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/* slagv2.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__2 = 2;
static integer c__1 = 1;
/* Subroutine */ int slagv2_(real *a, integer *lda, real *b, integer *ldb,
real *alphar, real *alphai, real *beta, real *csl, real *snl, real *
csr, real *snr)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset;
real r__1, r__2, r__3, r__4, r__5, r__6;
/* Local variables */
real r__, t, h1, h2, h3, wi, qq, rr, wr1, wr2, ulp;
extern /* Subroutine */ int srot_(integer *, real *, integer *, real *,
integer *, real *, real *), slag2_(real *, integer *, real *,
integer *, real *, real *, real *, real *, real *, real *);
real anorm, bnorm, scale1, scale2;
extern /* Subroutine */ int slasv2_(real *, real *, real *, real *, real *
, real *, real *, real *, real *);
extern doublereal slapy2_(real *, real *);
real ascale, bscale;
extern doublereal slamch_(char *);
real safmin;
extern /* Subroutine */ int slartg_(real *, real *, real *, real *, real *
);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 */
/* matrix pencil (A,B) where B is upper triangular. This routine */
/* computes orthogonal (rotation) matrices given by CSL, SNL and CSR, */
/* SNR such that */
/* 1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0 */
/* types), then */
/* [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ] */
/* [ 0 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ] */
/* [ b11 b12 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ] */
/* [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ], */
/* 2) if the pencil (A,B) has a pair of complex conjugate eigenvalues, */
/* then */
/* [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ] */
/* [ a21 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ] */
/* [ b11 0 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ] */
/* [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ] */
/* where b11 >= b22 > 0. */
/* Arguments */
/* ========= */
/* A (input/output) REAL array, dimension (LDA, 2) */
/* On entry, the 2 x 2 matrix A. */
/* On exit, A is overwritten by the ``A-part'' of the */
/* generalized Schur form. */
/* LDA (input) INTEGER */
/* THe leading dimension of the array A. LDA >= 2. */
/* B (input/output) REAL array, dimension (LDB, 2) */
/* On entry, the upper triangular 2 x 2 matrix B. */
/* On exit, B is overwritten by the ``B-part'' of the */
/* generalized Schur form. */
/* LDB (input) INTEGER */
/* THe leading dimension of the array B. LDB >= 2. */
/* ALPHAR (output) REAL array, dimension (2) */
/* ALPHAI (output) REAL array, dimension (2) */
/* BETA (output) REAL array, dimension (2) */
/* (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the */
/* pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may */
/* be zero. */
/* CSL (output) REAL */
/* The cosine of the left rotation matrix. */
/* SNL (output) REAL */
/* The sine of the left rotation matrix. */
/* CSR (output) REAL */
/* The cosine of the right rotation matrix. */
/* SNR (output) REAL */
/* The sine of the right rotation matrix. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--alphar;
--alphai;
--beta;
/* Function Body */
safmin = slamch_("S");
ulp = slamch_("P");
/* Scale A */
/* Computing MAX */
r__5 = (r__1 = a[a_dim1 + 1], dabs(r__1)) + (r__2 = a[a_dim1 + 2], dabs(
r__2)), r__6 = (r__3 = a[(a_dim1 << 1) + 1], dabs(r__3)) + (r__4 =
a[(a_dim1 << 1) + 2], dabs(r__4)), r__5 = max(r__5,r__6);
anorm = dmax(r__5,safmin);
ascale = 1.f / anorm;
a[a_dim1 + 1] = ascale * a[a_dim1 + 1];
a[(a_dim1 << 1) + 1] = ascale * a[(a_dim1 << 1) + 1];
a[a_dim1 + 2] = ascale * a[a_dim1 + 2];
a[(a_dim1 << 1) + 2] = ascale * a[(a_dim1 << 1) + 2];
/* Scale B */
/* Computing MAX */
r__4 = (r__3 = b[b_dim1 + 1], dabs(r__3)), r__5 = (r__1 = b[(b_dim1 << 1)
+ 1], dabs(r__1)) + (r__2 = b[(b_dim1 << 1) + 2], dabs(r__2)),
r__4 = max(r__4,r__5);
bnorm = dmax(r__4,safmin);
bscale = 1.f / bnorm;
b[b_dim1 + 1] = bscale * b[b_dim1 + 1];
b[(b_dim1 << 1) + 1] = bscale * b[(b_dim1 << 1) + 1];
b[(b_dim1 << 1) + 2] = bscale * b[(b_dim1 << 1) + 2];
/* Check if A can be deflated */
if ((r__1 = a[a_dim1 + 2], dabs(r__1)) <= ulp) {
*csl = 1.f;
*snl = 0.f;
*csr = 1.f;
*snr = 0.f;
a[a_dim1 + 2] = 0.f;
b[b_dim1 + 2] = 0.f;
/* Check if B is singular */
} else if ((r__1 = b[b_dim1 + 1], dabs(r__1)) <= ulp) {
slartg_(&a[a_dim1 + 1], &a[a_dim1 + 2], csl, snl, &r__);
*csr = 1.f;
*snr = 0.f;
srot_(&c__2, &a[a_dim1 + 1], lda, &a[a_dim1 + 2], lda, csl, snl);
srot_(&c__2, &b[b_dim1 + 1], ldb, &b[b_dim1 + 2], ldb, csl, snl);
a[a_dim1 + 2] = 0.f;
b[b_dim1 + 1] = 0.f;
b[b_dim1 + 2] = 0.f;
} else if ((r__1 = b[(b_dim1 << 1) + 2], dabs(r__1)) <= ulp) {
slartg_(&a[(a_dim1 << 1) + 2], &a[a_dim1 + 2], csr, snr, &t);
*snr = -(*snr);
srot_(&c__2, &a[a_dim1 + 1], &c__1, &a[(a_dim1 << 1) + 1], &c__1, csr,
snr);
srot_(&c__2, &b[b_dim1 + 1], &c__1, &b[(b_dim1 << 1) + 1], &c__1, csr,
snr);
*csl = 1.f;
*snl = 0.f;
a[a_dim1 + 2] = 0.f;
b[b_dim1 + 2] = 0.f;
b[(b_dim1 << 1) + 2] = 0.f;
} else {
/* B is nonsingular, first compute the eigenvalues of (A,B) */
slag2_(&a[a_offset], lda, &b[b_offset], ldb, &safmin, &scale1, &
scale2, &wr1, &wr2, &wi);
if (wi == 0.f) {
/* two real eigenvalues, compute s*A-w*B */
h1 = scale1 * a[a_dim1 + 1] - wr1 * b[b_dim1 + 1];
h2 = scale1 * a[(a_dim1 << 1) + 1] - wr1 * b[(b_dim1 << 1) + 1];
h3 = scale1 * a[(a_dim1 << 1) + 2] - wr1 * b[(b_dim1 << 1) + 2];
rr = slapy2_(&h1, &h2);
r__1 = scale1 * a[a_dim1 + 2];
qq = slapy2_(&r__1, &h3);
if (rr > qq) {
/* find right rotation matrix to zero 1,1 element of */
/* (sA - wB) */
slartg_(&h2, &h1, csr, snr, &t);
} else {
/* find right rotation matrix to zero 2,1 element of */
/* (sA - wB) */
r__1 = scale1 * a[a_dim1 + 2];
slartg_(&h3, &r__1, csr, snr, &t);
}
*snr = -(*snr);
srot_(&c__2, &a[a_dim1 + 1], &c__1, &a[(a_dim1 << 1) + 1], &c__1,
csr, snr);
srot_(&c__2, &b[b_dim1 + 1], &c__1, &b[(b_dim1 << 1) + 1], &c__1,
csr, snr);
/* compute inf norms of A and B */
/* Computing MAX */
r__5 = (r__1 = a[a_dim1 + 1], dabs(r__1)) + (r__2 = a[(a_dim1 <<
1) + 1], dabs(r__2)), r__6 = (r__3 = a[a_dim1 + 2], dabs(
r__3)) + (r__4 = a[(a_dim1 << 1) + 2], dabs(r__4));
h1 = dmax(r__5,r__6);
/* Computing MAX */
r__5 = (r__1 = b[b_dim1 + 1], dabs(r__1)) + (r__2 = b[(b_dim1 <<
1) + 1], dabs(r__2)), r__6 = (r__3 = b[b_dim1 + 2], dabs(
r__3)) + (r__4 = b[(b_dim1 << 1) + 2], dabs(r__4));
h2 = dmax(r__5,r__6);
if (scale1 * h1 >= dabs(wr1) * h2) {
/* find left rotation matrix Q to zero out B(2,1) */
slartg_(&b[b_dim1 + 1], &b[b_dim1 + 2], csl, snl, &r__);
} else {
/* find left rotation matrix Q to zero out A(2,1) */
slartg_(&a[a_dim1 + 1], &a[a_dim1 + 2], csl, snl, &r__);
}
srot_(&c__2, &a[a_dim1 + 1], lda, &a[a_dim1 + 2], lda, csl, snl);
srot_(&c__2, &b[b_dim1 + 1], ldb, &b[b_dim1 + 2], ldb, csl, snl);
a[a_dim1 + 2] = 0.f;
b[b_dim1 + 2] = 0.f;
} else {
/* a pair of complex conjugate eigenvalues */
/* first compute the SVD of the matrix B */
slasv2_(&b[b_dim1 + 1], &b[(b_dim1 << 1) + 1], &b[(b_dim1 << 1) +
2], &r__, &t, snr, csr, snl, csl);
/* Form (A,B) := Q(A,B)Z' where Q is left rotation matrix and */
/* Z is right rotation matrix computed from SLASV2 */
srot_(&c__2, &a[a_dim1 + 1], lda, &a[a_dim1 + 2], lda, csl, snl);
srot_(&c__2, &b[b_dim1 + 1], ldb, &b[b_dim1 + 2], ldb, csl, snl);
srot_(&c__2, &a[a_dim1 + 1], &c__1, &a[(a_dim1 << 1) + 1], &c__1,
csr, snr);
srot_(&c__2, &b[b_dim1 + 1], &c__1, &b[(b_dim1 << 1) + 1], &c__1,
csr, snr);
b[b_dim1 + 2] = 0.f;
b[(b_dim1 << 1) + 1] = 0.f;
}
}
/* Unscaling */
a[a_dim1 + 1] = anorm * a[a_dim1 + 1];
a[a_dim1 + 2] = anorm * a[a_dim1 + 2];
a[(a_dim1 << 1) + 1] = anorm * a[(a_dim1 << 1) + 1];
a[(a_dim1 << 1) + 2] = anorm * a[(a_dim1 << 1) + 2];
b[b_dim1 + 1] = bnorm * b[b_dim1 + 1];
b[b_dim1 + 2] = bnorm * b[b_dim1 + 2];
b[(b_dim1 << 1) + 1] = bnorm * b[(b_dim1 << 1) + 1];
b[(b_dim1 << 1) + 2] = bnorm * b[(b_dim1 << 1) + 2];
if (wi == 0.f) {
alphar[1] = a[a_dim1 + 1];
alphar[2] = a[(a_dim1 << 1) + 2];
alphai[1] = 0.f;
alphai[2] = 0.f;
beta[1] = b[b_dim1 + 1];
beta[2] = b[(b_dim1 << 1) + 2];
} else {
alphar[1] = anorm * wr1 / scale1 / bnorm;
alphai[1] = anorm * wi / scale1 / bnorm;
alphar[2] = alphar[1];
alphai[2] = -alphai[1];
beta[1] = 1.f;
beta[2] = 1.f;
}
return 0;
/* End of SLAGV2 */
} /* slagv2_ */
|
