org.jeometry.math.MatrixTestData Maven / Gradle / Ivy
package org.jeometry.math;
import org.jeometry.Jeometry;
/**
* A set of matrix data.
* @author Julien Seinturier - COMEX S.A. - [email protected] - https://github.com/jorigin/jeometry
* @version {@value Jeometry#version}
* @since 1.0.0
*
*/
public class MatrixTestData {
/**
* a 3 component vector.
*/
public static final double[] V_3_A = new double[] {-1.36528596, 0.2637087, -0.1998471};
/**
* a 4 component vector.
*/
public static final double[] V_4_A = new double[] {-1.36528596, 0.2637087, -0.1998471, 3.45692302};
/**
* a 4 component vector.
*/
public static final double[] V_PROD_M_4x4_A_X_V_4_A = new double[] {-1592.1687401217387, 48.8202233506501, -135.49691805832344, -1402.2024992659703};
/**
* A 4 component linear matrix
*/
public static final double[][] M_4L_A = new double[][] {{2.36987452, 1.036987452, -3.98542015, 0.006984548}};
/**
* A 4 component column matrix
*/
public static final double[][] M_4C_A = new double[][] {{ 2.36987452},
{ 1.036987452},
{-3.98542015},
{ 0.006984548}};
/**
* The result of the product {@link #M_4L_A} with {@link #V_4_A}
*/
public static final double[] V_PROD_M_4L_A_V_4_A = new double[] {-2.14147409220994684};
/**
* A 3x3 matrix.
*/
public static final double[][] M_3x3_A = new double[][]{
{-0.3489054, -0.7051164, -0.3809763},
{-0.8560400, -0.6291361, -0.7050437},
{-0.1990242, 0.5199935, 0.8552008}
};
/**
* The inverse of {@link #M_3x3_A}
*/
public static final double[][] M_3x3_A_INV = new double[][]{
{ 0.5070835964176541, -1.1977844683656990, -0.76157969102133000},
{-2.5807044250194540, 1.1069599186495120, -0.23705790083590658},
{ 1.6871726891994256, -0.9518233121942631, 1.13621944555775520},
};
/**
* The cofactor matrix of {@link #M_3x3_A}
*/
public static final double[][] M_3x3_A_COFACTOR = new double[][]{
{-0.17141955481292992, 0.87240685118954000, -0.5703485447336201},
{ 0.40491090971907000, -0.37420768053077996, 0.3217637675317800},
{ 0.25745193201225003, 0.08013739768601996, -0.3840988604310600}
};
/**
* The {@link MatrixTestData#M_3x3_A M_3x3_A} matrix determinant.
*/
public static final double M_3x3_A_DETERMINANT = -0.3380498916232778d;
/**
* A 4x4 matrix.
*/
public static final double[][] M_4x4_A = new double[][] {
{ 3.45692302, -1.36528596, 1.3685204, -459.0254136},
{22.65974148, 0.00698741, 8.1269853, 23.5410397},
{12.87456921, -3.12586921, 11.3685214, -33.2154242},
{36.25697942, -3.01127952, 6984.3652127, 12.6985412}
};
/**
* The inverse of {@link #M_4x4_A}
*/
public static final double[][] M_4x4_A_INV = new double[][] {
{ 0.0023362906372642535, 0.0443514687366402000, -8.724924050199067E-4, -5.0644838364482117E-5},
{ 0.0336722068448692500, 0.1844081481703914000, -0.334517281604580900, 3.23322649154155100E-4},
{ 6.5004947736464510E-6, -1.5033815455939636E-4, -1.414927212295284E-4, 1.43580902831110600E-4},
{-0.0022610663539576160, -2.1492488273757343E-4, 9.879670270111554E-4, -9.1500333970123050E-7},
};
/**
* The cofactor of {@link #M_4x4_A}
*/
public static final double[][] M_4x4_A_COFACTOR = new double[][] {
{ -510389.604736797160, -7356081.50289591800000000, -1420.107971669177, 493955.993433863740},
{-9689089.292630604000, -4.028608442532788E7, 32843.101820705080, 46952.8166568281000},
{ 190606.017346975920, 7.307915394281422E7, 30910.715006775317, -215832.77883597394},
{ 11063.948390032145, -70633.55751726116000000, -31366.902334349514, 199.893020771515400}
};
/**
* The {@link MatrixTestData#M_4x4_A M_4x4_A} matrix expressed within a single dimensional array in {@link Matrix#ROW_MAJOR}.
*/
public static final double[] M_4x4_A_ROWMAJOR = new double[] {
3.45692302, -1.36528596, 1.3685204, -459.0254136,
22.65974148, 0.00698741, 8.1269853, 23.5410397,
12.87456921, -3.12586921, 11.3685214, -33.2154242,
36.25697942, -3.01127952, 6984.3652127, 12.6985412
};
/**
* The {@link MatrixTestData#M_4x4_A M_4x4_A} matrix expressed within a single dimensional array in {@link Matrix#COLUMN_MAJOR}
*/
public static final double[] M_4x4_A_COLUMNMAJOR = new double[] {
3.45692302, 22.65974148, 12.87456921, 36.25697942,
-1.36528596, 0.00698741, -3.12586921, -3.01127952,
1.3685204, 8.1269853, 11.3685214, 6984.3652127,
-459.0254136, 23.5410397, -33.2154242, 12.6985412
};
/**
* The {@link MatrixTestData#M_4x4_A M_4x4_A} matrix determinant.
*/
public static final double M_4x4_A_DETERMINANT = -2.1846152041017145E8;
/**
* A 4x4 matrix.
*/
public static final double[][] M_4x4_B = new double[][] {
{0.37635972705741605, -0.6562297094791463, -0.34595043189408814, 0.35760795101456533},
{0.05485412293382774, -0.8277842762787191, -0.7645418241100518, 0.5903801510041287},
{0.6378734400547261, 0.4881916032381257, -0.5994457753638186, -0.2462926076270161},
{0.23311198402704603, 0.4246202954815326, 0.2418492075819768, 0.9927378463572852},
};
/**
* A 5x5 matrix.
*/
public static final double[][] M_5x5_A = new double[][] {
{-0.1180710, -0.3937494, 0.6888403, -0.7191015, -0.0774862},
{-0.3663894, -0.3909305, -0.2514673, -0.1998471, 0.4295696},
{ 0.0091618, -0.4103808, 0.2637087, 0.3439714, 0.3653926},
{-0.9802176, 0.7260585, 0.3678009, 0.7093690, -0.1036077},
{ 0.4253439, -0.5693282, 0.7328173, 0.9992786, -0.4779186}
};
/**
* The {@link MatrixTestData#M_5x5_A M_5x5_A} expressed within a single dimensional array in {@link Matrix#ROW_MAJOR}.
*/
public static final double[] M_5x5_A_ROWMAJOR = new double[] {
-0.1180710, -0.3937494, 0.6888403, -0.7191015, -0.0774862,
-0.3663894, -0.3909305, -0.2514673, -0.1998471, 0.4295696,
0.0091618, -0.4103808, 0.2637087, 0.3439714, 0.3653926,
-0.9802176, 0.7260585, 0.3678009, 0.7093690, -0.1036077,
0.4253439, -0.5693282, 0.7328173, 0.9992786, -0.4779186
};
/**
* The {@link MatrixTestData#M_5x5_A M_5x5_A} matrix expressed within a single dimensional array in {@link Matrix#COLUMN_MAJOR}.
*/
public static final double[] M_5x5_A_COLUMNMAJOR = new double[] {
-0.1180710, -0.3663894, 0.0091618, -0.9802176, 0.4253439,
-0.3937494, -0.3909305, -0.4103808, 0.7260585, -0.5693282,
0.6888403, -0.2514673, 0.2637087, 0.3678009, 0.7328173,
-0.7191015, -0.1998471, 0.3439714, 0.7093690, 0.9992786,
-0.0774862, 0.4295696, 0.3653926, -0.1036077, -0.4779186
};
/**
* The {@link MatrixTestData#M_5x5_A 5x5 C matrix} determinant.
*/
public static final double M_5x5_A_DETERMINANT = -0.4944084244983374;
/**
* A 4x3 matrix.
*/
public static final double[][] M_4x3_A = new double[][] {
{-0.6814359, -0.9401949, 0.4056839},
{-0.9660992, -0.9649611, -0.2315810},
{-0.3560276, -0.5212195, -0.9616091},
{-0.3269735, 0.8608128, 0.5911279}
};
/**
* The transpose of the {@link MatrixTestData#M_4x3_A} matrix.
*/
public static final double[][] M_4x3_A_TRANSPOSE = new double[][] {
{-0.6814359, -0.9660992, -0.3560276, -0.3269735},
{-0.9401949, -0.9649611, -0.5212195, 0.8608128},
{ 0.4056839, -0.2315810, -0.9616091, 0.5911279}
};
/**
* A 3x4 matrix.
*/
public static final double[][] M_3x4_A = new double[][] {
{ 0.2242035, 0.9148579, -0.6261270, 0.0339424},
{ 0.6411728, 0.6593071, -0.8716299, 0.9981717},
{-0.3769121, -0.5572688, 0.2030611, -0.3207281}
};
/**
* The matrix that represents the {@link MatrixTestData#M_4x3_A M_4x3_A}×{@link MatrixTestData#M_3x4_A M_3x4_A} product result.
*/
public static final double[][] M_4x4_PRODUCT_A = new double[][] {
{ -0.9085148810695599, -1.4693691695447202, 1.3285460214131, -1.09171973800408 },
{ -0.74802395133518, -1.39099632378469, 1.39896464829619, -0.9217140529808501 },
{ -0.05157229498608995, -0.13348363026040988, 0.48196359215223994, -0.22393592601267986 },
{ 0.255817891987, -0.06101143423428995, -0.42554815653352995, 0.6585493824073699 }
};
/**
* This matrix represent the {@link MatrixTestData#M_4x3_A M_4x3_A}×{@link MatrixTestData#M_4x4_A M_4x4_A} product result.
*/
public static final double[][] M_4x3_A_M_4x4_A_PRODUCT = new double[][] {
{ -0.6814359, -0.9401949, 0.4056839 },
{ -0.9660992, -0.9649611, -0.2315810 },
{ -0.3560276, -0.5212195, -0.9616091 },
{ -0.3269735, 0.8608128, 0.5911279 }
};
/**
* This matrix is dedicated to the testing of LU decomposition.
* @see #DECOMPOSITION_LU_L
* @see #DECOMPOSITION_LU_U
*/
public static final double[][] DECOMPOSITION_LU_INPUT = new double[][] {
{ 1, 2, 3, 4},
{-9, 8, -15, 4},
{ 2, 13, -21, 7},
{ 4, -5, 5, 3}
};
/**
* This matrix is the lower triangular matrix L resulting of the LU decomposition of the {@link #DECOMPOSITION_LU_INPUT input matrix}.
* @see #DECOMPOSITION_LU_INPUT
* @see #DECOMPOSITION_LU_U
*/
public static final double[][] DECOMPOSITION_LU_L = new double[][] {
{ 1.0000, 0, 0, 0},
{-0.2222222222222222, 1.0000, 0, 0},
{-0.1111111111111111, 0.195488721804511127, 1.0000, 0},
{-0.4444444444444444, -0.097744360902255650, -0.6641975308641974, 1.0000}
};
/**
* This matrix is the upper triangular matrix U resulting of the LU decomposition of the {@link #DECOMPOSITION_LU_INPUT input matrix}.
* @see #DECOMPOSITION_LU_INPUT
* @see #DECOMPOSITION_LU_L
*/
public static final double[][] DECOMPOSITION_LU_U = new double[][] {
{-9, 8, -15.0000, 4.0000},
{ 0, 14.777777777777779, -24.333333333333332, 7.888888888888889},
{ 0, 0, 6.090225563909774, 2.9022556390977443},
{ 0, 0, 0, 7.476543209876543},
};
/**
* This matrix is the permutation matrix P resulting of the LU decomposition of the {@link #DECOMPOSITION_LU_INPUT input matrix}.
* @see #DECOMPOSITION_LU_INPUT
* @see #DECOMPOSITION_LU_L
* @see #DECOMPOSITION_LU_U
*/
public static final double[][] DECOMPOSITION_LU_P = new double[][] {
{0, 1, 0, 0},
{0, 0, 1, 0},
{1, 0, 0, 0},
{0, 0, 0, 1}
};
/**
* This matrix is dedicated to the testing of Gauss Elimination based solvers. Matlab code:
* A = [9 3 4; 4 3 4; 1 1 1]
* @see #SOLVER_GAUSS_ELIMINATION_B
* @see #SOLVER_GAUSS_ELIMINATION_X
*/
public static final double[][] SOLVER_GAUSS_ELIMINATION_A = new double[][] {
{ 9.0d, 3.0d, 4.0d },
{ 4.0d, 3.0d, 4.0d },
{ 1.0d, 1.0d, 1.0d}};
/**
* This vector is dedicated to the testing of Gauss Elimination based solvers. Matlab code:
* B = [7; 8; 3]
* @see #SOLVER_GAUSS_ELIMINATION_A
* #see {@link #SOLVER_GAUSS_ELIMINATION_X}
*/
public static final double[] SOLVER_GAUSS_ELIMINATION_B = new double[] {7.0d, 8.0d, 3.0d};
/**
* This vector is dedicated to the testing of Gauss Elimination based solvers. Matlab code:
* B = [-1/5; 4; -4/5]
* @see #SOLVER_GAUSS_ELIMINATION_A
* @see #SOLVER_GAUSS_ELIMINATION_B
*/
public static final double[] SOLVER_GAUSS_ELIMINATION_X = new double[] {-1.0d/5.0d, 4.0d, -4.0d/5.0d};
/**
* This matrix is dedicated to the testing of Eigenvalue decomposition.
* Computing an eigenvalues decomposition from this matrix should provide {@link #DECOMPOSITION_EIGEN_V V} and {@link #DECOMPOSITION_EIGEN_D D} matrices.
* @see #DECOMPOSITION_EIGEN_V
* @see #DECOMPOSITION_EIGEN_D
*/
public static final double[][] DECOMPOSITION_EIGEN_INPUT = new double[][] {
{1.000000000000000, 0.500000000000000, 0.333333333333333, 0.250000000000000},
{0.500000000000000, 1.000000000000000, 0.666666666666667, 0.500000000000000},
{0.333333333333333, 0.666666666666667, 1.000000000000000, 0.750000000000000},
{0.250000000000000, 0.500000000000000, 0.750000000000000, 1.000000000000000}
};
/**
* This matrix is the V matrix computed from the Eigenvalues decomposition of the {@link #DECOMPOSITION_EIGEN_INPUT input matrix}.
* @see #DECOMPOSITION_EIGEN_INPUT
* @see #DECOMPOSITION_EIGEN_D
*/
public static final double[][] DECOMPOSITION_EIGEN_V = new double[][] {
{ 0.069318526074277, -0.442222850107573, -0.810476380106626, 0.377838497343619},
{-0.361796329835911, 0.742039806455369, -0.187714392599047, 0.532206396207443},
{ 0.769367037085765, 0.048636017022092, 0.300968104554782, 0.561361826396131},
{-0.521893398986829, -0.501448316705362, 0.466164717820999, 0.508790056532360}
};
/**
* This matrix is the D matrix computed from the Eigenvalues decomposition of the {@link #DECOMPOSITION_EIGEN_INPUT input matrix}.
* @see #DECOMPOSITION_EIGEN_INPUT
* @see #DECOMPOSITION_EIGEN_V
*/
public static final double[][] DECOMPOSITION_EIGEN_D = new double[][] {
{0.207775485918012, 0 , 0 , 0},
{0 , 0.407832884117875, 0 , 0},
{0 , 0 , 0.848229155477913, 0},
{0 , 0 , 0 , 2.536162474486201}
};
/**
* This matrix is dedicated to the testing of the Singular Values (SVD) decomposition.
* @see #DECOMPOSITION_SVD_U
* @see #DECOMPOSITION_SVD_S
* @see #DECOMPOSITION_SVD_V
*/
public static final double[][] DECOMPOSITION_SVD_INPUT = new double[][] {
{ 17, 24, 1, 8, 15},
{ 23, 5, 7, 14, 16},
{ 4, 6, 13, 20, 22},
{ 10, 12, 19, 21, 3},
{ 11, 18, 25, 2, 9}
};
/**
* This matrix is the U matrix obtained after the Singular Values (SVD) decomposition of the {@link #DECOMPOSITION_SVD_INPUT input matrix}.
* @see #DECOMPOSITION_SVD_INPUT
* @see #DECOMPOSITION_SVD_S
* @see #DECOMPOSITION_SVD_V
*/
public static final double[][] DECOMPOSITION_SVD_U = new double[][] {
{ 0.44721359549995793928183473374626, 0.54563487312996778094350033489632, 0.51166727360169272880036685827406, -0.19543950758485479560047750383079, -0.44975836315119696024624071783596},
{ 0.44721359549995793928183473374626, 0.44975836315119696024624071783596, -0.19543950758485479560047750383079, 0.51166727360169272880036685827406, 0.54563487312996778094350033489632},
{ 0.44721359549995793928183473374626, -3.6102493598044168843311881307351e-44, -0.63245553203367586639977870888654, -0.63245553203367586639977870888654, 1.7037410954189828268483469351314e-49},
{ 0.44721359549995793928183473374626, -0.44975836315119696024624071783596, -0.19543950758485479560047750383079, 0.51166727360169272880036685827406, -0.54563487312996778094350033489632},
{ 0.44721359549995793928183473374626, -0.54563487312996778094350033489632, 0.51166727360169272880036685827406, -0.19543950758485479560047750383079, 0.44975836315119696024624071783596}
};
/**
* This matrix is the S matrix obtained after the Singular Values (SVD) decomposition of the {@link #DECOMPOSITION_SVD_INPUT input matrix}.
* @see #DECOMPOSITION_SVD_INPUT
* @see #DECOMPOSITION_SVD_U
* @see #DECOMPOSITION_SVD_V
*/
public static final double[][] DECOMPOSITION_SVD_S = new double[][] {
{ 65.0, 0, 0, 0, 0},
{ 0, 22.547088685879657984674226396467, 0, 0, 0},
{ 0, 0, 21.687425355202639411956035427154, 0, 0},
{ 0, 0, 0, 13.403565997991492328585154445703, 0},
{ 0, 0, 0, 0, 11.900789544861194527298509087321}
};
/**
* This matrix is the V matrix obtained after the Singular Values (SVD) decomposition of the {@link #DECOMPOSITION_SVD_INPUT input matrix}.
* @see #DECOMPOSITION_SVD_INPUT
* @see #DECOMPOSITION_SVD_U
* @see #DECOMPOSITION_SVD_S
*/
public static final double[][] DECOMPOSITION_SVD_V = new double[][] {
{ 0.44721359549995793928183473374626, 0.40451643610455471341979148603303, 0.24656489623973259874361786663113, 0.6627260006535807384660483816136, 0.36927828655536965366206505316499},
{ 0.44721359549995793928183473374626, 0.0055661597144479252799165035570114, 0.6627260006535807384660483816136, -0.24656489623973259874361786663113, -0.54769427408549129087991810164138},
{ 0.44721359549995793928183473374626, -0.82016519163800527739941597918008, 1.0263687996129757425478176433711e-49, 2.7831673927115195568141887434356e-44, 0.35683197506024327443570609695277},
{ 0.44721359549995793928183473374626, 0.0055661597144479252799165035570114, -0.6627260006535807384660483816136, 0.24656489623973259874361786663113, -0.54769427408549129087991810164138},
{ 0.44721359549995793928183473374626, 0.40451643610455471341979148603303, -0.24656489623973259874361786663113, -0.6627260006535807384660483816136, 0.36927828655536965366206505316499}
};
}
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