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/* cgbequb.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 cgbequb_(integer *m, integer *n, integer *kl, integer *
ku, complex *ab, integer *ldab, real *r__, real *c__, real *rowcnd,
real *colcnd, real *amax, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
real r__1, r__2, r__3, r__4;
/* Builtin functions */
double log(doublereal), r_imag(complex *), pow_ri(real *, integer *);
/* Local variables */
integer i__, j, kd;
real radix, rcmin, rcmax;
extern doublereal slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
real bignum, logrdx, smlnum;
/* -- LAPACK routine (version 3.2) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- November 2008 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGBEQUB 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 an absolute value of at most */
/* the radix. */
/* R(i) and C(j) are restricted to be a power of the radix 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. */
/* This routine differs from CGEEQU by restricting the scaling factors */
/* to a power of the radix. Baring over- and underflow, scaling by */
/* these factors introduces no additional rounding errors. However, the */
/* scaled entries' magnitured are no longer approximately 1 but lie */
/* between sqrt(radix) and 1/sqrt(radix). */
/* 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. */
/* KL (input) INTEGER */
/* The number of subdiagonals within the band of A. KL >= 0. */
/* KU (input) INTEGER */
/* The number of superdiagonals within the band of A. KU >= 0. */
/* AB (input) DOUBLE PRECISION array, dimension (LDAB,N) */
/* On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */
/* The j-th column of A is stored in the j-th column of the */
/* array AB as follows: */
/* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) */
/* LDAB (input) INTEGER */
/* The leading dimension of the array A. LDAB >= max(1,M). */
/* R (output) REAL array, dimension (M) */
/* If INFO = 0 or INFO > M, R contains the row scale factors */
/* for A. */
/* C (output) REAL array, dimension (N) */
/* If INFO = 0, C contains the column scale factors for A. */
/* ROWCND (output) REAL */
/* 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) REAL */
/* 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) REAL */
/* 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 */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--r__;
--c__;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kl < 0) {
*info = -3;
} else if (*ku < 0) {
*info = -4;
} else if (*ldab < *kl + *ku + 1) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGBEQUB", &i__1);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
*rowcnd = 1.f;
*colcnd = 1.f;
*amax = 0.f;
return 0;
}
/* Get machine constants. Assume SMLNUM is a power of the radix. */
smlnum = slamch_("S");
bignum = 1.f / smlnum;
radix = slamch_("B");
logrdx = log(radix);
/* Compute row scale factors. */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
r__[i__] = 0.f;
/* L10: */
}
/* Find the maximum element in each row. */
kd = *ku + 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = j - *ku;
/* Computing MIN */
i__4 = j + *kl;
i__3 = min(i__4,*m);
for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
/* Computing MAX */
i__2 = kd + i__ - j + j * ab_dim1;
r__3 = r__[i__], r__4 = (r__1 = ab[i__2].r, dabs(r__1)) + (r__2 =
r_imag(&ab[kd + i__ - j + j * ab_dim1]), dabs(r__2));
r__[i__] = dmax(r__3,r__4);
/* L20: */
}
/* L30: */
}
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
if (r__[i__] > 0.f) {
i__3 = (integer) (log(r__[i__]) / logrdx);
r__[i__] = pow_ri(&radix, &i__3);
}
}
/* Find the maximum and minimum scale factors. */
rcmin = bignum;
rcmax = 0.f;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
r__1 = rcmax, r__2 = r__[i__];
rcmax = dmax(r__1,r__2);
/* Computing MIN */
r__1 = rcmin, r__2 = r__[i__];
rcmin = dmin(r__1,r__2);
/* L40: */
}
*amax = rcmax;
if (rcmin == 0.f) {
/* 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.f) {
*info = i__;
return 0;
}
/* L50: */
}
} else {
/* Invert the scale factors. */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MIN */
/* Computing MAX */
r__2 = r__[i__];
r__1 = dmax(r__2,smlnum);
r__[i__] = 1.f / dmin(r__1,bignum);
/* L60: */
}
/* Compute ROWCND = min(R(I)) / max(R(I)). */
*rowcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum);
}
/* Compute column scale factors. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
c__[j] = 0.f;
/* L70: */
}
/* Find the maximum element in each column, */
/* assuming the row scaling computed above. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__3 = j - *ku;
/* Computing MIN */
i__4 = j + *kl;
i__2 = min(i__4,*m);
for (i__ = max(i__3,1); i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = kd + i__ - j + j * ab_dim1;
r__3 = c__[j], r__4 = ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&ab[kd + i__ - j + j * ab_dim1]), dabs(r__2))) *
r__[i__];
c__[j] = dmax(r__3,r__4);
/* L80: */
}
if (c__[j] > 0.f) {
i__2 = (integer) (log(c__[j]) / logrdx);
c__[j] = pow_ri(&radix, &i__2);
}
/* L90: */
}
/* Find the maximum and minimum scale factors. */
rcmin = bignum;
rcmax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = rcmin, r__2 = c__[j];
rcmin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = rcmax, r__2 = c__[j];
rcmax = dmax(r__1,r__2);
/* L100: */
}
if (rcmin == 0.f) {
/* 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.f) {
*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 */
r__2 = c__[j];
r__1 = dmax(r__2,smlnum);
c__[j] = 1.f / dmin(r__1,bignum);
/* L120: */
}
/* Compute COLCND = min(C(J)) / max(C(J)). */
*colcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum);
}
return 0;
/* End of CGBEQUB */
} /* cgbequb_ */
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