| /*********************************************************************** |
| Copyright (c) 2006-2011, Skype Limited. All rights reserved. |
| Redistribution and use in source and binary forms, with or without |
| modification, are permitted provided that the following conditions |
| are met: |
| - Redistributions of source code must retain the above copyright notice, |
| this list of conditions and the following disclaimer. |
| - Redistributions in binary form must reproduce the above copyright |
| notice, this list of conditions and the following disclaimer in the |
| documentation and/or other materials provided with the distribution. |
| - Neither the name of Internet Society, IETF or IETF Trust, nor the |
| names of specific contributors, may be used to endorse or promote |
| products derived from this software without specific prior written |
| permission. |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
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| CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| POSSIBILITY OF SUCH DAMAGE. |
| ***********************************************************************/ |
| |
| #ifdef HAVE_CONFIG_H |
| #include "config.h" |
| #endif |
| |
| #include "main_FLP.h" |
| #include "tuning_parameters.h" |
| |
| /********************************************************************** |
| * LDL Factorisation. Finds the upper triangular matrix L and the diagonal |
| * Matrix D (only the diagonal elements returned in a vector)such that |
| * the symmetric matric A is given by A = L*D*L'. |
| **********************************************************************/ |
| static OPUS_INLINE void silk_LDL_FLP( |
| silk_float *A, /* I/O Pointer to Symetric Square Matrix */ |
| opus_int M, /* I Size of Matrix */ |
| silk_float *L, /* I/O Pointer to Square Upper triangular Matrix */ |
| silk_float *Dinv /* I/O Pointer to vector holding the inverse diagonal elements of D */ |
| ); |
| |
| /********************************************************************** |
| * Function to solve linear equation Ax = b, when A is a MxM lower |
| * triangular matrix, with ones on the diagonal. |
| **********************************************************************/ |
| static OPUS_INLINE void silk_SolveWithLowerTriangularWdiagOnes_FLP( |
| const silk_float *L, /* I Pointer to Lower Triangular Matrix */ |
| opus_int M, /* I Dim of Matrix equation */ |
| const silk_float *b, /* I b Vector */ |
| silk_float *x /* O x Vector */ |
| ); |
| |
| /********************************************************************** |
| * Function to solve linear equation (A^T)x = b, when A is a MxM lower |
| * triangular, with ones on the diagonal. (ie then A^T is upper triangular) |
| **********************************************************************/ |
| static OPUS_INLINE void silk_SolveWithUpperTriangularFromLowerWdiagOnes_FLP( |
| const silk_float *L, /* I Pointer to Lower Triangular Matrix */ |
| opus_int M, /* I Dim of Matrix equation */ |
| const silk_float *b, /* I b Vector */ |
| silk_float *x /* O x Vector */ |
| ); |
| |
| /********************************************************************** |
| * Function to solve linear equation Ax = b, when A is a MxM |
| * symmetric square matrix - using LDL factorisation |
| **********************************************************************/ |
| void silk_solve_LDL_FLP( |
| silk_float *A, /* I/O Symmetric square matrix, out: reg. */ |
| const opus_int M, /* I Size of matrix */ |
| const silk_float *b, /* I Pointer to b vector */ |
| silk_float *x /* O Pointer to x solution vector */ |
| ) |
| { |
| opus_int i; |
| silk_float L[ MAX_MATRIX_SIZE ][ MAX_MATRIX_SIZE ]; |
| silk_float T[ MAX_MATRIX_SIZE ]; |
| silk_float Dinv[ MAX_MATRIX_SIZE ]; /* inverse diagonal elements of D*/ |
| |
| silk_assert( M <= MAX_MATRIX_SIZE ); |
| |
| /*************************************************** |
| Factorize A by LDL such that A = L*D*(L^T), |
| where L is lower triangular with ones on diagonal |
| ****************************************************/ |
| silk_LDL_FLP( A, M, &L[ 0 ][ 0 ], Dinv ); |
| |
| /**************************************************** |
| * substitute D*(L^T) = T. ie: |
| L*D*(L^T)*x = b => L*T = b <=> T = inv(L)*b |
| ******************************************************/ |
| silk_SolveWithLowerTriangularWdiagOnes_FLP( &L[ 0 ][ 0 ], M, b, T ); |
| |
| /**************************************************** |
| D*(L^T)*x = T <=> (L^T)*x = inv(D)*T, because D is |
| diagonal just multiply with 1/d_i |
| ****************************************************/ |
| for( i = 0; i < M; i++ ) { |
| T[ i ] = T[ i ] * Dinv[ i ]; |
| } |
| /**************************************************** |
| x = inv(L') * inv(D) * T |
| *****************************************************/ |
| silk_SolveWithUpperTriangularFromLowerWdiagOnes_FLP( &L[ 0 ][ 0 ], M, T, x ); |
| } |
| |
| static OPUS_INLINE void silk_SolveWithUpperTriangularFromLowerWdiagOnes_FLP( |
| const silk_float *L, /* I Pointer to Lower Triangular Matrix */ |
| opus_int M, /* I Dim of Matrix equation */ |
| const silk_float *b, /* I b Vector */ |
| silk_float *x /* O x Vector */ |
| ) |
| { |
| opus_int i, j; |
| silk_float temp; |
| const silk_float *ptr1; |
| |
| for( i = M - 1; i >= 0; i-- ) { |
| ptr1 = matrix_adr( L, 0, i, M ); |
| temp = 0; |
| for( j = M - 1; j > i ; j-- ) { |
| temp += ptr1[ j * M ] * x[ j ]; |
| } |
| temp = b[ i ] - temp; |
| x[ i ] = temp; |
| } |
| } |
| |
| static OPUS_INLINE void silk_SolveWithLowerTriangularWdiagOnes_FLP( |
| const silk_float *L, /* I Pointer to Lower Triangular Matrix */ |
| opus_int M, /* I Dim of Matrix equation */ |
| const silk_float *b, /* I b Vector */ |
| silk_float *x /* O x Vector */ |
| ) |
| { |
| opus_int i, j; |
| silk_float temp; |
| const silk_float *ptr1; |
| |
| for( i = 0; i < M; i++ ) { |
| ptr1 = matrix_adr( L, i, 0, M ); |
| temp = 0; |
| for( j = 0; j < i; j++ ) { |
| temp += ptr1[ j ] * x[ j ]; |
| } |
| temp = b[ i ] - temp; |
| x[ i ] = temp; |
| } |
| } |
| |
| static OPUS_INLINE void silk_LDL_FLP( |
| silk_float *A, /* I/O Pointer to Symetric Square Matrix */ |
| opus_int M, /* I Size of Matrix */ |
| silk_float *L, /* I/O Pointer to Square Upper triangular Matrix */ |
| silk_float *Dinv /* I/O Pointer to vector holding the inverse diagonal elements of D */ |
| ) |
| { |
| opus_int i, j, k, loop_count, err = 1; |
| silk_float *ptr1, *ptr2; |
| double temp, diag_min_value; |
| silk_float v[ MAX_MATRIX_SIZE ], D[ MAX_MATRIX_SIZE ]; /* temp arrays*/ |
| |
| silk_assert( M <= MAX_MATRIX_SIZE ); |
| |
| diag_min_value = FIND_LTP_COND_FAC * 0.5f * ( A[ 0 ] + A[ M * M - 1 ] ); |
| for( loop_count = 0; loop_count < M && err == 1; loop_count++ ) { |
| err = 0; |
| for( j = 0; j < M; j++ ) { |
| ptr1 = matrix_adr( L, j, 0, M ); |
| temp = matrix_ptr( A, j, j, M ); /* element in row j column j*/ |
| for( i = 0; i < j; i++ ) { |
| v[ i ] = ptr1[ i ] * D[ i ]; |
| temp -= ptr1[ i ] * v[ i ]; |
| } |
| if( temp < diag_min_value ) { |
| /* Badly conditioned matrix: add white noise and run again */ |
| temp = ( loop_count + 1 ) * diag_min_value - temp; |
| for( i = 0; i < M; i++ ) { |
| matrix_ptr( A, i, i, M ) += ( silk_float )temp; |
| } |
| err = 1; |
| break; |
| } |
| D[ j ] = ( silk_float )temp; |
| Dinv[ j ] = ( silk_float )( 1.0f / temp ); |
| matrix_ptr( L, j, j, M ) = 1.0f; |
| |
| ptr1 = matrix_adr( A, j, 0, M ); |
| ptr2 = matrix_adr( L, j + 1, 0, M); |
| for( i = j + 1; i < M; i++ ) { |
| temp = 0.0; |
| for( k = 0; k < j; k++ ) { |
| temp += ptr2[ k ] * v[ k ]; |
| } |
| matrix_ptr( L, i, j, M ) = ( silk_float )( ( ptr1[ i ] - temp ) * Dinv[ j ] ); |
| ptr2 += M; /* go to next column*/ |
| } |
| } |
| } |
| silk_assert( err == 0 ); |
| } |
| |
