1 /***********************************************************************
2 Copyright (c) 2006-2011, Skype Limited. All rights reserved.
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4 modification, are permitted provided that the following conditions
5 are met:
6 - Redistributions of source code must retain the above copyright notice,
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8 - Redistributions in binary form must reproduce the above copyright
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11 - Neither the name of Internet Society, IETF or IETF Trust, nor the
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15 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
16 AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
19 LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
20 CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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24 ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
25 POSSIBILITY OF SUCH DAMAGE.
26 ***********************************************************************/
27
28 #ifdef HAVE_CONFIG_H
29 #include "config.h"
30 #endif
31
32 #include "main_FLP.h"
33 #include "tuning_parameters.h"
34
35 /**********************************************************************
36 * LDL Factorisation. Finds the upper triangular matrix L and the diagonal
37 * Matrix D (only the diagonal elements returned in a vector)such that
38 * the symmetric matric A is given by A = L*D*L'.
39 **********************************************************************/
40 static OPUS_INLINE void silk_LDL_FLP(
41 silk_float *A, /* I/O Pointer to Symetric Square Matrix */
42 opus_int M, /* I Size of Matrix */
43 silk_float *L, /* I/O Pointer to Square Upper triangular Matrix */
44 silk_float *Dinv /* I/O Pointer to vector holding the inverse diagonal elements of D */
45 );
46
47 /**********************************************************************
48 * Function to solve linear equation Ax = b, when A is a MxM lower
49 * triangular matrix, with ones on the diagonal.
50 **********************************************************************/
51 static OPUS_INLINE void silk_SolveWithLowerTriangularWdiagOnes_FLP(
52 const silk_float *L, /* I Pointer to Lower Triangular Matrix */
53 opus_int M, /* I Dim of Matrix equation */
54 const silk_float *b, /* I b Vector */
55 silk_float *x /* O x Vector */
56 );
57
58 /**********************************************************************
59 * Function to solve linear equation (A^T)x = b, when A is a MxM lower
60 * triangular, with ones on the diagonal. (ie then A^T is upper triangular)
61 **********************************************************************/
62 static OPUS_INLINE void silk_SolveWithUpperTriangularFromLowerWdiagOnes_FLP(
63 const silk_float *L, /* I Pointer to Lower Triangular Matrix */
64 opus_int M, /* I Dim of Matrix equation */
65 const silk_float *b, /* I b Vector */
66 silk_float *x /* O x Vector */
67 );
68
69 /**********************************************************************
70 * Function to solve linear equation Ax = b, when A is a MxM
71 * symmetric square matrix - using LDL factorisation
72 **********************************************************************/
silk_solve_LDL_FLP(silk_float * A,const opus_int M,const silk_float * b,silk_float * x)73 void silk_solve_LDL_FLP(
74 silk_float *A, /* I/O Symmetric square matrix, out: reg. */
75 const opus_int M, /* I Size of matrix */
76 const silk_float *b, /* I Pointer to b vector */
77 silk_float *x /* O Pointer to x solution vector */
78 )
79 {
80 opus_int i;
81 silk_float L[ MAX_MATRIX_SIZE ][ MAX_MATRIX_SIZE ];
82 silk_float T[ MAX_MATRIX_SIZE ];
83 silk_float Dinv[ MAX_MATRIX_SIZE ]; /* inverse diagonal elements of D*/
84
85 silk_assert( M <= MAX_MATRIX_SIZE );
86
87 /***************************************************
88 Factorize A by LDL such that A = L*D*(L^T),
89 where L is lower triangular with ones on diagonal
90 ****************************************************/
91 silk_LDL_FLP( A, M, &L[ 0 ][ 0 ], Dinv );
92
93 /****************************************************
94 * substitute D*(L^T) = T. ie:
95 L*D*(L^T)*x = b => L*T = b <=> T = inv(L)*b
96 ******************************************************/
97 silk_SolveWithLowerTriangularWdiagOnes_FLP( &L[ 0 ][ 0 ], M, b, T );
98
99 /****************************************************
100 D*(L^T)*x = T <=> (L^T)*x = inv(D)*T, because D is
101 diagonal just multiply with 1/d_i
102 ****************************************************/
103 for( i = 0; i < M; i++ ) {
104 T[ i ] = T[ i ] * Dinv[ i ];
105 }
106 /****************************************************
107 x = inv(L') * inv(D) * T
108 *****************************************************/
109 silk_SolveWithUpperTriangularFromLowerWdiagOnes_FLP( &L[ 0 ][ 0 ], M, T, x );
110 }
111
silk_SolveWithUpperTriangularFromLowerWdiagOnes_FLP(const silk_float * L,opus_int M,const silk_float * b,silk_float * x)112 static OPUS_INLINE void silk_SolveWithUpperTriangularFromLowerWdiagOnes_FLP(
113 const silk_float *L, /* I Pointer to Lower Triangular Matrix */
114 opus_int M, /* I Dim of Matrix equation */
115 const silk_float *b, /* I b Vector */
116 silk_float *x /* O x Vector */
117 )
118 {
119 opus_int i, j;
120 silk_float temp;
121 const silk_float *ptr1;
122
123 for( i = M - 1; i >= 0; i-- ) {
124 ptr1 = matrix_adr( L, 0, i, M );
125 temp = 0;
126 for( j = M - 1; j > i ; j-- ) {
127 temp += ptr1[ j * M ] * x[ j ];
128 }
129 temp = b[ i ] - temp;
130 x[ i ] = temp;
131 }
132 }
133
silk_SolveWithLowerTriangularWdiagOnes_FLP(const silk_float * L,opus_int M,const silk_float * b,silk_float * x)134 static OPUS_INLINE void silk_SolveWithLowerTriangularWdiagOnes_FLP(
135 const silk_float *L, /* I Pointer to Lower Triangular Matrix */
136 opus_int M, /* I Dim of Matrix equation */
137 const silk_float *b, /* I b Vector */
138 silk_float *x /* O x Vector */
139 )
140 {
141 opus_int i, j;
142 silk_float temp;
143 const silk_float *ptr1;
144
145 for( i = 0; i < M; i++ ) {
146 ptr1 = matrix_adr( L, i, 0, M );
147 temp = 0;
148 for( j = 0; j < i; j++ ) {
149 temp += ptr1[ j ] * x[ j ];
150 }
151 temp = b[ i ] - temp;
152 x[ i ] = temp;
153 }
154 }
155
silk_LDL_FLP(silk_float * A,opus_int M,silk_float * L,silk_float * Dinv)156 static OPUS_INLINE void silk_LDL_FLP(
157 silk_float *A, /* I/O Pointer to Symetric Square Matrix */
158 opus_int M, /* I Size of Matrix */
159 silk_float *L, /* I/O Pointer to Square Upper triangular Matrix */
160 silk_float *Dinv /* I/O Pointer to vector holding the inverse diagonal elements of D */
161 )
162 {
163 opus_int i, j, k, loop_count, err = 1;
164 silk_float *ptr1, *ptr2;
165 double temp, diag_min_value;
166 silk_float v[ MAX_MATRIX_SIZE ], D[ MAX_MATRIX_SIZE ]; /* temp arrays*/
167
168 silk_assert( M <= MAX_MATRIX_SIZE );
169
170 diag_min_value = FIND_LTP_COND_FAC * 0.5f * ( A[ 0 ] + A[ M * M - 1 ] );
171 for( loop_count = 0; loop_count < M && err == 1; loop_count++ ) {
172 err = 0;
173 for( j = 0; j < M; j++ ) {
174 ptr1 = matrix_adr( L, j, 0, M );
175 temp = matrix_ptr( A, j, j, M ); /* element in row j column j*/
176 for( i = 0; i < j; i++ ) {
177 v[ i ] = ptr1[ i ] * D[ i ];
178 temp -= ptr1[ i ] * v[ i ];
179 }
180 if( temp < diag_min_value ) {
181 /* Badly conditioned matrix: add white noise and run again */
182 temp = ( loop_count + 1 ) * diag_min_value - temp;
183 for( i = 0; i < M; i++ ) {
184 matrix_ptr( A, i, i, M ) += ( silk_float )temp;
185 }
186 err = 1;
187 break;
188 }
189 D[ j ] = ( silk_float )temp;
190 Dinv[ j ] = ( silk_float )( 1.0f / temp );
191 matrix_ptr( L, j, j, M ) = 1.0f;
192
193 ptr1 = matrix_adr( A, j, 0, M );
194 ptr2 = matrix_adr( L, j + 1, 0, M);
195 for( i = j + 1; i < M; i++ ) {
196 temp = 0.0;
197 for( k = 0; k < j; k++ ) {
198 temp += ptr2[ k ] * v[ k ];
199 }
200 matrix_ptr( L, i, j, M ) = ( silk_float )( ( ptr1[ i ] - temp ) * Dinv[ j ] );
201 ptr2 += M; /* go to next column*/
202 }
203 }
204 }
205 silk_assert( err == 0 );
206 }
207
208