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1 /***********************************************************************
2 Copyright (c) 2006-2011, Skype Limited. All rights reserved.
3 Redistribution and use in source and binary forms, with or without
4 modification, are permitted provided that the following conditions
5 are met:
6 - Redistributions of source code must retain the above copyright notice,
7 this list of conditions and the following disclaimer.
8 - Redistributions in binary form must reproduce the above copyright
9 notice, this list of conditions and the following disclaimer in the
10 documentation and/or other materials provided with the distribution.
11 - Neither the name of Internet Society, IETF or IETF Trust, nor the
12 names of specific contributors, may be used to endorse or promote
13 products derived from this software without specific prior written
14 permission.
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
21 SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
22 INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
23 CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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