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+/***********************************************************************
+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
+INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+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 );
+}
+