
* where n = min(numRows,numCols)
*
*
* @param a A square matrix. Not modified.
*/
public static double trace( DMatrix1Row a ) {
int N = Math.min(a.numRows, a.numCols);
double sum = 0;
int index = 0;
for( int i = 0; i < N; i++ ) {
sum += a.get(index);
index += 1 + a.numCols;
}
return sum;
}
/**
* Returns the determinant of the matrix. If the inverse of the matrix is also
* needed, then using {@link org.ejml.interfaces.decomposition.LUDecomposition_F64} 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 double det( DMatrixRMaj mat )
{
int numCol = mat.getNumCols();
int numRow = mat.getNumRows();
if( numCol != numRow ) {
throw new MatrixDimensionException("Must be a square matrix.");
} else if( numCol <= UnrolledDeterminantFromMinor_DDRM.MAX ) {
// slight performance boost overall by doing it this way
// when it was the case statement the VM did some strange optimization
// and made case 2 about 1/2 the speed
if( numCol >= 2 ) {
return UnrolledDeterminantFromMinor_DDRM.det(mat);
} else {
return mat.get(0);
}
} else {
LUDecompositionAlt_DDRM alg = new LUDecompositionAlt_DDRM();
if( alg.inputModified() ) {
mat = mat.copy();
}
if( !alg.decompose(mat) )
return 0.0;
return alg.computeDeterminant().real;
}
}
/**
*
* 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 mat 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( DMatrixRMaj mat) {
if( mat.numCols <= UnrolledInverseFromMinor_DDRM.MAX ) {
if( mat.numCols != mat.numRows ) {
throw new MatrixDimensionException("Must be a square matrix.");
}
if( mat.numCols >= 2 ) {
UnrolledInverseFromMinor_DDRM.inv(mat,mat);
} else {
mat.set(0, 1.0/mat.get(0));
}
} else {
LUDecompositionAlt_DDRM alg = new LUDecompositionAlt_DDRM();
LinearSolverLu_DDRM solver = new LinearSolverLu_DDRM(alg);
if( solver.setA(mat) ) {
solver.invert(mat);
} 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_DDRM} instead.
*
*
* @param mat The matrix that is to be inverted. Not modified.
* @param result Where the inverse matrix is stored. Modified.
* @return true if it could invert the matrix false if it could not.
*/
public static boolean invert(DMatrixRMaj mat, DMatrixRMaj result ) {
result.reshape(mat.numRows,mat.numCols);
if( mat.numCols <= UnrolledInverseFromMinor_DDRM.MAX ) {
if( mat.numCols != mat.numRows ) {
throw new MatrixDimensionException("Must be a square matrix.");
}
if( result.numCols >= 2 ) {
UnrolledInverseFromMinor_DDRM.inv(mat,result);
} else {
result.set(0, 1.0/mat.get(0));
}
} else {
LUDecompositionAlt_DDRM alg = new LUDecompositionAlt_DDRM();
LinearSolverLu_DDRM solver = new LinearSolverLu_DDRM(alg);
if( solver.modifiesA() )
mat = mat.copy();
if( !solver.setA(mat))
return false;
solver.invert(result);
}
return true;
}
/**
* Matrix inverse for symmetric positive definite matrices. For small matrices an unrolled
* cholesky is used. Otherwise a standard decomposition.
*
* @see UnrolledCholesky_DDRM
* @see LinearSolverFactory_DDRM#chol(int)
*
* @param mat (Input) SPD matrix
* @param result (Output) Inverted matrix.
* @return true if it could invert the matrix false if it could not.
*/
public static boolean invertSPD(DMatrixRMaj mat, DMatrixRMaj result ) {
if( mat.numRows != mat.numCols )
throw new IllegalArgumentException("Must be a square matrix");
result.reshape(mat.numRows,mat.numRows);
if( mat.numRows <= UnrolledCholesky_DDRM.MAX ) {
// L*L' = A
if( !UnrolledCholesky_DDRM.lower(mat,result) )
return false;
// L = inv(L)
TriangularSolver_DDRM.invertLower(result.data,result.numCols);
// inv(A) = inv(L')*inv(L)
SpecializedOps_DDRM.multLowerTranA(result);
} else {
LinearSolverDense solver = LinearSolverFactory_DDRM.chol(mat.numCols);
if( solver.modifiesA() )
mat = mat.copy();
if( !solver.setA(mat))
return false;
solver.invert(result);
}
return true;
}
/**
*
* Computes the Moore-Penrose pseudo-inverse:
*
* pinv(A) = (ATA)-1 AT
* or
* pinv(A) = AT(AAT)-1
*
*
* Internally it uses {@link SolvePseudoInverseSvd_DDRM} to compute the inverse. For performance reasons, this should only
* be used when a matrix is singular or nearly singular.
*
* @param A A m by n Matrix. Not modified.
* @param invA Where the computed pseudo inverse is stored. n by m. Modified.
*/
public static void pinv(DMatrixRMaj A , DMatrixRMaj invA )
{
LinearSolverDense solver = LinearSolverFactory_DDRM.pseudoInverse(true);
if( solver.modifiesA())
A = A.copy();
if( !solver.setA(A) )
throw new IllegalArgumentException("Invert failed, maybe a bug?");
solver.invert(invA);
}
/**
* Converts the columns in a matrix into a set of vectors.
*
* @param A Matrix. Not modified.
* @param v
* @return An array of vectors.
*/
public static DMatrixRMaj[] columnsToVector(DMatrixRMaj A, DMatrixRMaj[] v)
{
DMatrixRMaj[]ret;
if( v == null || v.length < A.numCols ) {
ret = new DMatrixRMaj[ A.numCols ];
} else {
ret = v;
}
for( int i = 0; i < ret.length; i++ ) {
if( ret[i] == null ) {
ret[i] = new DMatrixRMaj(A.numRows,1);
} else {
ret[i].reshape(A.numRows,1, false);
}
DMatrixRMaj u = ret[i];
for( int j = 0; j < A.numRows; j++ ) {
u.set(j,0, A.get(j,i));
}
}
return ret;
}
/**
* Converts the rows in a matrix into a set of vectors.
*
* @param A Matrix. Not modified.
* @param v
* @return An array of vectors.
*/
public static DMatrixRMaj[] rowsToVector(DMatrixRMaj A, DMatrixRMaj[] v)
{
DMatrixRMaj[]ret;
if( v == null || v.length < A.numRows ) {
ret = new DMatrixRMaj[ A.numRows ];
} else {
ret = v;
}
for( int i = 0; i < ret.length; i++ ) {
if( ret[i] == null ) {
ret[i] = new DMatrixRMaj(A.numCols,1);
} else {
ret[i].reshape(A.numCols,1, false);
}
DMatrixRMaj u = ret[i];
for( int j = 0; j < A.numCols; j++ ) {
u.set(j,0, A.get(i,j));
}
}
return ret;
}
/**
* 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.
*
* @see #identity(int)
*
* @param mat A square matrix.
*/
public static void setIdentity( DMatrix1Row mat )
{
int width = mat.numRows < mat.numCols ? mat.numRows : mat.numCols;
Arrays.fill(mat.data,0,mat.getNumElements(),0);
int index = 0;
for( int i = 0; i < width; i++ , index += mat.numCols + 1) {
mat.data[index] = 1;
}
}
/**
*
* Creates an identity matrix of the specified size.
*
* aij = 0 if i ≠ j
* aij = 1 if i = j
*
*
* @param width The width and height of the identity matrix.
* @return A new instance of an identity matrix.
*/
public static DMatrixRMaj identity(int width )
{
DMatrixRMaj ret = new DMatrixRMaj(width,width);
for( int i = 0; i < width; i++ ) {
ret.set(i,i,1.0);
}
return ret;
}
/**
* Creates a rectangular matrix which is zero except along the diagonals.
*
* @param numRows Number of rows in the matrix.
* @param numCols NUmber of columns in the matrix.
* @return A matrix with diagonal elements equal to one.
*/
public static DMatrixRMaj identity(int numRows , int numCols )
{
DMatrixRMaj ret = new DMatrixRMaj(numRows,numCols);
int small = numRows < numCols ? numRows : numCols;
for( int i = 0; i < small; i++ ) {
ret.set(i,i,1.0);
}
return ret;
}
/**
*
* Creates a new square matrix whose diagonal elements are specified by diagEl and all
* the other elements are zero.
*
* aij = 0 if i ≤ j
* aij = diag[i] if i = j
*
*
* @see #diagR
*
* @param diagEl Contains the values of the diagonal elements of the resulting matrix.
* @return A new matrix.
*/
public static DMatrixRMaj diag(double ...diagEl )
{
return diag(null,diagEl.length,diagEl);
}
/**
* @see #diag(double...)
*/
public static DMatrixRMaj diag(DMatrixRMaj ret , int width , double ...diagEl )
{
if( ret == null ) {
ret = new DMatrixRMaj(width,width);
} else {
if( ret.numRows != width || ret.numCols != width )
throw new IllegalArgumentException("Unexpected matrix size");
CommonOps_DDRM.fill(ret, 0);
}
for( int i = 0; i < width; i++ ) {
ret.unsafe_set(i, i, diagEl[i]);
}
return ret;
}
/**
*
* Creates a new rectangular matrix whose diagonal elements are specified by diagEl and all
* the other elements are zero.
*
* aij = 0 if i ≤ j
* aij = diag[i] if i = j
*
*
* @see #diag
*
* @param numRows Number of rows in the matrix.
* @param numCols Number of columns in the matrix.
* @param diagEl Contains the values of the diagonal elements of the resulting matrix.
* @return A new matrix.
*/
public static DMatrixRMaj diagR(int numRows , int numCols , double ...diagEl )
{
DMatrixRMaj ret = new DMatrixRMaj(numRows,numCols);
int o = Math.min(numRows,numCols);
for( int i = 0; i < o; i++ ) {
ret.set(i, i, diagEl[i]);
}
return ret;
}
/**
*
* The Kronecker product of two matrices is defined as:
* Cij = aijB
* where Cij is a sub matrix inside of C ∈ ℜ m*k × n*l,
* A ∈ ℜ m × n, and B ∈ ℜ k × l.
*
*
* @param A The left matrix in the operation. Not modified.
* @param B The right matrix in the operation. Not modified.
* @param C Where the results of the operation are stored. Modified.
*/
public static void kron(DMatrixRMaj A , DMatrixRMaj B , DMatrixRMaj C )
{
int numColsC = A.numCols*B.numCols;
int numRowsC = A.numRows*B.numRows;
if( C.numCols != numColsC || C.numRows != numRowsC) {
throw new MatrixDimensionException("C does not have the expected dimensions");
}
// TODO see comment below
// this will work well for small matrices
// but an alternative version should be made for large matrices
for( int i = 0; i < A.numRows; i++ ) {
for( int j = 0; j < A.numCols; j++ ) {
double a = A.get(i,j);
for( int rowB = 0; rowB < B.numRows; rowB++ ) {
for( int colB = 0; colB < B.numCols; colB++ ) {
double val = a*B.get(rowB,colB);
C.set(i*B.numRows+rowB,j*B.numCols+colB,val);
}
}
}
}
}
/**
*
* 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( DMatrix src,
int srcY0, int srcY1,
int srcX0, int srcX1,
DMatrix dst ,
int dstY0, int dstX0 )
{
if( srcY1 < srcY0 || srcY0 < 0 || srcY1 > src.getNumRows() )
throw new MatrixDimensionException("srcY1 < srcY0 || srcY0 < 0 || srcY1 > src.numRows. "+stringShapes(src,dst));
if( srcX1 < srcX0 || srcX0 < 0 || srcX1 > src.getNumCols() )
throw new MatrixDimensionException("srcX1 < srcX0 || srcX0 < 0 || srcX1 > src.numCols. "+stringShapes(src,dst));
int w = srcX1-srcX0;
int h = srcY1-srcY0;
if( dstY0+h > dst.getNumRows() )
throw new MatrixDimensionException("dst is too small in rows. "+dst.getNumRows()+" < "+(dstY0+h));
if( dstX0+w > dst.getNumCols() )
throw new MatrixDimensionException("dst is too small in columns. "+dst.getNumCols()+" < "+(dstX0+w));
// interestingly, the performance is only different for small matrices but identical for larger ones
if( src instanceof DMatrixRMaj && dst instanceof DMatrixRMaj) {
ImplCommonOps_DDRM.extract((DMatrixRMaj)src,srcY0,srcX0,(DMatrixRMaj)dst,dstY0,dstX0, h, w);
} else {
ImplCommonOps_DDMA.extract(src,srcY0,srcX0,dst,dstY0,dstX0, h, w);
}
}
/**
* Extract where the destination is reshaped to match the extracted region
* @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.
*/
public static void extract( DMatrix src,
int srcY0, int srcY1,
int srcX0, int srcX1,
DMatrix dst ) {
((ReshapeMatrix)dst).reshape(srcY1-srcY0,srcX1-srcX0);
extract(src,srcY0,srcY1,srcX0,srcX1,dst,0,0);
}
/**
*
* Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'. Uses the shape of dst
* to determine the size of the matrix extracted.
*
*
* @param src The original matrix which is to be copied. Not modified.
* @param srcY0 Start row in src.
* @param srcX0 Start column in src.
* @param dst Where the matrix is extracted into.
*/
public static void extract( DMatrix src,
int srcY0, int srcX0,
DMatrix dst ) {
extract(src,srcY0,srcY0+dst.getNumRows(),srcX0,srcX0+dst.getNumCols(),dst,0,0);
}
/**
*
* 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 DMatrixRMaj extract(DMatrixRMaj src,
int srcY0, int srcY1,
int srcX0, int srcX1 )
{
if( srcY1 <= srcY0 || srcY0 < 0 || srcY1 > src.numRows )
throw new MatrixDimensionException("srcY1 <= srcY0 || srcY0 < 0 || srcY1 > src.numRows");
if( srcX1 <= srcX0 || srcX0 < 0 || srcX1 > src.numCols )
throw new MatrixDimensionException("srcX1 <= srcX0 || srcX0 < 0 || srcX1 > src.numCols");
int w = srcX1-srcX0;
int h = srcY1-srcY0;
DMatrixRMaj dst = new DMatrixRMaj(h,w);
ImplCommonOps_DDRM.extract(src,srcY0,srcX0,dst,0,0, h, w);
return dst;
}
/**
* Extracts out a matrix from source given a sub matrix with arbitrary rows and columns specified in
* two array lists
*
* @param src Source matrix. Not modified.
* @param rows array of row indexes
* @param rowsSize maximum element in row array
* @param cols array of column indexes
* @param colsSize maximum element in column array
* @param dst output matrix. Must be correct shape.
*/
public static void extract( DMatrixRMaj src,
int rows[] , int rowsSize ,
int cols[] , int colsSize , DMatrixRMaj dst ) {
if( rowsSize != dst.numRows || colsSize != dst.numCols )
throw new MatrixDimensionException("Unexpected number of rows and/or columns in dst matrix");
int indexDst = 0;
for (int i = 0; i < rowsSize; i++) {
int indexSrcRow = src.numCols*rows[i];
for (int j = 0; j < colsSize; j++) {
dst.data[indexDst++] = src.data[indexSrcRow + cols[j]];
}
}
}
/**
* Extracts the elements from the source matrix by their 1D index.
*
* @param src Source matrix. Not modified.
* @param indexes array of row indexes
* @param length maximum element in row array
* @param dst output matrix. Must be a vector of the correct length.
*/
public static void extract(DMatrixRMaj src, int indexes[] , int length , DMatrixRMaj dst ) {
if( !MatrixFeatures_DDRM.isVector(dst))
throw new MatrixDimensionException("Dst must be a vector");
if( length != dst.getNumElements())
throw new MatrixDimensionException("Unexpected number of elements in dst vector");
for (int i = 0; i < length; i++) {
dst.data[i] = src.data[indexes[i]];
}
}
/**
* Inserts into the specified elements of dst the source matrix.
*
* for i in len(rows):
* for j in len(cols):
* dst(rows[i],cols[j]) = src(i,j)
*
*
* @param src Source matrix. Not modified.
* @param dst output matrix. Must be correct shape.
* @param rows array of row indexes
* @param rowsSize maximum element in row array
* @param cols array of column indexes
* @param colsSize maximum element in column array
*/
public static void insert( DMatrixRMaj src ,
DMatrixRMaj dst ,
int rows[] , int rowsSize ,
int cols[] , int colsSize ) {
if( rowsSize != src.numRows || colsSize != src.numCols )
throw new MatrixDimensionException("Unexpected number of rows and/or columns in dst matrix");
int indexSrc = 0;
for (int i = 0; i < rowsSize; i++) {
int indexDstRow = dst.numCols*rows[i];
for (int j = 0; j < colsSize; j++) {
dst.data[indexDstRow + cols[j]] = src.data[indexSrc++];
}
}
}
/**
*
* 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(DMatrixRMaj src, DMatrixRMaj dst )
{
int N = Math.min(src.numRows, src.numCols);
if( !MatrixFeatures_DDRM.isVector(dst) || dst.numCols*dst.numCols != N ) {
dst.reshape(N,1);
}
for( int i = 0; i < N; i++ ) {
dst.set( i , src.unsafe_get(i,i) );
}
}
/**
* Extracts the row from a matrix.
* @param a Input matrix
* @param row Which row is to be extracted
* @param out output. Storage for the extracted row. If null then a new vector will be returned.
* @return The extracted row.
*/
public static DMatrixRMaj extractRow(DMatrixRMaj a , int row , DMatrixRMaj out ) {
if( out == null)
out = new DMatrixRMaj(1,a.numCols);
else if( !MatrixFeatures_DDRM.isVector(out) || out.getNumElements() != a.numCols )
throw new MatrixDimensionException("Output must be a vector of length "+a.numCols);
System.arraycopy(a.data,a.getIndex(row,0),out.data,0,a.numCols);
return out;
}
/**
* Extracts the column from a matrix.
* @param a Input matrix
* @param column Which column is to be extracted
* @param out output. Storage for the extracted column. If null then a new vector will be returned.
* @return The extracted column.
*/
public static DMatrixRMaj extractColumn(DMatrixRMaj a , int column , DMatrixRMaj out ) {
if( out == null)
out = new DMatrixRMaj(a.numRows,1);
else if( !MatrixFeatures_DDRM.isVector(out) || out.getNumElements() != a.numRows )
throw new MatrixDimensionException("Output must be a vector of length "+a.numRows);
int index = column;
for (int i = 0; i < a.numRows; i++, index += a.numCols ) {
out.data[i] = a.data[index];
}
return out;
}
/**
* Removes columns from the matrix.
*
* @param A Matrix. Modified
* @param col0 First column
* @param col1 Last column, inclusive.
*/
public static void removeColumns( DMatrixRMaj A , int col0 , int col1 )
{
if( col1 < col0 ) {
throw new IllegalArgumentException("col1 must be >= col0");
} else if( col0 >= A.numCols || col1 >= A.numCols ) {
throw new IllegalArgumentException("Columns which are to be removed must be in bounds");
}
int step = col1-col0+1;
int offset = 0;
for (int row = 0, idx=0; row < A.numRows; row++) {
for (int i = 0; i < col0; i++,idx++) {
A.data[idx] = A.data[idx+offset];
}
offset += step;
for (int i = col1+1; i < A.numCols; i++,idx++) {
A.data[idx] = A.data[idx+offset];
}
}
A.numCols -= step;
}
/**
* Inserts matrix 'src' into matrix 'dest' with the (0,0) of src at (row,col) in dest.
* This is equivalent to calling extract(src,0,src.numRows,0,src.numCols,dest,destY0,destX0).
*
* @param src matrix that is being copied into dest. Not modified.
* @param dest Where src is being copied into. Modified.
* @param destY0 Start row for the copy into dest.
* @param destX0 Start column for the copy into dest.
*/
public static void insert(DMatrix src, DMatrix dest, int destY0, int destX0) {
extract(src, 0, src.getNumRows(), 0, src.getNumCols(), dest, destY0, destX0);
}
/**
*
* Returns the value of the element in the matrix that has the largest value.
*
* Max{ aij } for all i and j
*
*
* @param a A matrix. Not modified.
* @return The max element value of the matrix.
*/
public static double elementMax( DMatrixD1 a ) {
final int size = a.getNumElements();
double max = a.get(0);
for( int i = 1; i < size; i++ ) {
double val = a.get(i);
if( val >= max ) {
max = val;
}
}
return max;
}
/**
*
* Returns the absolute value of the element in the matrix that has the largest absolute value.
*
* Max{ |aij| } for all i and j
*
*
* @param a A matrix. Not modified.
* @return The max abs element value of the matrix.
*/
public static double elementMaxAbs( DMatrixD1 a ) {
final int size = a.getNumElements();
double max = 0;
for( int i = 0; i < size; i++ ) {
double val = Math.abs(a.get(i));
if( val > max ) {
max = val;
}
}
return max;
}
/**
*
* Returns the value of the element in the matrix that has the minimum value.
*
* Min{ aij } for all i and j
*
*
* @param a A matrix. Not modified.
* @return The value of element in the matrix with the minimum value.
*/
public static double elementMin( DMatrixD1 a ) {
final int size = a.getNumElements();
double min = a.get(0);
for( int i = 1; i < size; i++ ) {
double val = a.get(i);
if( val < min ) {
min = val;
}
}
return min;
}
/**
*
* Returns the absolute value of the element in the matrix that has the smallest absolute value.
*
* Min{ |aij| } for all i and j
*
*
* @param a A matrix. Not modified.
* @return The max element value of the matrix.
*/
public static double elementMinAbs( DMatrixD1 a ) {
final int size = a.getNumElements();
double min = Double.MAX_VALUE;
for( int i = 0; i < size; i++ ) {
double val = Math.abs(a.get(i));
if( val < min ) {
min = val;
}
}
return min;
}
/**
* Performs the an element by element multiplication operation:
*
* aij = aij * bij
*
* @param a The left matrix in the multiplication operation. Modified.
* @param b The right matrix in the multiplication operation. Not modified.
*/
public static void elementMult(DMatrixD1 a , DMatrixD1 b )
{
if( a.numCols != b.numCols || a.numRows != b.numRows ) {
throw new MatrixDimensionException("The 'a' and 'b' matrices do not have compatible dimensions");
}
int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
a.times(i, b.get(i));
}
}
/**
* Performs the an element by element multiplication operation:
*
* cij = aij * bij
*
* @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 elementMult(DMatrixD1 a , DMatrixD1 b , DMatrixD1 c )
{
if( a.numCols != b.numCols || a.numRows != b.numRows
|| a.numRows != c.numRows || a.numCols != c.numCols ) {
throw new MatrixDimensionException("The 'a' and 'b' matrices do not have compatible dimensions");
}
int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
c.set(i, a.get(i) * b.get(i));
}
}
/**
* Performs the an element by element division operation:
*
* aij = aij / bij
*
* @param a The left matrix in the division operation. Modified.
* @param b The right matrix in the division operation. Not modified.
*/
public static void elementDiv(DMatrixD1 a , DMatrixD1 b )
{
if( a.numCols != b.numCols || a.numRows != b.numRows ) {
throw new MatrixDimensionException("The 'a' and 'b' matrices do not have compatible dimensions");
}
int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
a.div(i, b.get(i));
}
}
/**
* Performs the an element by element division operation:
*
* cij = aij / bij
*
* @param a The left matrix in the division operation. Not modified.
* @param b The right matrix in the division operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void elementDiv(DMatrixD1 a , DMatrixD1 b , DMatrixD1 c )
{
if( a.numCols != b.numCols || a.numRows != b.numRows
|| a.numRows != c.numRows || a.numCols != c.numCols ) {
throw new MatrixDimensionException("The 'a' and 'b' matrices do not have compatible dimensions");
}
int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
c.set(i, a.get(i) / b.get(i));
}
}
/**
*
* Computes the sum of all the elements in the matrix:
*
* sum(i=1:m , j=1:n ; aij)
*
*
* @param mat An m by n matrix. Not modified.
* @return The sum of the elements.
*/
public static double elementSum( DMatrixD1 mat ) {
double total = 0;
int size = mat.getNumElements();
for( int i = 0; i < size; i++ ) {
total += mat.get(i);
}
return total;
}
/**
*
* Computes the sum of the absolute value all the elements in the matrix:
*
* sum(i=1:m , j=1:n ; |aij|)
*
*
* @param mat An m by n matrix. Not modified.
* @return The sum of the absolute value of each element.
*/
public static double elementSumAbs( DMatrixD1 mat ) {
double total = 0;
int size = mat.getNumElements();
for( int i = 0; i < size; i++ ) {
total += Math.abs(mat.get(i));
}
return total;
}
/**
*
* Element-wise power operation
* cij = aij ^ bij
*
*
* @param A left side
* @param B right side
* @param C output (modified)
*/
public static void elementPower(DMatrixD1 A , DMatrixD1 B , DMatrixD1 C ) {
if( A.numRows != B.numRows || A.numRows != C.numRows ||
A.numCols != B.numCols || A.numCols != C.numCols ) {
throw new MatrixDimensionException("All matrices must be the same shape");
}
int size = A.getNumElements();
for( int i = 0; i < size; i++ ) {
C.data[i] = Math.pow(A.data[i], B.data[i]);
}
}
/**
*
* Element-wise power operation
* cij = a ^ bij
*
*
* @param a left scalar
* @param B right side
* @param C output (modified)
*/
public static void elementPower(double a , DMatrixD1 B , DMatrixD1 C ) {
if( B.numRows != C.numRows || B.numCols != C.numCols ) {
throw new MatrixDimensionException("All matrices must be the same shape");
}
int size = B.getNumElements();
for( int i = 0; i < size; i++ ) {
C.data[i] = Math.pow(a, B.data[i]);
}
}
/**
*
* Element-wise power operation
* cij = aij ^ b
*
*
* @param A left side
* @param b right scalar
* @param C output (modified)
*/
public static void elementPower(DMatrixD1 A , double b, DMatrixD1 C ) {
if( A.numRows != C.numRows || A.numCols != C.numCols ) {
throw new MatrixDimensionException("All matrices must be the same shape");
}
int size = A.getNumElements();
for( int i = 0; i < size; i++ ) {
C.data[i] = Math.pow(A.data[i], b);
}
}
/**
*
* Element-wise log operation
* cij = Math.log(aij)
*
*
* @param A input
* @param C output (modified)
*/
public static void elementLog(DMatrixD1 A , DMatrixD1 C ) {
if( A.numCols != C.numCols || A.numRows != C.numRows ) {
throw new MatrixDimensionException("All matrices must be the same shape");
}
int size = A.getNumElements();
for( int i = 0; i < size; i++ ) {
C.data[i] = Math.log(A.data[i]);
}
}
/**
*
* Element-wise exp operation
* cij = Math.log(aij)
*
*
* @param A input
* @param C output (modified)
*/
public static void elementExp(DMatrixD1 A , DMatrixD1 C ) {
if( A.numCols != C.numCols || A.numRows != C.numRows ) {
throw new MatrixDimensionException("All matrices must be the same shape");
}
int size = A.getNumElements();
for( int i = 0; i < size; i++ ) {
C.data[i] = Math.exp(A.data[i]);
}
}
/**
* Multiplies every element in row i by value[i].
*
* @param values array. Not modified.
* @param A Matrix. Modified.
*/
public static void multRows(double[] values, DMatrixRMaj A) {
if( values.length < A.numRows ) {
throw new IllegalArgumentException("Not enough elements in values.");
}
int index = 0;
for (int row = 0; row < A.numRows; row++) {
double v = values[row];
for (int col = 0; col < A.numCols; col++, index++) {
A.data[index] *= v;
}
}
}
/**
* Divides every element in row i by value[i].
*
* @param values array. Not modified.
* @param A Matrix. Modified.
*/
public static void divideRows(double[] values, DMatrixRMaj A) {
if( values.length < A.numRows ) {
throw new IllegalArgumentException("Not enough elements in values.");
}
int index = 0;
for (int row = 0; row < A.numRows; row++) {
double v = values[row];
for (int col = 0; col < A.numCols; col++, index++) {
A.data[index] /= v;
}
}
}
/**
* Multiplies every element in column i by value[i].
*
* @param A Matrix. Modified.
* @param values array. Not modified.
*/
public static void multCols(DMatrixRMaj A , double values[] ) {
if( values.length < A.numCols ) {
throw new IllegalArgumentException("Not enough elements in values.");
}
int index = 0;
for (int row = 0; row < A.numRows; row++) {
for (int col = 0; col < A.numCols; col++, index++) {
A.data[index] *= values[col];
}
}
}
/**
* Divides every element in column i by value[i].
*
* @param A Matrix. Modified.
* @param values array. Not modified.
*/
public static void divideCols(DMatrixRMaj A , double values[] ) {
if( values.length < A.numCols ) {
throw new IllegalArgumentException("Not enough elements in values.");
}
int index = 0;
for (int row = 0; row < A.numRows; row++) {
for (int col = 0; col < A.numCols; col++, index++) {
A.data[index] /= values[col];
}
}
}
/**
* Equivalent to multiplying a matrix B by the inverse of two diagonal matrices.
* B = inv(A)*B*inv(C), where A=diag(a) and C=diag(c).
*
* @param diagA Array of length offsteA + B.numRows
* @param offsetA First index in A
* @param B Rectangular matrix
* @param diagC Array of length indexC + B.numCols
* @param offsetC First index in C
*/
public static void divideRowsCols( double []diagA , int offsetA ,
DMatrixRMaj B ,
double []diagC , int offsetC )
{
if( diagA.length-offsetA < B.numRows ) {
throw new IllegalArgumentException("Not enough elements in diagA.");
}
if( diagC.length-offsetC < B.numCols ) {
throw new IllegalArgumentException("Not enough elements in diagC.");
}
final int rows = B.numRows;
final int cols = B.numCols;
int index = 0;
for (int row = 0; row < rows; row++) {
double va = diagA[offsetA+row];
for (int col = 0; col < cols; col++, index++) {
B.data[index] /= va*diagC[offsetC+col];
}
}
}
/**
*
* Computes the sum of each row in the input matrix and returns the results in a vector:
*
* bj = sum(i=1:n ; aji)
*
*
* @param input INput matrix whose rows are summed.
* @param output Optional storage for output. Reshaped into a column. Modified.
* @return Vector containing the sum of each row in the input.
*/
public static DMatrixRMaj sumRows(DMatrixRMaj input , DMatrixRMaj output ) {
if( output == null ) {
output = new DMatrixRMaj(input.numRows,1);
} else {
output.reshape(input.numRows,1);
}
for( int row = 0; row < input.numRows; row++ ) {
double total = 0;
int end = (row+1)*input.numCols;
for( int index = row*input.numCols; index < end; index++ ) {
total += input.data[index];
}
output.set(row,total);
}
return output;
}
/**
*
* Finds the element with the minimum value along each row in the input matrix and returns the results in a vector:
*
* bj = min(i=1:n ; aji)
*
*
* @param input Input matrix
* @param output Optional storage for output. Reshaped into a column. Modified.
* @return Vector containing the sum of each row in the input.
*/
public static DMatrixRMaj minRows(DMatrixRMaj input , DMatrixRMaj output ) {
if( output == null ) {
output = new DMatrixRMaj(input.numRows,1);
} else {
output.reshape(input.numRows,1);
}
for( int row = 0; row < input.numRows; row++ ) {
double min = Double.MAX_VALUE;
int end = (row+1)*input.numCols;
for( int index = row*input.numCols; index < end; index++ ) {
double v = input.data[index];
if( v < min )
min = v;
}
output.set(row,min);
}
return output;
}
/**
*
* Finds the element with the maximum value along each row in the input matrix and returns the results in a vector:
*
* bj = max(i=1:n ; aji)
*
*
* @param input Input matrix
* @param output Optional storage for output. Reshaped into a column. Modified.
* @return Vector containing the sum of each row in the input.
*/
public static DMatrixRMaj maxRows(DMatrixRMaj input , DMatrixRMaj output ) {
if( output == null ) {
output = new DMatrixRMaj(input.numRows,1);
} else {
output.reshape(input.numRows,1);
}
for( int row = 0; row < input.numRows; row++ ) {
double max = -Double.MAX_VALUE;
int end = (row+1)*input.numCols;
for( int index = row*input.numCols; index < end; index++ ) {
double v = input.data[index];
if( v > max )
max = v;
}
output.set(row,max);
}
return output;
}
/**
*
* Computes the sum of each column in the input matrix and returns the results in a vector:
*
* bj = sum(i=1:m ; aij)
*
*
* @param input Input matrix
* @param output Optional storage for output. Reshaped into a row vector. Modified.
* @return Vector containing the sum of each column
*/
public static DMatrixRMaj sumCols(DMatrixRMaj input , DMatrixRMaj output ) {
if( output == null ) {
output = new DMatrixRMaj(1,input.numCols);
} else {
output.reshape(1,input.numCols);
}
for( int cols = 0; cols < input.numCols; cols++ ) {
double total = 0;
int index = cols;
int end = index + input.numCols*input.numRows;
for( ; index < end; index += input.numCols ) {
total += input.data[index];
}
output.set(cols, total);
}
return output;
}
/**
*
* Finds the element with the minimum value along column in the input matrix and returns the results in a vector:
*
* bj = min(i=1:m ; aij)
*
*
* @param input Input matrix
* @param output Optional storage for output. Reshaped into a row vector. Modified.
* @return Vector containing the minimum of each column
*/
public static DMatrixRMaj minCols(DMatrixRMaj input , DMatrixRMaj output ) {
if( output == null ) {
output = new DMatrixRMaj(1,input.numCols);
} else {
output.reshape(1,input.numCols);
}
for( int cols = 0; cols < input.numCols; cols++ ) {
double minimum = Double.MAX_VALUE;
int index = cols;
int end = index + input.numCols*input.numRows;
for( ; index < end; index += input.numCols ) {
double v = input.data[index];
if( v < minimum )
minimum = v;
}
output.set(cols, minimum);
}
return output;
}
/**
*
* Finds the element with the minimum value along column in the input matrix and returns the results in a vector:
*
* bj = min(i=1:m ; aij)
*
*
* @param input Input matrix
* @param output Optional storage for output. Reshaped into a row vector. Modified.
* @return Vector containing the maximum of each column
*/
public static DMatrixRMaj maxCols(DMatrixRMaj input , DMatrixRMaj output ) {
if( output == null ) {
output = new DMatrixRMaj(1,input.numCols);
} else {
output.reshape(1,input.numCols);
}
for( int cols = 0; cols < input.numCols; cols++ ) {
double maximum = -Double.MAX_VALUE;
int index = cols;
int end = index + input.numCols*input.numRows;
for( ; index < end; index += input.numCols ) {
double v = input.data[index];
if( v > maximum )
maximum = v;
}
output.set(cols, maximum);
}
return output;
}
/**
* Performs the following operation:
*
* a = a + b
* aij = aij + bij
*
*
* @param a A Matrix. Modified.
* @param b A Matrix. Not modified.
*/
public static void addEquals(DMatrixD1 a , DMatrixD1 b )
{
if( a.numCols != b.numCols || a.numRows != b.numRows ) {
throw new MatrixDimensionException("The 'a' and 'b' matrices do not have compatible dimensions");
}
final int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
a.plus(i, b.get(i));
}
}
/**
* Performs the following operation:
*
* a = a + β * b
* aij = aij + β * bij
*
*
* @param beta The number that matrix 'b' is multiplied by.
* @param a A Matrix. Modified.
* @param b A Matrix. Not modified.
*/
public static void addEquals(DMatrixD1 a , double beta, DMatrixD1 b )
{
if( a.numCols != b.numCols || a.numRows != b.numRows ) {
throw new MatrixDimensionException("The 'a' and 'b' matrices do not have compatible dimensions");
}
final int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
a.plus(i, beta * b.get(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 add(final DMatrixD1 a , final DMatrixD1 b , final DMatrixD1 c )
{
if( a.numCols != b.numCols || a.numRows != b.numRows ) {
throw new MatrixDimensionException("The matrices are not all the same dimension.");
}
c.reshape(a.numRows,a.numCols);
final int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
c.set(i, a.get(i) + b.get(i));
}
}
/**
* Performs the following operation:
*
* c = a + β * b
* cij = aij + β * bij
*
*
*
* Matrix C can be the same instance as Matrix A and/or B.
*
*
* @param a A Matrix. Not modified.
* @param beta Scaling factor for matrix b.
* @param b A Matrix. Not modified.
* @param c A Matrix where the results are stored. Modified.
*/
public static void add(DMatrixD1 a , double beta , DMatrixD1 b , DMatrixD1 c )
{
if( a.numCols != b.numCols || a.numRows != b.numRows ) {
throw new MatrixDimensionException("The matrices are not all the same dimension.");
}
c.reshape(a.numRows,a.numCols);
final int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
c.set(i, a.get(i) + beta * b.get(i));
}
}
/**
* Performs the following operation:
*
* c = α * a + β * b
* cij = α * aij + β * bij
*
*
*
* Matrix C can be the same instance as Matrix A and/or B.
*
*
* @param alpha A scaling factor for matrix a.
* @param a A Matrix. Not modified.
* @param beta A scaling factor for matrix b.
* @param b A Matrix. Not modified.
* @param c A Matrix where the results are stored. Modified.
*/
public static void add(double alpha , DMatrixD1 a , double beta , DMatrixD1 b , DMatrixD1 c )
{
if( a.numCols != b.numCols || a.numRows != b.numRows ) {
throw new MatrixDimensionException("The matrices are not all the same dimension.");
}
c.reshape(a.numRows,a.numCols);
final int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
c.set(i, alpha * a.get(i) + beta * b.get(i));
}
}
/**
* Performs the following operation:
*
* c = α * a + b
* cij = α * aij + bij
*
*
*
* Matrix C can be the same instance as Matrix A and/or B.
*
*
* @param alpha A scaling factor for matrix a.
* @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(double alpha , DMatrixD1 a , DMatrixD1 b , DMatrixD1 c )
{
if( a.numCols != b.numCols || a.numRows != b.numRows ) {
throw new MatrixDimensionException("The matrices are not all the same dimension.");
}
c.reshape(a.numRows,a.numCols);
final int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
c.set(i, alpha * a.get(i) + b.get(i));
}
}
/**
* Performs an in-place scalar addition:
*
* a = a + val
* aij = aij + val
*
*
* @param a A matrix. Modified.
* @param val The value that's added to each element.
*/
public static void add(DMatrixD1 a , double val ) {
final int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
a.plus(i, val);
}
}
/**
* Performs scalar addition:
*
* c = a + val
* cij = aij + val
*
*
* @param a A matrix. Not modified.
* @param c A matrix. Modified.
* @param val The value that's added to each element.
*/
public static void add(DMatrixD1 a , double val , DMatrixD1 c ) {
c.reshape(a.numRows,a.numCols);
final int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
c.data[i] = a.data[i] + val;
}
}
/**
* Performs matrix scalar subtraction:
*
* c = a - val
* cij = aij - val
*
*
* @param a (input) A matrix. Not modified.
* @param val (input) The value that's subtracted to each element.
* @param c (Output) A matrix. Modified.
*/
public static void subtract(DMatrixD1 a , double val , DMatrixD1 c ) {
c.reshape(a.numRows,a.numCols);
final int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
c.data[i] = a.data[i] - val;
}
}
/**
* Performs matrix scalar subtraction:
*
* c = val - a
* cij = val - aij
*
*
* @param val (input) The value that's subtracted to each element.
* @param a (input) A matrix. Not modified.
* @param c (Output) A matrix. Modified.
*/
public static void subtract(double val , DMatrixD1 a , DMatrixD1 c ) {
c.reshape(a.numRows,a.numCols);
final int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
c.data[i] = val - a.data[i];
}
}
/**
* Performs the following subtraction operation:
*
* a = a - b
* aij = aij - bij
*
*
* @param a A Matrix. Modified.
* @param b A Matrix. Not modified.
*/
public static void subtractEquals(DMatrixD1 a, DMatrixD1 b)
{
if( a.numCols != b.numCols || a.numRows != b.numRows ) {
throw new MatrixDimensionException("The 'a' and 'b' matrices do not have compatible dimensions");
}
final int length = a.getNumElements();
for( int i = 0; i < length; i++ ) {
a.data[i] -= b.data[i];
}
}
/**
* Performs the following subtraction 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. Modified.
*/
public static void subtract(DMatrixD1 a, DMatrixD1 b, DMatrixD1 c)
{
if( a.numCols != b.numCols || a.numRows != b.numRows ) {
throw new MatrixDimensionException("The 'a' and 'b' matrices do not have compatible dimensions");
}
c.reshape(a.numRows,a.numCols);
final int length = a.getNumElements();
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 alpha the amount each element is multiplied by.
*/
public static void scale( double alpha , DMatrixD1 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();
for( int i = 0; i < size; i++ ) {
a.data[i] *= alpha;
}
}
/**
*
* Performs an element by element scalar multiplication.
*
* bij = α*aij
*
*
* @param alpha the amount each element is multiplied by.
* @param a The matrix that is to be scaled. Not modified.
* @param b Where the scaled matrix is stored. Modified.
*/
public static void scale(double alpha , DMatrixD1 a , DMatrixD1 b)
{
b.reshape(a.numRows,a.numCols);
final int size = a.getNumElements();
for( int i = 0; i < size; i++ ) {
b.data[i] = a.data[i]*alpha;
}
}
/**
* In-place scaling of a row in A
*
* @param alpha scale factor
* @param A matrix
* @param row which row in A
*/
public static void scaleRow( double alpha , DMatrixRMaj A , int row ) {
int idx = row*A.numCols;
for (int col = 0; col < A.numCols; col++) {
A.data[idx++] *= alpha;
}
}
/**
* In-place scaling of a column in A
*
* @param alpha scale factor
* @param A matrix
* @param col which row in A
*/
public static void scaleCol( double alpha , DMatrixRMaj A , int col ) {
int idx = col;
for (int row = 0; row < A.numRows; row++, idx += A.numCols) {
A.data[idx] *= alpha;
}
}
/**
*
* Performs an in-place element by element scalar division with the scalar on top.
*
* aij = α/aij
*
*
* @param a The matrix whose elements are divide the scalar. Modified.
* @param alpha top value in division
*/
public static void divide( double alpha , DMatrixD1 a )
{
final int size = a.getNumElements();
for( int i = 0; i < size; i++ ) {
a.data[i] = alpha/a.data[i];
}
}
/**
*
* Performs an in-place element by element scalar division with the scalar on bottom.
*
* aij = aij/α
*
*
* @param a The matrix whose elements are to be divided. Modified.
* @param alpha the amount each element is divided by.
*/
public static void divide(DMatrixD1 a , double alpha)
{
final int size = a.getNumElements();
for( int i = 0; i < size; i++ ) {
a.data[i] /= alpha;
}
}
/**
*
* Performs an element by element scalar division with the scalar on top.
*
* bij = α/aij
*
*
* @param alpha The numerator.
* @param a The matrix whose elements are the divisor. Not modified.
* @param b Where the results are stored. Modified.
*/
public static void divide(double alpha , DMatrixD1 a , DMatrixD1 b)
{
b.reshape(a.numRows,a.numCols);
final int size = a.getNumElements();
for( int i = 0; i < size; i++ ) {
b.data[i] = alpha/a.data[i];
}
}
/**
*
* Performs an element by element scalar division with the scalar on botton.
*
* bij = aij /α
*
*
* @param a The matrix whose elements are to be divided. Not modified.
* @param alpha the amount each element is divided by.
* @param b Where the results are stored. Modified.
*/
public static void divide(DMatrixD1 a , double alpha , DMatrixD1 b)
{
b.reshape(a.numRows,a.numCols);
final int size = a.getNumElements();
for( int i = 0; i < size; i++ ) {
b.data[i] = a.data[i]/alpha;
}
}
/**
*
* Changes the sign of every element in the matrix.
*
* aij = -aij
*
*
* @param a A matrix. Modified.
*/
public static void changeSign( DMatrixD1 a )
{
final int size = a.getNumElements();
for( int i = 0; i < size; i++ ) {
a.data[i] = -a.data[i];
}
}
/**
*
* Changes the sign of every element in the matrix.
*
* outputij = -inputij
*
*
* @param input A matrix. Modified.
*/
public static T changeSign(T input , @Nullable T output)
{
if( output == null ) {
output = input.createLike();
} else {
output.reshape(input.numRows, input.numCols);
}
final int size = input.getNumElements();
for( int i = 0; i < size; i++ ) {
output.data[i] = -input.data[i];
}
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 value The value each element will have.
*/
public static void fill(DMatrixD1 a, double value)
{
Arrays.fill(a.data, 0, a.getNumElements(), value);
}
/**
*
* Puts the augmented system matrix into reduced row echelon form (RREF) using Gauss-Jordan
* elimination with row (partial) pivots. A matrix is said to be in RREF is the following conditions are true:
*
*
*
* - If a row has non-zero entries, then the first non-zero entry is 1. This is known as the leading one.
* - If a column contains a leading one then all other entries in that column are zero.
* - If a row contains a leading 1, then each row above contains a leading 1 further to the left.
*
*
*
* [1] Page 19 in, Otter Bretscherm "Linear Algebra with Applications" Prentice-Hall Inc, 1997
*
*
* @see RrefGaussJordanRowPivot_DDRM
*
* @param A Input matrix. Unmodified.
* @param numUnknowns Number of unknowns/columns that are reduced. Set to -1 to default to
* Math.min(A.numRows,A.numCols), which works for most systems.
* @param reduced Storage for reduced echelon matrix. If null then a new matrix is returned. Modified.
* @return Reduced echelon form of A
*/
public static DMatrixRMaj rref(DMatrixRMaj A , int numUnknowns, DMatrixRMaj reduced ) {
if( reduced == null ) {
reduced = new DMatrixRMaj(A.numRows,A.numCols);
}
reduced.reshape(A.numRows,A.numCols);
if( numUnknowns <= 0 )
numUnknowns = Math.min(A.numCols,A.numRows);
ReducedRowEchelonForm_F64 alg = new RrefGaussJordanRowPivot_DDRM();
alg.setTolerance(elementMaxAbs(A)* UtilEjml.EPS*Math.max(A.numRows,A.numCols));
reduced.set(A);
alg.reduce(reduced, numUnknowns);
return reduced;
}
/**
* Applies the > operator to each element in A. Results are stored in a boolean matrix.
*
* @param A Input matrx
* @param value value each element is compared against
* @param output (Optional) Storage for results. Can be null. Is reshaped.
* @return Boolean matrix with results
*/
public static BMatrixRMaj elementLessThan(DMatrixRMaj A , double value , BMatrixRMaj output )
{
if( output == null ) {
output = new BMatrixRMaj(A.numRows,A.numCols);
}
output.reshape(A.numRows, A.numCols);
int N = A.getNumElements();
for (int i = 0; i < N; i++) {
output.data[i] = A.data[i] < value;
}
return output;
}
/**
* Applies the ≥ operator to each element in A. Results are stored in a boolean matrix.
*
* @param A Input matrix
* @param value value each element is compared against
* @param output (Optional) Storage for results. Can be null. Is reshaped.
* @return Boolean matrix with results
*/
public static BMatrixRMaj elementLessThanOrEqual(DMatrixRMaj A , double value , BMatrixRMaj output )
{
if( output == null ) {
output = new BMatrixRMaj(A.numRows,A.numCols);
}
output.reshape(A.numRows, A.numCols);
int N = A.getNumElements();
for (int i = 0; i < N; i++) {
output.data[i] = A.data[i] <= value;
}
return output;
}
/**
* Applies the > operator to each element in A. Results are stored in a boolean matrix.
*
* @param A Input matrix
* @param value value each element is compared against
* @param output (Optional) Storage for results. Can be null. Is reshaped.
* @return Boolean matrix with results
*/
public static BMatrixRMaj elementMoreThan(DMatrixRMaj A , double value , BMatrixRMaj output )
{
if( output == null ) {
output = new BMatrixRMaj(A.numRows,A.numCols);
}
output.reshape(A.numRows, A.numCols);
int N = A.getNumElements();
for (int i = 0; i < N; i++) {
output.data[i] = A.data[i] > value;
}
return output;
}
/**
* Applies the ≥ operator to each element in A. Results are stored in a boolean matrix.
*
* @param A Input matrix
* @param value value each element is compared against
* @param output (Optional) Storage for results. Can be null. Is reshaped.
* @return Boolean matrix with results
*/
public static BMatrixRMaj elementMoreThanOrEqual(DMatrixRMaj A , double value , BMatrixRMaj output )
{
if( output == null ) {
output = new BMatrixRMaj(A.numRows,A.numCols);
}
output.reshape(A.numRows, A.numCols);
int N = A.getNumElements();
for (int i = 0; i < N; i++) {
output.data[i] = A.data[i] >= value;
}
return output;
}
/**
* Applies the < operator to each element in A. Results are stored in a boolean matrix.
*
* @param A Input matrix
* @param B Input matrix
* @param output (Optional) Storage for results. Can be null. Is reshaped.
* @return Boolean matrix with results
*/
public static BMatrixRMaj elementLessThan(DMatrixRMaj A , DMatrixRMaj B , BMatrixRMaj output )
{
if( output == null ) {
output = new BMatrixRMaj(A.numRows,A.numCols);
}
output.reshape(A.numRows, A.numCols);
int N = A.getNumElements();
for (int i = 0; i < N; i++) {
output.data[i] = A.data[i] < B.data[i];
}
return output;
}
/**
* Applies the A ≤ B operator to each element. Results are stored in a boolean matrix.
*
* @param A Input matrix
* @param B Input matrix
* @param output (Optional) Storage for results. Can be null. Is reshaped.
* @return Boolean matrix with results
*/
public static BMatrixRMaj elementLessThanOrEqual(DMatrixRMaj A , DMatrixRMaj B , BMatrixRMaj output )
{
if( output == null ) {
output = new BMatrixRMaj(A.numRows,A.numCols);
}
output.reshape(A.numRows, A.numCols);
int N = A.getNumElements();
for (int i = 0; i < N; i++) {
output.data[i] = A.data[i] <= B.data[i];
}
return output;
}
/**
* Returns a row matrix which contains all the elements in A which are flagged as true in 'marked'
*
* @param A Input matrix
* @param marked Input matrix marking elements in A
* @param output Storage for output row vector. Can be null. Will be reshaped.
* @return Row vector with marked elements
*/
public static DMatrixRMaj elements(DMatrixRMaj A , BMatrixRMaj marked , DMatrixRMaj output ) {
if( A.numRows != marked.numRows || A.numCols != marked.numCols )
throw new MatrixDimensionException("Input matrices must have the same shape");
if( output == null )
output = new DMatrixRMaj(1,1);
output.reshape(countTrue(marked),1);
int N = A.getNumElements();
int index = 0;
for (int i = 0; i < N; i++) {
if( marked.data[i] ) {
output.data[index++] = A.data[i];
}
}
return output;
}
/**
* Counts the number of elements in A which are true
* @param A input matrix
* @return number of true elements
*/
public static int countTrue(BMatrixRMaj A) {
int total = 0;
int N = A.getNumElements();
for (int i = 0; i < N; i++) {
if( A.data[i] )
total++;
}
return total;
}
/**
* output = [a , b]
*/
public static void concatColumns(DMatrixRMaj a , DMatrixRMaj b , DMatrixRMaj output ) {
int rows = Math.max(a.numRows , b.numRows);
int cols = a.numCols + b.numCols;
output.reshape(rows,cols);
output.zero();
insert(a,output,0,0);
insert(b,output,0,a.numCols);
}
/**
* Concatinates all the matrices together along their columns. If the rows do not match the upper elements
* are set to zero.
*
* A = [ m[0] , ... , m[n-1] ]
*
* @param m Set of matrices
* @return Resulting matrix
*/
public static DMatrixRMaj concatColumnsMulti(DMatrixRMaj ...m ) {
int rows = 0;
int cols = 0;
for (int i = 0; i < m.length; i++) {
rows = Math.max(rows,m[i].numRows);
cols += m[i].numCols;
}
DMatrixRMaj R = new DMatrixRMaj(rows,cols);
int col = 0;
for (int i = 0; i < m.length; i++) {
insert(m[i],R,0,col);
col += m[i].numCols;
}
return R;
}
/**
* output = [a ; b]
*/
public static void concatRows(DMatrixRMaj a , DMatrixRMaj b , DMatrixRMaj output ) {
int rows = a.numRows + b.numRows;
int cols = Math.max(a.numCols , b.numCols);
output.reshape(rows,cols);
output.zero();
insert(a,output,0,0);
insert(b,output,a.numRows,0);
}
/**
* Concatinates all the matrices together along their columns. If the rows do not match the upper elements
* are set to zero.
*
* A = [ m[0] ; ... ; m[n-1] ]
*
* @param m Set of matrices
* @return Resulting matrix
*/
public static DMatrixRMaj concatRowsMulti(DMatrixRMaj ...m ) {
int rows = 0;
int cols = 0;
for (int i = 0; i < m.length; i++) {
rows += m[i].numRows;
cols = Math.max(cols,m[i].numCols);
}
DMatrixRMaj R = new DMatrixRMaj(rows,cols);
int row = 0;
for (int i = 0; i < m.length; i++) {
insert(m[i],R,row,0);
row += m[i].numRows;
}
return R;
}
/**
* Applies the row permutation specified by the vector to the input matrix and save the results
* in the output matrix. output[perm[j],:] = input[j,:]
*
* @param pinv (Input) Inverse permutation vector. Specifies new order of the rows.
* @param input (Input) Matrix which is to be permuted
* @param output (Output) Matrix which has the permutation stored in it. Is reshaped.
*/
public static DMatrixRMaj permuteRowInv( int pinv[] , DMatrixRMaj input , DMatrixRMaj output ) {
if( input.numRows > pinv.length )
throw new MatrixDimensionException("permutation vector must have at least as many elements as input has rows");
if( output == null )
output = new DMatrixRMaj(1,1);
output.reshape(input.numRows,input.numCols);
int m = input.numCols;
for (int row = 0; row < input.numRows; row++) {
System.arraycopy(input.data,row*m,output.data,pinv[row]*m,m);
}
return output;
}
/**
* Performs absolute value of a matrix:
*
* c = abs(a)
* cij = abs(aij)
*
*
* @param a A matrix. Not modified.
* @param c A matrix. Modified.
*/
public static void abs(DMatrixD1 a , DMatrixD1 c ) {
c.reshape(a.numRows,a.numCols);
final int length = a.getNumElements();
for ( int i = 0; i < length; i++ ) {
c.data[i] = Math.abs(a.data[i]);
}
}
/**
* Performs absolute value of a matrix:
*
* a = abs(a)
* aij = abs(aij)
*
*
* @param a A matrix. Modified.
*/
public static void abs(DMatrixD1 a ) {
final int length = a.getNumElements();
for ( int i = 0; i < length; i++ ) {
a.data[i] = Math.abs(a.data[i]);
}
}
/**
* Given a symmetric matrix which is represented by a lower triangular matrix convert it back into
* a full symmetric matrix.
*
* @param A (Input) Lower triangular matrix (Output) symmetric matrix
*/
public static void symmLowerToFull( DMatrixRMaj A )
{
if( A.numRows != A.numCols )
throw new MatrixDimensionException("Must be a square matrix");
final int cols = A.numCols;
for (int row = 0; row < A.numRows; row++) {
for (int col = row+1; col < cols; col++) {
A.data[row*cols+col] = A.data[col*cols+row];
}
}
}
/**
* Given a symmetric matrix which is represented by a lower triangular matrix convert it back into
* a full symmetric matrix.
*
* @param A (Input) Lower triangular matrix (Output) symmetric matrix
*/
public static void symmUpperToFull( DMatrixRMaj A )
{
if( A.numRows != A.numCols )
throw new MatrixDimensionException("Must be a square matrix");
final int cols = A.numCols;
for (int row = 0; row < A.numRows; row++) {
for (int col = 0; col <= row; col++) {
A.data[row*cols+col] = A.data[col*cols+row];
}
}
}
}