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 OPUS_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 OPUS_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 OPUS_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 OPUS_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 OPUS_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 OPUS_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 } 207 208
