org.ejml.dense.row.SpecializedOps_FDRM Maven / Gradle / Ivy
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/*
* Copyright (c) 2009-2018, 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.data.FMatrix1Row;
import org.ejml.data.FMatrixD1;
import org.ejml.data.FMatrixRMaj;
import org.ejml.dense.row.mult.VectorVectorMult_FDRM;
import org.ejml.interfaces.linsol.LinearSolverDense;
/**
* This contains less common or more specialized matrix operations.
*
* @author Peter Abeles
*/
public class SpecializedOps_FDRM {
/**
*
* Creates a reflector from the provided vector.
*
* Q = I - γ u uT
* γ = 2/||u||2
*
*
*
* In practice {@link VectorVectorMult_FDRM#householder(float, FMatrixD1, FMatrixD1, FMatrixD1)} multHouseholder}
* should be used for performance reasons since there is no need to calculate Q explicitly.
*
*
* @param u A vector. Not modified.
* @return An orthogonal reflector.
*/
public static FMatrixRMaj createReflector(FMatrix1Row u ) {
if( !MatrixFeatures_FDRM.isVector(u))
throw new IllegalArgumentException("u must be a vector");
float norm = NormOps_FDRM.fastNormF(u);
float gamma = -2.0f/(norm*norm);
FMatrixRMaj Q = CommonOps_FDRM.identity(u.getNumElements());
CommonOps_FDRM.multAddTransB(gamma,u,u,Q);
return Q;
}
/**
*
* Creates a reflector from the provided vector and gamma.
*
* Q = I - γ u uT
*
*
*
* In practice {@link VectorVectorMult_FDRM#householder(float, FMatrixD1, FMatrixD1, FMatrixD1)} multHouseholder}
* should be used for performance reasons since there is no need to calculate Q explicitly.
*
*
* @param u A vector. Not modified.
* @param gamma To produce a reflector gamma needs to be equal to 2/||u||.
* @return An orthogonal reflector.
*/
public static FMatrixRMaj createReflector(FMatrixRMaj u , float gamma) {
if( !MatrixFeatures_FDRM.isVector(u))
throw new IllegalArgumentException("u must be a vector");
FMatrixRMaj Q = CommonOps_FDRM.identity(u.getNumElements());
CommonOps_FDRM.multAddTransB(-gamma,u,u,Q);
return Q;
}
/**
* Creates a copy of a matrix but swaps the rows as specified by the order array.
*
* @param order Specifies which row in the dest corresponds to a row in the src. Not modified.
* @param src The original matrix. Not modified.
* @param dst A Matrix that is a row swapped copy of src. Modified.
*/
public static FMatrixRMaj copyChangeRow(int order[] , FMatrixRMaj src , FMatrixRMaj dst )
{
if( dst == null ) {
dst = new FMatrixRMaj(src.numRows,src.numCols);
} else if( src.numRows != dst.numRows || src.numCols != dst.numCols ) {
throw new IllegalArgumentException("src and dst must have the same dimensions.");
}
for( int i = 0; i < src.numRows; i++ ) {
int indexDst = i*src.numCols;
int indexSrc = order[i]*src.numCols;
System.arraycopy(src.data,indexSrc,dst.data,indexDst,src.numCols);
}
return dst;
}
/**
* Copies just the upper or lower triangular portion of a matrix.
*
* @param src Matrix being copied. Not modified.
* @param dst Where just a triangle from src is copied. If null a new one will be created. Modified.
* @param upper If the upper or lower triangle should be copied.
* @return The copied matrix.
*/
public static FMatrixRMaj copyTriangle(FMatrixRMaj src , FMatrixRMaj dst , boolean upper ) {
if( dst == null ) {
dst = new FMatrixRMaj(src.numRows,src.numCols);
} else if( src.numRows != dst.numRows || src.numCols != dst.numCols ) {
throw new IllegalArgumentException("src and dst must have the same dimensions.");
}
if( upper ) {
int N = Math.min(src.numRows,src.numCols);
for( int i = 0; i < N; i++ ) {
int index = i*src.numCols+i;
System.arraycopy(src.data,index,dst.data,index,src.numCols-i);
}
} else {
for( int i = 0; i < src.numRows; i++ ) {
int length = Math.min(i+1,src.numCols);
int index = i*src.numCols;
System.arraycopy(src.data,index,dst.data,index,length);
}
}
return dst;
}
/**
* Performs L = L*LT
*/
public static void multLowerTranB( FMatrixRMaj mat ) {
int m = mat.numCols;
float[] L = mat.data;
for( int i = 0; i < m; i++ ) {
for( int j = m-1; j >= i; j-- ) {
float val = 0;
for( int k = 0; k <= i; k++ ) {
val += L[ i*m + k] * L[ j*m + k ];
}
L[ i*m + j ] = val;
}
}
// copy the results into the lower portion
for( int i = 0; i < m; i++ ) {
for (int j = 0; j < i; j++) {
L[i*m+j] = L[j*m+i];
}
}
}
/**
* Performs L = LT*L
*/
public static void multLowerTranA( FMatrixRMaj mat ) {
int m = mat.numCols;
float[] L = mat.data;
for( int i = 0; i < m; i++ ) {
for( int j = m-1; j >= i; j-- ) {
float val = 0;
for (int k = j; k < m; k++) {
val += L[ k*m + i] * L[ k*m + j ];
}
L[ i*m + j ] = val;
}
}
// copy the results into the lower portion
for( int i = 0; i < m; i++ ) {
for (int j = 0; j < i; j++) {
L[i*m+j] = L[j*m+i];
}
}
}
/**
*
* Computes the F norm of the difference between the two Matrices:
*
* Sqrt{∑i=1:m ∑j=1:n ( aij - bij)2}
*
*
* This is often used as a cost function.
*
*
* @see NormOps_FDRM#fastNormF
*
* @param a m by n matrix. Not modified.
* @param b m by n matrix. Not modified.
*
* @return The F normal of the difference matrix.
*/
public static float diffNormF(FMatrixD1 a , FMatrixD1 b )
{
if( a.numRows != b.numRows || a.numCols != b.numCols ) {
throw new IllegalArgumentException("Both matrices must have the same shape.");
}
final int size = a.getNumElements();
FMatrixRMaj diff = new FMatrixRMaj(size,1);
for( int i = 0; i < size; i++ ) {
diff.set(i , b.get(i) - a.get(i));
}
return NormOps_FDRM.normF(diff);
}
public static float diffNormF_fast(FMatrixD1 a , FMatrixD1 b )
{
if( a.numRows != b.numRows || a.numCols != b.numCols ) {
throw new IllegalArgumentException("Both matrices must have the same shape.");
}
final int size = a.getNumElements();
float total=0;
for( int i = 0; i < size; i++ ) {
float diff = b.get(i) - a.get(i);
total += diff*diff;
}
return (float)Math.sqrt(total);
}
/**
*
* Computes the p=1 p-norm of the difference between the two Matrices:
*
* ∑i=1:m ∑j=1:n | aij - bij|
*
* where |x| is the absolute value of x.
*
*
* This is often used as a cost function.
*
*
* @param a m by n matrix. Not modified.
* @param b m by n matrix. Not modified.
*
* @return The p=1 p-norm of the difference matrix.
*/
public static float diffNormP1(FMatrixD1 a , FMatrixD1 b )
{
if( a.numRows != b.numRows || a.numCols != b.numCols ) {
throw new IllegalArgumentException("Both matrices must have the same shape.");
}
final int size = a.getNumElements();
float total=0;
for( int i = 0; i < size; i++ ) {
total += Math.abs(b.get(i) - a.get(i));
}
return total;
}
/**
*
* Performs the following operation:
*
* B = A + αI
*
*
* @param A A square matrix. Not modified.
* @param B A square matrix that the results are saved to. Modified.
* @param alpha Scaling factor for the identity matrix.
*/
public static void addIdentity(FMatrix1Row A , FMatrix1Row B , float alpha )
{
if( A.numCols != A.numRows )
throw new IllegalArgumentException("A must be square");
if( B.numCols != A.numCols || B.numRows != A.numRows )
throw new IllegalArgumentException("B must be the same shape as A");
int n = A.numCols;
int index = 0;
for( int i = 0; i < n; i++ ) {
for( int j = 0; j < n; j++ , index++) {
if( i == j ) {
B.set( index , A.get(index) + alpha);
} else {
B.set( index , A.get(index) );
}
}
}
}
/**
*
* Extracts a row or column vector from matrix A. The first element in the matrix is at element (rowA,colA).
* The next 'length' elements are extracted along a row or column. The results are put into vector 'v'
* start at its element v0.
*
*
* @param A Matrix that the vector is being extracted from. Not modified.
* @param rowA Row of the first element that is extracted.
* @param colA Column of the first element that is extracted.
* @param length Length of the extracted vector.
* @param row If true a row vector is extracted, otherwise a column vector is extracted.
* @param offsetV First element in 'v' where the results are extracted to.
* @param v Vector where the results are written to. Modified.
*/
public static void subvector(FMatrix1Row A, int rowA, int colA, int length , boolean row, int offsetV, FMatrix1Row v) {
if( row ) {
for( int i = 0; i < length; i++ ) {
v.set( offsetV +i , A.get(rowA,colA+i) );
}
} else {
for( int i = 0; i < length; i++ ) {
v.set( offsetV +i , A.get(rowA+i,colA));
}
}
}
/**
* Takes a matrix and splits it into a set of row or column vectors.
*
* @param A original matrix.
* @param column If true then column vectors will be created.
* @return Set of vectors.
*/
public static FMatrixRMaj[] splitIntoVectors(FMatrix1Row A , boolean column )
{
int w = column ? A.numCols : A.numRows;
int M = column ? A.numRows : 1;
int N = column ? 1 : A.numCols;
int o = Math.max(M,N);
FMatrixRMaj[] ret = new FMatrixRMaj[w];
for( int i = 0; i < w; i++ ) {
FMatrixRMaj a = new FMatrixRMaj(M,N);
if( column )
subvector(A,0,i,o,false,0,a);
else
subvector(A,i,0,o,true,0,a);
ret[i] = a;
}
return ret;
}
/**
*
* Creates a pivot matrix that exchanges the rows in a matrix:
*
* A' = P*A
*
*
* For example, if element 0 in 'pivots' is 2 then the first row in A' will be the 3rd row in A.
*
*
* @param ret If null then a new matrix is declared otherwise the results are written to it. Is modified.
* @param pivots Specifies the new order of rows in a matrix.
* @param numPivots How many elements in pivots are being used.
* @param transposed If the transpose of the matrix is returned.
* @return A pivot matrix.
*/
public static FMatrixRMaj pivotMatrix(FMatrixRMaj ret, int pivots[], int numPivots, boolean transposed ) {
if( ret == null ) {
ret = new FMatrixRMaj(numPivots, numPivots);
} else {
if( ret.numCols != numPivots || ret.numRows != numPivots )
throw new IllegalArgumentException("Unexpected matrix dimension");
CommonOps_FDRM.fill(ret, 0);
}
if( transposed ) {
for( int i = 0; i < numPivots; i++ ) {
ret.set(pivots[i],i,1);
}
} else {
for( int i = 0; i < numPivots; i++ ) {
ret.set(i,pivots[i],1);
}
}
return ret;
}
/**
* Computes the product of the diagonal elements. For a diagonal or triangular
* matrix this is the determinant.
*
* @param T A matrix.
* @return product of the diagonal elements.
*/
public static float diagProd( FMatrix1Row T )
{
float prod = 1.0f;
int N = Math.min(T.numRows,T.numCols);
for( int i = 0; i < N; i++ ) {
prod *= T.unsafe_get(i,i);
}
return prod;
}
/**
*
* Returns the absolute value of the digonal 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 float elementDiagonalMaxAbs( FMatrixD1 a ) {
final int size = Math.min(a.numRows,a.numCols);
float max = 0;
for( int i = 0; i < size; i++ ) {
float val = Math.abs(a.get( i,i ));
if( val > max ) {
max = val;
}
}
return max;
}
/**
* Computes the quality of a triangular matrix, where the quality of a matrix
* is defined in {@link LinearSolverDense#quality()}. In
* this situation the quality os the absolute value of the product of
* each diagonal element divided by the magnitude of the largest diagonal element.
* If all diagonal elements are zero then zero is returned.
*
* @param T A matrix.
* @return the quality of the system.
*/
public static float qualityTriangular(FMatrixD1 T)
{
int N = Math.min(T.numRows,T.numCols);
// TODO make faster by just checking the upper triangular portion
float max = elementDiagonalMaxAbs(T);
if( max == 0.0f )
return 0.0f;
float quality = 1.0f;
for( int i = 0; i < N; i++ ) {
quality *= T.unsafe_get(i,i)/max;
}
return Math.abs(quality);
}
/**
* Sums up the square of each element in the matrix. This is equivalent to the
* Frobenius norm squared.
*
* @param m Matrix.
* @return Sum of elements squared.
*/
public static float elementSumSq( FMatrixD1 m ) {
// minimize round off error
float maxAbs = CommonOps_FDRM.elementMaxAbs(m);
if( maxAbs == 0)
return 0;
float total = 0;
int N = m.getNumElements();
for( int i = 0; i < N; i++ ) {
float d = m.data[i]/maxAbs;
total += d*d;
}
return maxAbs*total*maxAbs;
}
}