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A fast and easy to use dense matrix linear algebra library written in Java.
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/*
* Copyright (c) 2009-2014, 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.alg.fixed;
import org.ejml.data.FixedMatrix3_64F;
import org.ejml.data.FixedMatrix3x3_64F;
/**
* Common matrix operations for fixed sized matrices which are 3 x 3 or 3 element vectors.
* DO NOT MODIFY. Automatically generated code created by GenerateFixedOps
*
* @author Peter Abeles
*/
public class FixedOps3 {
/**
* 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( FixedMatrix3x3_64F a , FixedMatrix3x3_64F b , FixedMatrix3x3_64F c ) {
c.a11 = a.a11 + b.a11;
c.a12 = a.a12 + b.a12;
c.a13 = a.a13 + b.a13;
c.a21 = a.a21 + b.a21;
c.a22 = a.a22 + b.a22;
c.a23 = a.a23 + b.a23;
c.a31 = a.a31 + b.a31;
c.a32 = a.a32 + b.a32;
c.a33 = a.a33 + b.a33;
}
/**
* 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( FixedMatrix3x3_64F a , FixedMatrix3x3_64F b ) {
a.a11 += b.a11;
a.a12 += b.a12;
a.a13 += b.a13;
a.a21 += b.a21;
a.a22 += b.a22;
a.a23 += b.a23;
a.a31 += b.a31;
a.a32 += b.a32;
a.a33 += b.a33;
}
/**
* Performs an in-place transpose. This algorithm is only efficient for square
* matrices.
*
* @param m The matrix that is to be transposed. Modified.
*/
public static void transpose( FixedMatrix3x3_64F m ) {
double tmp;
tmp = m.a12; m.a12 = m.a21; m.a21 = tmp;
tmp = m.a13; m.a13 = m.a31; m.a31 = tmp;
tmp = m.a23; m.a23 = m.a32; m.a32 = tmp;
}
/**
*
* Transposes matrix 'a' and stores the results in 'b':
*
* bij = aji
* where 'b' is the transpose of 'a'.
*
*
* @param input The original matrix. Not modified.
* @param output Where the transpose is stored. If null a new matrix is created. Modified.
* @return The transposed matrix.
*/
public static FixedMatrix3x3_64F transpose( FixedMatrix3x3_64F input , FixedMatrix3x3_64F output ) {
if( input == null )
input = new FixedMatrix3x3_64F();
output.a11 = input.a11;
output.a12 = input.a21;
output.a13 = input.a31;
output.a21 = input.a12;
output.a22 = input.a22;
output.a23 = input.a32;
output.a31 = input.a13;
output.a32 = input.a23;
output.a33 = input.a33;
return output;
}
/**
* 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( FixedMatrix3x3_64F a , FixedMatrix3x3_64F b , FixedMatrix3x3_64F c) {
c.a11 = a.a11*b.a11 + a.a12*b.a21 + a.a13*b.a31;
c.a12 = a.a11*b.a12 + a.a12*b.a22 + a.a13*b.a32;
c.a13 = a.a11*b.a13 + a.a12*b.a23 + a.a13*b.a33;
c.a21 = a.a21*b.a11 + a.a22*b.a21 + a.a23*b.a31;
c.a22 = a.a21*b.a12 + a.a22*b.a22 + a.a23*b.a32;
c.a23 = a.a21*b.a13 + a.a22*b.a23 + a.a23*b.a33;
c.a31 = a.a31*b.a11 + a.a32*b.a21 + a.a33*b.a31;
c.a32 = a.a31*b.a12 + a.a32*b.a22 + a.a33*b.a32;
c.a33 = a.a31*b.a13 + a.a32*b.a23 + a.a33*b.a33;
}
/**
* 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( FixedMatrix3x3_64F a , FixedMatrix3x3_64F b , FixedMatrix3x3_64F c) {
c.a11 = a.a11*b.a11 + a.a21*b.a21 + a.a31*b.a31;
c.a12 = a.a11*b.a12 + a.a21*b.a22 + a.a31*b.a32;
c.a13 = a.a11*b.a13 + a.a21*b.a23 + a.a31*b.a33;
c.a21 = a.a12*b.a11 + a.a22*b.a21 + a.a32*b.a31;
c.a22 = a.a12*b.a12 + a.a22*b.a22 + a.a32*b.a32;
c.a23 = a.a12*b.a13 + a.a22*b.a23 + a.a32*b.a33;
c.a31 = a.a13*b.a11 + a.a23*b.a21 + a.a33*b.a31;
c.a32 = a.a13*b.a12 + a.a23*b.a22 + a.a33*b.a32;
c.a33 = a.a13*b.a13 + a.a23*b.a23 + a.a33*b.a33;
}
/**
*
* 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( FixedMatrix3x3_64F a , FixedMatrix3x3_64F b , FixedMatrix3x3_64F c) {
c.a11 = a.a11*b.a11 + a.a21*b.a12 + a.a31*b.a13;
c.a12 = a.a11*b.a21 + a.a21*b.a22 + a.a31*b.a23;
c.a13 = a.a11*b.a31 + a.a21*b.a32 + a.a31*b.a33;
c.a21 = a.a12*b.a11 + a.a22*b.a12 + a.a32*b.a13;
c.a22 = a.a12*b.a21 + a.a22*b.a22 + a.a32*b.a23;
c.a23 = a.a12*b.a31 + a.a22*b.a32 + a.a32*b.a33;
c.a31 = a.a13*b.a11 + a.a23*b.a12 + a.a33*b.a13;
c.a32 = a.a13*b.a21 + a.a23*b.a22 + a.a33*b.a23;
c.a33 = a.a13*b.a31 + a.a23*b.a32 + a.a33*b.a33;
}
/**
*
* 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( FixedMatrix3x3_64F a , FixedMatrix3x3_64F b , FixedMatrix3x3_64F c) {
c.a11 = a.a11*b.a11 + a.a12*b.a12 + a.a13*b.a13;
c.a12 = a.a11*b.a21 + a.a12*b.a22 + a.a13*b.a23;
c.a13 = a.a11*b.a31 + a.a12*b.a32 + a.a13*b.a33;
c.a21 = a.a21*b.a11 + a.a22*b.a12 + a.a23*b.a13;
c.a22 = a.a21*b.a21 + a.a22*b.a22 + a.a23*b.a23;
c.a23 = a.a21*b.a31 + a.a22*b.a32 + a.a23*b.a33;
c.a31 = a.a31*b.a11 + a.a32*b.a12 + a.a33*b.a13;
c.a32 = a.a31*b.a21 + a.a32*b.a22 + a.a33*b.a23;
c.a33 = a.a31*b.a31 + a.a32*b.a32 + a.a33*b.a33;
}
/**
* Performs matrix to vector multiplication:
*
* c = a * b
*
* ci = ∑k=1:n { aik * bk}
*
*
* @param a The left matrix in the multiplication operation. Not modified.
* @param b The right vector in the multiplication operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void mult( FixedMatrix3x3_64F a , FixedMatrix3_64F b , FixedMatrix3_64F c) {
c.a1 = a.a11*b.a1 + a.a12*b.a2 + a.a13*b.a3;
c.a2 = a.a21*b.a1 + a.a22*b.a2 + a.a23*b.a3;
c.a3 = a.a31*b.a1 + a.a32*b.a2 + a.a33*b.a3;
}
/**
* Performs vector to matrix multiplication:
*
* c = a * b
*
* cj = ∑k=1:n { bk * akj }
*
*
* @param a The left vector 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( FixedMatrix3_64F a , FixedMatrix3x3_64F b , FixedMatrix3_64F c) {
c.a1 = a.a1*b.a11 + a.a2*b.a21 + a.a3*b.a31;
c.a2 = a.a1*b.a12 + a.a2*b.a22 + a.a3*b.a32;
c.a3 = a.a1*b.a13 + a.a2*b.a23 + a.a3*b.a33;
}
/**
* Performs the vector dot product:
*
* c = a * b
*
* c> = ∑k=1:n { bk * ak }
*
*
* @param a The left vector in the multiplication operation. Not modified.
* @param b The right matrix in the multiplication operation. Not modified.
* @return The dot product
*/
public static double dot( FixedMatrix3_64F a , FixedMatrix3_64F b ) {
return a.a1*b.a1 + a.a2*b.a2 + a.a3*b.a3;
}
/**
* Sets all the diagonal elements equal to one and everything else equal to zero.
* If this is a square matrix then it will be an identity matrix.
*
* @param a A matrix.
*/
public static void setIdentity( FixedMatrix3x3_64F a ) {
a.a11 = 1; a.a21 = 0; a.a31 = 0;
a.a12 = 0; a.a22 = 1; a.a32 = 0;
a.a13 = 0; a.a23 = 0; a.a33 = 1;
}
/**
* Inverts matrix 'a' using minor matrices and stores the results in 'inv'. Scaling is applied to improve
* stability against overflow and underflow.
*
* WARNING: Potentially less stable than using LU decomposition.
*
* @param a Input matrix. Not modified.
* @param inv Inverted output matrix. Modified.
* @return true if it was successful or false if it failed. Not always reliable.
*/
public static boolean invert( FixedMatrix3x3_64F a , FixedMatrix3x3_64F inv ) {
double scale = 1.0/elementMaxAbs(a);
double a11 = a.a11*scale;
double a12 = a.a12*scale;
double a13 = a.a13*scale;
double a21 = a.a21*scale;
double a22 = a.a22*scale;
double a23 = a.a23*scale;
double a31 = a.a31*scale;
double a32 = a.a32*scale;
double a33 = a.a33*scale;
double m11 = a22*a33 - a23*a32;
double m12 = -( a21*a33 - a23*a31);
double m13 = a21*a32 - a22*a31;
double m21 = -( a12*a33 - a13*a32);
double m22 = a11*a33 - a13*a31;
double m23 = -( a11*a32 - a12*a31);
double m31 = a12*a23 - a13*a22;
double m32 = -( a11*a23 - a13*a21);
double m33 = a11*a22 - a12*a21;
double det = (a11*m11 + a12*m12 + a13*m13)/scale;
inv.a11 = m11/det;
inv.a12 = m21/det;
inv.a13 = m31/det;
inv.a21 = m12/det;
inv.a22 = m22/det;
inv.a23 = m32/det;
inv.a31 = m13/det;
inv.a32 = m23/det;
inv.a33 = m33/det;
return !Double.isNaN(det) && !Double.isInfinite(det);
}
/**
* Computes the determinant using minor matrices.
*
* WARNING: Potentially less stable than using LU decomposition.
*
* @param mat Input matrix. Not modified.
* @return The determinant.
*/
public static double det( FixedMatrix3x3_64F mat ) {
double a = mat.a11*(mat.a22*mat.a33 - mat.a23*mat.a32);
double b = mat.a12*(mat.a21*mat.a33 - mat.a23*mat.a31);
double c = mat.a13*(mat.a21*mat.a32 - mat.a31*mat.a22);
return a-b+c;
}
/**
*
* This computes the trace of the matrix:
*
* trace = ∑i=1:n { aii }
*
*
* The trace is only defined for square matrices.
*
*
* @param a A square matrix. Not modified.
*/
public static double trace( FixedMatrix3x3_64F a ) {
return a.a11 + a.a21 + a.a31;
}
/**
*
* Extracts all diagonal elements from 'input' and places them inside the 'out' vector. Elements
* are in sequential order.
*
*
*
* @param input Matrix. Not modified.
* @param out Vector containing diagonal elements. Modified.
*/
public static void diag( FixedMatrix3x3_64F input , FixedMatrix3_64F out ) {
out.a1 = input.a11;
out.a2 = input.a22;
out.a3 = input.a33;
}
/**
*
* 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( FixedMatrix3x3_64F a ) {
double max = a.a11;
max = Math.max(max,a.a12);
max = Math.max(max,a.a13);
max = Math.max(max,a.a21);
max = Math.max(max,a.a22);
max = Math.max(max,a.a23);
max = Math.max(max,a.a31);
max = Math.max(max,a.a32);
max = Math.max(max,a.a33);
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( FixedMatrix3x3_64F a ) {
double max = a.a11;
max = Math.max(max,Math.abs(a.a12));
max = Math.max(max,Math.abs(a.a13));
max = Math.max(max,Math.abs(a.a21));
max = Math.max(max,Math.abs(a.a22));
max = Math.max(max,Math.abs(a.a23));
max = Math.max(max,Math.abs(a.a31));
max = Math.max(max,Math.abs(a.a32));
max = Math.max(max,Math.abs(a.a33));
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( FixedMatrix3x3_64F a ) {
double min = a.a11;
min = Math.min(min,a.a12);
min = Math.min(min,a.a13);
min = Math.min(min,a.a21);
min = Math.min(min,a.a22);
min = Math.min(min,a.a23);
min = Math.min(min,a.a31);
min = Math.min(min,a.a32);
min = Math.min(min,a.a33);
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( FixedMatrix3x3_64F a ) {
double min = a.a11;
min = Math.min(min,Math.abs(a.a12));
min = Math.min(min,Math.abs(a.a13));
min = Math.min(min,Math.abs(a.a21));
min = Math.min(min,Math.abs(a.a22));
min = Math.min(min,Math.abs(a.a23));
min = Math.min(min,Math.abs(a.a31));
min = Math.min(min,Math.abs(a.a32));
min = Math.min(min,Math.abs(a.a33));
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( FixedMatrix3x3_64F a , FixedMatrix3x3_64F b) {
a.a11 *= b.a11; a.a12 *= b.a12; a.a13 *= b.a13;
a.a21 *= b.a21; a.a22 *= b.a22; a.a23 *= b.a23;
a.a31 *= b.a31; a.a32 *= b.a32; a.a33 *= b.a33;
}
/**
* 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( FixedMatrix3x3_64F a , FixedMatrix3x3_64F b , FixedMatrix3x3_64F c ) {
c.a11 = a.a11*b.a11; c.a12 = a.a12*b.a12; c.a13 = a.a13*b.a13;
c.a21 = a.a21*b.a21; c.a22 = a.a22*b.a22; c.a23 = a.a23*b.a23;
c.a31 = a.a31*b.a31; c.a32 = a.a32*b.a32; c.a33 = a.a33*b.a33;
}
/**
* 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( FixedMatrix3x3_64F a , FixedMatrix3x3_64F b) {
a.a11 /= b.a11; a.a12 /= b.a12; a.a13 /= b.a13;
a.a21 /= b.a21; a.a22 /= b.a22; a.a23 /= b.a23;
a.a31 /= b.a31; a.a32 /= b.a32; a.a33 /= b.a33;
}
/**
* 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( FixedMatrix3x3_64F a , FixedMatrix3x3_64F b , FixedMatrix3x3_64F c ) {
c.a11 = a.a11/b.a11; c.a12 = a.a12/b.a12; c.a13 = a.a13/b.a13;
c.a21 = a.a21/b.a21; c.a22 = a.a22/b.a22; c.a23 = a.a23/b.a23;
c.a31 = a.a31/b.a31; c.a32 = a.a32/b.a32; c.a33 = a.a33/b.a33;
}
/**
*
* 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 , FixedMatrix3x3_64F a ) {
a.a11 *= alpha; a.a12 *= alpha; a.a13 *= alpha;
a.a21 *= alpha; a.a22 *= alpha; a.a23 *= alpha;
a.a31 *= alpha; a.a32 *= alpha; a.a33 *= 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 , FixedMatrix3x3_64F a , FixedMatrix3x3_64F b ) {
b.a11 = a.a11*alpha; b.a12 = a.a12*alpha; b.a13 = a.a13*alpha;
b.a21 = a.a21*alpha; b.a22 = a.a22*alpha; b.a23 = a.a23*alpha;
b.a31 = a.a31*alpha; b.a32 = a.a32*alpha; b.a33 = a.a33*alpha;
}
/**
*
* Performs an in-place element by element scalar division. Scalar denominator.
*
* 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( FixedMatrix3x3_64F a , double alpha ) {
a.a11 /= alpha; a.a12 /= alpha; a.a13 /= alpha;
a.a21 /= alpha; a.a22 /= alpha; a.a23 /= alpha;
a.a31 /= alpha; a.a32 /= alpha; a.a33 /= alpha;
}
/**
*
* Performs an element by element scalar division. Scalar denominator.
*
* bij = *aij /α
*
*
* @param alpha the amount each element is divided by.
* @param a The matrix whose elements are to be divided. Not modified.
* @param b Where the results are stored. Modified.
*/
public static void divide( FixedMatrix3x3_64F a , double alpha , FixedMatrix3x3_64F b ) {
b.a11 = a.a11/alpha; b.a12 = a.a12/alpha; b.a13 = a.a13/alpha;
b.a21 = a.a21/alpha; b.a22 = a.a22/alpha; b.a23 = a.a23/alpha;
b.a31 = a.a31/alpha; b.a32 = a.a32/alpha; b.a33 = a.a33/alpha;
}
/**
*
* Changes the sign of every element in the matrix.
*
* aij = -aij
*
*
* @param a A matrix. Modified.
*/
public static void changeSign( FixedMatrix3x3_64F a )
{
a.a11 = -a.a11; a.a12 = -a.a12; a.a13 = -a.a13;
a.a21 = -a.a21; a.a22 = -a.a22; a.a23 = -a.a23;
a.a31 = -a.a31; a.a32 = -a.a32; a.a33 = -a.a33;
}
/**
*
* 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 v The value each element will have.
*/
public static void fill( FixedMatrix3x3_64F a , double v ) {
a.a11 = v; a.a12 = v; a.a13 = v;
a.a21 = v; a.a22 = v; a.a23 = v;
a.a31 = v; a.a32 = v; a.a33 = v;
}
}