CAMLprim value ml_gsl_linalg_exponential_ss(value A, value eA, value mode)
{
_DECLARE_MATRIX2(A, eA);
_CONVERT_MATRIX2(A, eA);
gsl_linalg_exponential_ss(&m_A, &m_eA, GSL_MODE_val(mode));
return Val_unit;
}
int
main(void)
{
ESL_STOPWATCH *w = NULL;
ESL_DMATRIX *Q = NULL;
ESL_DMATRIX *P = NULL;
double t = 5.0;
int esl_iterations = 100;
int i;
#ifdef HAVE_LIBGSL
gsl_matrix *Qg = NULL;
gsl_matrix *Pg = NULL;
int gsl_iterations = 100;
#endif
w = esl_stopwatch_Create();
Q = esl_dmatrix_Create(20, 20);
P = esl_dmatrix_Create(20, 20);
esl_rmx_SetWAG(Q, NULL);
esl_stopwatch_Start(w);
for (i = 0; i < esl_iterations; i++)
esl_dmx_Exp(Q, t, P);
esl_stopwatch_Stop(w);
printf("Easel takes: %g sec\n", w->user / (double) esl_iterations);
#ifdef HAVE_LIBGSL
if (esl_dmx_MorphGSL(Q, &Qg) != eslOK) esl_fatal("morph to gsl_matrix failed");
if ((Pg = gsl_matrix_alloc(20, 20)) == NULL) esl_fatal("gsl alloc failed");
gsl_matrix_scale(Qg, t);
esl_stopwatch_Start(w);
for (i = 0; i < gsl_iterations; i++)
gsl_linalg_exponential_ss(Qg, Pg, GSL_PREC_DOUBLE);
esl_stopwatch_Stop(w);
printf(" GSL takes: %g sec\n", w->user / (double) gsl_iterations);
gsl_matrix_free(Qg);
gsl_matrix_free(Pg);
#endif /*HAVE_LIBGSL*/
esl_dmatrix_Destroy(Q);
esl_dmatrix_Destroy(P);
esl_stopwatch_Destroy(w);
return 0;
}
void set_cdf(const Generator& gen, SummedCdf& cdf, GslContext& context)
{
gsl_matrix *A = (gsl_matrix *) context.get_input();
gsl_matrix *B = (gsl_matrix *) context.get_output();
const Stencil& bounds = cdf.bounds();
const int n = context.get_size();
// if (gen.get_size() != 4) throw 1;
// double *test_q = new double[(n-1) * (n-1)];
for (int i=0;i<bounds.N;i++)
{
double t = bounds.unmap(i);
for (int j=0;j<n-1;j++)
for (int k=0;k<n-1;k++)
{
gsl_matrix_set(A, j, k, gen.get_prob(j, k) * t);
// test_q[j * (n-1) + k] = gen.get_prob(j, k) * t;
}
gsl_linalg_exponential_ss(A, B, GSL_PREC_DOUBLE);
double d = 0;
for (int j=0;j<n-1;j++)
d += gsl_matrix_get(B, 0, j);
// std::cout << "x =" << t << std::endl;
// std::cout << "d =" << d << std::endl;
// std::cout << "approximation=" << mat_exp_3_5(test_q) << std::endl;
// std::cout << std::endl;
cdf.set(i, 1-d);
}
// delete test_q;
}
int
main(void)
{
char errbuf[eslERRBUFSIZE];
char *alphabet = "ACDEFGHIKLMNPQRSTVWY";
ESL_DMATRIX *Q = NULL;
ESL_DMATRIX *P = NULL;
gsl_matrix *Qg = NULL;
gsl_matrix *Pg = NULL;
ESL_DMATRIX *Pge = NULL;
double t = 15.0;
if ((Q = esl_dmatrix_Create(20, 20)) == NULL) esl_fatal("malloc failed");
if ((P = esl_dmatrix_Create(20, 20)) == NULL) esl_fatal("malloc failed");
if (esl_rmx_SetWAG(Q, NULL) != eslOK) esl_fatal("_SetWAG() failed");
if (esl_rmx_ValidateQ(Q, 0.0001, errbuf) != eslOK) esl_fatal("Q validation failed: %s", errbuf);
if (esl_dmx_Exp(Q, t, P) != eslOK) esl_fatal("matrix exponentiation failed");
if (esl_rmx_ValidateP(P, 0.0001, errbuf) != eslOK) esl_fatal("P validation failed: %s", errbuf);
if (esl_dmx_MorphGSL(Q, &Qg) != eslOK) esl_fatal("morph to gsl_matrix failed");
if ((Pg = gsl_matrix_alloc(20, 20)) == NULL) esl_fatal("gsl alloc failed");
gsl_matrix_scale(Qg, t);
if (gsl_linalg_exponential_ss(Qg, Pg, GSL_PREC_DOUBLE) != 0) esl_fatal("gsl's exponentiation failed");
if (esl_dmx_UnmorphGSL(Pg, &Pge) != eslOK) esl_fatal("morph from gsl_matrix failed");
esl_dmatrix_Dump(stdout, P, alphabet, alphabet);
if (esl_dmatrix_Compare(Pge, P, 0.00001) != eslOK) esl_fatal("whoops, different answers.");
esl_dmatrix_Destroy(Q);
esl_dmatrix_Destroy(P);
esl_dmatrix_Destroy(Pge);
gsl_matrix_free(Qg);
gsl_matrix_free(Pg);
return 0;
}
gsl_matrix* calc_Hs(double s, double tres, double* Qxx_m, double* Qyy_m, double* Qxy_m, double* Qyx_m, int kx, int ky) {
/*
*
*
* *H(s)
*I=eye(ky);
*expMat=mat_exp(-(s*I-Qyy)*tres);
*Hxx_s=Qxx+(Qxy*(s*I-Qyy)^-1)*(I-expMat)*Qyx;
*
*/
/* Initialise Qxx,Qxy,Qyx,Qyy */
gsl_matrix *Qxx=setup_matrix(Qxx_m,kx,kx);
gsl_matrix *Qxy=setup_matrix(Qxy_m,kx,ky);
gsl_matrix *Qyx=setup_matrix(Qyx_m,ky,kx);
gsl_matrix *Qyy=setup_matrix(Qyy_m,ky,ky);
gsl_matrix *ky_eye; //identitny matrix of dimension ky,ky
gsl_matrix *e_eye; //to hold the matrix exponential expMat
gsl_matrix *detected_tres; //matrix representing period in states y for tres followed by transition to x
gsl_matrix *seye2;
gsl_matrix *inv_sI_Qyy;
gsl_matrix *res;
gsl_matrix *res2;
gsl_matrix *res3;
gsl_matrix *eye3;
//printf("\tAllocate memory for the matrices\n");
//allocate memory for all the matrices
ky_eye=gsl_matrix_alloc(ky,ky);
e_eye=gsl_matrix_alloc(ky,ky);
seye2=gsl_matrix_alloc(ky,ky);
detected_tres=gsl_matrix_alloc(ky,ky);
inv_sI_Qyy=gsl_matrix_alloc(ky,ky);
res=gsl_matrix_alloc(kx,ky);
res2=gsl_matrix_alloc(ky,kx);
res3 = gsl_matrix_alloc(kx,kx);
eye3=gsl_matrix_alloc(ky,ky);
//printf("\tAllocated memory for the matrices\n");
gsl_matrix_set_identity(ky_eye);
//exp(-(s*I-Qyy)*tres)
//build from the identity matrix
gsl_matrix_memcpy (detected_tres,ky_eye);
gsl_matrix_scale(detected_tres,s);
gsl_matrix_sub(detected_tres,Qyy);
gsl_matrix_scale(detected_tres,-1);
gsl_matrix_scale(detected_tres,tres);
gsl_linalg_exponential_ss(detected_tres, e_eye, .01);
//printf("\tCalculated exp(-(s*I-Qyy)*tres)\n");
//(s*I-Qyy)
gsl_matrix_memcpy (seye2,ky_eye);
gsl_matrix_scale(seye2,s);
gsl_matrix_sub(seye2,Qyy);
//printf("\tCalculated s*I-Qyy\n");
//invert s*I-Qyy
int sc;
gsl_permutation * p = gsl_permutation_alloc (ky);
gsl_linalg_LU_decomp(seye2, p, &sc);
gsl_linalg_LU_invert(seye2, p, inv_sI_Qyy);
gsl_permutation_free(p);
//printf("\tInverted s*I-Qyy\n");
/*
for (int i=0; i<ky; i++){
for (int j=0; j<ky; j++){
mexPrintf("\t%f",gsl_matrix_get(inv_sI_Qyy,i,j));
}
mexPrintf("\n");
}
*/
//multiply Qxy * (s*I-Qyy)^-1
gsl_matrix_set_zero(res);
// res = (Qxy*(s*I-Qyy)^-1)
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans,
1.0, Qxy, inv_sI_Qyy,
0.0, res);
//printf("\tCalculated Qxy * (s*I-Qyy)^-1\n");
//res2 =(I-expMat)*Qyx;
gsl_matrix_set_zero(res2);
gsl_matrix_memcpy (eye3,ky_eye);
//printf("\tMemcpy (I-expMat)\n");
gsl_matrix_sub(eye3,e_eye);
//printf("\tSubtract (I-expMat)\n");
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans,
1.0, eye3, Qyx,
0.0, res2);
//res3 = (Qxy*(s*I-Qyy)^-1)*(I-expMat)*Qyx;
//res3 = res *res2
//res3 is the result we want to return
//printf("\t (I-expMat)*Qyx\n");
gsl_matrix_set_zero(res3);
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans,
1.0, res, res2,
0.0, res3);
gsl_matrix_add(res3,Qxx);
/*
for (int i=0; i<kx; i++){
for (int j=0; j<kx; j++){
mexPrintf("\t%f",gsl_matrix_get(res3,i,j));
}
mexPrintf("\n");
}
*/
//printf("\t Calced H(s)\n");
//cleanup
gsl_matrix_free(Qxx);
gsl_matrix_free(Qxy);
gsl_matrix_free(Qyx);
gsl_matrix_free(Qyy);
gsl_matrix_free(ky_eye);
gsl_matrix_free(e_eye);
gsl_matrix_free(detected_tres);
gsl_matrix_free(seye2);
gsl_matrix_free(inv_sI_Qyy);
gsl_matrix_free(res);
gsl_matrix_free(res2);
gsl_matrix_free(eye3);
//printf("\t Cleaned up H(s)\n");
return res3;
}
