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