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A fast and easy to use dense and sparse matrix linear algebra library written in Java.
/*
* 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.data.BMatrixRMaj;
import org.ejml.data.FMatrixD1;
import org.ejml.data.FMatrixRMaj;
import org.ejml.dense.row.mult.SubmatrixOps_FDRM;
import org.ejml.dense.row.mult.VectorVectorMult_FDRM;
import java.util.Random;
/**
* Contains a list of functions for creating random row real matrices and vectors with different structures.
*
* @author Peter Abeles
*/
public class RandomMatrices_FDRM {
/**
*
* Creates a randomly generated set of orthonormal vectors. At most it can generate the same
* number of vectors as the dimension of the vectors.
*
*
*
* This is done by creating random vectors then ensuring that they are orthogonal
* to all the ones previously created with reflectors.
*
*
*
* NOTE: This employs a brute force O(N3) algorithm.
*
*
* @param dimen dimension of the space which the vectors will span.
* @param numVectors How many vectors it should generate.
* @param rand Used to create random vectors.
* @return Array of N random orthogonal vectors of unit length.
*/
// is there a faster algorithm out there? This one is a bit sluggish
public static FMatrixRMaj[] span(int dimen, int numVectors , Random rand ) {
if( dimen < numVectors )
throw new IllegalArgumentException("The number of vectors must be less than or equal to the dimension");
FMatrixRMaj u[] = new FMatrixRMaj[numVectors];
u[0] = RandomMatrices_FDRM.rectangle(dimen,1,-1,1,rand);
NormOps_FDRM.normalizeF(u[0]);
for( int i = 1; i < numVectors; i++ ) {
// System.out.println(" i = "+i);
FMatrixRMaj a = new FMatrixRMaj(dimen,1);
FMatrixRMaj r=null;
for( int j = 0; j < i; j++ ) {
// System.out.println("j = "+j);
if( j == 0 )
r = RandomMatrices_FDRM.rectangle(dimen,1,-1,1,rand);
// find a vector that is normal to vector j
// u[i] = (1/2)*(r + Q[j]*r)
a.set(r);
VectorVectorMult_FDRM.householder(-2.0f,u[j],r,a);
CommonOps_FDRM.add(r,a,a);
CommonOps_FDRM.scale(0.5f,a);
// UtilEjml.print(a);
FMatrixRMaj t = a;
a = r;
r = t;
// normalize it so it doesn't get too small
float val = NormOps_FDRM.normF(r);
if( val == 0 || Float.isNaN(val) || Float.isInfinite(val))
throw new RuntimeException("Failed sanity check");
CommonOps_FDRM.divide(r,val);
}
u[i] = r;
}
return u;
}
/**
* Creates a random vector that is inside the specified span.
*
* @param span The span the random vector belongs in.
* @param rand RNG
* @return A random vector within the specified span.
*/
public static FMatrixRMaj insideSpan(FMatrixRMaj[] span , float min , float max , Random rand ) {
FMatrixRMaj A = new FMatrixRMaj(span.length,1);
FMatrixRMaj B = new FMatrixRMaj(span[0].getNumElements(),1);
for( int i = 0; i < span.length; i++ ) {
B.set(span[i]);
float val = rand.nextFloat()*(max-min)+min;
CommonOps_FDRM.scale(val,B);
CommonOps_FDRM.add(A,B,A);
}
return A;
}
/**
*
* Creates a random orthogonal or isometric matrix, depending on the number of rows and columns.
* The number of rows must be more than or equal to the number of columns.
*
*
* @param numRows Number of rows in the generated matrix.
* @param numCols Number of columns in the generated matrix.
* @param rand Random number generator used to create matrices.
* @return A new isometric matrix.
*/
public static FMatrixRMaj orthogonal(int numRows , int numCols , Random rand ) {
if( numRows < numCols ) {
throw new IllegalArgumentException("The number of rows must be more than or equal to the number of columns");
}
FMatrixRMaj u[] = span(numRows,numCols,rand);
FMatrixRMaj ret = new FMatrixRMaj(numRows,numCols);
for( int i = 0; i < numCols; i++ ) {
SubmatrixOps_FDRM.setSubMatrix(u[i], ret, 0, 0, 0, i, numRows, 1);
}
return ret;
}
/**
* Creates a random diagonal matrix where the diagonal elements are selected from a uniform
* distribution that goes from min to max.
*
* @param N Dimension of the matrix.
* @param min Minimum value of a diagonal element.
* @param max Maximum value of a diagonal element.
* @param rand Random number generator.
* @return A random diagonal matrix.
*/
public static FMatrixRMaj diagonal(int N , float min , float max , Random rand ) {
return diagonal(N,N,min,max,rand);
}
/**
* Creates a random matrix where all elements are zero but diagonal elements. Diagonal elements
* randomly drawn from a uniform distribution from min to max, inclusive.
*
* @param numRows Number of rows in the returned matrix..
* @param numCols Number of columns in the returned matrix.
* @param min Minimum value of a diagonal element.
* @param max Maximum value of a diagonal element.
* @param rand Random number generator.
* @return A random diagonal matrix.
*/
public static FMatrixRMaj diagonal(int numRows , int numCols , float min , float max , Random rand ) {
if( max < min )
throw new IllegalArgumentException("The max must be >= the min");
FMatrixRMaj ret = new FMatrixRMaj(numRows,numCols);
int N = Math.min(numRows,numCols);
float r = max-min;
for( int i = 0; i < N; i++ ) {
ret.set(i,i, rand.nextFloat()*r+min);
}
return ret;
}
/**
*
* Creates a random matrix which will have the provided singular values. The length of sv
* is assumed to be the rank of the matrix. This can be useful for testing purposes when one
* needs to ensure that a matrix is not singular but randomly generated.
*
*
* @param numRows Number of rows in generated matrix.
* @param numCols NUmber of columns in generated matrix.
* @param rand Random number generator.
* @param sv Singular values of the matrix.
* @return A new matrix with the specified singular values.
*/
public static FMatrixRMaj singular(int numRows, int numCols,
Random rand, float ...sv)
{
FMatrixRMaj U,V,S;
// speed it up in compact format
if( numRows > numCols ) {
U = RandomMatrices_FDRM.orthogonal(numRows, numCols, rand);
V = RandomMatrices_FDRM.orthogonal(numCols, numCols, rand);
S = new FMatrixRMaj(numCols, numCols);
} else {
U = RandomMatrices_FDRM.orthogonal(numRows, numRows, rand);
V = RandomMatrices_FDRM.orthogonal(numCols, numCols, rand);
S = new FMatrixRMaj(numRows, numCols);
}
int min = Math.min(numRows,numCols);
min = Math.min(min,sv.length);
for( int i = 0; i < min; i++ ) {
S.set(i,i,sv[i]);
}
FMatrixRMaj tmp = new FMatrixRMaj(numRows,numCols);
CommonOps_FDRM.mult(U,S,tmp);
S.reshape(numRows,numCols);
CommonOps_FDRM.multTransB(tmp,V,S);
return S;
}
/**
* Creates a new random symmetric matrix that will have the specified real eigenvalues.
*
* @param num Dimension of the resulting matrix.
* @param rand Random number generator.
* @param eigenvalues Set of real eigenvalues that the matrix will have.
* @return A random matrix with the specified eigenvalues.
*/
public static FMatrixRMaj symmetricWithEigenvalues(int num, Random rand , float ...eigenvalues ) {
FMatrixRMaj V = RandomMatrices_FDRM.orthogonal(num,num,rand);
FMatrixRMaj D = CommonOps_FDRM.diag(eigenvalues);
FMatrixRMaj temp = new FMatrixRMaj(num,num);
CommonOps_FDRM.mult(V,D,temp);
CommonOps_FDRM.multTransB(temp,V,D);
return D;
}
/**
* Returns a matrix where all the elements are selected independently from
* a uniform distribution between 0 and 1 inclusive.
*
* @param numRow Number of rows in the new matrix.
* @param numCol Number of columns in the new matrix.
* @param rand Random number generator used to fill the matrix.
* @return The randomly generated matrix.
*/
public static FMatrixRMaj rectangle(int numRow , int numCol , Random rand ) {
FMatrixRMaj mat = new FMatrixRMaj(numRow,numCol);
fillUniform(mat, 0, 1, rand);
return mat;
}
/**
* Returns new boolean matrix with true or false values selected with equal probability.
*
* @param numRow Number of rows in the new matrix.
* @param numCol Number of columns in the new matrix.
* @param rand Random number generator used to fill the matrix.
* @return The randomly generated matrix.
*/
public static BMatrixRMaj randomBinary(int numRow , int numCol , Random rand ) {
BMatrixRMaj mat = new BMatrixRMaj(numRow,numCol);
setRandomB(mat, rand);
return mat;
}
/**
*
* Adds random values to each element in the matrix from an uniform distribution.
*
* aij = aij + U(min,max)
*
*
* @param A The matrix who is to be randomized. Modified
* @param min The minimum value each element can be.
* @param max The maximum value each element can be..
* @param rand Random number generator used to fill the matrix.
*/
public static void addUniform(FMatrixRMaj A , float min , float max , Random rand ) {
float d[] = A.getData();
int size = A.getNumElements();
float r = max-min;
for( int i = 0; i < size; i++ ) {
d[i] += r*rand.nextFloat()+min;
}
}
/**
*
* Returns a matrix where all the elements are selected independently from
* a uniform distribution between 'min' and 'max' inclusive.
*
*
* @param numRow Number of rows in the new matrix.
* @param numCol Number of columns in the new matrix.
* @param min The minimum value each element can be.
* @param max The maximum value each element can be.
* @param rand Random number generator used to fill the matrix.
* @return The randomly generated matrix.
*/
public static FMatrixRMaj rectangle(int numRow , int numCol , float min , float max , Random rand ) {
FMatrixRMaj mat = new FMatrixRMaj(numRow,numCol);
fillUniform(mat,min,max,rand);
return mat;
}
/**
*
* Sets each element in the matrix to a value drawn from an uniform distribution from 0 to 1 inclusive.
*
*
* @param mat The matrix who is to be randomized. Modified.
* @param rand Random number generator used to fill the matrix.
*/
public static void fillUniform(FMatrixRMaj mat , Random rand )
{
fillUniform(mat,0,1,rand);
}
/**
*
* Sets each element in the matrix to a value drawn from an uniform distribution from 'min' to 'max' inclusive.
*
*
* @param min The minimum value each element can be.
* @param max The maximum value each element can be.
* @param mat The matrix who is to be randomized. Modified.
* @param rand Random number generator used to fill the matrix.
*/
public static void fillUniform(FMatrixD1 mat , float min , float max , Random rand )
{
float d[] = mat.getData();
int size = mat.getNumElements();
float r = max-min;
for( int i = 0; i < size; i++ ) {
d[i] = r*rand.nextFloat()+min;
}
}
/**
*
* Sets each element in the boolean matrix to true or false with equal probability
*
*
* @param mat The matrix who is to be randomized. Modified.
* @param rand Random number generator used to fill the matrix.
*/
public static void setRandomB(BMatrixRMaj mat , Random rand )
{
boolean d[] = mat.data;
int size = mat.getNumElements();
for( int i = 0; i < size; i++ ) {
d[i] = rand.nextBoolean();
}
}
/**
*
* Sets each element in the matrix to a value drawn from an Gaussian distribution with the specified mean and
* standard deviation
*
*
*
* @param numRow Number of rows in the new matrix.
* @param numCol Number of columns in the new matrix.
* @param mean Mean value in the distribution
* @param stdev Standard deviation in the distribution
* @param rand Random number generator used to fill the matrix.
*/
public static FMatrixRMaj rectangleGaussian(int numRow , int numCol , float mean , float stdev , Random rand )
{
FMatrixRMaj m = new FMatrixRMaj(numRow,numCol);
fillGaussian(m,mean,stdev,rand);
return m;
}
/**
*
* Sets each element in the matrix to a value drawn from an Gaussian distribution with the specified mean and
* standard deviation
*
*
* @param mat The matrix who is to be randomized. Modified.
* @param mean Mean value in the distribution
* @param stdev Standard deviation in the distribution
* @param rand Random number generator used to fill the matrix.
*/
public static void fillGaussian(FMatrixD1 mat , float mean , float stdev , Random rand )
{
float d[] = mat.getData();
int size = mat.getNumElements();
for( int i = 0; i < size; i++ ) {
d[i] = mean + stdev * (float)rand.nextGaussian();
}
}
/**
* Creates a random symmetric positive definite matrix.
*
* @param width The width of the square matrix it returns.
* @param rand Random number generator used to make the matrix.
* @return The random symmetric positive definite matrix.
*/
public static FMatrixRMaj symmetricPosDef(int width, Random rand) {
// This is not formally proven to work. It just seems to work.
FMatrixRMaj a = new FMatrixRMaj(width,1);
FMatrixRMaj b = new FMatrixRMaj(width,width);
for( int i = 0; i < width; i++ ) {
a.set(i,0,rand.nextFloat());
}
CommonOps_FDRM.multTransB(a,a,b);
for( int i = 0; i < width; i++ ) {
b.add(i,i,1);
}
return b;
}
/**
* Creates a random symmetric matrix whose values are selected from an uniform distribution
* from min to max, inclusive.
*
* @param length Width and height of the matrix.
* @param min Minimum value an element can have.
* @param max Maximum value an element can have.
* @param rand Random number generator.
* @return A symmetric matrix.
*/
public static FMatrixRMaj symmetric(int length, float min, float max, Random rand) {
FMatrixRMaj A = new FMatrixRMaj(length,length);
symmetric(A,min,max,rand);
return A;
}
/**
* Sets the provided square matrix to be a random symmetric matrix whose values are selected from an uniform distribution
* from min to max, inclusive.
*
* @param A The matrix that is to be modified. Must be square. Modified.
* @param min Minimum value an element can have.
* @param max Maximum value an element can have.
* @param rand Random number generator.
*/
public static void symmetric(FMatrixRMaj A, float min, float max, Random rand) {
if( A.numRows != A.numCols )
throw new IllegalArgumentException("A must be a square matrix");
float range = max-min;
int length = A.numRows;
for( int i = 0; i < length; i++ ) {
for( int j = i; j < length; j++ ) {
float val = rand.nextFloat()*range + min;
A.set(i,j,val);
A.set(j,i,val);
}
}
}
/**
* Creates an upper triangular matrix whose values are selected from a uniform distribution. If hessenberg
* is greater than zero then a hessenberg matrix of the specified degree is created instead.
*
* @param dimen Number of rows and columns in the matrix..
* @param hessenberg 0 for triangular matrix and > 0 for hessenberg matrix.
* @param min minimum value an element can be.
* @param max maximum value an element can be.
* @param rand random number generator used.
* @return The randomly generated matrix.
*/
public static FMatrixRMaj triangularUpper(int dimen , int hessenberg , float min , float max , Random rand )
{
if( hessenberg < 0 )
throw new RuntimeException("hessenberg must be more than or equal to 0");
float range = max-min;
FMatrixRMaj A = new FMatrixRMaj(dimen,dimen);
for( int i = 0; i < dimen; i++ ) {
int start = i <= hessenberg ? 0 : i-hessenberg;
for( int j = start; j < dimen; j++ ) {
A.set(i,j, rand.nextFloat()*range+min);
}
}
return A;
}
/**
* Creates a lower triangular matrix whose values are selected from a uniform distribution. If hessenberg
* is greater than zero then a hessenberg matrix of the specified degree is created instead.
*
* @param dimen Number of rows and columns in the matrix..
* @param hessenberg 0 for triangular matrix and > 0 for hessenberg matrix.
* @param min minimum value an element can be.
* @param max maximum value an element can be.
* @param rand random number generator used.
* @return The randomly generated matrix.
*/
public static FMatrixRMaj triangularLower(int dimen , int hessenberg , float min , float max , Random rand )
{
if( hessenberg < 0 )
throw new RuntimeException("hessenberg must be more than or equal to 0");
float range = max-min;
FMatrixRMaj A = new FMatrixRMaj(dimen,dimen);
for( int i = 0; i < dimen; i++ ) {
int end = Math.min(dimen,i+hessenberg+1);
for( int j = 0; j < end; j++ ) {
A.set(i,j, rand.nextFloat()*range+min);
}
}
return A;
}
}