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/* $Id: matrix.c,v 6.1 1999/04/02 20:43:30 vakatov Exp $
* ===========================================================================
*
* PUBLIC DOMAIN NOTICE
* National Center for Biotechnology Information (NCBI)
*
* This software/database is a "United States Government Work" under the
* terms of the United States Copyright Act. It was written as part of
* the author's official duties as a United States Government employee and
* thus cannot be copyrighted. This software/database is freely available
* to the public for use. The National Library of Medicine and the U.S.
* Government do not place any restriction on its use or reproduction.
* We would, however, appreciate having the NCBI and the author cited in
* any work or product based on this material
*
* Although all reasonable efforts have been taken to ensure the accuracy
* and reliability of the software and data, the NLM and the U.S.
* Government do not and cannot warrant the performance or results that
* may be obtained by using this software or data. The NLM and the U.S.
* Government disclaim all warranties, express or implied, including
* warranties of performance, merchantability or fitness for any particular
* purpose.
*
* ===========================================================================
*
* Author: Denis Vakatov
*
* File Description:
* Basic matrix & vector handling library.
* NOTE: most of advanced functions are valid for square matrices only!
*
* ===========================================================================
* $Log: matrix.c,v $
* Revision 6.1 1999/04/02 20:43:30 vakatov
* DLL'd for MS-Win
* Added detailed API function descriptions
*
* ==========================================================================
*/
#include <matrix.h>
#include <ncbimem.h>
#include <ncbierr.h>
typedef struct Nlm_MatrixTag {
Nlm_Uint4 n_row;
Nlm_Uint4 n_column;
Nlm_FloatHi m[1];
} Nlm_MatrixStruct;
#ifdef CHECK_RANGE_MATRIX
static Nlm_FloatHiPtr VALPtr(Nlm_Matrix mat, Nlm_Uint4 row, Nlm_Uint4 column)
{
ASSERT ( row < mat->n_row && column < mat->n_column );
return &mat->m[row * mat->n_column + column];
}
#define VAL(mat,row,column) (*VALPtr(mat,row,column))
#else /* CHECK_RANGE_MATRIX */
#define VAL(matrix, row, column) (matrix->m[row * matrix->n_column + column])
#endif /* CHECK_RANGE_MATRIX */
#define MAT_SIZE(mat) (sizeof(Nlm_MatrixStruct) + (mat->n_row * mat->n_column - 1) * sizeof(Nlm_FloatHi))
/***********************************************************************
* INTERNAL
***********************************************************************/
static Nlm_Boolean lu_decompose
(Nlm_Matrix mat,
Nlm_Uint4Ptr indx)
{
Nlm_Uint4 i, j, k, imax = UINT4_MAX;
Nlm_FloatHi max, temp, sum;
Nlm_Uint4 n = mat->n_row;
Nlm_FloatHiPtr row_scale = (Nlm_FloatHiPtr)
Nlm_MemNew(sizeof(Nlm_FloatHi) * n);
ASSERT ( mat->n_row == mat->n_column );
for (i = 0; i < n; i++)
{
max = 0.0;
for (j = 0; j < n; j++)
if ((temp = fabs( VAL(mat,i,j) )) > max)
max = temp;
if (max == 0.0) {
Nlm_MemFree( row_scale );
return FALSE;
}
row_scale[i] = 1.0 / max;
indx[i] = i;
}
for (j = 0; j < n; j++)
{
for (i = 0; i < j; i++)
{
sum = VAL(mat,i,j);
for (k = 0; k < i; k++)
sum -= VAL(mat,i,k) * VAL(mat,k,j);
VAL(mat,i,j) = sum;
}
max = 0.0;
for (i = j; i < n; i++)
{
sum = VAL(mat,i,j);
for (k = 0; k < j; k++)
sum -= VAL(mat,i,k) * VAL(mat,k,j);
VAL(mat,i,j) = sum;
if ((temp = row_scale[i] * fabs(sum)) >= max) {
max = temp;
imax = i;
}
}
if (j != imax)
{ /* row interchange */
for (k = 0; k < n; k++)
{
temp = VAL(mat,imax,k);
VAL(mat,imax,k) = VAL(mat,j,k);
VAL(mat,j,k) = temp;
}
row_scale[imax] = row_scale[j];
k = indx[j];
indx[j] = indx[imax];
indx[imax] = k;
}
if ((j+1) != n)
{
temp = 1.0 / VAL(mat,j,j);
for (i = j + 1; i < n; i++)
VAL(mat,i,j) *= temp;
}
}
Nlm_MemFree( row_scale );
return TRUE;
}
static Nlm_Matrix lu_back_subst
(const Nlm_Matrix mat,
Uint4Ptr indx,
const Nlm_Matrix vector)
{
Uint4 i,j;
Uint4 n = mat->n_row;
Uint4 i_nonzero = n; /* it means -- only zero nodes up to now */
Nlm_Matrix res_vector = Nlm_MatrixNew(vector->n_row, 1);
for (i = 0; i < res_vector->n_row; i++)
VAL(res_vector, i, 0) = VAL(vector, indx[i], 0);
ASSERT ( mat->n_row == mat->n_column );
ASSERT ( mat->n_row == res_vector->n_row );
for (i = 0; i < n; i++)
{
FloatHi sum = VAL(res_vector, i,0);
if (i_nonzero != n)
for (j = i_nonzero; j < i; j++)
sum -= VAL(mat, i,j) * VAL(res_vector, j,0);
else if ( sum )
i_nonzero = i;
VAL(res_vector, i,0) = sum;
}
for (i = n; i-- > 0; )
{
FloatHi sum = VAL(res_vector, i,0);
for (j = i+1; j < n; j++)
sum -= VAL(mat, i,j) * VAL(res_vector, j,0);
VAL(res_vector, i,0) = sum / VAL(mat, i,i);
}
return res_vector;
}
/***********************************************************************
* EXTERNAL
***********************************************************************/
NLM_EXTERN Nlm_Matrix Nlm_MatrixNew
(Nlm_Uint4 n_row,
Nlm_Uint4 n_column)
{
Nlm_Matrix mat = (Nlm_Matrix)
Nlm_MemNew(sizeof(Nlm_MatrixStruct) +
(n_row * n_column - 1) * sizeof(Nlm_FloatHi));
ASSERT ( n_row && n_column );
mat->n_row = n_row;
mat->n_column = n_column;
return mat;
}
NLM_EXTERN void Nlm_MatrixDelete
(Nlm_Matrix mat)
{
Nlm_MemFree( mat );
}
NLM_EXTERN void Nlm_MatrixSetNode
(Nlm_Matrix mat,
Nlm_Uint4 row,
Nlm_Uint4 column,
Nlm_FloatHi value)
{
VAL(mat, row, column) = value;
}
NLM_EXTERN void Nlm_MatrixSetRow
(Nlm_Matrix mat,
Nlm_Uint4 row,
const Nlm_Matrix mat_src,
Nlm_Uint4 row_src)
{
Uint4 j;
ASSERT ( mat->n_column == mat_src->n_column );
for (j = 0; j < mat->n_column; j++)
VAL(mat, row, j) = VAL(mat_src, row_src, j);
}
NLM_EXTERN void Nlm_MatrixSetColumn
(Nlm_Matrix mat,
Nlm_Uint4 column,
const Nlm_Matrix mat_src,
Nlm_Uint4 column_src)
{
Uint4 i;
ASSERT ( mat->n_row == mat_src->n_row );
for (i = 0; i < mat->n_row; i++)
VAL(mat, i, column) = VAL(mat_src, i, column_src);
}
NLM_EXTERN Nlm_FloatHi Nlm_MatrixNode
(const Nlm_Matrix mat,
Nlm_Uint4 row,
Nlm_Uint4 column)
{
return VAL(mat, row, column);
}
NLM_EXTERN Nlm_Matrix Nlm_MatrixRow
(const Nlm_Matrix mat,
Nlm_Uint4 row)
{
Uint4 j;
Nlm_Matrix row_mat = Nlm_MatrixNew(1, mat->n_column);
for (j = 0; j < mat->n_column; j++)
VAL(row_mat, 0, j) = VAL(mat, row, j);
return row_mat;
}
NLM_EXTERN Nlm_Matrix Nlm_MatrixColumn
(const Nlm_Matrix mat,
Nlm_Uint4 column)
{
Uint4 i;
Nlm_Matrix column_mat = Nlm_MatrixNew(mat->n_row, 1);
for (i = 0; i < mat->n_row; i++)
VAL(column_mat, i, 0) = VAL(mat, i, column);
return column_mat;
}
NLM_EXTERN Nlm_Boolean Nlm_MatrixCompare
(const Nlm_Matrix mat1,
const Nlm_Matrix mat2)
{
ASSERT ( mat1->n_row == mat1->n_row );
ASSERT ( mat1->n_column == mat1->n_column );
return (Nlm_Boolean)
(Nlm_MemCmp((VoidPtr)mat1, (VoidPtr)mat2, MAT_SIZE(mat1)) == 0);
}
NLM_EXTERN Nlm_Matrix Nlm_MatrixCopy
(const Nlm_Matrix mat)
{
size_t mat_size = MAT_SIZE( mat );
Nlm_Matrix c_mat = (Nlm_Matrix)Nlm_MemNew( mat_size );
Nlm_MemCpy((VoidPtr)c_mat, (VoidPtr)mat, mat_size);
return c_mat;
}
NLM_EXTERN Nlm_Matrix Nlm_MatrixTranspose
(const Nlm_Matrix mat)
{
Uint4 i,j;
Nlm_Matrix t_mat = Nlm_MatrixNew(mat->n_column, mat->n_row);
for (i = 0; i < mat->n_row; i++)
for (j = 0; j < mat->n_column; j++)
VAL(t_mat, i, j) = VAL(mat, j, i);
return t_mat;
}
NLM_EXTERN Nlm_Matrix Nlm_MatrixMultiply
(const Nlm_Matrix mat_left,
const Nlm_Matrix mat_right)
{
Uint4 n_row = mat_left->n_row;
Uint4 n_column = mat_right->n_column;
Nlm_Matrix mat = Nlm_MatrixNew(n_row, n_column);
ASSERT ( mat_left->n_column == mat_right->n_row );
{{
Uint4 n_sum = mat_left->n_column;
Uint4 i,j,k;
for (i = 0; i < n_row; i++)
for (j = 0; j < n_column; j++)
for (k = 0; k < n_sum; k++)
VAL(mat, i, j) += VAL(mat_left, i, k) * VAL(mat_right, k, j);
}}
return mat;
}
NLM_EXTERN Nlm_Matrix Nlm_MatrixSolve
(const Nlm_Matrix mat,
const Nlm_Matrix vector)
{
Nlm_Matrix d_mat = Nlm_MatrixCopy( mat );
Nlm_Uint4Ptr indx = (Uint4Ptr)Nlm_MemNew(sizeof(Nlm_Uint4) * mat->n_row);
ASSERT ( mat->n_row == mat->n_column );
ASSERT ( vector->n_row == mat->n_column );
ASSERT ( vector->n_column == 1 );
VERIFY ( lu_decompose(d_mat, indx) );
{{
Nlm_Matrix res_vector = lu_back_subst(d_mat, indx, vector);
Nlm_MemFree( indx );
Nlm_MatrixDelete( d_mat );
return res_vector;
}}
}
NLM_EXTERN Nlm_Matrix Nlm_MatrixInvert
(const Nlm_Matrix mat)
{
Nlm_Matrix res_matrix = Nlm_MatrixNew(mat->n_row, mat->n_column);
Nlm_Matrix unit_vector = Nlm_MatrixNew(mat->n_row, 1);
Uint4 j;
for (j = 0; j < mat->n_column; j++) {
VAL(unit_vector, j, 0) = 1.0;
{{
Nlm_Matrix res_vector = Nlm_MatrixSolve(mat, unit_vector);
Nlm_MatrixSetColumn(res_matrix, j, res_vector, 0);
Nlm_MatrixDelete( res_vector );
}}
VAL(unit_vector, j, 0) = 0;
}
Nlm_MatrixDelete( unit_vector );
return res_matrix;
}
NLM_EXTERN void Nlm_MatrixPrint
(const Nlm_Matrix mat,
FILE* fd,
const Char* descr)
{
Uint4 i,j;
if ( descr )
fprintf(fd, "\n%s:\n", descr);
for (i = 0; i < mat->n_row; i++) {
for (j = 0; j < mat->n_column; j++)
fprintf(fd, "%13g ", VAL(mat, i, j));
fprintf(fd, "\n");
}
}
/***********************************************************************
* TEST
***********************************************************************/
#ifdef TEST_MODULE_MATRIX
#include <ncbifile.h>
static void TestMatrix(Nlm_FloatHiPtr float_mat, Nlm_Uint4 dim, FILE *fd)
{
Nlm_Matrix mat = Nlm_MatrixNew(dim, dim);
Nlm_Matrix inv_mat, unit_mat, inv2_mat;
Nlm_Uint4 i,j;
for (i = 0; i < dim; i++)
for (j = 0; j < dim; j++)
Nlm_MatrixSetNode(mat, i, j, float_mat[i*dim + j]);
Nlm_MatrixPrint(mat, fd, "Original Matrix:");
inv_mat = Nlm_MatrixInvert( mat );
Nlm_MatrixPrint(inv_mat, fd, "Inverted Matrix:");
unit_mat = Nlm_MatrixMultiply(mat, inv_mat);
Nlm_MatrixPrint(unit_mat, fd, "Must be [1]:");
inv2_mat = Nlm_MatrixInvert( inv_mat );
Nlm_MatrixPrint(inv2_mat, fd, "Inverted Twice Matrix:");
Nlm_MatrixDelete( inv2_mat );
Nlm_MatrixDelete( unit_mat );
Nlm_MatrixDelete( inv_mat );
Nlm_MatrixDelete( mat );
}
static Nlm_FloatHi mat1[1][1] = {
{ 1 }
};
static Nlm_FloatHi mat2[2][2] = {
{ 3, 2 },
{ 4, 1 },
};
static Nlm_FloatHi mat3[3][3] = {
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 0, 8, 7 }
};
static Nlm_FloatHi mat4[4][4] = {
{ 0, 9, 4, 0 },
{ 1, 5, 6, 4 },
{ 9, 5, 2, 0 },
{ 0, 0, 7, 1 }
};
#define N_MAT 4
static Nlm_FloatHiPtr test_mat[N_MAT] = {
(Nlm_FloatHiPtr)mat1,
(Nlm_FloatHiPtr)mat2,
(Nlm_FloatHiPtr)mat3,
(Nlm_FloatHiPtr)mat4
};
Nlm_Int2 Nlm_Main( void )
{
Nlm_Uint4 dim;
FILE *fd = Nlm_FileOpen("matrix.log", "w");
ASSERT ( fd );
for (dim = 1; dim <= N_MAT; dim++)
TestMatrix(test_mat[dim-1], dim, fd);
Nlm_FileClose( fd );
return 0;
}
#endif /* TEST_MODULE_MATRIX */
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