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/* zla_porpvgrw.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"
doublereal zla_porpvgrw__(char *uplo, integer *ncols, doublecomplex *a,
integer *lda, doublecomplex *af, integer *ldaf, doublereal *work,
ftnlen uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, i__1, i__2, i__3;
doublereal ret_val, d__1, d__2, d__3, d__4;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
integer i__, j;
doublereal amax, umax;
extern logical lsame_(char *, char *);
logical upper;
doublereal rpvgrw;
/* -- LAPACK routine (version 3.2.1) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- April 2009 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLA_PORPVGRW computes the reciprocal pivot growth factor */
/* norm(A)/norm(U). The "max absolute element" norm is used. If this is */
/* much less than 1, the stability of the LU factorization of the */
/* (equilibrated) matrix A could be poor. This also means that the */
/* solution X, estimated condition numbers, and error bounds could be */
/* unreliable. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* NCOLS (input) INTEGER */
/* The number of columns of the matrix A. NCOLS >= 0. */
/* A (input) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input) COMPLEX*16 array, dimension (LDAF,N) */
/* The triangular factor U or L from the Cholesky factorization */
/* A = U**T*U or A = L*L**T, as computed by ZPOTRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* WORK (input) COMPLEX*16 array, dimension (2*N) */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--work;
/* Function Body */
upper = lsame_("Upper", uplo);
/* DPOTRF will have factored only the NCOLSxNCOLS leading minor, so */
/* we restrict the growth search to that minor and use only the first */
/* 2*NCOLS workspace entries. */
rpvgrw = 1.;
i__1 = *ncols << 1;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
}
/* Find the max magnitude entry of each column. */
if (upper) {
i__1 = *ncols;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * a_dim1;
d__3 = (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[i__
+ j * a_dim1]), abs(d__2)), d__4 = work[*ncols + j];
work[*ncols + j] = max(d__3,d__4);
}
}
} else {
i__1 = *ncols;
for (j = 1; j <= i__1; ++j) {
i__2 = *ncols;
for (i__ = j; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * a_dim1;
d__3 = (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[i__
+ j * a_dim1]), abs(d__2)), d__4 = work[*ncols + j];
work[*ncols + j] = max(d__3,d__4);
}
}
}
/* Now find the max magnitude entry of each column of the factor in */
/* AF. No pivoting, so no permutations. */
if (lsame_("Upper", uplo)) {
i__1 = *ncols;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * af_dim1;
d__3 = (d__1 = af[i__3].r, abs(d__1)) + (d__2 = d_imag(&af[
i__ + j * af_dim1]), abs(d__2)), d__4 = work[j];
work[j] = max(d__3,d__4);
}
}
} else {
i__1 = *ncols;
for (j = 1; j <= i__1; ++j) {
i__2 = *ncols;
for (i__ = j; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * af_dim1;
d__3 = (d__1 = af[i__3].r, abs(d__1)) + (d__2 = d_imag(&af[
i__ + j * af_dim1]), abs(d__2)), d__4 = work[j];
work[j] = max(d__3,d__4);
}
}
}
/* Compute the *inverse* of the max element growth factor. Dividing */
/* by zero would imply the largest entry of the factor's column is */
/* zero. Than can happen when either the column of A is zero or */
/* massive pivots made the factor underflow to zero. Neither counts */
/* as growth in itself, so simply ignore terms with zero */
/* denominators. */
if (lsame_("Upper", uplo)) {
i__1 = *ncols;
for (i__ = 1; i__ <= i__1; ++i__) {
umax = work[i__];
amax = work[*ncols + i__];
if (umax != 0.) {
/* Computing MIN */
d__1 = amax / umax;
rpvgrw = min(d__1,rpvgrw);
}
}
} else {
i__1 = *ncols;
for (i__ = 1; i__ <= i__1; ++i__) {
umax = work[i__];
amax = work[*ncols + i__];
if (umax != 0.) {
/* Computing MIN */
d__1 = amax / umax;
rpvgrw = min(d__1,rpvgrw);
}
}
}
ret_val = rpvgrw;
return ret_val;
} /* zla_porpvgrw__ */
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