/* nag_zgeevx (f08npc) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.1, 2017.
*/

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf08.h>
#include <nagx02.h>
#include <naga02.h>

int main(void)
{
/* Scalars */
double abnrm, eps, rcnd, tol;
Integer i, ihi, ilo, j, n, pda, pdvl, pdvr;
Integer exit_status = 0;
/* Arrays */
Complex *a = 0, *vl = 0, *vr = 0, *w = 0;
double *rconde = 0, *rcondv = 0, *scale = 0;

/* Nag Types */
NagError fail;
Nag_OrderType order;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J)  a[(J-1)*pda + I - 1]
#define VR(I, J) vr[(J)*pdvr + I]
order = Nag_ColMajor;
#else
#define A(I, J)  a[(I-1)*pda + J - 1]
#define VR(I, J) vr[(I)*pdvr + J]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_zgeevx (f08npc) Example Program Results\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%*[^\n]", &n);

pda = n;
pdvl = n;
pdvr = n;
/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, Complex)) ||
!(vl = NAG_ALLOC(n * n, Complex)) ||
!(vr = NAG_ALLOC(n * n, Complex)) ||
!(w = NAG_ALLOC(n, Complex)) ||
!(rconde = NAG_ALLOC(n, double)) ||
!(rcondv = NAG_ALLOC(n, double)) || !(scale = NAG_ALLOC(n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read the matrix A from data file */
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im);
scanf("%*[^\n]");

/* Solve the eigenvalue problem using nag_zgeevx (f08npc). */
nag_zgeevx(order, Nag_BalanceBoth, Nag_LeftVecs, Nag_RightVecs,
Nag_RCondBoth, n, a, pda, w, vl, pdvl, vr, pdvr, &ilo, &ihi,
scale, &abnrm, rconde, rcondv, &fail);

if (fail.code != NE_NOERROR) {
printf("Error from nag_zgeevx (f08npc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Compute the machine precision */
eps = nag_machine_precision;
tol = eps * abnrm;

/* Normalize the eigenvectors */
for (j = 0; j < n; j++)
for (i = n - 1; i >= 0; i--)
VR(i, j) = nag_complex_divide(VR(i, j), VR(0, j));

/* Print the eigenvalues/vectors, associated condition number and bounds. */
for (j = 0; j < n; ++j) {
/* Print information on j-th eigenvalue */
printf("\n\nEigenvalue %3" NAG_IFMT "%14s= ", j + 1, "");
if (w[j].im == 0.)
printf("%12.4e\n", w[j].re);
else
printf("(%13.4e, %13.4e)\n", w[j].re, w[j].im);

rcnd = rconde[j];
printf("\nReciprocal condition number = %9.1e\n", rcnd);
if (rcnd > 0.0)
printf("Error bound                 = %9.1e\n", tol / rcnd);
else
printf("Error bound is infinite\n");

/* Print information on j-th eigenvector */
printf("\nEigenvector %2" NAG_IFMT "\n", j + 1);
for (i = 0; i < n; ++i)
printf("%30s(%13.4e, %13.4e)\n", "", VR(i, j).re, VR(i, j).im);

rcnd = rcondv[j];
printf("\nReciprocal condition number = %9.1e\n", rcnd);
if (rcnd > 0.0)
printf("Error bound                 = %9.1e\n", tol / rcnd);
else
printf("Error bound is infinite\n");
}

END:
NAG_FREE(a);
NAG_FREE(vl);
NAG_FREE(vr);
NAG_FREE(w);
NAG_FREE(rconde);
NAG_FREE(rcondv);
NAG_FREE(scale);

return exit_status;
}

#undef A
#undef VR