/***********************************************************************
Copyright (c) 2006-2012 IETF Trust and Skype Limited. All rights reserved.

This file is extracted from RFC6716. Please see that RFC for additional
information.

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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
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***********************************************************************/

#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 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 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 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 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 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 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 );
}

