ref: 0dbd0ca3e63064cf5108d716f96e4bbbe21c160d
dir: /silk/float/solve_LS_FLP.c/
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***********************************************************************/
#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 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 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 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 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 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 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 );
}