G. C-language implementation

This implementation makes use of the C-language matrix source code available at

http://www.mymathlib.com/matrices/

It has been tested as a console application, and reproduces exactly the results given by the FORTRAN implementation of Magneto 1.2, using the test file mag.txt with a user norm of 0.569.

Copyright (C) 2013 www.sailboatinstruments.blogspot.com

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

#include <stdio.h>

#include <math.h>

#include <malloc.h>

#include <string.h>

#include <float.h>

// Forward declarations of mymathlib.com routines

void Matrix_x_Its_Transpose(double*, double*, int, int);

void Get_Submatrix(double*, int, int, double*, int, int, int);

int Choleski_LU_Decomposition(double*, int);

int Choleski_LU_Inverse(double*, int);

void Multiply_Matrices(double*, double*, int, int, double*, int);

void Identity_Matrix(double*, int);

int Hessenberg_Form_Elementary(double*, double*, int);

static void Hessenberg_Elementary_Transform(double*, double*, int[], int);

void Copy_Vector(double*, double*, int);

int QR_Hessenberg_Matrix(double*, double*, double[], double[], int, int);

static void One_Real_Eigenvalue(double[], double[], double[], int, double);

static void Two_Eigenvalues(double*, double*, double[], double[], int, int, double);

static void Update_Row(double*, double, double, int, int);

static void Update_Column(double*, double, double, int, int);

static void Update_Transformation(double*, double, double, int, int);

static void Double_QR_Iteration(double*, double*, int, int, int, double*, int);

static void Product_and_Sum_of_Shifts(double*, int, int, double*, double*, double*, int);

static int Two_Consecutive_Small_Subdiagonal(double*, int, int, int, double, double);

static void Double_QR_Step(double*, int, int, int, double, double, double*, int);

static void BackSubstitution(double*, double[], double[], int);

static void BackSubstitute_Real_Vector(double*, double[], double[], int, double, int);

static void BackSubstitute_Complex_Vector(double*, double[], double[], int, double, int);

static void Calculate_Eigenvectors(double*, double*, double[], double[], int);

static void Complex_Division(double, double, double, double, double*, double*);

void Transpose_Square_Matrix(double*, int);

int main()

{

int nlines = 0;

char buf[120];

double *D, *S, *C, *S11, *S12, *S12t, *S22, *S22_1, *S22a, *S22b, *SS, *E, *d, *U, *SSS;

double *eigen_real, *eigen_imag, *v1, *v2, *v, *Q, *Q_1, *B, *QB, J, hmb, *SSSS;

int *p;

int i, index;

double maxval, norm, btqb, *eigen_real3, *eigen_imag3, *Dz, *vdz, *SQ, *A_1, hm, norm1, norm2, norm3;

double x, y, z;

FILE *fp;

fp = fopen("c:\\MagCal\\mag.txt", "r");

while(fgets(buf, 100, fp) != NULL)

nlines++;

rewind(fp);

D = (double*)malloc(10 * nlines * sizeof(double));

for( i = 0; i < nlines; i++)

{

fgets(buf, 100, fp);

sscanf(buf, "%lf\t%lf\t%lf", &x, &y, &z);

D[i] = x * x;

D[nlines+i] = y * y;

D[nlines*2+i] = z * z;

D[nlines*3+i] = 2.0 * y * z;

D[nlines*4+i] = 2.0 * x * z;

D[nlines*5+i] = 2.0 * x * y;

D[nlines*6+i] = 2.0 * x;

D[nlines*7+i] = 2.0 * y;

D[nlines*8+i] = 2.0 * z;

D[nlines*9+i] = 1.0;

}

fclose(fp);

// allocate memory for matrix S

S = (double*)malloc(10 * 10 * sizeof(double));

Matrix_x_Its_Transpose(S, D, 10, nlines);

// Create pre-inverted constraint matrix C

C = (double*)malloc(6 * 6 * sizeof(double));

C[0] = 0.0; C[1] = 0.5; C[2] = 0.5; C[3] = 0.0; C[4] = 0.0; C[5] = 0.0;

C[6] = 0.5; C[7] = 0.0; C[8] = 0.5; C[9] = 0.0; C[10] = 0.0; C[11] = 0.0;

C[12] = 0.5; C[13] = 0.5; C[14] = 0.0; C[15] = 0.0; C[16] = 0.0; C[17] = 0.0;

C[18] = 0.0; C[19] = 0.0; C[20] = 0.0; C[21] = -0.25; C[22] = 0.0; C[23] = 0.0;

C[24] = 0.0; C[25] = 0.0; C[26] = 0.0; C[27] = 0.0; C[28] = -0.25; C[29] = 0.0;

C[30] = 0.0; C[31] = 0.0; C[32] = 0.0; C[33] = 0.0; C[34] = 0.0; C[35] = -0.25;

S11 = (double*)malloc(6 * 6 * sizeof(double));

Get_Submatrix(S11, 6, 6, S, 10, 0, 0);

S12 = (double*)malloc(6 * 4 * sizeof(double));

Get_Submatrix(S12, 6, 4, S, 10, 0, 6);

S12t = (double*)malloc(4 * 6 * sizeof(double));

Get_Submatrix(S12t, 4, 6, S, 10, 6, 0);

S22 = (double*)malloc(4 * 4 * sizeof(double));

Get_Submatrix(S22, 4, 4, S, 10, 6, 6);

S22_1 = (double*)malloc(4 * 4 * sizeof(double));

for(i = 0; i < 16; i++)

S22_1[i] = S22[i];

Choleski_LU_Decomposition(S22_1, 4);

Choleski_LU_Inverse(S22_1, 4);

// Calculate S22a = S22_1 * S12t 4*6 = 4x4 * 4x6 C = AB

S22a = (double*)malloc(4 * 6 * sizeof(double));

Multiply_Matrices(S22a, S22_1, 4, 4, S12t, 6);

// Then calculate S22b = S12 * S22a ( 6x6 = 6x4 * 4x6)

S22b = (double*)malloc(6 * 6 * sizeof(double));

Multiply_Matrices(S22b, S12, 6, 4, S22a, 6);

// Calculate SS = S11 - S22b

SS = (double*)malloc(6 * 6 * sizeof(double));

for(i = 0; i < 36; i++)

SS[i] = S11[i] - S22b[i];

E = (double*)malloc(6 * 6 * sizeof(double));

Multiply_Matrices(E, C, 6, 6, SS, 6);

SSS = (double*)malloc(6 * 6 * sizeof(double));

Hessenberg_Form_Elementary(E, SSS, 6);

eigen_real = (double*)malloc(6 * sizeof(double));

eigen_imag = (double*)malloc(6 * sizeof(double));

QR_Hessenberg_Matrix(E, SSS, eigen_real, eigen_imag, 6, 100);

index = 0;

maxval = eigen_real[0];

for(i = 1; i < 6; i++)

{

if(eigen_real[i] > maxval)

{

maxval = eigen_real[i];

index = i;

}

}

v1 = (double*)malloc(6 * sizeof(double));

v1[0] = SSS[index];

v1[1] = SSS[index+6];

v1[2] = SSS[index+12];

v1[3] = SSS[index+18];

v1[4] = SSS[index+24];

v1[5] = SSS[index+30];

// normalize v1

norm = sqrt(v1[0] * v1[0] + v1[1] * v1[1] + v1[2] * v1[2] + v1[3] * v1[3] + v1[4] * v1[4] + v1[5] * v1[5]);

v1[0] /= norm;

v1[1] /= norm;

v1[2] /= norm;

v1[3] /= norm;

v1[4] /= norm;

v1[5] /= norm;

if(v1[0] < 0.0)

{

v1[0] = -v1[0];

v1[1] = -v1[1];

v1[2] = -v1[2];

v1[3] = -v1[3];

v1[4] = -v1[4];

v1[5] = -v1[5];

}

// Calculate v2 = S22a * v1 ( 4x1 = 4x6 * 6x1)

v2 = (double*)malloc(4 * sizeof(double));

Multiply_Matrices(v2, S22a, 4, 6, v1, 1);

v = (double*)malloc(10 * sizeof(double));

v[0] = v1[0];

v[1] = v1[1];

v[2] = v1[2];

v[3] = v1[3];

v[4] = v1[4];

v[5] = v1[5];

v[6] = -v2[0];

v[7] = -v2[1];

v[8] = -v2[2];

v[9] = -v2[3];

Q = (double*)malloc(3 * 3 * sizeof(double));

Q[0] = v[0];

Q[1] = v[5];

Q[2] = v[4];

Q[3] = v[5];

Q[4] = v[1];

Q[5] = v[3];

Q[6] = v[4];

Q[7] = v[3];

Q[8] = v[2];

U = (double*)malloc(3 * sizeof(double));

U[0] = v[6];

U[1] = v[7];

U[2] = v[8];

Q_1 = (double*)malloc(3 * 3 * sizeof(double));

for(i = 0; i < 9; i++)

Q_1[i] = Q[i];

Choleski_LU_Decomposition(Q_1, 3);

Choleski_LU_Inverse(Q_1, 3);

// Calculate B = Q-1 * U ( 3x1 = 3x3 * 3x1)

B = (double*)malloc(3 * sizeof(double));

Multiply_Matrices(B, Q_1, 3, 3, U, 1);

B[0] = -B[0]; // x-axis combined bias

B[1] = -B[1]; // y-axis combined bias

B[2] = -B[2]; // z-axis combined bias

for(i = 0; i < 3; i++)

printf("%lf\r\n", B[i]);

// First calculate QB = Q * B ( 3x1 = 3x3 * 3x1)

QB = (double*)malloc(3 * sizeof(double));

Multiply_Matrices(QB, Q, 3, 3, B, 1);

// Then calculate btqb = BT * QB ( 1x1 = 1x3 * 3x1)

Multiply_Matrices(&btqb, B, 1, 3, QB, 1);

// Calculate hmb = sqrt(btqb - J).

J = v[9];

hmb = sqrt(btqb - J);

// Calculate SQ, the square root of matrix Q

SSSS = (double*)malloc(3 * 3 * sizeof(double));

Hessenberg_Form_Elementary(Q, SSSS, 3);

eigen_real3 = (double*)malloc(3 * sizeof(double));

eigen_imag3 = (double*)malloc(3 * sizeof(double));

QR_Hessenberg_Matrix(Q, SSSS, eigen_real3, eigen_imag3, 3, 100);

// normalize eigenvectors

norm1 = sqrt(SSSS[0] * SSSS[0] + SSSS[3] * SSSS[3] + SSSS[6] * SSSS[6]);

SSSS[0] /= norm1;

SSSS[3] /= norm1;

SSSS[6] /= norm1;

norm2 = sqrt(SSSS[1] * SSSS[1] + SSSS[4] * SSSS[4] + SSSS[7] * SSSS[7]);

SSSS[1] /= norm2;

SSSS[4] /= norm2;

SSSS[7] /= norm2;

norm3 = sqrt(SSSS[2] * SSSS[2] + SSSS[5] * SSSS[5] + SSSS[8] * SSSS[8]);

SSSS[2] /= norm3;

SSSS[5] /= norm3;

SSSS[8] /= norm3;

Dz = (double*)malloc(3 * 3 * sizeof(double));

for(i = 0; i < 9; i++)

Dz[i] = 0.0;

Dz[0] = sqrt(eigen_real3[0]);

Dz[4] = sqrt(eigen_real3[1]);

Dz[8] = sqrt(eigen_real3[2]);

vdz = (double*)malloc(3 * 3 * sizeof(double));

Multiply_Matrices(vdz, SSSS, 3, 3, Dz, 3);

Transpose_Square_Matrix(SSSS, 3);

SQ = (double*)malloc(3 * 3 * sizeof(double));

Multiply_Matrices(SQ, vdz, 3, 3, SSSS, 3);

hm = 0.569;

A_1 = (double*)malloc(3 * 3 * sizeof(double));

for(i = 0; i < 9; i++)

A_1[i] = SQ[i] * hm / hmb;

for(i = 0; i < 3; i++)

printf("%lf %lf %lf\r\n", A_1[i*3], A_1[i*3+1], A_1[i*3+2]);

free(D);

free(S);

free(C);

free(S11);

free(S12);

free(S12t);

free(S22);

free(S22_1);

free(S22a);

free(S22b);

free(SS);

free(E);

free(U);

free(SSS);

free(eigen_real);

free(eigen_imag);

free(v1);

free(v2);

free(v);

free(Q);

free(Q_1);

free(B);

free(QB);

free(SSSS);

free(eigen_real3);

free(eigen_imag3);

free(Dz);

free(vdz);

free(SQ);

free(A_1);

return 0;

}

// Place here the source code of all the routines which have been forward-declared, available at

// http://www.mymathlib.com/matrices/