void initialize_matrix (MATRIX *m, int rows, int cols) /***************************************************************************** Initializes a MATRIX to dimensions (rows, cols) and content zeros. ******************************************************************************/ { MROWS (*m) = rows; MCOLS (*m) = cols; { int i, j; for (i = 0; i < MROWS (*m); i++) for (j = 0; j < MCOLS (*m); j++) MDATA (*m, i, j) = 0; } }
int M_MatrixResize_SP(void *pA, Uint m, Uint n) { M_MatrixSP *A=pA; MROWS(A) = m; MCOLS(A) = n; /* no resizing of sparse matrices */ return 0; }
int inverse_matrix (MATRIX const *m, MATRIX *n) /***************************************************************************** ******************************************************************************/ { if (!M_SQUARE (*m)) { printf ("ERROR (inverse_matrix): MATRIX must be square!\n"); print_matrix ("MATRIX:", m); n->cols=0; n->rows=0; return -1; } else { float det; int res; res = determinant (m,&det); if (res == -1) { printf ("ERROR (inverse_matrix): singular MATRIX!\n"); print_matrix ("MATRIX:", m); return -1; } else { initialize_matrix (n, MROWS (*m), MCOLS (*m)); if (MROWS (*m) == 1) { MDATA (*n, 0, 0) = 1 / det ; } else if (MROWS (*m) == 2) { MDATA (*n, 0, 0) = MDATA (*m, 1, 1) / det ; MDATA (*n, 0, 1) = -MDATA (*m, 0, 1) / det ; MDATA (*n, 1, 0) = -MDATA (*m, 1, 0) / det ; MDATA (*n, 1, 1) = MDATA (*m, 0, 0) / det ; } else { MDATA (*n, 0, 0) = cross_product (m, 1, 1, 2, 2) / det ; MDATA (*n, 0, 1) = -cross_product (m, 0, 1, 2, 2) / det ; MDATA (*n, 0, 2) = cross_product (m, 0, 1, 1, 2) / det ; MDATA (*n, 1, 0) = -cross_product (m, 1, 0, 2, 2) / det ; MDATA (*n, 1, 1) = cross_product (m, 0, 0, 2, 2) / det ; MDATA (*n, 1, 2) = -cross_product (m, 0, 0, 1, 2) / det ; MDATA (*n, 2, 0) = cross_product (m, 1, 0, 2, 1) / det ; MDATA (*n, 2, 1) = -cross_product (m, 0, 0, 2, 1) / det ; MDATA (*n, 2, 2) = cross_product (m, 0, 0, 1, 1) / det ; } } } return 1; }
void print_matrix (char *message, MATRIX const *m) /***************************************************************************** Print to stdout the contents of MATRIX m. ******************************************************************************/ { int i, j; printf ("%s\n",message); printf("%d %d \n",MROWS (*m),MCOLS (*m)); if ((MROWS (*m) <= MAX_ROWS) && (MCOLS (*m) <= MAX_COLS)) for (i = 0; i < MROWS (*m); i++) { for (j = 0; j < MCOLS (*m); j++) printf ("%10.5f ", MDATA (*m, i, j)); printf ("\n"); } else printf ("Dimension incorrecta!"); printf ("\n"); }
MATRIX create_matrix (int rows, int cols) /***************************************************************************** Creates a MATRIX of dimensions (rows, cols) and initializaes it to zeros. ******************************************************************************/ { MATRIX m; MROWS (m) = rows; MCOLS (m) = cols; { int i, j; for (i = 0; i < MROWS (m); i++) for (j = 0; j < MCOLS (m); j++) MDATA (m, i, j) = 0; } return m; }
void * M_MatrixNew_SP(Uint m, Uint n) { M_MatrixSP *A; int error; A = Malloc(sizeof(M_MatrixSP)); MMATRIX(A)->ops = &mMatOps_SP; A->d = spCreate(0, 0, &error); MROWS(A) = m; MCOLS(A) = n; return (A); }
/** * Computes the Lomb-Scargle periodogram of the matrix "data". "data" should contain at least three * columns: time, measurement and measurement error. The periodogram is calculated in "samples" intervals * between "Pmin" and "Pmax", spaced logarithmically. * * The function returns a matrix of "samples" rows and several columns, including period, power (z) and * an estimation of the upper bound for the false alarm probability. The estimation is calculated using * the method of Baluev, 2008 (Baluev08). The column PS_Z_LS contains the unnormalized LS periodogram * (z = 1/2 * (Chi^2_0 - Chi^2_SC)), while the column PS_Z contains z_1 = 1/2 * N_H * z / Chi^2_0 (z_1 in Baluev08). * The FAP upper bound is estimated as ~ tau(z_1). (Another estimate of the FAP can be calculated by * estimating the indep. frequencies through your own algorithm, or using the ok_periodogram_boot routine.) * * @param data Input data containing the data; each row containing (t_i, x_i, sigma_i) * @param samples Number of frequencies sampled * @param Pmin Minimum period sampled * @param Pmax Maximum period sampled * @param method Method to compute periodogram (ignored) * @param timecol Time column (e.g. 0) in the matrix data * @param valcol Value column (e.g. 1) in the matrix data * @param sigmacol Sigma column (e.g. 2) in the matrix data * @param p If not NULL, it is used to return additional info for the periodogram and reuse matrices to save space/speed. If you pass * a value different than NULL, you are responsible for deallocating the workspace and its fields. p->buf is an array of * gsl_matrix*, sized the same as the value of omp_get_max_threads(). * @return A matrix containing: {PS_TIME, PS_Z, PS_FAP, PS_Z_LS} (period, power, FAP upper limit, unnormalized * LS power). You are responsible for deallocating it. */ gsl_matrix* ok_periodogram_ls(const gsl_matrix* data, const unsigned int samples, const double Pmin, const double Pmax, const int method, unsigned int timecol, unsigned int valcol, unsigned int sigcol, ok_periodogram_workspace* p) { gsl_matrix* ret = NULL; gsl_matrix* buf = NULL; gsl_vector* bufv = gsl_vector_alloc(data->size1); int ndata = data->size1; // If no pre-allocated buffers are passed through p, or p is null, // allocate those buffers. if (p != NULL) { if (p->per != NULL && MROWS(p->per) == samples && MCOLS(p->per) == PS_SIZE) ret = p->per; if (p->buf != NULL && MROWS(p->buf) == ndata && MCOLS(p->per) == 5) ret = p->buf; } ret = (ret != NULL ? ret : gsl_matrix_alloc(samples, PS_SIZE)); buf = (buf != NULL ? buf : gsl_matrix_alloc(ndata, 5)); double fmin = 1. / Pmax; double fmax = 1. / Pmin; double df = (fmax - fmin) / (double) samples; gsl_matrix_get_col(bufv, data, timecol); double W = 2. * M_PI * gsl_stats_sd(bufv->data, 1, ndata) / Pmin; gsl_matrix_get_col(bufv, data, valcol); double avg = gsl_stats_mean(bufv->data, 1, ndata); double z1_max = 0.; double xa[ndata]; // pre-calculate cdf, sdf for (int i = 0; i < ndata; i++) { double t = MGET(data, i, timecol) - MGET(data, 0, timecol); MSET(buf, i, BUF_CDF, cos(2 * M_PI * df * t)); MSET(buf, i, BUF_SDF, sin(2 * M_PI * df * t)); MSET(buf, i, BUF_C, cos(2 * M_PI * fmin * t)); MSET(buf, i, BUF_S, sin(2 * M_PI * fmin * t)); MSET(buf, i, BUF_SIG, 1. / (MGET(data, i, sigcol) * MGET(data, i, sigcol))); xa[i] = MGET(data, i, valcol) - avg; } // Calculate periodogram by looping over all angular frequencies for (int i = 0; i < samples; i++) { // Current frequency double f = fmin + df * i; double w = 2 * M_PI*f; // Calculate tau(w) double s_2wt = 0.; double c_2wt = 0.; for (int j = 0; j < ndata; j++) { double cos_wt = C(j); double sin_wt = S(j); c_2wt += (1. - 2. * sin_wt * sin_wt) * SIG(j); s_2wt += (2. * sin_wt * cos_wt) * SIG(j); } double tau = atan2(s_2wt, c_2wt) / (2. * w); double numa = 0.; double numb = 0.; double dena = 0.; double denb = 0.; double numa_w = 0.; double numb_w = 0.; double dena_w = 0.; double denb_w = 0.; double coswtau = cos(w * tau); double sinwtau = sin(w * tau); double chi2_h = 0.; double chi2_h_w = 0; for (int j = 0; j < ndata; j++) { double sig = SIG(j); const double cos_wt = C(j); const double sin_wt = S(j); double cos_wdf = CDF(j); double sin_wdf = SDF(j); double c = cos_wt * coswtau + sin_wt * sinwtau; double s = sin_wt * coswtau - cos_wt * sinwtau; double x = xa[j]; MSET(buf, j, BUF_C, cos_wt * cos_wdf - sin_wt * sin_wdf); MSET(buf, j, BUF_S, sin_wt * cos_wdf + cos_wt * sin_wdf); numa += x * c * sig; numb += x * s * sig; dena += c * c * sig; denb += s * s * sig; chi2_h += x * x * sig; numa_w += c; numb_w += s; dena_w += c*c; denb_w += s*s; chi2_h_w += 1; } double z = 0.5 * (numa * numa / dena + numb * numb / denb); double z_1 = z * ndata / chi2_h; double w_1 = 0.5 * (numa_w * numa_w / dena_w + numb_w * numb_w / denb_w) * ndata / chi2_h_w; double fap_single = pow(1. - 2. * z_1 / (double) ndata, 0.5 * (double) (ndata - 3.)); double tau_z = W * fap_single * sqrt(z_1); MSET(ret, samples - i - 1, PS_TIME, 1. / f); MSET(ret, samples - i - 1, PS_Z, z_1); MSET(ret, samples - i - 1, PS_Z_LS, z); MSET(ret, samples - i - 1, PS_FAP, MIN(fap_single + tau_z, 1.)); MSET(ret, samples - i - 1, PS_TAU, tau); MSET(ret, samples - i - 1, PS_WIN, w_1); z1_max = MAX(z1_max, z_1); } if (p != NULL && p->calc_z_fap) { gsl_root_fsolver * s = gsl_root_fsolver_alloc(gsl_root_fsolver_brent); double pars[3]; pars[0] = ndata; pars[1] = W; pars[2] = 0.; gsl_function F; F.function = _baluev_tau; F.params = pars; double zz = z1_max; while (_baluev_tau(zz, pars) > 1e-3) zz *= 2; p->z_fap_3 = _find_z(s, &F, 1e-3, 0.1, zz); p->z_fap_2 = _find_z(s, &F, 1e-2, 0.1, p->z_fap_3); p->z_fap_1 = _find_z(s, &F, 1e-1, 0.1, p->z_fap_2); gsl_root_fsolver_free(s); p->calc_z_fap = false; } if (p == NULL) { gsl_matrix_free(buf); } else { p->per = ret; p->buf = buf; p->zmax = z1_max; }; gsl_vector_free(bufv); return ret; }