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/* cla_syrpvgrw.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 cla_syrpvgrw__(char *uplo, integer *n, integer *info, complex *a,
integer *lda, complex *af, integer *ldaf, integer *ipiv, real *work,
ftnlen uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, i__1, i__2, i__3;
real ret_val, r__1, r__2, r__3, r__4;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, j, k, kp;
real tmp, amax, umax;
extern logical lsame_(char *, char *);
integer ncols;
logical upper;
real 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 */
/* ======= */
/* CLA_SYRPVGRW 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. */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* INFO (input) INTEGER */
/* The value of INFO returned from CSYTRF, .i.e., the pivot in */
/* column INFO is exactly 0. */
/* NCOLS (input) INTEGER */
/* The number of columns of the matrix A. NCOLS >= 0. */
/* A (input) COMPLEX 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 array, dimension (LDAF,N) */
/* The block diagonal matrix D and the multipliers used to */
/* obtain the factor U or L as computed by CSYTRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* IPIV (input) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D */
/* as determined by CSYTRF. */
/* WORK (input) COMPLEX array, dimension (2*N) */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. 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;
--ipiv;
--work;
/* Function Body */
upper = lsame_("Upper", uplo);
if (*info == 0) {
if (upper) {
ncols = 1;
} else {
ncols = *n;
}
} else {
ncols = *info;
}
rpvgrw = 1.f;
i__1 = *n << 1;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.f;
}
/* Find the max magnitude entry of each column of A. Compute the max */
/* for all N columns so we can apply the pivot permutation while */
/* looping below. Assume a full factorization is the common case. */
if (upper) {
i__1 = *n;
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;
r__3 = (r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&a[i__
+ j * a_dim1]), dabs(r__2)), r__4 = work[*n + i__];
work[*n + i__] = dmax(r__3,r__4);
/* Computing MAX */
i__3 = i__ + j * a_dim1;
r__3 = (r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&a[i__
+ j * a_dim1]), dabs(r__2)), r__4 = work[*n + j];
work[*n + j] = dmax(r__3,r__4);
}
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * a_dim1;
r__3 = (r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&a[i__
+ j * a_dim1]), dabs(r__2)), r__4 = work[*n + i__];
work[*n + i__] = dmax(r__3,r__4);
/* Computing MAX */
i__3 = i__ + j * a_dim1;
r__3 = (r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&a[i__
+ j * a_dim1]), dabs(r__2)), r__4 = work[*n + j];
work[*n + j] = dmax(r__3,r__4);
}
}
}
/* Now find the max magnitude entry of each column of U or L. Also */
/* permute the magnitudes of A above so they're in the same order as */
/* the factor. */
/* The iteration orders and permutations were copied from csytrs. */
/* Calls to SSWAP would be severe overkill. */
if (upper) {
k = *n;
while(k < ncols && k > 0) {
if (ipiv[k] > 0) {
/* 1x1 pivot */
kp = ipiv[k];
if (kp != k) {
tmp = work[*n + k];
work[*n + k] = work[*n + kp];
work[*n + kp] = tmp;
}
i__1 = k;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
i__2 = i__ + k * af_dim1;
r__3 = (r__1 = af[i__2].r, dabs(r__1)) + (r__2 = r_imag(&
af[i__ + k * af_dim1]), dabs(r__2)), r__4 = work[
k];
work[k] = dmax(r__3,r__4);
}
--k;
} else {
/* 2x2 pivot */
kp = -ipiv[k];
tmp = work[*n + k - 1];
work[*n + k - 1] = work[*n + kp];
work[*n + kp] = tmp;
i__1 = k - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
i__2 = i__ + k * af_dim1;
r__3 = (r__1 = af[i__2].r, dabs(r__1)) + (r__2 = r_imag(&
af[i__ + k * af_dim1]), dabs(r__2)), r__4 = work[
k];
work[k] = dmax(r__3,r__4);
/* Computing MAX */
i__2 = i__ + (k - 1) * af_dim1;
r__3 = (r__1 = af[i__2].r, dabs(r__1)) + (r__2 = r_imag(&
af[i__ + (k - 1) * af_dim1]), dabs(r__2)), r__4 =
work[k - 1];
work[k - 1] = dmax(r__3,r__4);
}
/* Computing MAX */
i__1 = k + k * af_dim1;
r__3 = (r__1 = af[i__1].r, dabs(r__1)) + (r__2 = r_imag(&af[k
+ k * af_dim1]), dabs(r__2)), r__4 = work[k];
work[k] = dmax(r__3,r__4);
k += -2;
}
}
k = ncols;
while(k <= *n) {
if (ipiv[k] > 0) {
kp = ipiv[k];
if (kp != k) {
tmp = work[*n + k];
work[*n + k] = work[*n + kp];
work[*n + kp] = tmp;
}
++k;
} else {
kp = -ipiv[k];
tmp = work[*n + k];
work[*n + k] = work[*n + kp];
work[*n + kp] = tmp;
k += 2;
}
}
} else {
k = 1;
while(k <= ncols) {
if (ipiv[k] > 0) {
/* 1x1 pivot */
kp = ipiv[k];
if (kp != k) {
tmp = work[*n + k];
work[*n + k] = work[*n + kp];
work[*n + kp] = tmp;
}
i__1 = *n;
for (i__ = k; i__ <= i__1; ++i__) {
/* Computing MAX */
i__2 = i__ + k * af_dim1;
r__3 = (r__1 = af[i__2].r, dabs(r__1)) + (r__2 = r_imag(&
af[i__ + k * af_dim1]), dabs(r__2)), r__4 = work[
k];
work[k] = dmax(r__3,r__4);
}
++k;
} else {
/* 2x2 pivot */
kp = -ipiv[k];
tmp = work[*n + k + 1];
work[*n + k + 1] = work[*n + kp];
work[*n + kp] = tmp;
i__1 = *n;
for (i__ = k + 1; i__ <= i__1; ++i__) {
/* Computing MAX */
i__2 = i__ + k * af_dim1;
r__3 = (r__1 = af[i__2].r, dabs(r__1)) + (r__2 = r_imag(&
af[i__ + k * af_dim1]), dabs(r__2)), r__4 = work[
k];
work[k] = dmax(r__3,r__4);
/* Computing MAX */
i__2 = i__ + (k + 1) * af_dim1;
r__3 = (r__1 = af[i__2].r, dabs(r__1)) + (r__2 = r_imag(&
af[i__ + (k + 1) * af_dim1]), dabs(r__2)), r__4 =
work[k + 1];
work[k + 1] = dmax(r__3,r__4);
}
/* Computing MAX */
i__1 = k + k * af_dim1;
r__3 = (r__1 = af[i__1].r, dabs(r__1)) + (r__2 = r_imag(&af[k
+ k * af_dim1]), dabs(r__2)), r__4 = work[k];
work[k] = dmax(r__3,r__4);
k += 2;
}
}
k = ncols;
while(k >= 1) {
if (ipiv[k] > 0) {
kp = ipiv[k];
if (kp != k) {
tmp = work[*n + k];
work[*n + k] = work[*n + kp];
work[*n + kp] = tmp;
}
--k;
} else {
kp = -ipiv[k];
tmp = work[*n + k];
work[*n + k] = work[*n + kp];
work[*n + kp] = tmp;
k += -2;
}
}
}
/* 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 (upper) {
i__1 = *n;
for (i__ = ncols; i__ <= i__1; ++i__) {
umax = work[i__];
amax = work[*n + i__];
if (umax != 0.f) {
/* Computing MIN */
r__1 = amax / umax;
rpvgrw = dmin(r__1,rpvgrw);
}
}
} else {
i__1 = ncols;
for (i__ = 1; i__ <= i__1; ++i__) {
umax = work[i__];
amax = work[*n + i__];
if (umax != 0.f) {
/* Computing MIN */
r__1 = amax / umax;
rpvgrw = dmin(r__1,rpvgrw);
}
}
}
ret_val = rpvgrw;
return ret_val;
} /* cla_syrpvgrw__ */
|
