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/* deri21.f -- translated by f2c (version 19991025).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#include "f2c.h"
/* Subroutine */ int deri21_(a, nvar, minear, nfirst, vnert, pnert, b, ncut)
doublereal *a;
integer *nvar, *minear, *nfirst;
doublereal *vnert, *pnert, *b;
integer *ncut;
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
/* Builtin functions */
double sqrt();
/* Local variables */
static doublereal work[4];
static integer i__, j, l;
extern /* Subroutine */ int hqrii_(), mtxmc_();
static doublereal cutoff;
extern /* Subroutine */ int mxm_();
static doublereal sum, sum2;
/* *********************************************************************** */
/* LEAST-SQUARE ANALYSIS OF A SET OF NVAR POINTS {A} : */
/* PRODUCE A SUBSET OF NCUT ORTHONORMALIZED VECTORS B, OPTIMUM IN A */
/* LEAST-SQUARE SENSE WITH RESPECT TO THE INITIAL SPACE {A}. */
/* EACH NEW HIERARCHIZED VECTOR B EXTRACTS A MAXIMUM PERCENTAGE FROM */
/* THE REMAINING DISPERSION OF THE SET {A} OUT OF THE PREVIOUS */
/* {B} SUBSPACE. */
/* INPUT */
/* A(MINEAR,NVAR): ORIGINAL SET {A}. */
/* NFIRST : MAXIMUM ALLOWED SIZE OF THE BASIS B. */
/* OUTPUT */
/* VNERT(NVAR) : LOWEST EIGENVECTOR OF A'* A. */
/* PNERT(NVAR) : SQUARE ROOT OF THE ASSOCIATED EIGENVALUES */
/* IN DECREASING ORDER. */
/* B(MINEAR,NCUT): OPTIMUM ORTHONORMALIZED SUBSET {B}. */
/* *********************************************************************** */
/* VNERT = A' * A */
/* Parameter adjustments */
--pnert;
--vnert;
b_dim1 = *minear;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
a_dim1 = *minear;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
/* Function Body */
cutoff = .85;
sum2 = 0.;
mtxmc_(&a[a_offset], nvar, &a[a_offset], minear, work);
i__1 = *nvar * (*nvar + 1) / 2;
for (i__ = 1; i__ <= i__1; ++i__) {
/* L10: */
work[i__ - 1] = -work[i__ - 1];
}
/* DIAGONALIZE IN DECREASING ORDER OF EIGENVALUES */
if (abs(work[0]) < 1e-28 && *nvar == 1) {
pnert[1] = sqrt(-work[0]);
work[0] = 1e15;
vnert[1] = 1.;
*ncut = 1;
goto L50;
} else {
hqrii_(work, nvar, nvar, &pnert[1], &vnert[1]);
/* FIND NCUT ACCORDING TO CUTOFF, BUILD WORK = VNERT * (PNERT)**-0.5 */
sum = 0.;
i__1 = *nvar;
for (i__ = 1; i__ <= i__1; ++i__) {
/* L20: */
sum -= pnert[i__];
}
l = 1;
i__1 = *nfirst;
for (i__ = 1; i__ <= i__1; ++i__) {
sum2 -= pnert[i__] / sum;
pnert[i__] = sqrt(-pnert[i__]);
i__2 = *nvar;
for (j = 1; j <= i__2; ++j) {
work[l - 1] = vnert[l] / pnert[i__];
/* L30: */
++l;
}
if (sum2 >= cutoff) {
*ncut = i__;
goto L50;
}
/* L40: */
}
*ncut = *nfirst;
/* ORTHONORMALIZED BASIS */
/* B(MINEAR,NCUT) = A(MINEAR,NVAR)*WORK(NVAR,NCUT) */
}
L50:
mxm_(&a[a_offset], minear, work, nvar, &b[b_offset], ncut);
return 0;
} /* deri21_ */
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