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-rw-r--r--libs/qm-dsp/hmm/hmm.c837
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diff --git a/libs/qm-dsp/hmm/hmm.c b/libs/qm-dsp/hmm/hmm.c
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index fbe202613d..0000000000
--- a/libs/qm-dsp/hmm/hmm.c
+++ /dev/null
@@ -1,837 +0,0 @@
-/*
- * hmm.c
- *
- * Created by Mark Levy on 12/02/2006.
- * Copyright 2006 Centre for Digital Music, Queen Mary, University of London.
-
- This program is free software; you can redistribute it and/or
- modify it under the terms of the GNU General Public License as
- published by the Free Software Foundation; either version 2 of the
- License, or (at your option) any later version. See the file
- COPYING included with this distribution for more information.
- *
- */
-
-#include <stdio.h>
-#include <math.h>
-#include <stdlib.h>
-#include <float.h>
-#include <time.h> /* to seed random number generator */
-
-#include <clapack.h> /* LAPACK for matrix inversion */
-
-#include "maths/nan-inf.h"
-
-#ifdef ATLAS_ORDER
-#define HAVE_ATLAS 1
-#endif
-
-#ifdef HAVE_ATLAS
-// Using ATLAS C interface to LAPACK
-#define dgetrf_(m, n, a, lda, ipiv, info) \
- clapack_dgetrf(CblasColMajor, *m, *n, a, *lda, ipiv)
-#define dgetri_(n, a, lda, ipiv, work, lwork, info) \
- clapack_dgetri(CblasColMajor, *n, a, *lda, ipiv)
-#endif
-
-#ifdef _MAC_OS_X
-#include <vecLib/cblas.h>
-#else
-#include <cblas.h> /* BLAS for matrix multiplication */
-#endif
-
-#include "hmm.h"
-
-model_t* hmm_init(double** x, int T, int L, int N)
-{
- int i, j, d, e, t;
- double s, ss;
-
- model_t* model;
- model = (model_t*) malloc(sizeof(model_t));
- model->N = N;
- model->L = L;
- model->p0 = (double*) malloc(N*sizeof(double));
- model->a = (double**) malloc(N*sizeof(double*));
- model->mu = (double**) malloc(N*sizeof(double*));
- for (i = 0; i < N; i++)
- {
- model->a[i] = (double*) malloc(N*sizeof(double));
- model->mu[i] = (double*) malloc(L*sizeof(double));
- }
- model->cov = (double**) malloc(L*sizeof(double*));
- for (i = 0; i < L; i++)
- model->cov[i] = (double*) malloc(L*sizeof(double));
-
- srand(time(0));
- double* global_mean = (double*) malloc(L*sizeof(double));
-
- /* find global mean */
- for (d = 0; d < L; d++)
- {
- global_mean[d] = 0;
- for (t = 0; t < T; t++)
- global_mean[d] += x[t][d];
- global_mean[d] /= T;
- }
-
- /* calculate global diagonal covariance */
- for (d = 0; d < L; d++)
- {
- for (e = 0; e < L; e++)
- model->cov[d][e] = 0;
- for (t = 0; t < T; t++)
- model->cov[d][d] += (x[t][d] - global_mean[d]) * (x[t][d] - global_mean[d]);
- model->cov[d][d] /= T-1;
- }
-
- /* set all means close to global mean */
- for (i = 0; i < N; i++)
- {
- for (d = 0; d < L; d++)
- {
- /* add some random noise related to covariance */
- /* ideally the random number would be Gaussian(0,1), as a hack we make it uniform on [-0.25,0.25] */
- model->mu[i][d] = global_mean[d] + (0.5 * rand() / (double) RAND_MAX - 0.25) * sqrt(model->cov[d][d]);
- }
- }
-
- /* random intial and transition probs */
- s = 0;
- for (i = 0; i < N; i++)
- {
- model->p0[i] = 1 + rand() / (double) RAND_MAX;
- s += model->p0[i];
- ss = 0;
- for (j = 0; j < N; j++)
- {
- model->a[i][j] = 1 + rand() / (double) RAND_MAX;
- ss += model->a[i][j];
- }
- for (j = 0; j < N; j++)
- {
- model->a[i][j] /= ss;
- }
- }
- for (i = 0; i < N; i++)
- model->p0[i] /= s;
-
- free(global_mean);
-
- return model;
-}
-
-void hmm_close(model_t* model)
-{
- int i;
-
- for (i = 0; i < model->N; i++)
- {
- free(model->a[i]);
- free(model->mu[i]);
- }
- free(model->a);
- free(model->mu);
- for (i = 0; i < model->L; i++)
- free(model->cov[i]);
- free(model->cov);
- free(model);
-}
-
-void hmm_train(double** x, int T, model_t* model)
-{
- int i, t;
- double loglik; /* overall log-likelihood at each iteration */
-
- int N = model->N;
- int L = model->L;
- double* p0 = model->p0;
- double** a = model->a;
- double** mu = model->mu;
- double** cov = model->cov;
-
- /* allocate memory */
- double** gamma = (double**) malloc(T*sizeof(double*));
- double*** xi = (double***) malloc(T*sizeof(double**));
- for (t = 0; t < T; t++)
- {
- gamma[t] = (double*) malloc(N*sizeof(double));
- xi[t] = (double**) malloc(N*sizeof(double*));
- for (i = 0; i < N; i++)
- xi[t][i] = (double*) malloc(N*sizeof(double));
- }
-
- /* temporary memory */
- double* gauss_y = (double*) malloc(L*sizeof(double));
- double* gauss_z = (double*) malloc(L*sizeof(double));
-
- /* obs probs P(j|{x}) */
- double** b = (double**) malloc(T*sizeof(double*));
- for (t = 0; t < T; t++)
- b[t] = (double*) malloc(N*sizeof(double));
-
- /* inverse covariance and its determinant */
- double** icov = (double**) malloc(L*sizeof(double*));
- for (i = 0; i < L; i++)
- icov[i] = (double*) malloc(L*sizeof(double));
- double detcov;
-
- double thresh = 0.0001;
- int niter = 50;
- int iter = 0;
- double loglik1, loglik2;
- int foundnan = 0;
-
- while (iter < niter && !foundnan && !(iter > 1 && (loglik - loglik1) < thresh * (loglik1 - loglik2)))
- {
- ++iter;
-/*
- fprintf(stderr, "calculating obsprobs...\n");
- fflush(stderr);
-*/
- /* precalculate obs probs */
- invert(cov, L, icov, &detcov);
-
- for (t = 0; t < T; t++)
- {
- //int allzero = 1;
- for (i = 0; i < N; i++)
- {
- b[t][i] = exp(loggauss(x[t], L, mu[i], icov, detcov, gauss_y, gauss_z));
-
- //if (b[t][i] != 0)
- // allzero = 0;
- }
- /*
- if (allzero)
- {
- printf("all the b[t][i] were zero for t = %d, correcting...\n", t);
- for (i = 0; i < N; i++)
- {
- b[t][i] = 0.00001;
- }
- }
- */
- }
-/*
- fprintf(stderr, "forwards-backwards...\n");
- fflush(stderr);
-*/
- forward_backwards(xi, gamma, &loglik, &loglik1, &loglik2, iter, N, T, p0, a, b);
-/*
- fprintf(stderr, "iteration %d: loglik = %f\n", iter, loglik);
- fprintf(stderr, "re-estimation...\n");
- fflush(stderr);
-*/
- if (ISNAN(loglik)) {
- foundnan = 1;
- continue;
- }
-
- baum_welch(p0, a, mu, cov, N, T, L, x, xi, gamma);
-
- /*
- printf("a:\n");
- for (i = 0; i < model->N; i++)
- {
- for (j = 0; j < model->N; j++)
- printf("%f ", model->a[i][j]);
- printf("\n");
- }
- printf("\n\n");
- */
- //hmm_print(model);
- }
-
- /* deallocate memory */
- for (t = 0; t < T; t++)
- {
- free(gamma[t]);
- free(b[t]);
- for (i = 0; i < N; i++)
- free(xi[t][i]);
- free(xi[t]);
- }
- free(gamma);
- free(xi);
- free(b);
-
- for (i = 0; i < L; i++)
- free(icov[i]);
- free(icov);
-
- free(gauss_y);
- free(gauss_z);
-}
-
-void mlss_reestimate(double* p0, double** a, double** mu, double** cov, int N, int T, int L, int* q, double** x)
-{
- /* fit a single Gaussian to observations in each state */
-
- /* calculate the mean observation in each state */
-
- /* calculate the overall covariance */
-
- /* count transitions */
-
- /* estimate initial probs from transitions (???) */
-}
-
-void baum_welch(double* p0, double** a, double** mu, double** cov, int N, int T, int L, double** x, double*** xi, double** gamma)
-{
- int i, j, t;
-
- double* sum_gamma = (double*) malloc(N*sizeof(double));
-
- /* temporary memory */
- double* u = (double*) malloc(L*L*sizeof(double));
- double* yy = (double*) malloc(T*L*sizeof(double));
- double* yy2 = (double*) malloc(T*L*sizeof(double));
-
- /* re-estimate transition probs */
- for (i = 0; i < N; i++)
- {
- sum_gamma[i] = 0;
- for (t = 0; t < T-1; t++)
- sum_gamma[i] += gamma[t][i];
- }
-
- for (i = 0; i < N; i++)
- {
- if (sum_gamma[i] == 0)
- {
-/* fprintf(stderr, "sum_gamma[%d] was zero...\n", i); */
- }
- //double s = 0;
- for (j = 0; j < N; j++)
- {
- a[i][j] = 0;
- if (sum_gamma[i] == 0.) continue;
- for (t = 0; t < T-1; t++)
- a[i][j] += xi[t][i][j];
- //s += a[i][j];
- a[i][j] /= sum_gamma[i];
- }
- /*
- for (j = 0; j < N; j++)
- {
- a[i][j] /= s;
- }
- */
- }
-
- /* NB: now we need to sum gamma over all t */
- for (i = 0; i < N; i++)
- sum_gamma[i] += gamma[T-1][i];
-
- /* re-estimate initial probs */
- for (i = 0; i < N; i++)
- p0[i] = gamma[0][i];
-
- /* re-estimate covariance */
- int d, e;
- double sum_sum_gamma = 0;
- for (i = 0; i < N; i++)
- sum_sum_gamma += sum_gamma[i];
-
- /*
- for (d = 0; d < L; d++)
- {
- for (e = d; e < L; e++)
- {
- cov[d][e] = 0;
- for (t = 0; t < T; t++)
- for (j = 0; j < N; j++)
- cov[d][e] += gamma[t][j] * (x[t][d] - mu[j][d]) * (x[t][e] - mu[j][e]);
-
- cov[d][e] /= sum_sum_gamma;
-
- if (ISNAN(cov[d][e]))
- {
- printf("cov[%d][%d] was nan\n", d, e);
- for (j = 0; j < N; j++)
- for (i = 0; i < L; i++)
- if (ISNAN(mu[j][i]))
- printf("mu[%d][%d] was nan\n", j, i);
- for (t = 0; t < T; t++)
- for (j = 0; j < N; j++)
- if (ISNAN(gamma[t][j]))
- printf("gamma[%d][%d] was nan\n", t, j);
- exit(-1);
- }
- }
- }
- for (d = 0; d < L; d++)
- for (e = 0; e < d; e++)
- cov[d][e] = cov[e][d];
- */
-
- /* using BLAS */
- for (d = 0; d < L; d++)
- for (e = 0; e < L; e++)
- cov[d][e] = 0;
-
- for (j = 0; j < N; j++)
- {
- for (d = 0; d < L; d++)
- for (t = 0; t < T; t++)
- {
- yy[d*T+t] = x[t][d] - mu[j][d];
- yy2[d*T+t] = gamma[t][j] * (x[t][d] - mu[j][d]);
- }
-
- cblas_dgemm(CblasColMajor, CblasTrans, CblasNoTrans, L, L, T, 1.0, yy, T, yy2, T, 0, u, L);
-
- for (e = 0; e < L; e++)
- for (d = 0; d < L; d++)
- cov[d][e] += u[e*L+d];
- }
-
- for (d = 0; d < L; d++)
- for (e = 0; e < L; e++)
- cov[d][e] /= T; /* sum_sum_gamma; */
-
- //printf("sum_sum_gamma = %f\n", sum_sum_gamma); /* fine, = T IS THIS ALWAYS TRUE with pooled cov?? */
-
- /* re-estimate means */
- for (j = 0; j < N; j++)
- {
- for (d = 0; d < L; d++)
- {
- mu[j][d] = 0;
- for (t = 0; t < T; t++)
- mu[j][d] += gamma[t][j] * x[t][d];
- mu[j][d] /= sum_gamma[j];
- }
- }
-
- /* deallocate memory */
- free(sum_gamma);
- free(yy);
- free(yy2);
- free(u);
-}
-
-void forward_backwards(double*** xi, double** gamma, double* loglik, double* loglik1, double* loglik2, int iter, int N, int T, double* p0, double** a, double** b)
-{
- /* forwards-backwards with scaling */
- int i, j, t;
-
- double** alpha = (double**) malloc(T*sizeof(double*));
- double** beta = (double**) malloc(T*sizeof(double*));
- for (t = 0; t < T; t++)
- {
- alpha[t] = (double*) malloc(N*sizeof(double));
- beta[t] = (double*) malloc(N*sizeof(double));
- }
-
- /* scaling coefficients */
- double* c = (double*) malloc(T*sizeof(double));
-
- /* calculate forward probs and scale coefficients */
- c[0] = 0;
- for (i = 0; i < N; i++)
- {
- alpha[0][i] = p0[i] * b[0][i];
- c[0] += alpha[0][i];
-
- //printf("p0[%d] = %f, b[0][%d] = %f\n", i, p0[i], i, b[0][i]);
- }
- c[0] = 1 / c[0];
- for (i = 0; i < N; i++)
- {
- alpha[0][i] *= c[0];
-
- //printf("alpha[0][%d] = %f\n", i, alpha[0][i]); /* OK agrees with Matlab */
- }
-
- *loglik1 = *loglik;
- *loglik = -log(c[0]);
- if (iter == 2)
- *loglik2 = *loglik;
-
- for (t = 1; t < T; t++)
- {
- c[t] = 0;
- for (j = 0; j < N; j++)
- {
- alpha[t][j] = 0;
- for (i = 0; i < N; i++)
- alpha[t][j] += alpha[t-1][i] * a[i][j];
- alpha[t][j] *= b[t][j];
-
- c[t] += alpha[t][j];
- }
-
- /*
- if (c[t] == 0)
- {
- printf("c[%d] = 0, going to blow up so exiting\n", t);
- for (i = 0; i < N; i++)
- if (b[t][i] == 0)
- fprintf(stderr, "b[%d][%d] was zero\n", t, i);
- fprintf(stderr, "x[t] was \n");
- for (i = 0; i < L; i++)
- fprintf(stderr, "%f ", x[t][i]);
- fprintf(stderr, "\n\n");
- exit(-1);
- }
- */
-
- c[t] = 1 / c[t];
- for (j = 0; j < N; j++)
- alpha[t][j] *= c[t];
-
- //printf("c[%d] = %e\n", t, c[t]);
-
- *loglik -= log(c[t]);
- }
-
- /* calculate backwards probs using same coefficients */
- for (i = 0; i < N; i++)
- beta[T-1][i] = 1;
- t = T - 1;
- while (1)
- {
- for (i = 0; i < N; i++)
- beta[t][i] *= c[t];
-
- if (t == 0)
- break;
-
- for (i = 0; i < N; i++)
- {
- beta[t-1][i] = 0;
- for (j = 0; j < N; j++)
- beta[t-1][i] += a[i][j] * b[t][j] * beta[t][j];
- }
-
- t--;
- }
-
- /*
- printf("alpha:\n");
- for (t = 0; t < T; t++)
- {
- for (i = 0; i < N; i++)
- printf("%4.4e\t\t", alpha[t][i]);
- printf("\n");
- }
- printf("\n\n");printf("beta:\n");
- for (t = 0; t < T; t++)
- {
- for (i = 0; i < N; i++)
- printf("%4.4e\t\t", beta[t][i]);
- printf("\n");
- }
- printf("\n\n");
- */
-
- /* calculate posterior probs */
- double tot;
- for (t = 0; t < T; t++)
- {
- tot = 0;
- for (i = 0; i < N; i++)
- {
- gamma[t][i] = alpha[t][i] * beta[t][i];
- tot += gamma[t][i];
- }
- for (i = 0; i < N; i++)
- {
- gamma[t][i] /= tot;
-
- //printf("gamma[%d][%d] = %f\n", t, i, gamma[t][i]);
- }
- }
-
- for (t = 0; t < T-1; t++)
- {
- tot = 0;
- for (i = 0; i < N; i++)
- {
- for (j = 0; j < N; j++)
- {
- xi[t][i][j] = alpha[t][i] * a[i][j] * b[t+1][j] * beta[t+1][j];
- tot += xi[t][i][j];
- }
- }
- for (i = 0; i < N; i++)
- for (j = 0; j < N; j++)
- xi[t][i][j] /= tot;
- }
-
- /*
- // CHECK - fine
- // gamma[t][i] = \sum_j{xi[t][i][j]}
- tot = 0;
- for (j = 0; j < N; j++)
- tot += xi[3][1][j];
- printf("gamma[3][1] = %f, sum_j(xi[3][1][j]) = %f\n", gamma[3][1], tot);
- */
-
- for (t = 0; t < T; t++)
- {
- free(alpha[t]);
- free(beta[t]);
- }
- free(alpha);
- free(beta);
- free(c);
-}
-
-void viterbi_decode(double** x, int T, model_t* model, int* q)
-{
- int i, j, t;
- double max;
- int havemax;
-
- int N = model->N;
- int L = model->L;
- double* p0 = model->p0;
- double** a = model->a;
- double** mu = model->mu;
- double** cov = model->cov;
-
- /* inverse covariance and its determinant */
- double** icov = (double**) malloc(L*sizeof(double*));
- for (i = 0; i < L; i++)
- icov[i] = (double*) malloc(L*sizeof(double));
- double detcov;
-
- double** logb = (double**) malloc(T*sizeof(double*));
- double** phi = (double**) malloc(T*sizeof(double*));
- int** psi = (int**) malloc(T*sizeof(int*));
- for (t = 0; t < T; t++)
- {
- logb[t] = (double*) malloc(N*sizeof(double));
- phi[t] = (double*) malloc(N*sizeof(double));
- psi[t] = (int*) malloc(N*sizeof(int));
- }
-
- /* temporary memory */
- double* gauss_y = (double*) malloc(L*sizeof(double));
- double* gauss_z = (double*) malloc(L*sizeof(double));
-
- /* calculate observation logprobs */
- invert(cov, L, icov, &detcov);
- for (t = 0; t < T; t++)
- for (i = 0; i < N; i++)
- logb[t][i] = loggauss(x[t], L, mu[i], icov, detcov, gauss_y, gauss_z);
-
- /* initialise */
- for (i = 0; i < N; i++)
- {
- phi[0][i] = log(p0[i]) + logb[0][i];
- psi[0][i] = 0;
- }
-
- for (t = 1; t < T; t++)
- {
- for (j = 0; j < N; j++)
- {
- max = -1000000;
- havemax = 0;
-
- psi[t][j] = 0;
- for (i = 0; i < N; i++)
- {
- if (phi[t-1][i] + log(a[i][j]) > max || !havemax)
- {
- max = phi[t-1][i] + log(a[i][j]);
- phi[t][j] = max + logb[t][j];
- psi[t][j] = i;
- havemax = 1;
- }
- }
- }
- }
-
- /* find maximising state at time T-1 */
- max = phi[T-1][0];
- q[T-1] = 0;
- for (i = 1; i < N; i++)
- {
- if (phi[T-1][i] > max)
- {
- max = phi[T-1][i];
- q[T-1] = i;
- }
- }
-
-
- /* track back */
- t = T - 2;
- while (t >= 0)
- {
- q[t] = psi[t+1][q[t+1]];
- t--;
- }
-
- /* de-allocate memory */
- for (i = 0; i < L; i++)
- free(icov[i]);
- free(icov);
- for (t = 0; t < T; t++)
- {
- free(logb[t]);
- free(phi[t]);
- free(psi[t]);
- }
- free(logb);
- free(phi);
- free(psi);
-
- free(gauss_y);
- free(gauss_z);
-}
-
-/* invert matrix and calculate determinant using LAPACK */
-void invert(double** cov, int L, double** icov, double* detcov)
-{
- /* copy square matrix into a vector in column-major order */
- double* a = (double*) malloc(L*L*sizeof(double));
- int i, j;
- for(j=0; j < L; j++)
- for (i=0; i < L; i++)
- a[j*L+i] = cov[i][j];
-
- int M = (int) L;
- int* ipiv = (int *) malloc(L*L*sizeof(int));
- int ret;
-
- /* LU decomposition */
- ret = dgetrf_(&M, &M, a, &M, ipiv, &ret); /* ret should be zero, negative if cov is singular */
- if (ret < 0)
- {
- fprintf(stderr, "Covariance matrix was singular, couldn't invert\n");
- exit(-1);
- }
-
- /* find determinant */
- double det = 1;
- for(i = 0; i < L; i++)
- det *= a[i*L+i];
- // TODO: get this to work!!! If detcov < 0 then cov is bad anyway...
- /*
- int sign = 1;
- for (i = 0; i < L; i++)
- if (ipiv[i] != i)
- sign = -sign;
- det *= sign;
- */
- if (det < 0)
- det = -det;
- *detcov = det;
-
- /* allocate required working storage */
-#ifndef HAVE_ATLAS
- int lwork = -1;
- double lwbest = 0.0;
- dgetri_(&M, a, &M, ipiv, &lwbest, &lwork, &ret);
- lwork = (int) lwbest;
- double* work = (double*) malloc(lwork*sizeof(double));
-#endif
-
- /* find inverse */
- dgetri_(&M, a, &M, ipiv, work, &lwork, &ret);
-
- for(j=0; j < L; j++)
- for (i=0; i < L; i++)
- icov[i][j] = a[j*L+i];
-
-#ifndef HAVE_ATLAS
- free(work);
-#endif
- free(a);
-}
-
-/* probability of multivariate Gaussian given mean, inverse and determinant of covariance */
-double gauss(double* x, int L, double* mu, double** icov, double detcov, double* y, double* z)
-{
- int i, j;
- double s = 0;
- for (i = 0; i < L; i++)
- y[i] = x[i] - mu[i];
- for (i = 0; i < L; i++)
- {
- //z[i] = 0;
- //for (j = 0; j < L; j++)
- // z[i] += icov[i][j] * y[j];
- z[i] = cblas_ddot(L, &icov[i][0], 1, y, 1);
- }
- s = cblas_ddot(L, z, 1, y, 1);
- //for (i = 0; i < L; i++)
- // s += z[i] * y[i];
-
- return exp(-s/2.0) / (pow(2*PI, L/2.0) * sqrt(detcov));
-}
-
-/* log probability of multivariate Gaussian given mean, inverse and determinant of covariance */
-double loggauss(double* x, int L, double* mu, double** icov, double detcov, double* y, double* z)
-{
- int i, j;
- double s = 0;
- double ret;
- for (i = 0; i < L; i++)
- y[i] = x[i] - mu[i];
- for (i = 0; i < L; i++)
- {
- //z[i] = 0;
- //for (j = 0; j < L; j++)
- // z[i] += icov[i][j] * y[j];
- z[i] = cblas_ddot(L, &icov[i][0], 1, y, 1);
- }
- s = cblas_ddot(L, z, 1, y, 1);
- //for (i = 0; i < L; i++)
- // s += z[i] * y[i];
-
- ret = -0.5 * (s + L * log(2*PI) + log(detcov));
-
- /*
- // TEST
- if (ISINF(ret) > 0)
- printf("loggauss returning infinity\n");
- if (ISINF(ret) < 0)
- printf("loggauss returning -infinity\n");
- if (ISNAN(ret))
- printf("loggauss returning nan\n");
- */
-
- return ret;
-}
-
-void hmm_print(model_t* model)
-{
- int i, j;
- printf("p0:\n");
- for (i = 0; i < model->N; i++)
- printf("%f ", model->p0[i]);
- printf("\n\n");
- printf("a:\n");
- for (i = 0; i < model->N; i++)
- {
- for (j = 0; j < model->N; j++)
- printf("%f ", model->a[i][j]);
- printf("\n");
- }
- printf("\n\n");
- printf("mu:\n");
- for (i = 0; i < model->N; i++)
- {
- for (j = 0; j < model->L; j++)
- printf("%f ", model->mu[i][j]);
- printf("\n");
- }
- printf("\n\n");
- printf("cov:\n");
- for (i = 0; i < model->L; i++)
- {
- for (j = 0; j < model->L; j++)
- printf("%f ", model->cov[i][j]);
- printf("\n");
- }
- printf("\n\n");
-}
-
-
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