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/* sdisna.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Subroutine */ int sdisna_(char *job, integer *m, integer *n, real *d__,
real *sep, integer *info)
{
/* System generated locals */
integer i__1;
real r__1, r__2, r__3;
/* Local variables */
integer i__, k;
real eps;
logical decr, left, incr, sing, eigen;
extern logical lsame_(char *, char *);
real anorm;
logical right;
real oldgap;
extern doublereal slamch_(char *);
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
real newgap, thresh;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SDISNA computes the reciprocal condition numbers for the eigenvectors */
/* of a real symmetric or complex Hermitian matrix or for the left or */
/* right singular vectors of a general m-by-n matrix. The reciprocal */
/* condition number is the 'gap' between the corresponding eigenvalue or */
/* singular value and the nearest other one. */
/* The bound on the error, measured by angle in radians, in the I-th */
/* computed vector is given by */
/* SLAMCH( 'E' ) * ( ANORM / SEP( I ) ) */
/* where ANORM = 2-norm(A) = max( abs( D(j) ) ). SEP(I) is not allowed */
/* to be smaller than SLAMCH( 'E' )*ANORM in order to limit the size of */
/* the error bound. */
/* SDISNA may also be used to compute error bounds for eigenvectors of */
/* the generalized symmetric definite eigenproblem. */
/* Arguments */
/* ========= */
/* JOB (input) CHARACTER*1 */
/* Specifies for which problem the reciprocal condition numbers */
/* should be computed: */
/* = 'E': the eigenvectors of a symmetric/Hermitian matrix; */
/* = 'L': the left singular vectors of a general matrix; */
/* = 'R': the right singular vectors of a general matrix. */
/* M (input) INTEGER */
/* The number of rows of the matrix. M >= 0. */
/* N (input) INTEGER */
/* If JOB = 'L' or 'R', the number of columns of the matrix, */
/* in which case N >= 0. Ignored if JOB = 'E'. */
/* D (input) REAL array, dimension (M) if JOB = 'E' */
/* dimension (min(M,N)) if JOB = 'L' or 'R' */
/* The eigenvalues (if JOB = 'E') or singular values (if JOB = */
/* 'L' or 'R') of the matrix, in either increasing or decreasing */
/* order. If singular values, they must be non-negative. */
/* SEP (output) REAL array, dimension (M) if JOB = 'E' */
/* dimension (min(M,N)) if JOB = 'L' or 'R' */
/* The reciprocal condition numbers of the vectors. */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
--sep;
--d__;
/* Function Body */
*info = 0;
eigen = lsame_(job, "E");
left = lsame_(job, "L");
right = lsame_(job, "R");
sing = left || right;
if (eigen) {
k = *m;
} else if (sing) {
k = min(*m,*n);
}
if (! eigen && ! sing) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (k < 0) {
*info = -3;
} else {
incr = TRUE_;
decr = TRUE_;
i__1 = k - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
if (incr) {
incr = incr && d__[i__] <= d__[i__ + 1];
}
if (decr) {
decr = decr && d__[i__] >= d__[i__ + 1];
}
/* L10: */
}
if (sing && k > 0) {
if (incr) {
incr = incr && 0.f <= d__[1];
}
if (decr) {
decr = decr && d__[k] >= 0.f;
}
}
if (! (incr || decr)) {
*info = -4;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SDISNA", &i__1);
return 0;
}
/* Quick return if possible */
if (k == 0) {
return 0;
}
/* Compute reciprocal condition numbers */
if (k == 1) {
sep[1] = slamch_("O");
} else {
oldgap = (r__1 = d__[2] - d__[1], dabs(r__1));
sep[1] = oldgap;
i__1 = k - 1;
for (i__ = 2; i__ <= i__1; ++i__) {
newgap = (r__1 = d__[i__ + 1] - d__[i__], dabs(r__1));
sep[i__] = dmin(oldgap,newgap);
oldgap = newgap;
/* L20: */
}
sep[k] = oldgap;
}
if (sing) {
if (left && *m > *n || right && *m < *n) {
if (incr) {
sep[1] = dmin(sep[1],d__[1]);
}
if (decr) {
/* Computing MIN */
r__1 = sep[k], r__2 = d__[k];
sep[k] = dmin(r__1,r__2);
}
}
}
/* Ensure that reciprocal condition numbers are not less than */
/* threshold, in order to limit the size of the error bound */
eps = slamch_("E");
safmin = slamch_("S");
/* Computing MAX */
r__2 = dabs(d__[1]), r__3 = (r__1 = d__[k], dabs(r__1));
anorm = dmax(r__2,r__3);
if (anorm == 0.f) {
thresh = eps;
} else {
/* Computing MAX */
r__1 = eps * anorm;
thresh = dmax(r__1,safmin);
}
i__1 = k;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
r__1 = sep[i__];
sep[i__] = dmax(r__1,thresh);
/* L30: */
}
return 0;
/* End of SDISNA */
} /* sdisna_ */
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