1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
|
/***********************************************************************
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 );
}
|
