ref: 8d6467c7ed09535845f7c84074e7ffc1f2a364c8
dir: /silk/fixed/solve_LS_FIX.c/
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#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "main_FIX.h"
#include "tuning_parameters.h"
/*****************************/
/* Internal function headers */
/*****************************/
typedef struct {
opus_int32 Q36_part;
opus_int32 Q48_part;
} inv_D_t;
/* Factorize square matrix A into LDL form */
static inline void silk_LDL_factorize_FIX(
opus_int32 *A, /* I/O Pointer to Symetric Square Matrix */
opus_int M, /* I Size of Matrix */
opus_int32 *L_Q16, /* I/O Pointer to Square Upper triangular Matrix */
inv_D_t *inv_D /* I/O Pointer to vector holding inverted diagonal elements of D */
);
/* Solve Lx = b, when L is lower triangular and has ones on the diagonal */
static inline void silk_LS_SolveFirst_FIX(
const opus_int32 *L_Q16, /* I Pointer to Lower Triangular Matrix */
opus_int M, /* I Dim of Matrix equation */
const opus_int32 *b, /* I b Vector */
opus_int32 *x_Q16 /* O x Vector */
);
/* Solve L^t*x = b, where L is lower triangular with ones on the diagonal */
static inline void silk_LS_SolveLast_FIX(
const opus_int32 *L_Q16, /* I Pointer to Lower Triangular Matrix */
const opus_int M, /* I Dim of Matrix equation */
const opus_int32 *b, /* I b Vector */
opus_int32 *x_Q16 /* O x Vector */
);
static inline void silk_LS_divide_Q16_FIX(
opus_int32 T[], /* I/O Numenator vector */
inv_D_t *inv_D, /* I 1 / D vector */
opus_int M /* I dimension */
);
/* Solves Ax = b, assuming A is symmetric */
void silk_solve_LDL_FIX(
opus_int32 *A, /* I Pointer to symetric square matrix A */
opus_int M, /* I Size of matrix */
const opus_int32 *b, /* I Pointer to b vector */
opus_int32 *x_Q16 /* O Pointer to x solution vector */
)
{
opus_int32 L_Q16[ MAX_MATRIX_SIZE * MAX_MATRIX_SIZE ];
opus_int32 Y[ MAX_MATRIX_SIZE ];
inv_D_t inv_D[ MAX_MATRIX_SIZE ];
silk_assert( M <= MAX_MATRIX_SIZE );
/***************************************************
Factorize A by LDL such that A = L*D*L',
where L is lower triangular with ones on diagonal
****************************************************/
silk_LDL_factorize_FIX( A, M, L_Q16, inv_D );
/****************************************************
* substitute D*L'*x = Y. ie:
L*D*L'*x = b => L*Y = b <=> Y = inv(L)*b
******************************************************/
silk_LS_SolveFirst_FIX( L_Q16, M, b, Y );
/****************************************************
D*L'*x = Y <=> L'*x = inv(D)*Y, because D is
diagonal just multiply with 1/d_i
****************************************************/
silk_LS_divide_Q16_FIX( Y, inv_D, M );
/****************************************************
x = inv(L') * inv(D) * Y
*****************************************************/
silk_LS_SolveLast_FIX( L_Q16, M, Y, x_Q16 );
}
static inline void silk_LDL_factorize_FIX(
opus_int32 *A, /* I Pointer to Symetric Square Matrix */
opus_int M, /* I Size of Matrix */
opus_int32 *L_Q16, /* I/O Pointer to Square Upper triangular Matrix */
inv_D_t *inv_D /* I/O Pointer to vector holding inverted diagonal elements of D */
)
{
opus_int i, j, k, status, loop_count;
const opus_int32 *ptr1, *ptr2;
opus_int32 diag_min_value, tmp_32, err;
opus_int32 v_Q0[ MAX_MATRIX_SIZE ], D_Q0[ MAX_MATRIX_SIZE ];
opus_int32 one_div_diag_Q36, one_div_diag_Q40, one_div_diag_Q48;
silk_assert( M <= MAX_MATRIX_SIZE );
status = 1;
diag_min_value = silk_max_32( silk_SMMUL( silk_ADD_SAT32( A[ 0 ], A[ silk_SMULBB( M, M ) - 1 ] ), SILK_FIX_CONST( FIND_LTP_COND_FAC, 31 ) ), 1 << 9 );
for( loop_count = 0; loop_count < M && status == 1; loop_count++ ) {
status = 0;
for( j = 0; j < M; j++ ) {
ptr1 = matrix_adr( L_Q16, j, 0, M );
tmp_32 = 0;
for( i = 0; i < j; i++ ) {
v_Q0[ i ] = silk_SMULWW( D_Q0[ i ], ptr1[ i ] ); /* Q0 */
tmp_32 = silk_SMLAWW( tmp_32, v_Q0[ i ], ptr1[ i ] ); /* Q0 */
}
tmp_32 = silk_SUB32( matrix_ptr( A, j, j, M ), tmp_32 );
if( tmp_32 < diag_min_value ) {
tmp_32 = silk_SUB32( silk_SMULBB( loop_count + 1, diag_min_value ), tmp_32 );
/* Matrix not positive semi-definite, or ill conditioned */
for( i = 0; i < M; i++ ) {
matrix_ptr( A, i, i, M ) = silk_ADD32( matrix_ptr( A, i, i, M ), tmp_32 );
}
status = 1;
break;
}
D_Q0[ j ] = tmp_32; /* always < max(Correlation) */
/* two-step division */
one_div_diag_Q36 = silk_INVERSE32_varQ( tmp_32, 36 ); /* Q36 */
one_div_diag_Q40 = silk_LSHIFT( one_div_diag_Q36, 4 ); /* Q40 */
err = silk_SUB32( 1 << 24, silk_SMULWW( tmp_32, one_div_diag_Q40 ) ); /* Q24 */
one_div_diag_Q48 = silk_SMULWW( err, one_div_diag_Q40 ); /* Q48 */
/* Save 1/Ds */
inv_D[ j ].Q36_part = one_div_diag_Q36;
inv_D[ j ].Q48_part = one_div_diag_Q48;
matrix_ptr( L_Q16, j, j, M ) = 65536; /* 1.0 in Q16 */
ptr1 = matrix_adr( A, j, 0, M );
ptr2 = matrix_adr( L_Q16, j + 1, 0, M );
for( i = j + 1; i < M; i++ ) {
tmp_32 = 0;
for( k = 0; k < j; k++ ) {
tmp_32 = silk_SMLAWW( tmp_32, v_Q0[ k ], ptr2[ k ] ); /* Q0 */
}
tmp_32 = silk_SUB32( ptr1[ i ], tmp_32 ); /* always < max(Correlation) */
/* tmp_32 / D_Q0[j] : Divide to Q16 */
matrix_ptr( L_Q16, i, j, M ) = silk_ADD32( silk_SMMUL( tmp_32, one_div_diag_Q48 ),
silk_RSHIFT( silk_SMULWW( tmp_32, one_div_diag_Q36 ), 4 ) );
/* go to next column */
ptr2 += M;
}
}
}
silk_assert( status == 0 );
}
static inline void silk_LS_divide_Q16_FIX(
opus_int32 T[], /* I/O Numenator vector */
inv_D_t *inv_D, /* I 1 / D vector */
opus_int M /* I Order */
)
{
opus_int i;
opus_int32 tmp_32;
opus_int32 one_div_diag_Q36, one_div_diag_Q48;
for( i = 0; i < M; i++ ) {
one_div_diag_Q36 = inv_D[ i ].Q36_part;
one_div_diag_Q48 = inv_D[ i ].Q48_part;
tmp_32 = T[ i ];
T[ i ] = silk_ADD32( silk_SMMUL( tmp_32, one_div_diag_Q48 ), silk_RSHIFT( silk_SMULWW( tmp_32, one_div_diag_Q36 ), 4 ) );
}
}
/* Solve Lx = b, when L is lower triangular and has ones on the diagonal */
static inline void silk_LS_SolveFirst_FIX(
const opus_int32 *L_Q16, /* I Pointer to Lower Triangular Matrix */
opus_int M, /* I Dim of Matrix equation */
const opus_int32 *b, /* I b Vector */
opus_int32 *x_Q16 /* O x Vector */
)
{
opus_int i, j;
const opus_int32 *ptr32;
opus_int32 tmp_32;
for( i = 0; i < M; i++ ) {
ptr32 = matrix_adr( L_Q16, i, 0, M );
tmp_32 = 0;
for( j = 0; j < i; j++ ) {
tmp_32 = silk_SMLAWW( tmp_32, ptr32[ j ], x_Q16[ j ] );
}
x_Q16[ i ] = silk_SUB32( b[ i ], tmp_32 );
}
}
/* Solve L^t*x = b, where L is lower triangular with ones on the diagonal */
static inline void silk_LS_SolveLast_FIX(
const opus_int32 *L_Q16, /* I Pointer to Lower Triangular Matrix */
const opus_int M, /* I Dim of Matrix equation */
const opus_int32 *b, /* I b Vector */
opus_int32 *x_Q16 /* O x Vector */
)
{
opus_int i, j;
const opus_int32 *ptr32;
opus_int32 tmp_32;
for( i = M - 1; i >= 0; i-- ) {
ptr32 = matrix_adr( L_Q16, 0, i, M );
tmp_32 = 0;
for( j = M - 1; j > i; j-- ) {
tmp_32 = silk_SMLAWW( tmp_32, ptr32[ silk_SMULBB( j, M ) ], x_Q16[ j ] );
}
x_Q16[ i ] = silk_SUB32( b[ i ], tmp_32 );
}
}