Alexandre Lision | 744f742 | 2013-09-25 11:39:37 -0400 | [diff] [blame] | 1 | /*********************************************************************** |
| 2 | Copyright (c) 2006-2011, Skype Limited. All rights reserved. |
| 3 | Redistribution and use in source and binary forms, with or without |
| 4 | modification, are permitted provided that the following conditions |
| 5 | are met: |
| 6 | - Redistributions of source code must retain the above copyright notice, |
| 7 | this list of conditions and the following disclaimer. |
| 8 | - Redistributions in binary form must reproduce the above copyright |
| 9 | notice, this list of conditions and the following disclaimer in the |
| 10 | documentation and/or other materials provided with the distribution. |
| 11 | - Neither the name of Internet Society, IETF or IETF Trust, nor the |
| 12 | names of specific contributors, may be used to endorse or promote |
| 13 | products derived from this software without specific prior written |
| 14 | permission. |
| 15 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” |
| 16 | AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 17 | IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| 18 | ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| 19 | LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| 20 | CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| 21 | SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| 22 | INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| 23 | CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| 24 | ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| 25 | POSSIBILITY OF SUCH DAMAGE. |
| 26 | ***********************************************************************/ |
| 27 | |
| 28 | #ifdef HAVE_CONFIG_H |
| 29 | #include "config.h" |
| 30 | #endif |
| 31 | |
| 32 | #include "main_FLP.h" |
| 33 | #include "tuning_parameters.h" |
| 34 | |
| 35 | /********************************************************************** |
| 36 | * LDL Factorisation. Finds the upper triangular matrix L and the diagonal |
| 37 | * Matrix D (only the diagonal elements returned in a vector)such that |
| 38 | * the symmetric matric A is given by A = L*D*L'. |
| 39 | **********************************************************************/ |
| 40 | static inline void silk_LDL_FLP( |
| 41 | silk_float *A, /* I/O Pointer to Symetric Square Matrix */ |
| 42 | opus_int M, /* I Size of Matrix */ |
| 43 | silk_float *L, /* I/O Pointer to Square Upper triangular Matrix */ |
| 44 | silk_float *Dinv /* I/O Pointer to vector holding the inverse diagonal elements of D */ |
| 45 | ); |
| 46 | |
| 47 | /********************************************************************** |
| 48 | * Function to solve linear equation Ax = b, when A is a MxM lower |
| 49 | * triangular matrix, with ones on the diagonal. |
| 50 | **********************************************************************/ |
| 51 | static inline void silk_SolveWithLowerTriangularWdiagOnes_FLP( |
| 52 | const silk_float *L, /* I Pointer to Lower Triangular Matrix */ |
| 53 | opus_int M, /* I Dim of Matrix equation */ |
| 54 | const silk_float *b, /* I b Vector */ |
| 55 | silk_float *x /* O x Vector */ |
| 56 | ); |
| 57 | |
| 58 | /********************************************************************** |
| 59 | * Function to solve linear equation (A^T)x = b, when A is a MxM lower |
| 60 | * triangular, with ones on the diagonal. (ie then A^T is upper triangular) |
| 61 | **********************************************************************/ |
| 62 | static inline void silk_SolveWithUpperTriangularFromLowerWdiagOnes_FLP( |
| 63 | const silk_float *L, /* I Pointer to Lower Triangular Matrix */ |
| 64 | opus_int M, /* I Dim of Matrix equation */ |
| 65 | const silk_float *b, /* I b Vector */ |
| 66 | silk_float *x /* O x Vector */ |
| 67 | ); |
| 68 | |
| 69 | /********************************************************************** |
| 70 | * Function to solve linear equation Ax = b, when A is a MxM |
| 71 | * symmetric square matrix - using LDL factorisation |
| 72 | **********************************************************************/ |
| 73 | void silk_solve_LDL_FLP( |
| 74 | silk_float *A, /* I/O Symmetric square matrix, out: reg. */ |
| 75 | const opus_int M, /* I Size of matrix */ |
| 76 | const silk_float *b, /* I Pointer to b vector */ |
| 77 | silk_float *x /* O Pointer to x solution vector */ |
| 78 | ) |
| 79 | { |
| 80 | opus_int i; |
| 81 | silk_float L[ MAX_MATRIX_SIZE ][ MAX_MATRIX_SIZE ]; |
| 82 | silk_float T[ MAX_MATRIX_SIZE ]; |
| 83 | silk_float Dinv[ MAX_MATRIX_SIZE ]; /* inverse diagonal elements of D*/ |
| 84 | |
| 85 | silk_assert( M <= MAX_MATRIX_SIZE ); |
| 86 | |
| 87 | /*************************************************** |
| 88 | Factorize A by LDL such that A = L*D*(L^T), |
| 89 | where L is lower triangular with ones on diagonal |
| 90 | ****************************************************/ |
| 91 | silk_LDL_FLP( A, M, &L[ 0 ][ 0 ], Dinv ); |
| 92 | |
| 93 | /**************************************************** |
| 94 | * substitute D*(L^T) = T. ie: |
| 95 | L*D*(L^T)*x = b => L*T = b <=> T = inv(L)*b |
| 96 | ******************************************************/ |
| 97 | silk_SolveWithLowerTriangularWdiagOnes_FLP( &L[ 0 ][ 0 ], M, b, T ); |
| 98 | |
| 99 | /**************************************************** |
| 100 | D*(L^T)*x = T <=> (L^T)*x = inv(D)*T, because D is |
| 101 | diagonal just multiply with 1/d_i |
| 102 | ****************************************************/ |
| 103 | for( i = 0; i < M; i++ ) { |
| 104 | T[ i ] = T[ i ] * Dinv[ i ]; |
| 105 | } |
| 106 | /**************************************************** |
| 107 | x = inv(L') * inv(D) * T |
| 108 | *****************************************************/ |
| 109 | silk_SolveWithUpperTriangularFromLowerWdiagOnes_FLP( &L[ 0 ][ 0 ], M, T, x ); |
| 110 | } |
| 111 | |
| 112 | static inline void silk_SolveWithUpperTriangularFromLowerWdiagOnes_FLP( |
| 113 | const silk_float *L, /* I Pointer to Lower Triangular Matrix */ |
| 114 | opus_int M, /* I Dim of Matrix equation */ |
| 115 | const silk_float *b, /* I b Vector */ |
| 116 | silk_float *x /* O x Vector */ |
| 117 | ) |
| 118 | { |
| 119 | opus_int i, j; |
| 120 | silk_float temp; |
| 121 | const silk_float *ptr1; |
| 122 | |
| 123 | for( i = M - 1; i >= 0; i-- ) { |
| 124 | ptr1 = matrix_adr( L, 0, i, M ); |
| 125 | temp = 0; |
| 126 | for( j = M - 1; j > i ; j-- ) { |
| 127 | temp += ptr1[ j * M ] * x[ j ]; |
| 128 | } |
| 129 | temp = b[ i ] - temp; |
| 130 | x[ i ] = temp; |
| 131 | } |
| 132 | } |
| 133 | |
| 134 | static inline void silk_SolveWithLowerTriangularWdiagOnes_FLP( |
| 135 | const silk_float *L, /* I Pointer to Lower Triangular Matrix */ |
| 136 | opus_int M, /* I Dim of Matrix equation */ |
| 137 | const silk_float *b, /* I b Vector */ |
| 138 | silk_float *x /* O x Vector */ |
| 139 | ) |
| 140 | { |
| 141 | opus_int i, j; |
| 142 | silk_float temp; |
| 143 | const silk_float *ptr1; |
| 144 | |
| 145 | for( i = 0; i < M; i++ ) { |
| 146 | ptr1 = matrix_adr( L, i, 0, M ); |
| 147 | temp = 0; |
| 148 | for( j = 0; j < i; j++ ) { |
| 149 | temp += ptr1[ j ] * x[ j ]; |
| 150 | } |
| 151 | temp = b[ i ] - temp; |
| 152 | x[ i ] = temp; |
| 153 | } |
| 154 | } |
| 155 | |
| 156 | static inline void silk_LDL_FLP( |
| 157 | silk_float *A, /* I/O Pointer to Symetric Square Matrix */ |
| 158 | opus_int M, /* I Size of Matrix */ |
| 159 | silk_float *L, /* I/O Pointer to Square Upper triangular Matrix */ |
| 160 | silk_float *Dinv /* I/O Pointer to vector holding the inverse diagonal elements of D */ |
| 161 | ) |
| 162 | { |
| 163 | opus_int i, j, k, loop_count, err = 1; |
| 164 | silk_float *ptr1, *ptr2; |
| 165 | double temp, diag_min_value; |
| 166 | silk_float v[ MAX_MATRIX_SIZE ], D[ MAX_MATRIX_SIZE ]; /* temp arrays*/ |
| 167 | |
| 168 | silk_assert( M <= MAX_MATRIX_SIZE ); |
| 169 | |
| 170 | diag_min_value = FIND_LTP_COND_FAC * 0.5f * ( A[ 0 ] + A[ M * M - 1 ] ); |
| 171 | for( loop_count = 0; loop_count < M && err == 1; loop_count++ ) { |
| 172 | err = 0; |
| 173 | for( j = 0; j < M; j++ ) { |
| 174 | ptr1 = matrix_adr( L, j, 0, M ); |
| 175 | temp = matrix_ptr( A, j, j, M ); /* element in row j column j*/ |
| 176 | for( i = 0; i < j; i++ ) { |
| 177 | v[ i ] = ptr1[ i ] * D[ i ]; |
| 178 | temp -= ptr1[ i ] * v[ i ]; |
| 179 | } |
| 180 | if( temp < diag_min_value ) { |
| 181 | /* Badly conditioned matrix: add white noise and run again */ |
| 182 | temp = ( loop_count + 1 ) * diag_min_value - temp; |
| 183 | for( i = 0; i < M; i++ ) { |
| 184 | matrix_ptr( A, i, i, M ) += ( silk_float )temp; |
| 185 | } |
| 186 | err = 1; |
| 187 | break; |
| 188 | } |
| 189 | D[ j ] = ( silk_float )temp; |
| 190 | Dinv[ j ] = ( silk_float )( 1.0f / temp ); |
| 191 | matrix_ptr( L, j, j, M ) = 1.0f; |
| 192 | |
| 193 | ptr1 = matrix_adr( A, j, 0, M ); |
| 194 | ptr2 = matrix_adr( L, j + 1, 0, M); |
| 195 | for( i = j + 1; i < M; i++ ) { |
| 196 | temp = 0.0; |
| 197 | for( k = 0; k < j; k++ ) { |
| 198 | temp += ptr2[ k ] * v[ k ]; |
| 199 | } |
| 200 | matrix_ptr( L, i, j, M ) = ( silk_float )( ( ptr1[ i ] - temp ) * Dinv[ j ] ); |
| 201 | ptr2 += M; /* go to next column*/ |
| 202 | } |
| 203 | } |
| 204 | } |
| 205 | silk_assert( err == 0 ); |
| 206 | } |
| 207 | |