diff options
Diffstat (limited to 'converter/other/fiasco/codec/approx.c')
| -rw-r--r-- | converter/other/fiasco/codec/approx.c | 563 |
1 files changed, 285 insertions, 278 deletions
diff --git a/converter/other/fiasco/codec/approx.c b/converter/other/fiasco/codec/approx.c index d47bac62..d8fefcaa 100644 --- a/converter/other/fiasco/codec/approx.c +++ b/converter/other/fiasco/codec/approx.c @@ -294,9 +294,9 @@ static bool_t used [MAXSTATES]; static void matching_pursuit (mp_t *mp, bool_t full_search, real_t price, - unsigned max_edges, int y_state, const range_t *range, - const domain_pool_t *domain_pool, const coeff_t *coeff, - const wfa_t *wfa, const coding_t *c) + unsigned max_edges, int y_state, const range_t *range, + const domain_pool_t *domain_pool, const coeff_t *coeff, + const wfa_t *wfa, const coding_t *c) /* * Find an approximation of the current 'range' with a linear * combination of vectors of the 'domain_pool'. The linear @@ -320,303 +320,310 @@ matching_pursuit (mp_t *mp, bool_t full_search, real_t price, * vectors, factors, rate, distortion and costs are stored in 'mp' */ { - unsigned n; /* current vector of the OB */ - int index; /* best fitting domain image */ - unsigned domain; /* counter */ - real_t norm; /* norm of range image */ - real_t additional_bits; /* bits for mc, nd, and tree */ - word_t *domain_blocks; /* current set of domain images */ - const real_t min_norm = 2e-3; /* lower bound of norm */ - unsigned best_n = 0; - unsigned size = size_of_level (range->level); + unsigned n; /* current vector of the OB */ + int index; /* best fitting domain image */ + unsigned domain; /* counter */ + real_t norm; /* norm of range image */ + real_t additional_bits; /* bits for mc, nd, and tree */ + word_t *domain_blocks; /* current set of domain images */ + const real_t min_norm = 2e-3; /* lower bound of norm */ + unsigned best_n = 0; + unsigned size = size_of_level (range->level); - /* - * Initialize domain pool and inner product arrays - */ - domain_blocks = domain_pool->generate (range->level, y_state, wfa, - domain_pool->model); - for (domain = 0; domain_blocks [domain] >= 0; domain++) - { - used [domain] = NO; - rem_denominator [domain] /* norm of domain */ - = get_ip_state_state (domain_blocks [domain], domain_blocks [domain], - range->level, c); - if (rem_denominator [domain] / size < min_norm) - used [domain] = YES; /* don't use domains with small norm */ - else - rem_numerator [domain] /* inner product <s_domain, b> */ - = get_ip_image_state (range->image, range->address, - range->level, domain_blocks [domain], c); - if (!used [domain] && fabs (rem_numerator [domain]) < min_norm) - used [domain] = YES; - } + /* + * Initialize domain pool and inner product arrays + */ + domain_blocks = domain_pool->generate (range->level, y_state, wfa, + domain_pool->model); + for (domain = 0; domain_blocks [domain] >= 0; domain++) + { + used [domain] = NO; + rem_denominator [domain] = /* norm of domain */ + get_ip_state_state (domain_blocks [domain], domain_blocks [domain], + range->level, c); + if (rem_denominator [domain] / size < min_norm) + used [domain] = YES; /* don't use domains with small norm */ + else + rem_numerator [domain] /* inner product <s_domain, b> */ + = get_ip_image_state (range->image, range->address, + range->level, domain_blocks [domain], c); + if (!used [domain] && fabs (rem_numerator [domain]) < min_norm) + used [domain] = YES; + } - /* - * Exclude all domain blocks given in array 'mp->exclude' - */ - for (n = 0; isdomain (mp->exclude [n]); n++) - used [mp->exclude [n]] = YES; + /* + * Exclude all domain blocks given in array 'mp->exclude' + */ + for (n = 0; isdomain (mp->exclude [n]); n++) + used [mp->exclude [n]] = YES; - /* - * Compute the approximation costs if 'range' is approximated with - * no linear combination, i.e. the error is equal to the square - * of the image norm and the size of the automaton is determined by - * storing only zero elements in the current matrix row - */ - for (norm = 0, n = 0; n < size; n++) - norm += square (c->pixels [range->address * size + n]); - - additional_bits = range->tree_bits + range->mv_tree_bits - + range->mv_coord_bits + range->nd_tree_bits - + range->nd_weights_bits; - - mp->err = norm; - mp->weights_bits = 0; - mp->matrix_bits = domain_pool->bits (domain_blocks, NULL, range->level, - y_state, wfa, domain_pool->model); - mp->costs = (mp->matrix_bits + mp->weights_bits - + additional_bits) * price + mp->err; - - n = 0; - do - { - /* - * Current approximation is: b = d_0 o_0 + ... + d_(n-1) o_(n-1) - * with corresponding costs 'range->err + range->bits * p'. - * For all remaining state images s_i (used[s_i] == NO) set - * o_n : = s_i - \sum(k = 0, ... , n-1) {(<s_i, o_k> / ||o_k||^2) o_k} - * and try to beat current costs. - * Choose that vector for the next orthogonalization step, - * which has minimal costs: s_index. - * (No progress is indicated by index == -1) - */ - - real_t min_matrix_bits = 0; - real_t min_weights_bits = 0; - real_t min_error = 0; - real_t min_weight [MAXEDGES]; - real_t min_costs = full_search ? MAXCOSTS : mp->costs; - - for (index = -1, domain = 0; domain_blocks [domain] >= 0; domain++) - if (!used [domain]) - { - real_t matrix_bits, weights_bits; + /* + * Compute the approximation costs if 'range' is approximated with + * no linear combination, i.e. the error is equal to the square + * of the image norm and the size of the automaton is determined by + * storing only zero elements in the current matrix row + */ + for (norm = 0, n = 0; n < size; n++) + norm += square (c->pixels [range->address * size + n]); + + additional_bits = range->tree_bits + range->mv_tree_bits + + range->mv_coord_bits + range->nd_tree_bits + + range->nd_weights_bits; + + mp->err = norm; + mp->weights_bits = 0; + mp->matrix_bits = domain_pool->bits (domain_blocks, NULL, range->level, + y_state, wfa, domain_pool->model); + mp->costs = (mp->matrix_bits + mp->weights_bits + + additional_bits) * price + mp->err; + + n = 0; + do + { /* - * To speed up the search through the domain images, - * the costs of using domain image 'domain' as next vector - * can be approximated in a first step: - * improvement of image quality - * <= square (rem_numerator[domain]) / rem_denominator[domain] + * Current approximation is: b = d_0 o_0 + ... + d_(n-1) o_(n-1) + * with corresponding costs 'range->err + range->bits * p'. + * For all remaining state images s_i (used[s_i] == NO) set + * o_n : = s_i - \sum(k = 0, ... , n-1) {(<s_i, o_k> / ||o_k||^2) o_k} + * and try to beat current costs. + * Choose that vector for the next orthogonalization step, + * which has minimal costs: s_index. + * (No progress is indicated by index == -1) */ - { - word_t vectors [MAXEDGES + 1]; - word_t states [MAXEDGES + 1]; - real_t weights [MAXEDGES + 1]; - unsigned i, k; + + real_t min_matrix_bits = 0; + real_t min_weights_bits = 0; + real_t min_error = 0; + real_t min_weight [MAXEDGES]; + real_t min_costs = full_search ? MAXCOSTS : mp->costs; + + for (index = -1, domain = 0; domain_blocks [domain] >= 0; domain++) + if (!used [domain]) + { + real_t matrix_bits, weights_bits; + /* + * To speed up the search through the domain images, + * the costs of using domain image 'domain' as next vector + * can be approximated in a first step: + * improvement of image quality + * <= square (rem_numerator[domain]) / rem_denominator[domain] + */ + { + word_t vectors [MAXEDGES + 1]; + word_t states [MAXEDGES + 1]; + real_t weights [MAXEDGES + 1]; + unsigned i, k; - for (i = 0, k = 0; k < n; k++) - if (mp->weight [k] != 0) - { - vectors [i] = mp->indices [k]; - states [i] = domain_blocks [vectors [i]]; - weights [i] = mp->weight [k]; - i++; - } - vectors [i] = domain; - states [i] = domain_blocks [domain]; - weights [i] = 0.5; - vectors [i + 1] = -1; - states [i + 1] = -1; - - weights_bits = coeff->bits (weights, states, range->level, - coeff); - matrix_bits = domain_pool->bits (domain_blocks, vectors, - range->level, y_state, - wfa, domain_pool->model); - } - if (((matrix_bits + weights_bits + additional_bits) * price + - mp->err - - square (rem_numerator [domain]) / rem_denominator [domain]) - < min_costs) - { - /* - * 1.) Compute the weights (linear factors) c_i of the - * linear combination - * b = c_0 v_0 + ... + c_(n-1) v_(n-1) + c_n v_'domain' - * Use backward substitution to obtain c_i from the linear - * factors of the lin. comb. b = d_0 o_0 + ... + d_n o_n - * of the corresponding orthogonal vectors {o_0, ..., o_n}. - * Vector o_n of the orthogonal basis is obtained by using - * vector 'v_domain' in step n of the Gram Schmidt - * orthogonalization (see above for definition of o_n). - * Recursive formula for the coefficients c_i: - * c_n := <b, o_n> / ||o_n||^2 - * for i = n - 1, ... , 0: - * c_i := <b, o_i> / ||o_i||^2 + - * \sum (k = i + 1, ... , n){ c_k <v_k, o_i> - * / ||o_i||^2 } - * 2.) Because linear factors are stored with reduced precision - * factor c_i is rounded with the given precision in step i - * of the recursive formula. - */ - - unsigned k; /* counter */ - int l; /* counter */ - real_t m_bits; /* number of matrix bits to store */ - real_t w_bits; /* number of weights bits to store */ - real_t r [MAXEDGES]; /* rounded linear factors */ - real_t f [MAXEDGES]; /* linear factors */ - int v [MAXEDGES]; /* mapping of domains to vectors */ - real_t costs; /* current approximation costs */ - real_t m_err; /* current approximation error */ - - f [n] = rem_numerator [domain] / rem_denominator [domain]; - v [n] = domain; /* corresponding mapping */ - for (k = 0; k < n; k++) - { - f [k] = ip_image_ortho_vector [k] / norm_ortho_vector [k]; - v [k] = mp->indices [k]; - } + for (i = 0, k = 0; k < n; k++) + if (mp->weight [k] != 0) + { + vectors [i] = mp->indices [k]; + states [i] = domain_blocks [vectors [i]]; + weights [i] = mp->weight [k]; + i++; + } + vectors [i] = domain; + states [i] = domain_blocks [domain]; + weights [i] = 0.5; + vectors [i + 1] = -1; + states [i + 1] = -1; + + weights_bits = coeff->bits (weights, states, range->level, + coeff); + matrix_bits = domain_pool->bits (domain_blocks, vectors, + range->level, y_state, + wfa, domain_pool->model); + } + if (((matrix_bits + weights_bits + additional_bits) * price + + mp->err - + square (rem_numerator[domain]) / rem_denominator[domain]) + < min_costs) + { + /* + * 1.) Compute the weights (linear factors) c_i of the + * linear combination + * b = c_0 v_0 + ... + c_(n-1) v_(n-1) + c_n v_'domain' + * Use backward substitution to obtain c_i from the linear + * factors of the lin. comb. b = d_0 o_0 + ... + d_n o_n + * of the corresponding orthogonal vectors {o_0, ..., o_n}. + * Vector o_n of the orthogonal basis is obtained by using + * vector 'v_domain' in step n of the Gram Schmidt + * orthogonalization (see above for definition of o_n). + * Recursive formula for the coefficients c_i: + * c_n := <b, o_n> / ||o_n||^2 + * for i = n - 1, ... , 0: + * c_i := <b, o_i> / ||o_i||^2 + + * \sum (k = i + 1, ... , n){ c_k <v_k, o_i> + * / ||o_i||^2 } + * 2.) Because linear factors are stored with reduced + * precision factor c_i is rounded with the given + * precision in step i of the recursive formula. + */ + + unsigned k; /* counter */ + int l; /* counter */ + real_t m_bits; /* number of matrix bits to store */ + real_t w_bits; /* number of weights bits to store */ + real_t r [MAXEDGES]; /* rounded linear factors */ + real_t f [MAXEDGES]; /* linear factors */ + int v [MAXEDGES]; /* mapping of domains to vectors*/ + real_t costs; /* current approximation costs */ + real_t m_err; /* current approximation error */ + + f [n] = rem_numerator [domain] / rem_denominator [domain]; + v [n] = domain; /* corresponding mapping */ + for (k = 0; k < n; k++) + { + f[k] = ip_image_ortho_vector[k] / norm_ortho_vector[k]; + v [k] = mp->indices [k]; + } - for (l = n; l >= 0; l--) - { - rpf_t *rpf = domain_blocks [v [l]] - ? coeff->rpf : coeff->dc_rpf; + for (l = n; l >= 0; --l) { + rpf_t * const rpf = domain_blocks[v[l]] + ? coeff->rpf : coeff->dc_rpf; + + unsigned int k; - r [l] = f [l] = btor (rtob (f [l], rpf), rpf); + r[l] = f[l] = btor(rtob(f[l], rpf), rpf); + + { + real_t const fl = f[l]; - for (k = 0; k < (unsigned) l; k++) - f [k] -= f [l] * ip_domain_ortho_vector [v [l]][k] - / norm_ortho_vector [k] ; - } - - /* - * Compute the number of output bits of the linear combination - * and store the weights with reduced precision. The - * resulting linear combination is - * b = r_0 v_0 + ... + r_(n-1) v_(n-1) + r_n v_'domain' - */ - { - word_t vectors [MAXEDGES + 1]; - word_t states [MAXEDGES + 1]; - real_t weights [MAXEDGES + 1]; - int i; + for (k = 0; k < l; ++k) { + f[k] -= fl * ip_domain_ortho_vector[v[l]][k] + / norm_ortho_vector[k]; + } + } + } + + /* + * Compute the number of output bits of the linear + * combination and store the weights with reduced + * precision. The resulting linear combination is + * b = r_0 v_0 + ... + r_(n-1) v_(n-1) + r_n v_'domain' + */ + { + word_t vectors [MAXEDGES + 1]; + word_t states [MAXEDGES + 1]; + real_t weights [MAXEDGES + 1]; + int i; - for (i = 0, k = 0; k <= n; k++) - if (f [k] != 0) - { - vectors [i] = v [k]; - states [i] = domain_blocks [v [k]]; - weights [i] = f [k]; - i++; - } - vectors [i] = -1; - states [i] = -1; - - w_bits = coeff->bits (weights, states, range->level, coeff); - m_bits = domain_pool->bits (domain_blocks, vectors, - range->level, y_state, - wfa, domain_pool->model); - } + for (i = 0, k = 0; k <= n; k++) + if (f [k] != 0) + { + vectors [i] = v [k]; + states [i] = domain_blocks [v [k]]; + weights [i] = f [k]; + i++; + } + vectors [i] = -1; + states [i] = -1; + + w_bits = + coeff->bits(weights, states, range->level, coeff); + m_bits = domain_pool->bits (domain_blocks, vectors, + range->level, y_state, + wfa, domain_pool->model); + } - /* - * To compute the approximation error, the corresponding - * linear factors of the linear combination - * b = r_0 o_0 + ... + r_(n-1) o_(n-1) + r_n o_'domain' - * with orthogonal vectors must be computed with following - * formula: - * r_i := r_i + - * \sum (k = i + 1, ... , n) { r_k <v_k, o_i> - * / ||o_i||^2 } - */ - for (l = 0; (unsigned) l <= n; l++) - { - /* - * compute <v_n, o_n> - */ - real_t a; - - a = get_ip_state_state (domain_blocks [v [l]], - domain_blocks [domain], - range->level, c); - for (k = 0; k < n; k++) - a -= ip_domain_ortho_vector [v [l]][k] - / norm_ortho_vector [k] - * ip_domain_ortho_vector [domain][k]; - ip_domain_ortho_vector [v [l]][n] = a; - } - norm_ortho_vector [n] = rem_denominator [domain]; - ip_image_ortho_vector [n] = rem_numerator [domain]; + /* + * To compute the approximation error, the corresponding + * linear factors of the linear combination + * b = r_0 o_0 + ... + r_(n-1) o_(n-1) + r_n o_'domain' + * with orthogonal vectors must be computed with following + * formula: + * r_i := r_i + + * \sum (k = i + 1, ... , n) { r_k <v_k, o_i> + * / ||o_i||^2 } + */ + for (l = 0; (unsigned) l <= n; l++) + { + /* + * compute <v_n, o_n> + */ + real_t a; + + a = get_ip_state_state (domain_blocks [v [l]], + domain_blocks [domain], + range->level, c); + for (k = 0; k < n; k++) + a -= ip_domain_ortho_vector [v [l]][k] + / norm_ortho_vector [k] + * ip_domain_ortho_vector [domain][k]; + ip_domain_ortho_vector [v [l]][n] = a; + } + norm_ortho_vector [n] = rem_denominator [domain]; + ip_image_ortho_vector [n] = rem_numerator [domain]; - for (k = 0; k <= n; k++) - for (l = k + 1; (unsigned) l <= n; l++) - r [k] += ip_domain_ortho_vector [v [l]][k] * r [l] - / norm_ortho_vector [k]; - /* - * Compute approximation error: - * error := ||b||^2 + - * \sum (k = 0, ... , n){r_k^2 ||o_k||^2 - 2 r_k <b, o_k>} - */ - m_err = norm; - for (k = 0; k <= n; k++) - m_err += square (r [k]) * norm_ortho_vector [k] - - 2 * r [k] * ip_image_ortho_vector [k]; - if (m_err < 0) /* TODO: return MAXCOSTS */ - warning ("Negative image norm: %f" - " (current domain: %d, level = %d)", - (double) m_err, domain, range->level); - - costs = (m_bits + w_bits + additional_bits) * price + m_err; - if (costs < min_costs) /* found a better approximation */ - { - index = domain; - min_costs = costs; - min_matrix_bits = m_bits; - min_weights_bits = w_bits; - min_error = m_err; - for (k = 0; k <= n; k++) - min_weight [k] = f [k]; - } - } - } + for (k = 0; k <= n; k++) + for (l = k + 1; (unsigned) l <= n; l++) + r [k] += ip_domain_ortho_vector [v [l]][k] * r [l] + / norm_ortho_vector [k]; + /* + * Compute approximation error: + * error := ||b||^2 + + * \sum (k = 0, ... , n){r_k^2 ||o_k||^2 - 2 r_k <b, o_k>} + */ + m_err = norm; + for (k = 0; k <= n; k++) + m_err += square (r [k]) * norm_ortho_vector [k] + - 2 * r [k] * ip_image_ortho_vector [k]; + if (m_err < 0) /* TODO: return MAXCOSTS */ + warning ("Negative image norm: %f" + " (current domain: %d, level = %d)", + (double) m_err, domain, range->level); + + costs = (m_bits + w_bits + additional_bits) * price + m_err; + if (costs < min_costs) /* found a better approximation */ + { + index = domain; + min_costs = costs; + min_matrix_bits = m_bits; + min_weights_bits = w_bits; + min_error = m_err; + for (k = 0; k <= n; k++) + min_weight [k] = f [k]; + } + } + } - if (index >= 0) /* found a better approximation */ - { - if (min_costs < mp->costs) - { - unsigned k; + if (index >= 0) /* found a better approximation */ + { + if (min_costs < mp->costs) + { + unsigned k; - mp->costs = min_costs; - mp->err = min_error; - mp->matrix_bits = min_matrix_bits; - mp->weights_bits = min_weights_bits; + mp->costs = min_costs; + mp->err = min_error; + mp->matrix_bits = min_matrix_bits; + mp->weights_bits = min_weights_bits; - for (k = 0; k <= n; k++) - mp->weight [k] = min_weight [k]; + for (k = 0; k <= n; k++) + mp->weight [k] = min_weight [k]; - best_n = n + 1; - } + best_n = n + 1; + } - mp->indices [n] = index; - mp->into [n] = domain_blocks [index]; + mp->indices [n] = index; + mp->into [n] = domain_blocks [index]; - used [index] = YES; + used [index] = YES; - /* - * Gram-Schmidt orthogonalization step n - */ - orthogonalize (index, n, range->level, min_norm, domain_blocks, c); - n++; - } - } - while (n < max_edges && index >= 0); + /* + * Gram-Schmidt orthogonalization step n + */ + orthogonalize (index, n, range->level, min_norm, domain_blocks, c); + n++; + } + } + while (n < max_edges && index >= 0); - mp->indices [best_n] = NO_EDGE; + mp->indices [best_n] = NO_EDGE; - mp->costs = (mp->matrix_bits + mp->weights_bits + additional_bits) * price - + mp->err; + mp->costs = (mp->matrix_bits + mp->weights_bits + additional_bits) * price + + mp->err; - Free (domain_blocks); + Free (domain_blocks); } static void |