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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.fixed;
import org.ejml.UtilEjml;
import org.ejml.data.FMatrix4;
import org.ejml.data.FMatrix4x4;
/**
* Common matrix operations for fixed sized matrices which are 4 x 4 or 4 element vectors.
* DO NOT MODIFY. Automatically generated code created by GenerateCommonOps_DDF
*
* @author Peter Abeles
*/
public class CommonOps_FDF4 {
/**
* 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( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c ) {
c.a11 = a.a11 + b.a11;
c.a12 = a.a12 + b.a12;
c.a13 = a.a13 + b.a13;
c.a14 = a.a14 + b.a14;
c.a21 = a.a21 + b.a21;
c.a22 = a.a22 + b.a22;
c.a23 = a.a23 + b.a23;
c.a24 = a.a24 + b.a24;
c.a31 = a.a31 + b.a31;
c.a32 = a.a32 + b.a32;
c.a33 = a.a33 + b.a33;
c.a34 = a.a34 + b.a34;
c.a41 = a.a41 + b.a41;
c.a42 = a.a42 + b.a42;
c.a43 = a.a43 + b.a43;
c.a44 = a.a44 + b.a44;
}
/**
* Performs the following operation:
*
* c = a + b
* ci = ai + bi
*
*
*
* Vector C can be the same instance as Vector A and/or B.
*
*
* @param a A Vector. Not modified.
* @param b A Vector. Not modified.
* @param c A Vector where the results are stored. Modified.
*/
public static void add( FMatrix4 a , FMatrix4 b , FMatrix4 c ) {
c.a1 = a.a1 + b.a1;
c.a2 = a.a2 + b.a2;
c.a3 = a.a3 + b.a3;
c.a4 = a.a4 + b.a4;
}
/**
* 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( FMatrix4x4 a , FMatrix4x4 b ) {
a.a11 += b.a11;
a.a12 += b.a12;
a.a13 += b.a13;
a.a14 += b.a14;
a.a21 += b.a21;
a.a22 += b.a22;
a.a23 += b.a23;
a.a24 += b.a24;
a.a31 += b.a31;
a.a32 += b.a32;
a.a33 += b.a33;
a.a34 += b.a34;
a.a41 += b.a41;
a.a42 += b.a42;
a.a43 += b.a43;
a.a44 += b.a44;
}
/**
* Performs the following operation:
*
* a = a + b
* ai = ai + bi
*
*
* @param a A Vector. Modified.
* @param b A Vector. Not modified.
*/
public static void addEquals( FMatrix4 a , FMatrix4 b ) {
a.a1 += b.a1;
a.a2 += b.a2;
a.a3 += b.a3;
a.a4 += b.a4;
}
/**
* Performs the following operation:
*
* c = a - b
* cij = aij - bij
*
*
*
* Matrix C can be the same instance as Matrix A and/or B.
*
*
* @param a A Matrix. Not modified.
* @param b A Matrix. Not modified.
* @param c A Matrix where the results are stored. Modified.
*/
public static void subtract( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c ) {
c.a11 = a.a11 - b.a11;
c.a12 = a.a12 - b.a12;
c.a13 = a.a13 - b.a13;
c.a14 = a.a14 - b.a14;
c.a21 = a.a21 - b.a21;
c.a22 = a.a22 - b.a22;
c.a23 = a.a23 - b.a23;
c.a24 = a.a24 - b.a24;
c.a31 = a.a31 - b.a31;
c.a32 = a.a32 - b.a32;
c.a33 = a.a33 - b.a33;
c.a34 = a.a34 - b.a34;
c.a41 = a.a41 - b.a41;
c.a42 = a.a42 - b.a42;
c.a43 = a.a43 - b.a43;
c.a44 = a.a44 - b.a44;
}
/**
* Performs the following operation:
*
* c = a - b
* ci = ai - bi
*
*
*
* Vector C can be the same instance as Vector A and/or B.
*
*
* @param a A Vector. Not modified.
* @param b A Vector. Not modified.
* @param c A Vector where the results are stored. Modified.
*/
public static void subtract( FMatrix4 a , FMatrix4 b , FMatrix4 c ) {
c.a1 = a.a1 - b.a1;
c.a2 = a.a2 - b.a2;
c.a3 = a.a3 - b.a3;
c.a4 = a.a4 - b.a4;
}
/**
* Performs the following operation:
*
* a = a - b
* aij = aij - bij
*
*
* @param a A Matrix. Modified.
* @param b A Matrix. Not modified.
*/
public static void subtractEquals( FMatrix4x4 a , FMatrix4x4 b ) {
a.a11 -= b.a11;
a.a12 -= b.a12;
a.a13 -= b.a13;
a.a14 -= b.a14;
a.a21 -= b.a21;
a.a22 -= b.a22;
a.a23 -= b.a23;
a.a24 -= b.a24;
a.a31 -= b.a31;
a.a32 -= b.a32;
a.a33 -= b.a33;
a.a34 -= b.a34;
a.a41 -= b.a41;
a.a42 -= b.a42;
a.a43 -= b.a43;
a.a44 -= b.a44;
}
/**
* Performs the following operation:
*
* a = a - b
* ai = ai - bi
*
*
* @param a A Vector. Modified.
* @param b A Vector. Not modified.
*/
public static void subtractEquals( FMatrix4 a , FMatrix4 b ) {
a.a1 -= b.a1;
a.a2 -= b.a2;
a.a3 -= b.a3;
a.a4 -= b.a4;
}
/**
* 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( FMatrix4x4 m ) {
float tmp;
tmp = m.a12; m.a12 = m.a21; m.a21 = tmp;
tmp = m.a13; m.a13 = m.a31; m.a31 = tmp;
tmp = m.a14; m.a14 = m.a41; m.a41 = tmp;
tmp = m.a23; m.a23 = m.a32; m.a32 = tmp;
tmp = m.a24; m.a24 = m.a42; m.a42 = tmp;
tmp = m.a34; m.a34 = m.a43; m.a43 = 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 FMatrix4x4 transpose( FMatrix4x4 input , FMatrix4x4 output ) {
if( input == null )
input = new FMatrix4x4();
UtilEjml.checkSameInstance(input,output);
output.a11 = input.a11;
output.a12 = input.a21;
output.a13 = input.a31;
output.a14 = input.a41;
output.a21 = input.a12;
output.a22 = input.a22;
output.a23 = input.a32;
output.a24 = input.a42;
output.a31 = input.a13;
output.a32 = input.a23;
output.a33 = input.a33;
output.a34 = input.a43;
output.a41 = input.a14;
output.a42 = input.a24;
output.a43 = input.a34;
output.a44 = input.a44;
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 (Output) Where the results of the operation are stored. Modified.
*/
public static void mult( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 = a.a11*b.a11 + a.a12*b.a21 + a.a13*b.a31 + a.a14*b.a41;
c.a12 = a.a11*b.a12 + a.a12*b.a22 + a.a13*b.a32 + a.a14*b.a42;
c.a13 = a.a11*b.a13 + a.a12*b.a23 + a.a13*b.a33 + a.a14*b.a43;
c.a14 = a.a11*b.a14 + a.a12*b.a24 + a.a13*b.a34 + a.a14*b.a44;
c.a21 = a.a21*b.a11 + a.a22*b.a21 + a.a23*b.a31 + a.a24*b.a41;
c.a22 = a.a21*b.a12 + a.a22*b.a22 + a.a23*b.a32 + a.a24*b.a42;
c.a23 = a.a21*b.a13 + a.a22*b.a23 + a.a23*b.a33 + a.a24*b.a43;
c.a24 = a.a21*b.a14 + a.a22*b.a24 + a.a23*b.a34 + a.a24*b.a44;
c.a31 = a.a31*b.a11 + a.a32*b.a21 + a.a33*b.a31 + a.a34*b.a41;
c.a32 = a.a31*b.a12 + a.a32*b.a22 + a.a33*b.a32 + a.a34*b.a42;
c.a33 = a.a31*b.a13 + a.a32*b.a23 + a.a33*b.a33 + a.a34*b.a43;
c.a34 = a.a31*b.a14 + a.a32*b.a24 + a.a33*b.a34 + a.a34*b.a44;
c.a41 = a.a41*b.a11 + a.a42*b.a21 + a.a43*b.a31 + a.a44*b.a41;
c.a42 = a.a41*b.a12 + a.a42*b.a22 + a.a43*b.a32 + a.a44*b.a42;
c.a43 = a.a41*b.a13 + a.a42*b.a23 + a.a43*b.a33 + a.a44*b.a43;
c.a44 = a.a41*b.a14 + a.a42*b.a24 + a.a43*b.a34 + a.a44*b.a44;
}
/**
* Performs the following operation:
*
* c = α * a * b
*
* cij = α ∑k=1:n { aik * bkj}
*
*
* @param alpha Scaling factor.
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void mult( float alpha , FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 = alpha*(a.a11*b.a11 + a.a12*b.a21 + a.a13*b.a31 + a.a14*b.a41);
c.a12 = alpha*(a.a11*b.a12 + a.a12*b.a22 + a.a13*b.a32 + a.a14*b.a42);
c.a13 = alpha*(a.a11*b.a13 + a.a12*b.a23 + a.a13*b.a33 + a.a14*b.a43);
c.a14 = alpha*(a.a11*b.a14 + a.a12*b.a24 + a.a13*b.a34 + a.a14*b.a44);
c.a21 = alpha*(a.a21*b.a11 + a.a22*b.a21 + a.a23*b.a31 + a.a24*b.a41);
c.a22 = alpha*(a.a21*b.a12 + a.a22*b.a22 + a.a23*b.a32 + a.a24*b.a42);
c.a23 = alpha*(a.a21*b.a13 + a.a22*b.a23 + a.a23*b.a33 + a.a24*b.a43);
c.a24 = alpha*(a.a21*b.a14 + a.a22*b.a24 + a.a23*b.a34 + a.a24*b.a44);
c.a31 = alpha*(a.a31*b.a11 + a.a32*b.a21 + a.a33*b.a31 + a.a34*b.a41);
c.a32 = alpha*(a.a31*b.a12 + a.a32*b.a22 + a.a33*b.a32 + a.a34*b.a42);
c.a33 = alpha*(a.a31*b.a13 + a.a32*b.a23 + a.a33*b.a33 + a.a34*b.a43);
c.a34 = alpha*(a.a31*b.a14 + a.a32*b.a24 + a.a33*b.a34 + a.a34*b.a44);
c.a41 = alpha*(a.a41*b.a11 + a.a42*b.a21 + a.a43*b.a31 + a.a44*b.a41);
c.a42 = alpha*(a.a41*b.a12 + a.a42*b.a22 + a.a43*b.a32 + a.a44*b.a42);
c.a43 = alpha*(a.a41*b.a13 + a.a42*b.a23 + a.a43*b.a33 + a.a44*b.a43);
c.a44 = alpha*(a.a41*b.a14 + a.a42*b.a24 + a.a43*b.a34 + a.a44*b.a44);
}
/**
* Performs the following operation:
*
* c = aT * b
*
* cij = ∑k=1:n { aki * bkj}
*
*
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multTransA( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 = a.a11*b.a11 + a.a21*b.a21 + a.a31*b.a31 + a.a41*b.a41;
c.a12 = a.a11*b.a12 + a.a21*b.a22 + a.a31*b.a32 + a.a41*b.a42;
c.a13 = a.a11*b.a13 + a.a21*b.a23 + a.a31*b.a33 + a.a41*b.a43;
c.a14 = a.a11*b.a14 + a.a21*b.a24 + a.a31*b.a34 + a.a41*b.a44;
c.a21 = a.a12*b.a11 + a.a22*b.a21 + a.a32*b.a31 + a.a42*b.a41;
c.a22 = a.a12*b.a12 + a.a22*b.a22 + a.a32*b.a32 + a.a42*b.a42;
c.a23 = a.a12*b.a13 + a.a22*b.a23 + a.a32*b.a33 + a.a42*b.a43;
c.a24 = a.a12*b.a14 + a.a22*b.a24 + a.a32*b.a34 + a.a42*b.a44;
c.a31 = a.a13*b.a11 + a.a23*b.a21 + a.a33*b.a31 + a.a43*b.a41;
c.a32 = a.a13*b.a12 + a.a23*b.a22 + a.a33*b.a32 + a.a43*b.a42;
c.a33 = a.a13*b.a13 + a.a23*b.a23 + a.a33*b.a33 + a.a43*b.a43;
c.a34 = a.a13*b.a14 + a.a23*b.a24 + a.a33*b.a34 + a.a43*b.a44;
c.a41 = a.a14*b.a11 + a.a24*b.a21 + a.a34*b.a31 + a.a44*b.a41;
c.a42 = a.a14*b.a12 + a.a24*b.a22 + a.a34*b.a32 + a.a44*b.a42;
c.a43 = a.a14*b.a13 + a.a24*b.a23 + a.a34*b.a33 + a.a44*b.a43;
c.a44 = a.a14*b.a14 + a.a24*b.a24 + a.a34*b.a34 + a.a44*b.a44;
}
/**
* Performs the following operation:
*
* c = α * aT * b
*
* cij = α * ∑k=1:n { aki * bkj}
*
*
* @param alpha Scaling factor.
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multTransA( float alpha , FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 = alpha*(a.a11*b.a11 + a.a21*b.a21 + a.a31*b.a31 + a.a41*b.a41);
c.a12 = alpha*(a.a11*b.a12 + a.a21*b.a22 + a.a31*b.a32 + a.a41*b.a42);
c.a13 = alpha*(a.a11*b.a13 + a.a21*b.a23 + a.a31*b.a33 + a.a41*b.a43);
c.a14 = alpha*(a.a11*b.a14 + a.a21*b.a24 + a.a31*b.a34 + a.a41*b.a44);
c.a21 = alpha*(a.a12*b.a11 + a.a22*b.a21 + a.a32*b.a31 + a.a42*b.a41);
c.a22 = alpha*(a.a12*b.a12 + a.a22*b.a22 + a.a32*b.a32 + a.a42*b.a42);
c.a23 = alpha*(a.a12*b.a13 + a.a22*b.a23 + a.a32*b.a33 + a.a42*b.a43);
c.a24 = alpha*(a.a12*b.a14 + a.a22*b.a24 + a.a32*b.a34 + a.a42*b.a44);
c.a31 = alpha*(a.a13*b.a11 + a.a23*b.a21 + a.a33*b.a31 + a.a43*b.a41);
c.a32 = alpha*(a.a13*b.a12 + a.a23*b.a22 + a.a33*b.a32 + a.a43*b.a42);
c.a33 = alpha*(a.a13*b.a13 + a.a23*b.a23 + a.a33*b.a33 + a.a43*b.a43);
c.a34 = alpha*(a.a13*b.a14 + a.a23*b.a24 + a.a33*b.a34 + a.a43*b.a44);
c.a41 = alpha*(a.a14*b.a11 + a.a24*b.a21 + a.a34*b.a31 + a.a44*b.a41);
c.a42 = alpha*(a.a14*b.a12 + a.a24*b.a22 + a.a34*b.a32 + a.a44*b.a42);
c.a43 = alpha*(a.a14*b.a13 + a.a24*b.a23 + a.a34*b.a33 + a.a44*b.a43);
c.a44 = alpha*(a.a14*b.a14 + a.a24*b.a24 + a.a34*b.a34 + a.a44*b.a44);
}
/**
*
* Performs the following operation:
*
* c = aT * bT
* cij = ∑k=1:n { aki * bjk}
*
*
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multTransAB( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 = a.a11*b.a11 + a.a21*b.a12 + a.a31*b.a13 + a.a41*b.a14;
c.a12 = a.a11*b.a21 + a.a21*b.a22 + a.a31*b.a23 + a.a41*b.a24;
c.a13 = a.a11*b.a31 + a.a21*b.a32 + a.a31*b.a33 + a.a41*b.a34;
c.a14 = a.a11*b.a41 + a.a21*b.a42 + a.a31*b.a43 + a.a41*b.a44;
c.a21 = a.a12*b.a11 + a.a22*b.a12 + a.a32*b.a13 + a.a42*b.a14;
c.a22 = a.a12*b.a21 + a.a22*b.a22 + a.a32*b.a23 + a.a42*b.a24;
c.a23 = a.a12*b.a31 + a.a22*b.a32 + a.a32*b.a33 + a.a42*b.a34;
c.a24 = a.a12*b.a41 + a.a22*b.a42 + a.a32*b.a43 + a.a42*b.a44;
c.a31 = a.a13*b.a11 + a.a23*b.a12 + a.a33*b.a13 + a.a43*b.a14;
c.a32 = a.a13*b.a21 + a.a23*b.a22 + a.a33*b.a23 + a.a43*b.a24;
c.a33 = a.a13*b.a31 + a.a23*b.a32 + a.a33*b.a33 + a.a43*b.a34;
c.a34 = a.a13*b.a41 + a.a23*b.a42 + a.a33*b.a43 + a.a43*b.a44;
c.a41 = a.a14*b.a11 + a.a24*b.a12 + a.a34*b.a13 + a.a44*b.a14;
c.a42 = a.a14*b.a21 + a.a24*b.a22 + a.a34*b.a23 + a.a44*b.a24;
c.a43 = a.a14*b.a31 + a.a24*b.a32 + a.a34*b.a33 + a.a44*b.a34;
c.a44 = a.a14*b.a41 + a.a24*b.a42 + a.a34*b.a43 + a.a44*b.a44;
}
/**
*
* Performs the following operation:
*
* c = α*aT * bT
* cij = α*∑k=1:n { aki * bjk}
*
*
* @param alpha Scaling factor.
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multTransAB( float alpha , FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 = alpha*(a.a11*b.a11 + a.a21*b.a12 + a.a31*b.a13 + a.a41*b.a14);
c.a12 = alpha*(a.a11*b.a21 + a.a21*b.a22 + a.a31*b.a23 + a.a41*b.a24);
c.a13 = alpha*(a.a11*b.a31 + a.a21*b.a32 + a.a31*b.a33 + a.a41*b.a34);
c.a14 = alpha*(a.a11*b.a41 + a.a21*b.a42 + a.a31*b.a43 + a.a41*b.a44);
c.a21 = alpha*(a.a12*b.a11 + a.a22*b.a12 + a.a32*b.a13 + a.a42*b.a14);
c.a22 = alpha*(a.a12*b.a21 + a.a22*b.a22 + a.a32*b.a23 + a.a42*b.a24);
c.a23 = alpha*(a.a12*b.a31 + a.a22*b.a32 + a.a32*b.a33 + a.a42*b.a34);
c.a24 = alpha*(a.a12*b.a41 + a.a22*b.a42 + a.a32*b.a43 + a.a42*b.a44);
c.a31 = alpha*(a.a13*b.a11 + a.a23*b.a12 + a.a33*b.a13 + a.a43*b.a14);
c.a32 = alpha*(a.a13*b.a21 + a.a23*b.a22 + a.a33*b.a23 + a.a43*b.a24);
c.a33 = alpha*(a.a13*b.a31 + a.a23*b.a32 + a.a33*b.a33 + a.a43*b.a34);
c.a34 = alpha*(a.a13*b.a41 + a.a23*b.a42 + a.a33*b.a43 + a.a43*b.a44);
c.a41 = alpha*(a.a14*b.a11 + a.a24*b.a12 + a.a34*b.a13 + a.a44*b.a14);
c.a42 = alpha*(a.a14*b.a21 + a.a24*b.a22 + a.a34*b.a23 + a.a44*b.a24);
c.a43 = alpha*(a.a14*b.a31 + a.a24*b.a32 + a.a34*b.a33 + a.a44*b.a34);
c.a44 = alpha*(a.a14*b.a41 + a.a24*b.a42 + a.a34*b.a43 + a.a44*b.a44);
}
/**
*
* Performs the following operation:
*
* c = a * bT
* cij = ∑k=1:n { aik * bjk}
*
*
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multTransB( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 = a.a11*b.a11 + a.a12*b.a12 + a.a13*b.a13 + a.a14*b.a14;
c.a12 = a.a11*b.a21 + a.a12*b.a22 + a.a13*b.a23 + a.a14*b.a24;
c.a13 = a.a11*b.a31 + a.a12*b.a32 + a.a13*b.a33 + a.a14*b.a34;
c.a14 = a.a11*b.a41 + a.a12*b.a42 + a.a13*b.a43 + a.a14*b.a44;
c.a21 = a.a21*b.a11 + a.a22*b.a12 + a.a23*b.a13 + a.a24*b.a14;
c.a22 = a.a21*b.a21 + a.a22*b.a22 + a.a23*b.a23 + a.a24*b.a24;
c.a23 = a.a21*b.a31 + a.a22*b.a32 + a.a23*b.a33 + a.a24*b.a34;
c.a24 = a.a21*b.a41 + a.a22*b.a42 + a.a23*b.a43 + a.a24*b.a44;
c.a31 = a.a31*b.a11 + a.a32*b.a12 + a.a33*b.a13 + a.a34*b.a14;
c.a32 = a.a31*b.a21 + a.a32*b.a22 + a.a33*b.a23 + a.a34*b.a24;
c.a33 = a.a31*b.a31 + a.a32*b.a32 + a.a33*b.a33 + a.a34*b.a34;
c.a34 = a.a31*b.a41 + a.a32*b.a42 + a.a33*b.a43 + a.a34*b.a44;
c.a41 = a.a41*b.a11 + a.a42*b.a12 + a.a43*b.a13 + a.a44*b.a14;
c.a42 = a.a41*b.a21 + a.a42*b.a22 + a.a43*b.a23 + a.a44*b.a24;
c.a43 = a.a41*b.a31 + a.a42*b.a32 + a.a43*b.a33 + a.a44*b.a34;
c.a44 = a.a41*b.a41 + a.a42*b.a42 + a.a43*b.a43 + a.a44*b.a44;
}
/**
*
* Performs the following operation:
*
* c = α * a * bT
* cij = α*∑k=1:n { aik * bjk}
*
*
* @param alpha Scaling factor.
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multTransB( float alpha , FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 = alpha*(a.a11*b.a11 + a.a12*b.a12 + a.a13*b.a13 + a.a14*b.a14);
c.a12 = alpha*(a.a11*b.a21 + a.a12*b.a22 + a.a13*b.a23 + a.a14*b.a24);
c.a13 = alpha*(a.a11*b.a31 + a.a12*b.a32 + a.a13*b.a33 + a.a14*b.a34);
c.a14 = alpha*(a.a11*b.a41 + a.a12*b.a42 + a.a13*b.a43 + a.a14*b.a44);
c.a21 = alpha*(a.a21*b.a11 + a.a22*b.a12 + a.a23*b.a13 + a.a24*b.a14);
c.a22 = alpha*(a.a21*b.a21 + a.a22*b.a22 + a.a23*b.a23 + a.a24*b.a24);
c.a23 = alpha*(a.a21*b.a31 + a.a22*b.a32 + a.a23*b.a33 + a.a24*b.a34);
c.a24 = alpha*(a.a21*b.a41 + a.a22*b.a42 + a.a23*b.a43 + a.a24*b.a44);
c.a31 = alpha*(a.a31*b.a11 + a.a32*b.a12 + a.a33*b.a13 + a.a34*b.a14);
c.a32 = alpha*(a.a31*b.a21 + a.a32*b.a22 + a.a33*b.a23 + a.a34*b.a24);
c.a33 = alpha*(a.a31*b.a31 + a.a32*b.a32 + a.a33*b.a33 + a.a34*b.a34);
c.a34 = alpha*(a.a31*b.a41 + a.a32*b.a42 + a.a33*b.a43 + a.a34*b.a44);
c.a41 = alpha*(a.a41*b.a11 + a.a42*b.a12 + a.a43*b.a13 + a.a44*b.a14);
c.a42 = alpha*(a.a41*b.a21 + a.a42*b.a22 + a.a43*b.a23 + a.a44*b.a24);
c.a43 = alpha*(a.a41*b.a31 + a.a42*b.a32 + a.a43*b.a33 + a.a44*b.a34);
c.a44 = alpha*(a.a41*b.a41 + a.a42*b.a42 + a.a43*b.a43 + a.a44*b.a44);
}
/**
* 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 (Output) Where the results of the operation are stored. Modified.
*/
public static void multAdd( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 += a.a11*b.a11 + a.a12*b.a21 + a.a13*b.a31 + a.a14*b.a41;
c.a12 += a.a11*b.a12 + a.a12*b.a22 + a.a13*b.a32 + a.a14*b.a42;
c.a13 += a.a11*b.a13 + a.a12*b.a23 + a.a13*b.a33 + a.a14*b.a43;
c.a14 += a.a11*b.a14 + a.a12*b.a24 + a.a13*b.a34 + a.a14*b.a44;
c.a21 += a.a21*b.a11 + a.a22*b.a21 + a.a23*b.a31 + a.a24*b.a41;
c.a22 += a.a21*b.a12 + a.a22*b.a22 + a.a23*b.a32 + a.a24*b.a42;
c.a23 += a.a21*b.a13 + a.a22*b.a23 + a.a23*b.a33 + a.a24*b.a43;
c.a24 += a.a21*b.a14 + a.a22*b.a24 + a.a23*b.a34 + a.a24*b.a44;
c.a31 += a.a31*b.a11 + a.a32*b.a21 + a.a33*b.a31 + a.a34*b.a41;
c.a32 += a.a31*b.a12 + a.a32*b.a22 + a.a33*b.a32 + a.a34*b.a42;
c.a33 += a.a31*b.a13 + a.a32*b.a23 + a.a33*b.a33 + a.a34*b.a43;
c.a34 += a.a31*b.a14 + a.a32*b.a24 + a.a33*b.a34 + a.a34*b.a44;
c.a41 += a.a41*b.a11 + a.a42*b.a21 + a.a43*b.a31 + a.a44*b.a41;
c.a42 += a.a41*b.a12 + a.a42*b.a22 + a.a43*b.a32 + a.a44*b.a42;
c.a43 += a.a41*b.a13 + a.a42*b.a23 + a.a43*b.a33 + a.a44*b.a43;
c.a44 += a.a41*b.a14 + a.a42*b.a24 + a.a43*b.a34 + a.a44*b.a44;
}
/**
* Performs the following operation:
*
* c += α * a * b
*
* cij += α ∑k=1:n { aik * bkj}
*
*
* @param alpha Scaling factor.
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multAdd( float alpha , FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 += alpha*(a.a11*b.a11 + a.a12*b.a21 + a.a13*b.a31 + a.a14*b.a41);
c.a12 += alpha*(a.a11*b.a12 + a.a12*b.a22 + a.a13*b.a32 + a.a14*b.a42);
c.a13 += alpha*(a.a11*b.a13 + a.a12*b.a23 + a.a13*b.a33 + a.a14*b.a43);
c.a14 += alpha*(a.a11*b.a14 + a.a12*b.a24 + a.a13*b.a34 + a.a14*b.a44);
c.a21 += alpha*(a.a21*b.a11 + a.a22*b.a21 + a.a23*b.a31 + a.a24*b.a41);
c.a22 += alpha*(a.a21*b.a12 + a.a22*b.a22 + a.a23*b.a32 + a.a24*b.a42);
c.a23 += alpha*(a.a21*b.a13 + a.a22*b.a23 + a.a23*b.a33 + a.a24*b.a43);
c.a24 += alpha*(a.a21*b.a14 + a.a22*b.a24 + a.a23*b.a34 + a.a24*b.a44);
c.a31 += alpha*(a.a31*b.a11 + a.a32*b.a21 + a.a33*b.a31 + a.a34*b.a41);
c.a32 += alpha*(a.a31*b.a12 + a.a32*b.a22 + a.a33*b.a32 + a.a34*b.a42);
c.a33 += alpha*(a.a31*b.a13 + a.a32*b.a23 + a.a33*b.a33 + a.a34*b.a43);
c.a34 += alpha*(a.a31*b.a14 + a.a32*b.a24 + a.a33*b.a34 + a.a34*b.a44);
c.a41 += alpha*(a.a41*b.a11 + a.a42*b.a21 + a.a43*b.a31 + a.a44*b.a41);
c.a42 += alpha*(a.a41*b.a12 + a.a42*b.a22 + a.a43*b.a32 + a.a44*b.a42);
c.a43 += alpha*(a.a41*b.a13 + a.a42*b.a23 + a.a43*b.a33 + a.a44*b.a43);
c.a44 += alpha*(a.a41*b.a14 + a.a42*b.a24 + a.a43*b.a34 + a.a44*b.a44);
}
/**
* Performs the following operation:
*
* c += aT * b
*
* cij += ∑k=1:n { aki * bkj}
*
*
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multAddTransA( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 += a.a11*b.a11 + a.a21*b.a21 + a.a31*b.a31 + a.a41*b.a41;
c.a12 += a.a11*b.a12 + a.a21*b.a22 + a.a31*b.a32 + a.a41*b.a42;
c.a13 += a.a11*b.a13 + a.a21*b.a23 + a.a31*b.a33 + a.a41*b.a43;
c.a14 += a.a11*b.a14 + a.a21*b.a24 + a.a31*b.a34 + a.a41*b.a44;
c.a21 += a.a12*b.a11 + a.a22*b.a21 + a.a32*b.a31 + a.a42*b.a41;
c.a22 += a.a12*b.a12 + a.a22*b.a22 + a.a32*b.a32 + a.a42*b.a42;
c.a23 += a.a12*b.a13 + a.a22*b.a23 + a.a32*b.a33 + a.a42*b.a43;
c.a24 += a.a12*b.a14 + a.a22*b.a24 + a.a32*b.a34 + a.a42*b.a44;
c.a31 += a.a13*b.a11 + a.a23*b.a21 + a.a33*b.a31 + a.a43*b.a41;
c.a32 += a.a13*b.a12 + a.a23*b.a22 + a.a33*b.a32 + a.a43*b.a42;
c.a33 += a.a13*b.a13 + a.a23*b.a23 + a.a33*b.a33 + a.a43*b.a43;
c.a34 += a.a13*b.a14 + a.a23*b.a24 + a.a33*b.a34 + a.a43*b.a44;
c.a41 += a.a14*b.a11 + a.a24*b.a21 + a.a34*b.a31 + a.a44*b.a41;
c.a42 += a.a14*b.a12 + a.a24*b.a22 + a.a34*b.a32 + a.a44*b.a42;
c.a43 += a.a14*b.a13 + a.a24*b.a23 + a.a34*b.a33 + a.a44*b.a43;
c.a44 += a.a14*b.a14 + a.a24*b.a24 + a.a34*b.a34 + a.a44*b.a44;
}
/**
* Performs the following operation:
*
* c += α * aT * b
*
* cij += α * ∑k=1:n { aki * bkj}
*
*
* @param alpha Scaling factor.
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multAddTransA( float alpha , FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 += alpha*(a.a11*b.a11 + a.a21*b.a21 + a.a31*b.a31 + a.a41*b.a41);
c.a12 += alpha*(a.a11*b.a12 + a.a21*b.a22 + a.a31*b.a32 + a.a41*b.a42);
c.a13 += alpha*(a.a11*b.a13 + a.a21*b.a23 + a.a31*b.a33 + a.a41*b.a43);
c.a14 += alpha*(a.a11*b.a14 + a.a21*b.a24 + a.a31*b.a34 + a.a41*b.a44);
c.a21 += alpha*(a.a12*b.a11 + a.a22*b.a21 + a.a32*b.a31 + a.a42*b.a41);
c.a22 += alpha*(a.a12*b.a12 + a.a22*b.a22 + a.a32*b.a32 + a.a42*b.a42);
c.a23 += alpha*(a.a12*b.a13 + a.a22*b.a23 + a.a32*b.a33 + a.a42*b.a43);
c.a24 += alpha*(a.a12*b.a14 + a.a22*b.a24 + a.a32*b.a34 + a.a42*b.a44);
c.a31 += alpha*(a.a13*b.a11 + a.a23*b.a21 + a.a33*b.a31 + a.a43*b.a41);
c.a32 += alpha*(a.a13*b.a12 + a.a23*b.a22 + a.a33*b.a32 + a.a43*b.a42);
c.a33 += alpha*(a.a13*b.a13 + a.a23*b.a23 + a.a33*b.a33 + a.a43*b.a43);
c.a34 += alpha*(a.a13*b.a14 + a.a23*b.a24 + a.a33*b.a34 + a.a43*b.a44);
c.a41 += alpha*(a.a14*b.a11 + a.a24*b.a21 + a.a34*b.a31 + a.a44*b.a41);
c.a42 += alpha*(a.a14*b.a12 + a.a24*b.a22 + a.a34*b.a32 + a.a44*b.a42);
c.a43 += alpha*(a.a14*b.a13 + a.a24*b.a23 + a.a34*b.a33 + a.a44*b.a43);
c.a44 += alpha*(a.a14*b.a14 + a.a24*b.a24 + a.a34*b.a34 + a.a44*b.a44);
}
/**
*
* Performs the following operation:
*
* c += aT * bT
* cij += ∑k=1:n { aki * bjk}
*
*
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multAddTransAB( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 += a.a11*b.a11 + a.a21*b.a12 + a.a31*b.a13 + a.a41*b.a14;
c.a12 += a.a11*b.a21 + a.a21*b.a22 + a.a31*b.a23 + a.a41*b.a24;
c.a13 += a.a11*b.a31 + a.a21*b.a32 + a.a31*b.a33 + a.a41*b.a34;
c.a14 += a.a11*b.a41 + a.a21*b.a42 + a.a31*b.a43 + a.a41*b.a44;
c.a21 += a.a12*b.a11 + a.a22*b.a12 + a.a32*b.a13 + a.a42*b.a14;
c.a22 += a.a12*b.a21 + a.a22*b.a22 + a.a32*b.a23 + a.a42*b.a24;
c.a23 += a.a12*b.a31 + a.a22*b.a32 + a.a32*b.a33 + a.a42*b.a34;
c.a24 += a.a12*b.a41 + a.a22*b.a42 + a.a32*b.a43 + a.a42*b.a44;
c.a31 += a.a13*b.a11 + a.a23*b.a12 + a.a33*b.a13 + a.a43*b.a14;
c.a32 += a.a13*b.a21 + a.a23*b.a22 + a.a33*b.a23 + a.a43*b.a24;
c.a33 += a.a13*b.a31 + a.a23*b.a32 + a.a33*b.a33 + a.a43*b.a34;
c.a34 += a.a13*b.a41 + a.a23*b.a42 + a.a33*b.a43 + a.a43*b.a44;
c.a41 += a.a14*b.a11 + a.a24*b.a12 + a.a34*b.a13 + a.a44*b.a14;
c.a42 += a.a14*b.a21 + a.a24*b.a22 + a.a34*b.a23 + a.a44*b.a24;
c.a43 += a.a14*b.a31 + a.a24*b.a32 + a.a34*b.a33 + a.a44*b.a34;
c.a44 += a.a14*b.a41 + a.a24*b.a42 + a.a34*b.a43 + a.a44*b.a44;
}
/**
*
* Performs the following operation:
*
* c += α*aT * bT
* cij += α*∑k=1:n { aki * bjk}
*
*
* @param alpha Scaling factor.
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multAddTransAB( float alpha , FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 += alpha*(a.a11*b.a11 + a.a21*b.a12 + a.a31*b.a13 + a.a41*b.a14);
c.a12 += alpha*(a.a11*b.a21 + a.a21*b.a22 + a.a31*b.a23 + a.a41*b.a24);
c.a13 += alpha*(a.a11*b.a31 + a.a21*b.a32 + a.a31*b.a33 + a.a41*b.a34);
c.a14 += alpha*(a.a11*b.a41 + a.a21*b.a42 + a.a31*b.a43 + a.a41*b.a44);
c.a21 += alpha*(a.a12*b.a11 + a.a22*b.a12 + a.a32*b.a13 + a.a42*b.a14);
c.a22 += alpha*(a.a12*b.a21 + a.a22*b.a22 + a.a32*b.a23 + a.a42*b.a24);
c.a23 += alpha*(a.a12*b.a31 + a.a22*b.a32 + a.a32*b.a33 + a.a42*b.a34);
c.a24 += alpha*(a.a12*b.a41 + a.a22*b.a42 + a.a32*b.a43 + a.a42*b.a44);
c.a31 += alpha*(a.a13*b.a11 + a.a23*b.a12 + a.a33*b.a13 + a.a43*b.a14);
c.a32 += alpha*(a.a13*b.a21 + a.a23*b.a22 + a.a33*b.a23 + a.a43*b.a24);
c.a33 += alpha*(a.a13*b.a31 + a.a23*b.a32 + a.a33*b.a33 + a.a43*b.a34);
c.a34 += alpha*(a.a13*b.a41 + a.a23*b.a42 + a.a33*b.a43 + a.a43*b.a44);
c.a41 += alpha*(a.a14*b.a11 + a.a24*b.a12 + a.a34*b.a13 + a.a44*b.a14);
c.a42 += alpha*(a.a14*b.a21 + a.a24*b.a22 + a.a34*b.a23 + a.a44*b.a24);
c.a43 += alpha*(a.a14*b.a31 + a.a24*b.a32 + a.a34*b.a33 + a.a44*b.a34);
c.a44 += alpha*(a.a14*b.a41 + a.a24*b.a42 + a.a34*b.a43 + a.a44*b.a44);
}
/**
*
* Performs the following operation:
*
* c += a * bT
* cij += ∑k=1:n { aik * bjk}
*
*
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multAddTransB( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 += a.a11*b.a11 + a.a12*b.a12 + a.a13*b.a13 + a.a14*b.a14;
c.a12 += a.a11*b.a21 + a.a12*b.a22 + a.a13*b.a23 + a.a14*b.a24;
c.a13 += a.a11*b.a31 + a.a12*b.a32 + a.a13*b.a33 + a.a14*b.a34;
c.a14 += a.a11*b.a41 + a.a12*b.a42 + a.a13*b.a43 + a.a14*b.a44;
c.a21 += a.a21*b.a11 + a.a22*b.a12 + a.a23*b.a13 + a.a24*b.a14;
c.a22 += a.a21*b.a21 + a.a22*b.a22 + a.a23*b.a23 + a.a24*b.a24;
c.a23 += a.a21*b.a31 + a.a22*b.a32 + a.a23*b.a33 + a.a24*b.a34;
c.a24 += a.a21*b.a41 + a.a22*b.a42 + a.a23*b.a43 + a.a24*b.a44;
c.a31 += a.a31*b.a11 + a.a32*b.a12 + a.a33*b.a13 + a.a34*b.a14;
c.a32 += a.a31*b.a21 + a.a32*b.a22 + a.a33*b.a23 + a.a34*b.a24;
c.a33 += a.a31*b.a31 + a.a32*b.a32 + a.a33*b.a33 + a.a34*b.a34;
c.a34 += a.a31*b.a41 + a.a32*b.a42 + a.a33*b.a43 + a.a34*b.a44;
c.a41 += a.a41*b.a11 + a.a42*b.a12 + a.a43*b.a13 + a.a44*b.a14;
c.a42 += a.a41*b.a21 + a.a42*b.a22 + a.a43*b.a23 + a.a44*b.a24;
c.a43 += a.a41*b.a31 + a.a42*b.a32 + a.a43*b.a33 + a.a44*b.a34;
c.a44 += a.a41*b.a41 + a.a42*b.a42 + a.a43*b.a43 + a.a44*b.a44;
}
/**
*
* Performs the following operation:
*
* c += α * a * bT
* cij += α*∑k=1:n { aik * bjk}
*
*
* @param alpha Scaling factor.
* @param a (Input) The left matrix in the multiplication operation. Not modified.
* @param b (Input) The right matrix in the multiplication operation. Not modified.
* @param c (Output) Where the results of the operation are stored. Modified.
*/
public static void multAddTransB( float alpha , FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c) {
UtilEjml.checkSameInstance(a,c);
UtilEjml.checkSameInstance(b,c);
c.a11 += alpha*(a.a11*b.a11 + a.a12*b.a12 + a.a13*b.a13 + a.a14*b.a14);
c.a12 += alpha*(a.a11*b.a21 + a.a12*b.a22 + a.a13*b.a23 + a.a14*b.a24);
c.a13 += alpha*(a.a11*b.a31 + a.a12*b.a32 + a.a13*b.a33 + a.a14*b.a34);
c.a14 += alpha*(a.a11*b.a41 + a.a12*b.a42 + a.a13*b.a43 + a.a14*b.a44);
c.a21 += alpha*(a.a21*b.a11 + a.a22*b.a12 + a.a23*b.a13 + a.a24*b.a14);
c.a22 += alpha*(a.a21*b.a21 + a.a22*b.a22 + a.a23*b.a23 + a.a24*b.a24);
c.a23 += alpha*(a.a21*b.a31 + a.a22*b.a32 + a.a23*b.a33 + a.a24*b.a34);
c.a24 += alpha*(a.a21*b.a41 + a.a22*b.a42 + a.a23*b.a43 + a.a24*b.a44);
c.a31 += alpha*(a.a31*b.a11 + a.a32*b.a12 + a.a33*b.a13 + a.a34*b.a14);
c.a32 += alpha*(a.a31*b.a21 + a.a32*b.a22 + a.a33*b.a23 + a.a34*b.a24);
c.a33 += alpha*(a.a31*b.a31 + a.a32*b.a32 + a.a33*b.a33 + a.a34*b.a34);
c.a34 += alpha*(a.a31*b.a41 + a.a32*b.a42 + a.a33*b.a43 + a.a34*b.a44);
c.a41 += alpha*(a.a41*b.a11 + a.a42*b.a12 + a.a43*b.a13 + a.a44*b.a14);
c.a42 += alpha*(a.a41*b.a21 + a.a42*b.a22 + a.a43*b.a23 + a.a44*b.a24);
c.a43 += alpha*(a.a41*b.a31 + a.a42*b.a32 + a.a43*b.a33 + a.a44*b.a34);
c.a44 += alpha*(a.a41*b.a41 + a.a42*b.a42 + a.a43*b.a43 + a.a44*b.a44);
}
/**
* C = αA + βu*vT
*
* @param alpha scale factor applied to A
* @param A matrix
* @param beta scale factor applies to outer product
* @param u vector
* @param v vector
* @param C Storage for solution. Can be same instance as A.
*/
public static void multAddOuter( float alpha , FMatrix4x4 A , float beta , FMatrix4 u , FMatrix4 v , FMatrix4x4 C ) {
C.a11 = alpha*A.a11 + beta*u.a1*v.a1;
C.a12 = alpha*A.a12 + beta*u.a1*v.a2;
C.a13 = alpha*A.a13 + beta*u.a1*v.a3;
C.a14 = alpha*A.a14 + beta*u.a1*v.a4;
C.a21 = alpha*A.a21 + beta*u.a2*v.a1;
C.a22 = alpha*A.a22 + beta*u.a2*v.a2;
C.a23 = alpha*A.a23 + beta*u.a2*v.a3;
C.a24 = alpha*A.a24 + beta*u.a2*v.a4;
C.a31 = alpha*A.a31 + beta*u.a3*v.a1;
C.a32 = alpha*A.a32 + beta*u.a3*v.a2;
C.a33 = alpha*A.a33 + beta*u.a3*v.a3;
C.a34 = alpha*A.a34 + beta*u.a3*v.a4;
C.a41 = alpha*A.a41 + beta*u.a4*v.a1;
C.a42 = alpha*A.a42 + beta*u.a4*v.a2;
C.a43 = alpha*A.a43 + beta*u.a4*v.a3;
C.a44 = alpha*A.a44 + beta*u.a4*v.a4;
}
/**
* 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( FMatrix4x4 a , FMatrix4 b , FMatrix4 c) {
c.a1 = a.a11*b.a1 + a.a12*b.a2 + a.a13*b.a3 + a.a14*b.a4;
c.a2 = a.a21*b.a1 + a.a22*b.a2 + a.a23*b.a3 + a.a24*b.a4;
c.a3 = a.a31*b.a1 + a.a32*b.a2 + a.a33*b.a3 + a.a34*b.a4;
c.a4 = a.a41*b.a1 + a.a42*b.a2 + a.a43*b.a3 + a.a44*b.a4;
}
/**
* 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( FMatrix4 a , FMatrix4x4 b , FMatrix4 c) {
c.a1 = a.a1*b.a11 + a.a2*b.a21 + a.a3*b.a31 + a.a4*b.a41;
c.a2 = a.a1*b.a12 + a.a2*b.a22 + a.a3*b.a32 + a.a4*b.a42;
c.a3 = a.a1*b.a13 + a.a2*b.a23 + a.a3*b.a33 + a.a4*b.a43;
c.a4 = a.a1*b.a14 + a.a2*b.a24 + a.a3*b.a34 + a.a4*b.a44;
}
/**
* 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 float dot( FMatrix4 a , FMatrix4 b ) {
return a.a1*b.a1 + a.a2*b.a2 + a.a3*b.a3 + a.a4*b.a4;
}
/**
* 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( FMatrix4x4 a ) {
a.a11 = 1; a.a21 = 0; a.a31 = 0; a.a41 = 0;
a.a12 = 0; a.a22 = 1; a.a32 = 0; a.a42 = 0;
a.a13 = 0; a.a23 = 0; a.a33 = 1; a.a43 = 0;
a.a14 = 0; a.a24 = 0; a.a34 = 0; a.a44 = 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( FMatrix4x4 a , FMatrix4x4 inv ) {
float scale = 1.0f/elementMaxAbs(a);
float a11 = a.a11*scale;
float a12 = a.a12*scale;
float a13 = a.a13*scale;
float a14 = a.a14*scale;
float a21 = a.a21*scale;
float a22 = a.a22*scale;
float a23 = a.a23*scale;
float a24 = a.a24*scale;
float a31 = a.a31*scale;
float a32 = a.a32*scale;
float a33 = a.a33*scale;
float a34 = a.a34*scale;
float a41 = a.a41*scale;
float a42 = a.a42*scale;
float a43 = a.a43*scale;
float a44 = a.a44*scale;
float m11 = + a22*(a33*a44 - a34*a43) - a23*(a32*a44 - a34*a42) + a24*(a32*a43 - a33*a42);
float m12 = -( + a21*(a33*a44 - a34*a43) - a23*(a31*a44 - a34*a41) + a24*(a31*a43 - a33*a41));
float m13 = + a21*(a32*a44 - a34*a42) - a22*(a31*a44 - a34*a41) + a24*(a31*a42 - a32*a41);
float m14 = -( + a21*(a32*a43 - a33*a42) - a22*(a31*a43 - a33*a41) + a23*(a31*a42 - a32*a41));
float m21 = -( + a12*(a33*a44 - a34*a43) - a13*(a32*a44 - a34*a42) + a14*(a32*a43 - a33*a42));
float m22 = + a11*(a33*a44 - a34*a43) - a13*(a31*a44 - a34*a41) + a14*(a31*a43 - a33*a41);
float m23 = -( + a11*(a32*a44 - a34*a42) - a12*(a31*a44 - a34*a41) + a14*(a31*a42 - a32*a41));
float m24 = + a11*(a32*a43 - a33*a42) - a12*(a31*a43 - a33*a41) + a13*(a31*a42 - a32*a41);
float m31 = + a12*(a23*a44 - a24*a43) - a13*(a22*a44 - a24*a42) + a14*(a22*a43 - a23*a42);
float m32 = -( + a11*(a23*a44 - a24*a43) - a13*(a21*a44 - a24*a41) + a14*(a21*a43 - a23*a41));
float m33 = + a11*(a22*a44 - a24*a42) - a12*(a21*a44 - a24*a41) + a14*(a21*a42 - a22*a41);
float m34 = -( + a11*(a22*a43 - a23*a42) - a12*(a21*a43 - a23*a41) + a13*(a21*a42 - a22*a41));
float m41 = -( + a12*(a23*a34 - a24*a33) - a13*(a22*a34 - a24*a32) + a14*(a22*a33 - a23*a32));
float m42 = + a11*(a23*a34 - a24*a33) - a13*(a21*a34 - a24*a31) + a14*(a21*a33 - a23*a31);
float m43 = -( + a11*(a22*a34 - a24*a32) - a12*(a21*a34 - a24*a31) + a14*(a21*a32 - a22*a31));
float m44 = + a11*(a22*a33 - a23*a32) - a12*(a21*a33 - a23*a31) + a13*(a21*a32 - a22*a31);
float det = (a11*m11 + a12*m12 + a13*m13 + a14*m14)/scale;
inv.a11 = m11/det;
inv.a12 = m21/det;
inv.a13 = m31/det;
inv.a14 = m41/det;
inv.a21 = m12/det;
inv.a22 = m22/det;
inv.a23 = m32/det;
inv.a24 = m42/det;
inv.a31 = m13/det;
inv.a32 = m23/det;
inv.a33 = m33/det;
inv.a34 = m43/det;
inv.a41 = m14/det;
inv.a42 = m24/det;
inv.a43 = m34/det;
inv.a44 = m44/det;
return !Float.isNaN(det) && !Float.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 float det( FMatrix4x4 mat ) {
float a11 = mat.a22;
float a12 = mat.a23;
float a13 = mat.a24;
float a21 = mat.a32;
float a22 = mat.a33;
float a23 = mat.a34;
float a31 = mat.a42;
float a32 = mat.a43;
float a33 = mat.a44;
float ret = 0;
ret += mat.a11 * ( + a11*(a22*a33 - a23*a32) - a12*(a21*a33 - a23*a31) + a13*(a21*a32 - a22*a31));
a11 = mat.a21;
a21 = mat.a31;
a31 = mat.a41;
ret -= mat.a12 * ( + a11*(a22*a33 - a23*a32) - a12*(a21*a33 - a23*a31) + a13*(a21*a32 - a22*a31));
a12 = mat.a22;
a22 = mat.a32;
a32 = mat.a42;
ret += mat.a13 * ( + a11*(a22*a33 - a23*a32) - a12*(a21*a33 - a23*a31) + a13*(a21*a32 - a22*a31));
a13 = mat.a23;
a23 = mat.a33;
a33 = mat.a43;
ret -= mat.a14 * ( + a11*(a22*a33 - a23*a32) - a12*(a21*a33 - a23*a31) + a13*(a21*a32 - a22*a31));
return ret;
}
/**
* Performs a lower Cholesky decomposition of matrix 'A' and stores result in A.
*
* @param A (Input) SPD Matrix. (Output) lower cholesky.
* @return true if it was successful or false if it failed. Not always reliable.
*/
public static boolean cholL( FMatrix4x4 A ) {
A.a11 = (float)Math.sqrt(A.a11);
A.a12 = 0;
A.a13 = 0;
A.a14 = 0;
A.a21 = (A.a21)/A.a11;
A.a22 = (float)Math.sqrt(A.a22-A.a21*A.a21);
A.a23 = 0;
A.a24 = 0;
A.a31 = (A.a31)/A.a11;
A.a32 = (A.a32-A.a31*A.a21)/A.a22;
A.a33 = (float)Math.sqrt(A.a33-A.a31*A.a31-A.a32*A.a32);
A.a34 = 0;
A.a41 = (A.a41)/A.a11;
A.a42 = (A.a42-A.a41*A.a21)/A.a22;
A.a43 = (A.a43-A.a41*A.a31-A.a42*A.a32)/A.a33;
A.a44 = (float)Math.sqrt(A.a44-A.a41*A.a41-A.a42*A.a42-A.a43*A.a43);
return !UtilEjml.isUncountable(A.a44);
}
/**
* Performs an upper Cholesky decomposition of matrix 'A' and stores result in A.
*
* @param A (Input) SPD Matrix. (Output) upper cholesky.
* @return true if it was successful or false if it failed. Not always reliable.
*/
public static boolean cholU( FMatrix4x4 A ) {
A.a11 = (float)Math.sqrt(A.a11);
A.a21 = 0;
A.a31 = 0;
A.a41 = 0;
A.a12 = (A.a12)/A.a11;
A.a22 = (float)Math.sqrt(A.a22-A.a12*A.a12);
A.a32 = 0;
A.a42 = 0;
A.a13 = (A.a13)/A.a11;
A.a23 = (A.a23-A.a12*A.a13)/A.a22;
A.a33 = (float)Math.sqrt(A.a33-A.a13*A.a13-A.a23*A.a23);
A.a43 = 0;
A.a14 = (A.a14)/A.a11;
A.a24 = (A.a24-A.a12*A.a14)/A.a22;
A.a34 = (A.a34-A.a13*A.a14-A.a23*A.a24)/A.a33;
A.a44 = (float)Math.sqrt(A.a44-A.a14*A.a14-A.a24*A.a24-A.a34*A.a34);
return !UtilEjml.isUncountable(A.a44);
}
/**
*
* 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 float trace( FMatrix4x4 a ) {
return a.a11 + a.a22 + a.a33 + a.a44;
}
/**
*
* 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( FMatrix4x4 input , FMatrix4 out ) {
out.a1 = input.a11;
out.a2 = input.a22;
out.a3 = input.a33;
out.a4 = input.a44;
}
/**
*
* 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 float elementMax( FMatrix4x4 a ) {
float max = a.a11;
if( a.a12 > max ) max = a.a12;
if( a.a13 > max ) max = a.a13;
if( a.a14 > max ) max = a.a14;
if( a.a21 > max ) max = a.a21;
if( a.a22 > max ) max = a.a22;
if( a.a23 > max ) max = a.a23;
if( a.a24 > max ) max = a.a24;
if( a.a31 > max ) max = a.a31;
if( a.a32 > max ) max = a.a32;
if( a.a33 > max ) max = a.a33;
if( a.a34 > max ) max = a.a34;
if( a.a41 > max ) max = a.a41;
if( a.a42 > max ) max = a.a42;
if( a.a43 > max ) max = a.a43;
if( a.a44 > max ) max = a.a44;
return max;
}
/**
*
* Returns the value of the element in the vector that has the largest value.
*
* Max{ ai } for all i
*
*
* @param a A vector. Not modified.
* @return The max element value of the matrix.
*/
public static float elementMax( FMatrix4 a ) {
float max = a.a1;
if( a.a2 > max ) max = a.a2;
if( a.a3 > max ) max = a.a3;
if( a.a4 > max ) max = a.a4;
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 float elementMaxAbs( FMatrix4x4 a ) {
float max = Math.abs(a.a11);
float tmp = Math.abs(a.a12); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a13); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a14); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a21); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a22); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a23); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a24); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a31); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a32); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a33); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a34); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a41); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a42); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a43); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a44); if( tmp > max ) max = tmp;
return max;
}
/**
*
* Returns the absolute value of the element in the vector that has the largest absolute value.
*
* Max{ |ai| } for all i
*
*
* @param a A matrix. Not modified.
* @return The max abs element value of the vector.
*/
public static float elementMaxAbs( FMatrix4 a ) {
float max = Math.abs(a.a1);
float tmp = Math.abs(a.a2); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a2); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a3); if( tmp > max ) max = tmp;
tmp = Math.abs(a.a4); if( tmp > max ) max = tmp;
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 float elementMin( FMatrix4x4 a ) {
float min = a.a11;
if( a.a12 < min ) min = a.a12;
if( a.a13 < min ) min = a.a13;
if( a.a14 < min ) min = a.a14;
if( a.a21 < min ) min = a.a21;
if( a.a22 < min ) min = a.a22;
if( a.a23 < min ) min = a.a23;
if( a.a24 < min ) min = a.a24;
if( a.a31 < min ) min = a.a31;
if( a.a32 < min ) min = a.a32;
if( a.a33 < min ) min = a.a33;
if( a.a34 < min ) min = a.a34;
if( a.a41 < min ) min = a.a41;
if( a.a42 < min ) min = a.a42;
if( a.a43 < min ) min = a.a43;
if( a.a44 < min ) min = a.a44;
return min;
}
/**
*
* Returns the value of the element in the vector that has the minimum value.
*
* Min{ ai } for all
*
*
* @param a A matrix. Not modified.
* @return The value of element in the vector with the minimum value.
*/
public static float elementMin( FMatrix4 a ) {
float min = a.a1;
if( a.a2 < min ) min = a.a2;
if( a.a3 < min ) min = a.a3;
if( a.a4 < min ) min = a.a4;
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 float elementMinAbs( FMatrix4x4 a ) {
float min = Math.abs(a.a11);
float tmp = Math.abs(a.a12); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a13); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a14); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a21); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a22); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a23); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a24); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a31); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a32); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a33); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a34); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a41); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a42); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a43); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a44); if( tmp < min ) min = tmp;
return min;
}
/**
*
* Returns the absolute value of the element in the vector that has the smallest absolute value.
*
* Min{ |ai| } for all i
*
*
* @param a A matrix. Not modified.
* @return The max element value of the vector.
*/
public static float elementMinAbs( FMatrix4 a ) {
float min = Math.abs(a.a1);
float tmp = Math.abs(a.a1); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a2); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a3); if( tmp < min ) min = tmp;
tmp = Math.abs(a.a4); if( tmp < min ) min = tmp;
return min;
}
/**
* Performs 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( FMatrix4x4 a , FMatrix4x4 b) {
a.a11 *= b.a11; a.a12 *= b.a12; a.a13 *= b.a13; a.a14 *= b.a14;
a.a21 *= b.a21; a.a22 *= b.a22; a.a23 *= b.a23; a.a24 *= b.a24;
a.a31 *= b.a31; a.a32 *= b.a32; a.a33 *= b.a33; a.a34 *= b.a34;
a.a41 *= b.a41; a.a42 *= b.a42; a.a43 *= b.a43; a.a44 *= b.a44;
}
/**
* Performs an element by element multiplication operation:
*
* ai = ai * bi
*
* @param a The left vector in the multiplication operation. Modified.
* @param b The right vector in the multiplication operation. Not modified.
*/
public static void elementMult( FMatrix4 a , FMatrix4 b) {
a.a1 *= b.a1;
a.a2 *= b.a2;
a.a3 *= b.a3;
a.a4 *= b.a4;
}
/**
* Performs 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( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c ) {
c.a11 = a.a11*b.a11; c.a12 = a.a12*b.a12; c.a13 = a.a13*b.a13; c.a14 = a.a14*b.a14;
c.a21 = a.a21*b.a21; c.a22 = a.a22*b.a22; c.a23 = a.a23*b.a23; c.a24 = a.a24*b.a24;
c.a31 = a.a31*b.a31; c.a32 = a.a32*b.a32; c.a33 = a.a33*b.a33; c.a34 = a.a34*b.a34;
c.a41 = a.a41*b.a41; c.a42 = a.a42*b.a42; c.a43 = a.a43*b.a43; c.a44 = a.a44*b.a44;
}
/**
* Performs an element by element multiplication operation:
*
* ci = ai * bj
*
* @param a The left vector 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 elementMult( FMatrix4 a , FMatrix4 b , FMatrix4 c ) {
c.a1 = a.a1*b.a1;
c.a2 = a.a2*b.a2;
c.a3 = a.a3*b.a3;
c.a4 = a.a4*b.a4;
}
/**
* Performs 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( FMatrix4x4 a , FMatrix4x4 b) {
a.a11 /= b.a11; a.a12 /= b.a12; a.a13 /= b.a13; a.a14 /= b.a14;
a.a21 /= b.a21; a.a22 /= b.a22; a.a23 /= b.a23; a.a24 /= b.a24;
a.a31 /= b.a31; a.a32 /= b.a32; a.a33 /= b.a33; a.a34 /= b.a34;
a.a41 /= b.a41; a.a42 /= b.a42; a.a43 /= b.a43; a.a44 /= b.a44;
}
/**
* Performs an element by element division operation:
*
* ai = ai / bi
*
* @param a The left vector in the division operation. Modified.
* @param b The right vector in the division operation. Not modified.
*/
public static void elementDiv( FMatrix4 a , FMatrix4 b) {
a.a1 /= b.a1;
a.a2 /= b.a2;
a.a3 /= b.a3;
a.a4 /= b.a4;
}
/**
* Performs 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( FMatrix4x4 a , FMatrix4x4 b , FMatrix4x4 c ) {
c.a11 = a.a11/b.a11; c.a12 = a.a12/b.a12; c.a13 = a.a13/b.a13; c.a14 = a.a14/b.a14;
c.a21 = a.a21/b.a21; c.a22 = a.a22/b.a22; c.a23 = a.a23/b.a23; c.a24 = a.a24/b.a24;
c.a31 = a.a31/b.a31; c.a32 = a.a32/b.a32; c.a33 = a.a33/b.a33; c.a34 = a.a34/b.a34;
c.a41 = a.a41/b.a41; c.a42 = a.a42/b.a42; c.a43 = a.a43/b.a43; c.a44 = a.a44/b.a44;
}
/**
* Performs an element by element division operation:
*
* ci = ai / bi
*
* @param a The left vector in the division operation. Not modified.
* @param b The right vector in the division operation. Not modified.
* @param c Where the results of the operation are stored. Modified.
*/
public static void elementDiv( FMatrix4 a , FMatrix4 b , FMatrix4 c ) {
c.a1 = a.a1/b.a1;
c.a2 = a.a2/b.a2;
c.a3 = a.a3/b.a3;
c.a4 = a.a4/b.a4;
}
/**
*
* 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( float alpha , FMatrix4x4 a ) {
a.a11 *= alpha; a.a12 *= alpha; a.a13 *= alpha; a.a14 *= alpha;
a.a21 *= alpha; a.a22 *= alpha; a.a23 *= alpha; a.a24 *= alpha;
a.a31 *= alpha; a.a32 *= alpha; a.a33 *= alpha; a.a34 *= alpha;
a.a41 *= alpha; a.a42 *= alpha; a.a43 *= alpha; a.a44 *= alpha;
}
/**
*
* Performs an in-place element by element scalar multiplication.
*
* aij = α*aij
*
*
* @param a The vector that is to be scaled. Modified.
* @param alpha the amount each element is multiplied by.
*/
public static void scale( float alpha , FMatrix4 a ) {
a.a1 *= alpha;
a.a2 *= alpha;
a.a3 *= alpha;
a.a4 *= 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( float alpha , FMatrix4x4 a , FMatrix4x4 b ) {
b.a11 = a.a11*alpha; b.a12 = a.a12*alpha; b.a13 = a.a13*alpha; b.a14 = a.a14*alpha;
b.a21 = a.a21*alpha; b.a22 = a.a22*alpha; b.a23 = a.a23*alpha; b.a24 = a.a24*alpha;
b.a31 = a.a31*alpha; b.a32 = a.a32*alpha; b.a33 = a.a33*alpha; b.a34 = a.a34*alpha;
b.a41 = a.a41*alpha; b.a42 = a.a42*alpha; b.a43 = a.a43*alpha; b.a44 = a.a44*alpha;
}
/**
*
* Performs an element by element scalar multiplication.
*
* bi = α*ai
*
*
* @param alpha the amount each element is multiplied by.
* @param a The vector that is to be scaled. Not modified.
* @param b Where the scaled matrix is stored. Modified.
*/
public static void scale( float alpha , FMatrix4 a , FMatrix4 b ) {
b.a1 = a.a1*alpha;
b.a2 = a.a2*alpha;
b.a3 = a.a3*alpha;
b.a4 = a.a4*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( FMatrix4x4 a , float alpha ) {
a.a11 /= alpha; a.a12 /= alpha; a.a13 /= alpha; a.a14 /= alpha;
a.a21 /= alpha; a.a22 /= alpha; a.a23 /= alpha; a.a24 /= alpha;
a.a31 /= alpha; a.a32 /= alpha; a.a33 /= alpha; a.a34 /= alpha;
a.a41 /= alpha; a.a42 /= alpha; a.a43 /= alpha; a.a44 /= alpha;
}
/**
*
* Performs an in-place element by element scalar division. Scalar denominator.
*
* ai = ai/α
*
*
* @param a The vector whose elements are to be divided. Modified.
* @param alpha the amount each element is divided by.
*/
public static void divide( FMatrix4 a , float alpha ) {
a.a1 /= alpha;
a.a2 /= alpha;
a.a3 /= alpha;
a.a4 /= 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( FMatrix4x4 a , float alpha , FMatrix4x4 b ) {
b.a11 = a.a11/alpha; b.a12 = a.a12/alpha; b.a13 = a.a13/alpha; b.a14 = a.a14/alpha;
b.a21 = a.a21/alpha; b.a22 = a.a22/alpha; b.a23 = a.a23/alpha; b.a24 = a.a24/alpha;
b.a31 = a.a31/alpha; b.a32 = a.a32/alpha; b.a33 = a.a33/alpha; b.a34 = a.a34/alpha;
b.a41 = a.a41/alpha; b.a42 = a.a42/alpha; b.a43 = a.a43/alpha; b.a44 = a.a44/alpha;
}
/**
*
* Performs an element by element scalar division. Scalar denominator.
*
* bi = ai /α
*
*
* @param alpha the amount each element is divided by.
* @param a The vector whose elements are to be divided. Not modified.
* @param b Where the results are stored. Modified.
*/
public static void divide( FMatrix4 a , float alpha , FMatrix4 b ) {
b.a1 = a.a1/alpha;
b.a2 = a.a2/alpha;
b.a3 = a.a3/alpha;
b.a4 = a.a4/alpha;
}
/**
*
* Changes the sign of every element in the matrix.
*
* aij = -aij
*
*
* @param a A matrix. Modified.
*/
public static void changeSign( FMatrix4x4 a )
{
a.a11 = -a.a11; a.a12 = -a.a12; a.a13 = -a.a13; a.a14 = -a.a14;
a.a21 = -a.a21; a.a22 = -a.a22; a.a23 = -a.a23; a.a24 = -a.a24;
a.a31 = -a.a31; a.a32 = -a.a32; a.a33 = -a.a33; a.a34 = -a.a34;
a.a41 = -a.a41; a.a42 = -a.a42; a.a43 = -a.a43; a.a44 = -a.a44;
}
/**
*
* Changes the sign of every element in the vector.
*
* ai = -ai
*
*
* @param a A vector. Modified.
*/
public static void changeSign( FMatrix4 a )
{
a.a1 = -a.a1;
a.a2 = -a.a2;
a.a3 = -a.a3;
a.a4 = -a.a4;
}
/**
*
* 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( FMatrix4x4 a , float v ) {
a.a11 = v; a.a12 = v; a.a13 = v; a.a14 = v;
a.a21 = v; a.a22 = v; a.a23 = v; a.a24 = v;
a.a31 = v; a.a32 = v; a.a33 = v; a.a34 = v;
a.a41 = v; a.a42 = v; a.a43 = v; a.a44 = v;
}
/**
*
* Sets every element in the vector to the specified value.
*
* ai = value
*
*
* @param a A vector whose elements are about to be set. Modified.
* @param v The value each element will have.
*/
public static void fill( FMatrix4 a , float v ) {
a.a1 = v;
a.a2 = v;
a.a3 = v;
a.a4 = v;
}
/**
* Extracts the row from the matrix a.
* @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 FMatrix4 extractRow( FMatrix4x4 a , int row , FMatrix4 out ) {
if( out == null) out = new FMatrix4();
switch( row ) {
case 0:
out.a1 = a.a11;
out.a2 = a.a12;
out.a3 = a.a13;
out.a4 = a.a14;
break;
case 1:
out.a1 = a.a21;
out.a2 = a.a22;
out.a3 = a.a23;
out.a4 = a.a24;
break;
case 2:
out.a1 = a.a31;
out.a2 = a.a32;
out.a3 = a.a33;
out.a4 = a.a34;
break;
case 3:
out.a1 = a.a41;
out.a2 = a.a42;
out.a3 = a.a43;
out.a4 = a.a44;
break;
default:
throw new IllegalArgumentException("Out of bounds row. row = "+row);
}
return out;
}
/**
* Extracts the column from the matrix a.
* @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 FMatrix4 extractColumn( FMatrix4x4 a , int column , FMatrix4 out ) {
if( out == null) out = new FMatrix4();
switch( column ) {
case 0:
out.a1 = a.a11;
out.a2 = a.a21;
out.a3 = a.a31;
out.a4 = a.a41;
break;
case 1:
out.a1 = a.a12;
out.a2 = a.a22;
out.a3 = a.a32;
out.a4 = a.a42;
break;
case 2:
out.a1 = a.a13;
out.a2 = a.a23;
out.a3 = a.a33;
out.a4 = a.a43;
break;
case 3:
out.a1 = a.a14;
out.a2 = a.a24;
out.a3 = a.a34;
out.a4 = a.a44;
break;
default:
throw new IllegalArgumentException("Out of bounds column. column = "+column);
}
return out;
}
}