#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int zgeequ_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublereal *r__, doublereal *c__, doublereal *rowcnd,
doublereal *colcnd, doublereal *amax, integer *info)
{
/* -- LAPACK routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
ZGEEQU computes row and column scalings intended to equilibrate an
M-by-N matrix A and reduce its condition number. R returns the row
scale factors and C the column scale factors, chosen to try to make
the largest element in each row and column of the matrix B with
elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
R(i) and C(j) are restricted to be between SMLNUM = smallest safe
number and BIGNUM = largest safe number. Use of these scaling
factors is not guaranteed to reduce the condition number of A but
works well in practice.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input) COMPLEX*16 array, dimension (LDA,N)
The M-by-N matrix whose equilibration factors are
to be computed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
R (output) DOUBLE PRECISION array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale factors
for A.
C (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND (output) DOUBLE PRECISION
If INFO = 0 or INFO > M, ROWCND contains the ratio of the
smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
AMAX is neither too large nor too small, it is not worth
scaling by R.
COLCND (output) DOUBLE PRECISION
If INFO = 0, COLCND contains the ratio of the smallest
C(i) to the largest C(i). If COLCND >= 0.1, it is not
worth scaling by C.
AMAX (output) DOUBLE PRECISION
Absolute value of largest matrix element. If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is
<= M: the i-th row of A is exactly zero
> M: the (i-M)-th column of A is exactly zero
=====================================================================
Test the input parameters.
Parameter adjustments */
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1, d__2, d__3, d__4;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
static integer i__, j;
static doublereal rcmin, rcmax;
extern doublereal dlamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static doublereal bignum, smlnum;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--r__;
--c__;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEEQU", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
*rowcnd = 1.;
*colcnd = 1.;
*amax = 0.;
return 0;
}
/* Get machine constants. */
smlnum = dlamch_("S");
bignum = 1. / smlnum;
/* Compute row scale factors. */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
r__[i__] = 0.;
/* L10: */
}
/* Find the maximum element in each row. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * a_dim1;
d__3 = r__[i__], d__4 = (d__1 = a[i__3].r, abs(d__1)) + (d__2 =
d_imag(&a[i__ + j * a_dim1]), abs(d__2));
r__[i__] = max(d__3,d__4);
/* L20: */
}
/* L30: */
}
/* Find the maximum and minimum scale factors. */
rcmin = bignum;
rcmax = 0.;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
d__1 = rcmax, d__2 = r__[i__];
rcmax = max(d__1,d__2);
/* Computing MIN */
d__1 = rcmin, d__2 = r__[i__];
rcmin = min(d__1,d__2);
/* L40: */
}
*amax = rcmax;
if (rcmin == 0.) {
/* Find the first zero scale factor and return an error code. */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
if (r__[i__] == 0.) {
*info = i__;
return 0;
}
/* L50: */
}
} else {
/* Invert the scale factors. */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MIN
Computing MAX */
d__2 = r__[i__];
d__1 = max(d__2,smlnum);
r__[i__] = 1. / min(d__1,bignum);
/* L60: */
}
/* Compute ROWCND = min(R(I)) / max(R(I)) */
*rowcnd = max(rcmin,smlnum) / min(rcmax,bignum);
}
/* Compute column scale factors */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
c__[j] = 0.;
/* L70: */
}
/* Find the maximum element in each column,
assuming the row scaling computed above. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * a_dim1;
d__3 = c__[j], d__4 = ((d__1 = a[i__3].r, abs(d__1)) + (d__2 =
d_imag(&a[i__ + j * a_dim1]), abs(d__2))) * r__[i__];
c__[j] = max(d__3,d__4);
/* L80: */
}
/* L90: */
}
/* Find the maximum and minimum scale factors. */
rcmin = bignum;
rcmax = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
d__1 = rcmin, d__2 = c__[j];
rcmin = min(d__1,d__2);
/* Computing MAX */
d__1 = rcmax, d__2 = c__[j];
rcmax = max(d__1,d__2);
/* L100: */
}
if (rcmin == 0.) {
/* Find the first zero scale factor and return an error code. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (c__[j] == 0.) {
*info = *m + j;
return 0;
}
/* L110: */
}
} else {
/* Invert the scale factors. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN
Computing MAX */
d__2 = c__[j];
d__1 = max(d__2,smlnum);
c__[j] = 1. / min(d__1,bignum);
/* L120: */
}
/* Compute COLCND = min(C(J)) / max(C(J)) */
*colcnd = max(rcmin,smlnum) / min(rcmax,bignum);
}
return 0;
/* End of ZGEEQU */
} /* zgeequ_ */