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matrix.c
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matrix.c
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/*****************************************************************************
Major portions of this software are copyrighted by the Medical College
of Wisconsin, 1994-2000, and are released under the Gnu General Public
License, Version 2. See the file README.Copyright for details.
******************************************************************************/
/*!
This file contains matrix and vector arithmetic routines.
File: matrix.c
Author: B. Douglas Ward
Date: 23 April 1997
Mod: Changed print format for functions matrix_print and vector_print.
Date: 05 August 1997
Mod: Changed initialization in function vector_create.
Date: 04 November 1997
Mod: Added routines matrix_file_write and matrix_file_read.
Date: 02 July 1999
Mod: Added routine for calculating square root of matrix.
Date: 30 September 1999
Mod: Added routines matrix_sprint and vector_sprint.
Date: 04 October 1999
Mod: Modified matrix_file_read to use mri_read_ascii routine.
Date: 12 January 2000
Mod: Changed return type of vector_dot from float to double.
Date: 13 April 2000
Mod: Added functions column_to_vector and matrix_extract_rows.
Date: 21 April 2000
Mod: Added test for missing matrix file name.
Date: 08 May 2000
Mod: Added "register" declarations and a few other things to speed
up calculations (including vector_create_noinit) -- RWCox.
Date: 28 Dec 2001
Mod: Allow matrices and vectors with zero rows and columns.
Date: 26 February 2002
Mod: Corrected errors in vector_multiply and vector_multiply_subtract
routines that would produce segmentation fault for certain input
matrices.
Date: 18 March 2003
Mod: UNROLL_VECMUL defined to allow unrolling by 2 of vector-multiply
dot product loops.
Mod: 'ipr' added to matrix_print() function.
Date: 03 Aug 2004 - RWCox
Mod: Added USE_SCSLBLAS stuff for SGI Altix, and USE_SUNPERF for Solaris.
Date: 01 Mar 2005
Mod: Freed memory for an orphaned matrix in matrix_sqrt function
Date: 26 Mar 2008 - drg
*/
/*---------------------------------------------------------------------*/
/** Vectorization macros:
- DOTP(n,x,y,z) computes the n-long dot product of vectors
x and y and puts the result into the place pointed to by z.
- VSUB(n,x,y,z) computes vector x-y into vector z.
- These are intended to be the fast method for doing these things. **/
/*---------------------------------------------------------------------*/
#include "mrilib.h"
#include "matrix.h"
#undef SETUP_BLAS1 /* define this to use BLAS-1 functions */
#undef SETUP_BLAS2 /* define this to use BLAS-2 functions */
#undef DOTP
#undef VSUB
#undef MATVEC
#undef SUBMATVEC
#if defined(USE_SCSLBLAS) /** SGI Altix **/
# include <scsl_blas.h>
# define SETUP_BLAS1
# undef SETUP_BLAS2 /* don't use this */
# define TRANSA "T"
#elif defined(USE_SUNPERF) /** Sun Solaris **/
# include <sunperf.h>
# define SETUP_BLAS1
# undef SETUP_BLAS2
# define TRANSA 'T'
#elif defined(USE_ACML)
# ifndef _ACML_COMPLEX
# define _ACML_COMPLEX
/* typedef struct { float real, imag; } complex; */
/* typedef struct { double real, imag; } doublecomplex; */
# endif
# include <acml.h>
# define SETUP_BLAS1
#endif
/* double precision BLAS-1 functions */
#ifdef SETUP_BLAS1
# define DOTP(n,x,y,z) *(z)=ddot(n,x,1,y,1)
# define VSUB(n,x,y,z) (memcpy(z,x,sizeof(double)*n),daxpy(n,-1.0,y,1,z,1))
#endif
/*.......................................................................
BLAS-2 function operate on matrix-vector structs defined in matrix.h:
MATVEC(m,v,z): [z] = [m][v] where m=matrix, z,v = matrices
SUBMATVEC(m,v,z): [z] = [z] - [m][v]
.........................................................................*/
#ifdef DONT_USE_MATRIX_MAT
# undef SETUP_BLAS2
#endif
#ifdef SETUP_BLAS2 /* doesn't seem to help much */
# define MATVEC(m,v,z) dgemv( TRANSA , (m).cols , (m).rows , \
1.0 , (m).mat , (m).cols , \
(v).elts , 1 , 0.0 , (z).elts , 1 )
# define SUBMATVEC(m,v,z) dgemv( TRANSA , (m).cols , (m).rows , \
-1.0 , (m).mat , (m).cols , \
(v).elts , 1 , 1.0 , (z).elts , 1 )
#endif
/*---------------------------------------------------------------------------*/
static double flops=0.0 ;
double get_matrix_flops(void){ return flops; }
static double dotnum=0.0 , dotsum=0.0 ;
double get_matrix_dotlen(void){ return (dotnum > 0.0) ? dotsum/dotnum : 0.0 ; }
#ifndef USE_OMP
# define ENABLE_FLOPS
#else
# undef ENABLE_FLOPS
#endif
/*---------------------------------------------------------------------------*/
/*!
Routine to print and error message and stop.
*/
void matrix_error (char *message)
{
printf ("Matrix error: %s \n", message);
EXIT (1);
}
/*---------------------------------------------------------------------------*/
/*!
Initialize matrix data structure.
*/
void matrix_initialize (matrix *m)
{
m->rows = 0;
m->cols = 0;
m->elts = NULL;
#ifndef DONT_USE_MATRIX_MAT
m->mat = NULL ; /* 04 Mar 2005 */
#endif
}
/*---------------------------------------------------------------------------*/
/*!
Destroy matrix data structure by deallocating memory.
*/
void matrix_destroy (matrix *m)
{
if (m->elts != NULL){
#ifdef DONT_USE_MATRIX_MAT
int i ;
for( i=0 ; i < m->rows ; i++ )
if( m->elts[i] != NULL ) free(m->elts[i]) ;
#endif
free(m->elts) ;
}
#ifndef DONT_USE_MATRIX_MAT
if( m->mat != NULL) free (m->mat ) ;
#endif
matrix_initialize (m);
}
/*---------------------------------------------------------------------------*/
/*!
Create matrix data structure by allocating memory and initializing values.
*/
void matrix_create (int rows, int cols, matrix *m)
{
register int i ;
matrix_destroy (m);
if ((rows < 0) || (cols < 0))
matrix_error ("Illegal dimensions for new matrix");
m->rows = rows;
m->cols = cols;
if ((rows < 1) || (cols < 1)) return;
m->elts = (double **) malloc (sizeof(double *) * rows);
if (m->elts == NULL)
matrix_error ("Memory allocation error");
#ifdef DONT_USE_MATRIX_MAT
for (i = 0; i < rows; i++){
m->elts[i] = (double *) calloc (sizeof(double) , cols);
if (m->elts[i] == NULL) matrix_error ("Memory allocation error");
}
#else
m->mat = (double *) calloc( sizeof(double) , rows*cols ) ;
if( m->mat == NULL )
matrix_error ("Memory allocation error");
for (i = 0; i < rows; i++)
m->elts[i] = m->mat + (i*cols) ; /* 04 Mar 2005: offsets into mat */
#endif
}
/*---------------------------------------------------------------------------*/
/*!
Print contents of matrix m.
*/
void matrix_print (matrix m)
{
int i=0, j=0;
int rows, cols;
double val ;
int ipr ;
rows = m.rows; if( rows < 1 ) return ;
cols = m.cols; if( cols < 1 ) return ;
for( i=0 ; i < rows ; i++ ){
for( j=0 ; j < cols ; j++ ){
val = (int)m.elts[i][j] ;
if( val != m.elts[i][j] || fabs(val) > 99.0 ) goto zork ;
}
}
zork:
ipr = (i==rows && j==cols) ;
for (i = 0; i < rows; i++)
{
for (j = 0; j < cols; j++)
if( ipr ) printf (" %3d" , (int)m.elts[i][j]);
else printf (" %10.4g", m.elts[i][j]);
printf (" \n");
}
printf (" \n"); fflush(stdout) ;
}
/*---------------------------------------------------------------------------*/
/*!
Print label and contents of matrix m.
*/
void matrix_sprint (char * s, matrix m)
{
printf ("%s \n", s);
matrix_print (m);
}
/*---------------------------------------------------------------------------*/
/*!
Print contents of matrix m to specified file.
*/
void matrix_file_write (char * filename, matrix m)
{
int i, j;
int rows, cols;
FILE * outfile = NULL;
/*----- First, check for empty file name -----*/
if (filename == NULL) matrix_error ("Missing matrix file name");
outfile = fopen (filename, "w");
rows = m.rows;
cols = m.cols;
for (i = 0; i < rows; i++)
{
for (j = 0; j < cols; j++)
fprintf (outfile, " %g", m.elts[i][j]);
fprintf (outfile, " \n");
}
fprintf (outfile, " \n");
fclose (outfile);
}
/*---------------------------------------------------------------------------*/
/*!
Manual entry of matrix data.
*/
void matrix_enter (matrix * m)
{
int rows, cols;
int i, j;
float fval;
printf ("Enter number of rows: "); fflush(stdout) ;
scanf ("%d", &rows);
printf ("Enter number of cols: "); fflush(stdout) ;
scanf ("%d", &cols);
matrix_create (rows, cols, m);
for (i = 0; i < rows; i++)
for (j = 0; j < cols; j++)
{
printf ("elts[%d][%d] = ", i, j); fflush(stdout);
scanf ("%f", &fval);
m->elts[i][j] = fval;
}
}
/*---------------------------------------------------------------------------*/
/*!
Read contents of matrix m from specified file.
If unable to read matrix from file, or matrix has wrong dimensions:
If error_exit flag is set, then print error message and exit.
Otherwise, return null matrix.
*/
void matrix_file_read (char * filename, int rows, int cols, matrix * m,
int error_exit)
{
int i, j;
MRI_IMAGE * flim; /* pointer to image structure
-- used to read ASCII file */
float * far; /* pointer to MRI_IMAGE floating point data */
char message [80]; /* error message */
/*----- First, check for empty file name -----*/
if (filename == NULL) matrix_error ("Missing matrix file name");
/*----- Read the matrix file -----*/
flim = mri_read_1D(filename);
if (flim == NULL) {
if (error_exit)
{
sprintf (message, "Unable to read matrix from file: %s", filename);
matrix_error (message);
}
else
{
matrix_destroy (m);
return;
}
}
/*----- Set pointer to data -----*/
far = MRI_FLOAT_PTR(flim);
/*----- Test for correct dimensions -----*/
if ( (rows != flim->nx) || (cols != flim->ny) ) {
if (error_exit)
{
sprintf (message,
"In matrix file: %s Expected: %d x %d Actual: %d x %d",
filename, rows, cols, flim->nx, flim->ny);
matrix_error (message);
}
else
{
matrix_destroy (m);
return;
}
}
matrix_create (rows, cols, m);
/*----- Copy data from image structure to matrix structure -----*/
for (i = 0; i < rows; i++)
for (j = 0; j < cols; j++)
m->elts[i][j] = far[i + j*rows];
{ mri_free (flim); flim = NULL; }
}
/*---------------------------------------------------------------------------*/
/*!
Convert simple array to matrix structure.
*/
void array_to_matrix (int rows, int cols, float ** f, matrix * m)
{
register int i, j;
matrix_create (rows, cols, m);
for (i = 0; i < rows; i++)
for (j = 0; j < cols; j++)
m->elts[i][j] = f[i][j];
}
/*---------------------------------------------------------------------------*/
/*!
Make a copy of the first matrix, return copy as the second matrix.
*/
void matrix_equate (matrix a, matrix * b)
{
register int i;
register int rows, cols;
rows = a.rows;
cols = a.cols;
matrix_create (rows, cols, b);
for (i = 0; i < rows; i++){
#if 0
for (j = 0; j < cols; j++)
b->elts[i][j] = a.elts[i][j];
#else
if( cols > 0 )
memcpy( b->elts[i] , a.elts[i] , sizeof(double)*cols ) ; /* RWCox */
#endif
}
}
/*---------------------------------------------------------------------------*/
/*!
Extending a matrix with nradd rows and ncadd columns (zero-filled).
*/
void matrix_enlarge( int nradd , int ncadd , matrix *a )
{
int i , rows, cols ;
matrix *b ;
if( ncadd < 0 ) ncadd = 0 ; /* no subtraction allowed */
if( nradd < 0 ) nradd = 0 ;
if( nradd == 0 && ncadd == 0 ) return ; /* nothing to do? */
rows = a->rows ; cols = a->cols ;
/* create bigger matrix with extra rows/columns */
b = (matrix *)malloc(sizeof(matrix)) ;
matrix_initialize( b ) ;
matrix_create( rows+nradd , cols+ncadd, b ) ; /* zero-filled */
/* copy row data from a into b */
if( cols > 0 ){
for( i=0 ; i < rows ; i++ ){
memcpy( b->elts[i] , a->elts[i] , sizeof(double)*cols ) ;
}
}
/* destroy contents of a, replace with contents of b */
matrix_destroy(a) ; *a = *b ; return ;
}
/*---------------------------------------------------------------------------*/
/*!
Extract p columns (specified by list) from matrix a. Result is matrix b.
*/
void matrix_extract (matrix a, int p, int *list, matrix * b)
{
register int i, j;
register int rows, cols;
rows = a.rows;
cols = p;
matrix_create (rows, cols, b);
for (i = 0; i < rows; i++)
for (j = 0; j < cols; j++)
b->elts[i][j] = a.elts[i][list[j]];
}
/*---------------------------------------------------------------------------*/
/*!
Extract p rows (specified by list) from matrix a. Result is matrix b.
*/
void matrix_extract_rows (matrix a, int p, int * list, matrix * b)
{
register int i, j;
register int rows, cols;
rows = p;
cols = a.cols;
matrix_create (rows, cols, b);
for (i = 0; i < rows; i++)
for (j = 0; j < cols; j++)
b->elts[i][j] = a.elts[list[i]][j];
}
/*---------------------------------------------------------------------------*/
/*!
Add columns that are all 0 except for a single 1, as indicated. [16 Aug 2019]
For use in 3dDeconvolve experimentation [RWC].
*/
void matrix_augment_01_columns( matrix a, int nadd, int *addlist, matrix *b )
{
int arows,brows , acols,bcols , i,j,k,aa ;
if( b == NULL ) return ; /* bad input */
if( nadd <= 0 || addlist == NULL ){ /* nothing to do but copy input */
matrix_equate(a,b) ; return ;
}
/* check addlist for bad entries */
for( aa=0 ; aa < nadd ; aa++ ){
if( addlist[aa] < 0 || addlist[aa] >= a.rows ){
fprintf(stderr,"** ERROR: bad index in matrix_augment_01_columns\n") ;
return ;
}
}
arows = brows = a.rows ;
acols = a.cols ;
bcols = acols + nadd ;
matrix_create( brows , bcols , b ) ;
/* copy original part */
for( i=0 ; i < brows ; i++ )
for( j=0 ; j < acols ; j++ ) b->elts[i][j] = a.elts[i][j] ;
/* add new cols */
for( aa=0 ; aa < nadd ; aa++ ){
k = addlist[aa] ; j = acols+aa ;
for( i=0 ; i < brows ; i++ )
b->elts[i][j] = (i==k) ? 1.0 : 0.0 ;
}
return ;
}
/*---------------------------------------------------------------------------*/
/*! Return value is number of rows deleted.
If this is zero, the output matrix *b is not created.
If the output matrix would have no rows
(return value == number of rows input), then *b is also not created.
*//*-------------------------------------------------------------------------*/
int matrix_delete_allzero_rows( matrix a , matrix *b )
{
int ii , jj , rows , cols , np=0 , *lp ;
rows = a.rows ;
cols = a.cols ; if( rows < 1 || cols < 1 || b == NULL ) return 0 ;
/* make list of rows to keep */
lp = (int *)malloc(sizeof(int)*rows) ;
for( ii=0 ; ii < rows ; ii++ ){
for( jj=0 ; jj < cols && a.elts[ii][jj] == 0.0 ; jj++ ) ; /*nada*/
if( jj < cols ) lp[np++] = ii ;
}
if( np > 0 && np < rows )
matrix_extract_rows( a , np , lp , b ) ;
free(lp) ; return (rows-np) ;
}
/*---------------------------------------------------------------------------*/
/*!
Create n x n identity matrix.
*/
void matrix_identity (int n, matrix * m)
{
register int i, j;
if (n < 0)
matrix_error ("Illegal dimensions for identity matrix");
matrix_create (n, n, m);
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
if (i == j)
m->elts[i][j] = 1.0;
else
m->elts[i][j] = 0.0;
}
/*---------------------------------------------------------------------------*/
/*!
Add matrix a to matrix b. Result is matrix c.
*/
void matrix_add (matrix a, matrix b, matrix * c)
{
register int rows, cols;
register int i, j;
if ((a.rows != b.rows) || (a.cols != b.cols))
matrix_error ("Incompatible dimensions for matrix addition");
rows = a.rows;
cols = a.cols;
matrix_create (rows, cols, c);
for (i = 0; i < rows; i++)
for (j = 0; j < cols; j++)
c->elts[i][j] = a.elts[i][j] + b.elts[i][j];
#ifdef ENABLE_FLOPS
flops += rows*cols ;
#endif
}
/*---------------------------------------------------------------------------*/
/*!
Subtract matrix b from matrix a. Result is matrix c.
*/
void matrix_subtract (matrix a, matrix b, matrix * c)
{
register int rows, cols;
register int i, j;
if ((a.rows != b.rows) || (a.cols != b.cols))
matrix_error ("Incompatible dimensions for matrix subtraction");
rows = a.rows;
cols = a.cols;
matrix_create (rows, cols, c);
for (i = 0; i < rows; i++)
for (j = 0; j < cols; j++)
c->elts[i][j] = a.elts[i][j] - b.elts[i][j];
#ifdef ENABLE_FLOPS
flops += rows*cols ;
#endif
}
/*---------------------------------------------------------------------------*/
/*!
Multiply matrix a by matrix b. Result is matrix c.
*/
void matrix_multiply (matrix a, matrix b, matrix * c)
{
int rows, cols;
register int i, j, k;
register double sum ;
if (a.cols != b.rows)
matrix_error ("Incompatible dimensions for matrix multiplication");
rows = a.rows;
cols = b.cols;
matrix_create (rows, cols, c);
for (i = 0; i < rows; i++)
for (j = 0; j < cols; j++)
{
sum = 0.0 ;
for (k = 0; k < a.cols; k++)
sum += a.elts[i][k] * b.elts[k][j];
c->elts[i][j] = sum;
}
#ifdef ENABLE_FLOPS
flops += 2.0*rows*cols*cols ;
#endif
}
/*---------------------------------------------------------------------------*/
/*!
Multiply matrix a by scalar constant k. Result is matrix c.
*/
void matrix_scale (double k, matrix a, matrix * c)
{
register int rows, cols;
register int i, j;
rows = a.rows;
cols = a.cols;
matrix_create (rows, cols, c);
for (i = 0; i < rows; i++)
for (j = 0; j < cols; j++)
c->elts[i][j] = k * a.elts[i][j];
#ifdef ENABLE_FLOPS
flops += rows*cols ;
#endif
}
/*---------------------------------------------------------------------------*/
/*!
Take transpose of matrix a. Result is matrix t.
*/
void matrix_transpose (matrix a, matrix * t)
{
register int rows, cols;
register int i, j;
rows = a.cols;
cols = a.rows;
matrix_create (rows, cols, t);
for (i = 0; i < rows; i++)
for (j = 0; j < cols; j++)
t->elts[i][j] = a.elts[j][i];
}
/*---------------------------------------------------------------------------*/
/*!
Use Gaussian elimination to calculate inverse of matrix a. Result is
matrix ainv.
*/
int matrix_inverse (matrix a, matrix * ainv)
{
const double epsilon = 1.0e-10;
matrix tmp;
register int i, j, ii, n;
register double fval;
register double fmax;
register double * p;
matrix_initialize (&tmp);
if (a.rows != a.cols)
matrix_error ("Illegal dimensions for matrix inversion");
#if 0
matrix_sprint("matrix_inverse:",a) ;
#endif
n = a.rows;
matrix_identity (n, ainv);
matrix_equate (a, &tmp);
for (i = 0; i < n; i++)
{
fmax = fabs(tmp.elts[i][i]);
for (j = i+1; j < n; j++)
if (fabs(tmp.elts[j][i]) > fmax)
{
fmax = fabs(tmp.elts[j][i]);
p = tmp.elts[i];
tmp.elts[i] = tmp.elts[j];
tmp.elts[j] = p;
p = ainv->elts[i];
ainv->elts[i] = ainv->elts[j];
ainv->elts[j] = p;
}
if (fmax < epsilon)
{
matrix_destroy (&tmp);
return (0);
}
fval = 1.0 / tmp.elts[i][i]; /* RWCox: change division by this to */
for (j = 0; j < n; j++) /* multiplication by 1.0/this */
{
tmp.elts[i][j] *= fval;
ainv->elts[i][j] *= fval;
}
for (ii = 0; ii < n; ii++)
if (ii != i)
{
fval = tmp.elts[ii][i];
for (j = 0; j < n; j++)
{
tmp.elts[ii][j] -= fval*tmp.elts[i][j];
ainv->elts[ii][j] -= fval*ainv->elts[i][j];
}
}
}
matrix_destroy (&tmp);
#ifdef ENABLE_FLOPS
flops += 3.0*n*n*n ;
#endif
return (1);
}
/*---------------------------------------------------------------------------*/
/*!
Use Gaussian elimination to calculate inverse of matrix a, with diagonal
scaling applied for stability. Result is matrix ainv.
*/
int matrix_inverse_dsc (matrix a, matrix * ainv) /* 15 Jul 2004 - RWCox */
{
matrix atmp;
register int i, j, n;
register double *diag ;
int mir ;
if (a.rows != a.cols)
matrix_error ("Illegal dimensions for matrix inversion");
matrix_initialize (&atmp);
n = a.rows;
matrix_equate (a, &atmp);
diag = (double *)malloc( sizeof(double)*n ) ;
for( i=0 ; i < n ; i++ ){
diag[i] = fabs(atmp.elts[i][i]) ;
if( diag[i] == 0.0 ) diag[i] = 1.0 ; /* shouldn't happen? */
diag[i] = 1.0 / sqrt(diag[i]) ;
}
for( i=0 ; i < n ; i++ ) /* scale a */
for( j=0 ; j < n ; j++ )
atmp.elts[i][j] *= diag[i]*diag[j] ;
mir = matrix_inverse( atmp , ainv ) ; /* invert */
for( i=0 ; i < n ; i++ ) /* scale inverse */
for( j=0 ; j < n ; j++ )
ainv->elts[i][j] *= diag[i]*diag[j] ;
matrix_destroy (&atmp);
free((void *)diag) ;
#ifdef ENABLE_FLOPS
flops += 4.0*n*n + 4.0*n ;
#endif
return (mir);
}
/*---------------------------------------------------------------------------*/
/*!
Calculate square root of symmetric positive definite matrix a.
Result is matrix s.
*/
int matrix_sqrt (matrix a, matrix * s)
{
const int MAX_ITER = 100;
int n;
int ok;
int iter;
register float sse, psse;
register int i, j;
matrix x, xinv, axinv, xtemp, error;
matrix_initialize (&x);
matrix_initialize (&xinv);
matrix_initialize (&axinv);
matrix_initialize (&xtemp);
matrix_initialize (&error);
if (a.rows != a.cols)
matrix_error ("Illegal dimensions for matrix square root");
n = a.rows;
matrix_identity (n, &x);
psse = 1.0e+30;
for (iter = 0; iter < MAX_ITER; iter++)
{
ok = matrix_inverse (x, &xinv);
if (! ok) return (0);
matrix_multiply (a, xinv, &axinv);
matrix_add (x, axinv, &xtemp);
matrix_scale (0.5, xtemp, &x);
matrix_multiply (x, x, &xtemp);
matrix_subtract (a, xtemp, &error);
sse = 0.0;
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
sse += error.elts[i][j] * error.elts[i][j] ;
if (sse >= psse) break;
psse = sse;
}
if (iter == MAX_ITER) return (0);
matrix_equate (x, s);
matrix_destroy (&x);
matrix_destroy (&xinv);
matrix_destroy (&axinv);
matrix_destroy (&xtemp);
matrix_destroy (&error); /* destroy error matrix too - 26 Mar 2008 drg */
return (1);
}
/*---------------------------------------------------------------------------*/
/*!
Initialize vector data structure.
*/
void vector_initialize (vector * v)
{
v->dim = 0;
v->elts = NULL;
}
/*---------------------------------------------------------------------------*/
/*!
Destroy vector data structure by deallocating memory.
*/
void vector_destroy (vector * v)
{
if (v->elts != NULL) free (v->elts);
vector_initialize (v);
}
/*---------------------------------------------------------------------------*/
/*!
Create vector v by allocating memory and initializing values.
*/
void vector_create (int dim, vector * v)
{
vector_destroy (v);
if (dim < 0) matrix_error ("Illegal dimensions for new vector");
v->dim = dim;
if (dim < 1) return;
v->elts = (double *) calloc (sizeof(double) , dim);
if (v->elts == NULL)