#include <stdio.h>

#include <errno.h>

#include <string.h>

#include <stdlib.h>

#include <time.h>

#include <math.h>

#include <gsl/gsl_matrix.h>

#include <gsl/gsl_rng.h>

#include <gsl/gsl_randist.h>

#include <gsl/gsl_vector.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_cdf.h>

#include <gsl/gsl_blas.h>

#include <gsl/gsl_linalg.h>

#include <gsl/gsl_sf_gamma.h>

#include <gsl/gsl_permutation.h>

#include "invwishpdf.h"

int main(int argc, char *argv[]){

int args;

int m, n;

double pdf, dof;

args = 1;

m = atoi(argv[args++]);

n = atoi(argv[args++]);

// allocate space for matrix X, test_copy, and Scale.

gsl_matrix *X = gsl_matrix_alloc(m, n);

gsl_matrix *inv = gsl_matrix_alloc(m,n);

gsl_matrix *Scale = gsl_matrix_alloc(m, n);

gsl_matrix_set_identity(Scale);

fill_matrix(X);

dof = m + 1;

pdf = iwishpdf(X, Scale, inv, dof);

// Print the data

printf("\n%s", "Inverse Wishart matrix");

print_matrix(X);

printf("\n%s", "Scale matrix");

print_matrix(Scale);

printf("\n%s", "Wishart matrix");

print_matrix(inv);

printf("\n%s", "Density");

printf("\n%f\n", pdf);

return(0);

}

gsl_matrix fill_matrix(gsl_matrix *X)

{

int i,j;

int step = 0;

int n = X->size1;

int m = X->size2;

// Create a test matrix

double a_vect[] = {0.17955079, -0.09332222, -0.01273225, -0.09332222, 0.28282278, 0.01724885, -0.01273225, 0.01724885, 0.14424177};

for (i = 0; i < m; ++i){

for (j = 0; j < n; ++j){

gsl_matrix_set(X, i, j, a_vect[step++]);

}

}

return(*X);

}

double iwishpdf(gsl_matrix *X, gsl_matrix *Scale, gsl_matrix *inv, double dof)

{

double X_det, scale_det, denom, pdf, trace, numerator;

int m = X->size1;

int n = X->size2;

// Allocate matrix for inv(X)

gsl_matrix *for_mult = gsl_matrix_alloc(m, n);

// Get determinant of X and Scale matrix

X_det = matrix_determ(X);

scale_det = matrix_determ(Scale);

// Invert X

inv_matrix(X,inv);

// Multiple Scale * inv(X)

gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Scale, inv, 1.0, for_mult);

// Get trace of above.

trace = matrix_trace(for_mult);

numerator = pow(scale_det, dof / 2.0) * pow(X_det, (-dof-m-1)/ 2.0) * exp(-0.5 * trace);

denom = pow(2,dof * m / 2) * mv_gamma(dof/2, m);

pdf = (numerator/denom);

return(pdf);

}

gsl_matrix inv_matrix(gsl_matrix *X, gsl_matrix *inv)

{

int s;

int n = X->size1;

int m = X->size2;

gsl_matrix *a_copy = gsl_matrix_alloc(m, n);

gsl_matrix_memcpy( a_copy, X );

gsl_permutation *P = gsl_permutation_alloc(n);

gsl_linalg_LU_decomp(a_copy, P, &s);

gsl_linalg_LU_invert(a_copy, P, inv);

return(*inv);

}

double matrix_determ(gsl_matrix *X)

{

int s;

int n = X->size1;

int m = X->size2;

gsl_matrix *a_copy = gsl_matrix_alloc(m, n);

gsl_matrix_memcpy(a_copy, X );

gsl_permutation *P = gsl_permutation_alloc(n);

gsl_linalg_LU_decomp(a_copy, P, &s);

double my_det = gsl_linalg_LU_det (a_copy, s);

return(my_det);

}

double matrix_trace(gsl_matrix *X){

int i, m;

m = X->size1;

double trace = 0.0;

for(i=0;i<m;i++){

trace += gsl_matrix_get(X,i,i);

}

return(trace);

}

double mv_gamma(double a, double d){

double val = 1.0;

int i;

for(i = 1; i <= d; i++){

val *= gsl_sf_gamma(a - (0.5 * (i - 1)));

}

val *= pow(M_PI, (d * (d - 1) / 4.0));

return(val);

}

void print_matrix(gsl_matrix *X)

{

int i, j;

int n = X->size1;

int m = X->size2;

printf("\n");

for(i=0; i<m; i++){

for(j=0; j<n; j++){

printf("%05.2f ", gsl_matrix_get(X, i, j));

}

printf("\n");

}

}