/* dla_porcond.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"
/* Table of constant values */
static integer c__1 = 1;
doublereal dla_porcond__(char *uplo, integer *n, doublereal *a, integer *lda,
doublereal *af, integer *ldaf, integer *cmode, doublereal *c__,
integer *info, doublereal *work, integer *iwork, ftnlen uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, i__1, i__2;
doublereal ret_val, d__1;
/* Local variables */
integer i__, j;
logical up;
doublereal tmp;
integer kase;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *), xerbla_(char *,
integer *);
doublereal ainvnm;
extern /* Subroutine */ int dpotrs_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *);
/* -- 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 */
/* ======= */
/* DLA_PORCOND Estimates the Skeel condition number of op(A) * op2(C) */
/* where op2 is determined by CMODE as follows */
/* CMODE = 1 op2(C) = C */
/* CMODE = 0 op2(C) = I */
/* CMODE = -1 op2(C) = inv(C) */
/* The Skeel condition number cond(A) = norminf( |inv(A)||A| ) */
/* is computed by computing scaling factors R such that */
/* diag(R)*A*op2(C) is row equilibrated and computing the standard */
/* infinity-norm condition number. */
/* Arguments */
/* ========== */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* A (input) REAL 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) DOUBLE PRECISION 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 DPOTRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* CMODE (input) INTEGER */
/* Determines op2(C) in the formula op(A) * op2(C) as follows: */
/* CMODE = 1 op2(C) = C */
/* CMODE = 0 op2(C) = I */
/* CMODE = -1 op2(C) = inv(C) */
/* C (input) DOUBLE PRECISION array, dimension (N) */
/* The vector C in the formula op(A) * op2(C). */
/* INFO (output) INTEGER */
/* = 0: Successful exit. */
/* i > 0: The ith argument is invalid. */
/* WORK (input) DOUBLE PRECISION array, dimension (3*N). */
/* Workspace. */
/* IWORK (input) INTEGER array, dimension (N). */
/* Workspace. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. 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;
--c__;
--work;
--iwork;
/* Function Body */
ret_val = 0.;
*info = 0;
if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DLA_PORCOND", &i__1);
return ret_val;
}
if (*n == 0) {
ret_val = 1.;
return ret_val;
}
up = FALSE_;
if (lsame_(uplo, "U")) {
up = TRUE_;
}
/* Compute the equilibration matrix R such that */
/* inv(R)*A*C has unit 1-norm. */
if (up) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 0.;
if (*cmode == 1) {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
tmp += (d__1 = a[j + i__ * a_dim1] * c__[j], abs(d__1));
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
tmp += (d__1 = a[i__ + j * a_dim1] * c__[j], abs(d__1));
}
} else if (*cmode == 0) {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
tmp += (d__1 = a[j + i__ * a_dim1], abs(d__1));
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
tmp += (d__1 = a[i__ + j * a_dim1], abs(d__1));
}
} else {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
tmp += (d__1 = a[j + i__ * a_dim1] / c__[j], abs(d__1));
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
tmp += (d__1 = a[i__ + j * a_dim1] / c__[j], abs(d__1));
}
}
work[(*n << 1) + i__] = tmp;
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 0.;
if (*cmode == 1) {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
tmp += (d__1 = a[i__ + j * a_dim1] * c__[j], abs(d__1));
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
tmp += (d__1 = a[j + i__ * a_dim1] * c__[j], abs(d__1));
}
} else if (*cmode == 0) {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
tmp += (d__1 = a[i__ + j * a_dim1], abs(d__1));
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
tmp += (d__1 = a[j + i__ * a_dim1], abs(d__1));
}
} else {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
tmp += (d__1 = a[i__ + j * a_dim1] / c__[j], abs(d__1));
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
tmp += (d__1 = a[j + i__ * a_dim1] / c__[j], abs(d__1));
}
}
work[(*n << 1) + i__] = tmp;
}
}
/* Estimate the norm of inv(op(A)). */
ainvnm = 0.;
kase = 0;
L10:
dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
if (kase != 0) {
if (kase == 2) {
/* Multiply by R. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] *= work[(*n << 1) + i__];
}
if (up) {
dpotrs_("Upper", n, &c__1, &af[af_offset], ldaf, &work[1], n,
info);
} else {
dpotrs_("Lower", n, &c__1, &af[af_offset], ldaf, &work[1], n,
info);
}
/* Multiply by inv(C). */
if (*cmode == 1) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] /= c__[i__];
}
} else if (*cmode == -1) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] *= c__[i__];
}
}
} else {
/* Multiply by inv(C'). */
if (*cmode == 1) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] /= c__[i__];
}
} else if (*cmode == -1) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] *= c__[i__];
}
}
if (up) {
dpotrs_("Upper", n, &c__1, &af[af_offset], ldaf, &work[1], n,
info);
} else {
dpotrs_("Lower", n, &c__1, &af[af_offset], ldaf, &work[1], n,
info);
}
/* Multiply by R. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] *= work[(*n << 1) + i__];
}
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) {
ret_val = 1. / ainvnm;
}
return ret_val;
} /* dla_porcond__ */