1/***********************************************************************
2Copyright (c) 2006-2011, Skype Limited. All rights reserved.
3Redistribution and use in source and binary forms, with or without
4modification, are permitted provided that the following conditions
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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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14permission.
15THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
16AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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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 **********************************************************************/
40static 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 **********************************************************************/
51static 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 **********************************************************************/
62static 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 **********************************************************************/
73void 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
112static 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
134static 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
156static 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