void matlib_xvwrite_csv
(
char* file_name,
matlib_index n,
matlib_xv v[n]
)
{
FILE *fp = fopen(file_name, "w+");
if(fp==NULL)
{
term_exec("failed to create the file '%s'", file_name );
}
matlib_index i, j;
for (i=0; i<v->len; i++)
{
for (j=0; j<n-1; j++)
{
fprintf(fp, "% 0.16f\t", v[j].elem_p[i]);
}
fprintf(fp, "% 0.16f\n", v[j].elem_p[i]);
}
fclose(fp);
}
void matlib_xmwrite_csv(char* file_name, matlib_xm M)
{
FILE *fp = fopen(file_name, "w+");
#if 1
if(fp==NULL)
{
term_exec("failed to create the file '%s'", file_name );
}
#endif
matlib_index i, j, col_st, row_st;
if(M.order == MATLIB_COL_MAJOR)
{
col_st = 1;
row_st = M.lenc;
}
else if(M.order == MATLIB_ROW_MAJOR)
{
col_st = M.lenr;
row_st = 1;
}
else
{
term_exec( "Storage order unknown (order: %d)", M.order);
}
for (i=0; i<M.lenc; i++)
{
for (j=0; j<M.lenr-1; j++)
{
fprintf(fp, "% 0.16f\t", M.elem_p[i*col_st+j*row_st]);
}
fprintf(fp, "% 0.16f\n", M.elem_p[i*col_st+j*row_st]);
}
fclose(fp);
}
void matlib_xzvwrite_csv
(
char* file_name,
matlib_index m,
matlib_xv u[m],
matlib_index n,
matlib_zv v[n]
)
{
FILE *fp = fopen(file_name, "w+");
if(fp==NULL)
{
term_exec("failed to create the file '%s'", file_name );
}
matlib_index i, j, k;
for (i=0; i<u->len; i++)
{
for (j=0; j<m-1; j++)
{
fprintf(fp, "% 0.16f\t", u[j].elem_p[i]);
}
if(n>0)
{
fprintf(fp, "% 0.16f\t", u[j].elem_p[i]);
for (k=0; k<n-1; k++)
{
fprintf(fp, "% 0.16f%+0.16fi\t", v[k].elem_p[i]);
}
fprintf(fp, "% 0.16f%+0.16fi\n", v[k].elem_p[i]);
}
else
{
fprintf(fp, "% 0.16f\n", u[j].elem_p[i]);
}
}
fclose(fp);
}
static void execterm(char **args)
{
if (!mainterm())
term_exec(args);
}
void jacobi_find_zeros
(
matlib_index n,
double a,
double b,
double *zeros,
double tol
)
/*
* Description: This function calculates the zeros of the Jacobi polynomial
* $J^{(a,b)_n(x)}$. A combination of bisection and Newton's method is used to
* find the roots.
*
* Input(s):
* n - order of the Jacobi polynomials
* a,b - Jacobi polynomial parameters, $a,b \in[-1/2,1/2]$
* tol - numerical tolerance
*
* Output(s):
* zeros - roots of the Jacobi polynomial
*
**/
{
double JP[2], dJP, *C, e;
double x, xa, xb, xmid;
double JPa, tmp;
matlib_index i, j = 0;
double theta = M_PI/(n+0.5);
/* Perform the check on a and b parameters. */
bool param_valid = ((fabs(a)<0.5) & (fabs(b)<0.5));
if (!param_valid)
{
term_exec( "parameters outside the range (-0.5,0.5): a=%0.4f, b=%0.4f", a, b);
}
/* Coefficients for the recurrence relation for Jacobi polynomials */
double C1[n+1], D[n-1], E[n-1];
C1[0] = 0.5*(a-b);
C1[1] = 0.5*(a+b+2);
for( i=2; i<(n+1); i++){
tmp = 2*i*(i+a+b)*(2*i-2+a+b);
C1[i] = (2*i-1+a+b)*(a*a-b*b)/tmp;
D[i-2] = (2*i-2+a+b)*(2*i-1+a+b)*(2*i+a+b)/tmp;
E[i-2] = 2*(i-1+a)*(i-1+b)*(2*i+a+b)/tmp;
}
C = calloc(3, sizeof(double));
tmp = 2.0*n+a+b;
*(C+0) = n*(a-b)/tmp;
*(C+1) = n*(2.0*n+a+b)/tmp;
*(C+2) = 2.0*(n+a)*(n+b)/tmp;
if(n>0)
{
for( i=0; i<n; i++)
{
/* Determine the bracketting interval */
xa = -cos((i+0.5)*theta);
xb = -cos((i+1)*theta);
jacobi_calcjp( n, a, b, xa, C1, D, E, JP);
JPa = *(JP+1);
jacobi_calcjp( n, a, b, xb, C1, D, E, JP);
tmp = JPa**(JP+1);
/* exit if the bracketting interval does not contain even one root
* */
if(tmp>0)
{
term_exec("Root does not lie in: [% 0.16f, % 0.16f]", xa, xb);
}
xmid = 0.5*(xa+xb);
jacobi_calcjp( n, a, b, xmid, C1, D, E, JP);
e = fabs(*(JP+1));
if(e>tol)
{
tmp = JPa**(JP+1);
if(tmp<0)
xb = xmid;
else
{
xa = xmid;
JPa = *(JP+1);
}
}
x = xmid;
while(e>tol && j<JCOBI_ITER_MAX)
{
/* Newton step is only used to find a better bracketting
* interval.
* */
dJP = ((*(C+0)-x**(C+1))**(JP+1)+*(C+2)**(JP+0))/(1-x*x);
xmid = x-*(JP+1)/dJP;
jacobi_calcjp( n, a, b, xmid, C1, D, E, JP);
e = fabs(*(JP+1));
if(e>tol)
{
if(xmid>xa && xmid<xb)
{
tmp = JPa**(JP+1);
if(tmp<0)
xb = xmid;
else
{
xa = xmid;
JPa = *(JP+1);
}
}
else
xmid = 0.5*(xa+xb);
x = xmid;
}
j++;
}
if (j>JCOBI_ITER_MAX)
{
term_exec("Threshold iteration reached (j=%d)", j);
}
j = 0;
*zeros = xmid;
zeros++;
}
}
}
