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/* lapack/double/dlagv2.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__2 = 2;
static integer c__1 = 1;
/*< >*/
/* Subroutine */ int dlagv2_(doublereal *a, integer *lda, doublereal *b,
integer *ldb, doublereal *alphar, doublereal *alphai, doublereal *
beta, doublereal *csl, doublereal *snl, doublereal *csr, doublereal *
snr)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
/* Local variables */
doublereal r__, t, h1, h2, h3, wi, qq, rr, wr1, wr2, ulp;
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *), dlag2_(
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *);
doublereal anorm, bnorm, scale1, scale2;
extern /* Subroutine */ int dlasv2_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *);
extern doublereal dlapy2_(doublereal *, doublereal *);
doublereal ascale, bscale;
extern doublereal dlamch_(char *, ftnlen);
doublereal safmin;
extern /* Subroutine */ int dlartg_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/*< INTEGER LDA, LDB >*/
/*< DOUBLE PRECISION CSL, CSR, SNL, SNR >*/
/* .. */
/* .. Array Arguments .. */
/*< >*/
/* .. */
/* Purpose */
/* ======= */
/* DLAGV2 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (2) */
/* ALPHAI (output) DOUBLE PRECISION array, dimension (2) */
/* BETA (output) DOUBLE PRECISION 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) DOUBLE PRECISION */
/* The cosine of the left rotation matrix. */
/* SNL (output) DOUBLE PRECISION */
/* The sine of the left rotation matrix. */
/* CSR (output) DOUBLE PRECISION */
/* The cosine of the right rotation matrix. */
/* SNR (output) DOUBLE PRECISION */
/* The sine of the right rotation matrix. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
/* ===================================================================== */
/* .. Parameters .. */
/*< DOUBLE PRECISION ZERO, ONE >*/
/*< PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL DLAG2, DLARTG, DLASV2, DROT >*/
/* .. */
/* .. External Functions .. */
/*< DOUBLE PRECISION DLAMCH, DLAPY2 >*/
/*< EXTERNAL DLAMCH, DLAPY2 >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, MAX >*/
/* .. */
/* .. Executable Statements .. */
/*< SAFMIN = DLAMCH( 'S' ) >*/
/* 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 = dlamch_("S", (ftnlen)1);
/*< ULP = DLAMCH( 'P' ) >*/
ulp = dlamch_("P", (ftnlen)1);
/* Scale A */
/*< >*/
/* Computing MAX */
d__5 = (d__1 = a[a_dim1 + 1], abs(d__1)) + (d__2 = a[a_dim1 + 2], abs(
d__2)), d__6 = (d__3 = a[(a_dim1 << 1) + 1], abs(d__3)) + (d__4 =
a[(a_dim1 << 1) + 2], abs(d__4)), d__5 = max(d__5,d__6);
anorm = max(d__5,safmin);
/*< ASCALE = ONE / ANORM >*/
ascale = 1. / anorm;
/*< A( 1, 1 ) = ASCALE*A( 1, 1 ) >*/
a[a_dim1 + 1] = ascale * a[a_dim1 + 1];
/*< A( 1, 2 ) = ASCALE*A( 1, 2 ) >*/
a[(a_dim1 << 1) + 1] = ascale * a[(a_dim1 << 1) + 1];
/*< A( 2, 1 ) = ASCALE*A( 2, 1 ) >*/
a[a_dim1 + 2] = ascale * a[a_dim1 + 2];
/*< A( 2, 2 ) = ASCALE*A( 2, 2 ) >*/
a[(a_dim1 << 1) + 2] = ascale * a[(a_dim1 << 1) + 2];
/* Scale B */
/*< >*/
/* Computing MAX */
d__4 = (d__3 = b[b_dim1 + 1], abs(d__3)), d__5 = (d__1 = b[(b_dim1 << 1)
+ 1], abs(d__1)) + (d__2 = b[(b_dim1 << 1) + 2], abs(d__2)), d__4
= max(d__4,d__5);
bnorm = max(d__4,safmin);
/*< BSCALE = ONE / BNORM >*/
bscale = 1. / bnorm;
/*< B( 1, 1 ) = BSCALE*B( 1, 1 ) >*/
b[b_dim1 + 1] = bscale * b[b_dim1 + 1];
/*< B( 1, 2 ) = BSCALE*B( 1, 2 ) >*/
b[(b_dim1 << 1) + 1] = bscale * b[(b_dim1 << 1) + 1];
/*< B( 2, 2 ) = BSCALE*B( 2, 2 ) >*/
b[(b_dim1 << 1) + 2] = bscale * b[(b_dim1 << 1) + 2];
/* Check if A can be deflated */
/*< IF( ABS( A( 2, 1 ) ).LE.ULP ) THEN >*/
if ((d__1 = a[a_dim1 + 2], abs(d__1)) <= ulp) {
/*< CSL = ONE >*/
*csl = 1.;
/*< SNL = ZERO >*/
*snl = 0.;
/*< CSR = ONE >*/
*csr = 1.;
/*< SNR = ZERO >*/
*snr = 0.;
/*< A( 2, 1 ) = ZERO >*/
a[a_dim1 + 2] = 0.;
/*< B( 2, 1 ) = ZERO >*/
b[b_dim1 + 2] = 0.;
/* Check if B is singular */
/*< ELSE IF( ABS( B( 1, 1 ) ).LE.ULP ) THEN >*/
} else if ((d__1 = b[b_dim1 + 1], abs(d__1)) <= ulp) {
/*< CALL DLARTG( A( 1, 1 ), A( 2, 1 ), CSL, SNL, R ) >*/
dlartg_(&a[a_dim1 + 1], &a[a_dim1 + 2], csl, snl, &r__);
/*< CSR = ONE >*/
*csr = 1.;
/*< SNR = ZERO >*/
*snr = 0.;
/*< CALL DROT( 2, A( 1, 1 ), LDA, A( 2, 1 ), LDA, CSL, SNL ) >*/
drot_(&c__2, &a[a_dim1 + 1], lda, &a[a_dim1 + 2], lda, csl, snl);
/*< CALL DROT( 2, B( 1, 1 ), LDB, B( 2, 1 ), LDB, CSL, SNL ) >*/
drot_(&c__2, &b[b_dim1 + 1], ldb, &b[b_dim1 + 2], ldb, csl, snl);
/*< A( 2, 1 ) = ZERO >*/
a[a_dim1 + 2] = 0.;
/*< B( 1, 1 ) = ZERO >*/
b[b_dim1 + 1] = 0.;
/*< B( 2, 1 ) = ZERO >*/
b[b_dim1 + 2] = 0.;
/*< ELSE IF( ABS( B( 2, 2 ) ).LE.ULP ) THEN >*/
} else if ((d__1 = b[(b_dim1 << 1) + 2], abs(d__1)) <= ulp) {
/*< CALL DLARTG( A( 2, 2 ), A( 2, 1 ), CSR, SNR, T ) >*/
dlartg_(&a[(a_dim1 << 1) + 2], &a[a_dim1 + 2], csr, snr, &t);
/*< SNR = -SNR >*/
*snr = -(*snr);
/*< CALL DROT( 2, A( 1, 1 ), 1, A( 1, 2 ), 1, CSR, SNR ) >*/
drot_(&c__2, &a[a_dim1 + 1], &c__1, &a[(a_dim1 << 1) + 1], &c__1, csr,
snr);
/*< CALL DROT( 2, B( 1, 1 ), 1, B( 1, 2 ), 1, CSR, SNR ) >*/
drot_(&c__2, &b[b_dim1 + 1], &c__1, &b[(b_dim1 << 1) + 1], &c__1, csr,
snr);
/*< CSL = ONE >*/
*csl = 1.;
/*< SNL = ZERO >*/
*snl = 0.;
/*< A( 2, 1 ) = ZERO >*/
a[a_dim1 + 2] = 0.;
/*< B( 2, 1 ) = ZERO >*/
b[b_dim1 + 2] = 0.;
/*< B( 2, 2 ) = ZERO >*/
b[(b_dim1 << 1) + 2] = 0.;
/*< ELSE >*/
} else {
/* B is nonsingular, first compute the eigenvalues of (A,B) */
/*< >*/
dlag2_(&a[a_offset], lda, &b[b_offset], ldb, &safmin, &scale1, &
scale2, &wr1, &wr2, &wi);
/*< IF( WI.EQ.ZERO ) THEN >*/
if (wi == 0.) {
/* two real eigenvalues, compute s*A-w*B */
/*< H1 = SCALE1*A( 1, 1 ) - WR1*B( 1, 1 ) >*/
h1 = scale1 * a[a_dim1 + 1] - wr1 * b[b_dim1 + 1];
/*< H2 = SCALE1*A( 1, 2 ) - WR1*B( 1, 2 ) >*/
h2 = scale1 * a[(a_dim1 << 1) + 1] - wr1 * b[(b_dim1 << 1) + 1];
/*< H3 = SCALE1*A( 2, 2 ) - WR1*B( 2, 2 ) >*/
h3 = scale1 * a[(a_dim1 << 1) + 2] - wr1 * b[(b_dim1 << 1) + 2];
/*< RR = DLAPY2( H1, H2 ) >*/
rr = dlapy2_(&h1, &h2);
/*< QQ = DLAPY2( SCALE1*A( 2, 1 ), H3 ) >*/
d__1 = scale1 * a[a_dim1 + 2];
qq = dlapy2_(&d__1, &h3);
/*< IF( RR.GT.QQ ) THEN >*/
if (rr > qq) {
/* find right rotation matrix to zero 1,1 element of */
/* (sA - wB) */
/*< CALL DLARTG( H2, H1, CSR, SNR, T ) >*/
dlartg_(&h2, &h1, csr, snr, &t);
/*< ELSE >*/
} else {
/* find right rotation matrix to zero 2,1 element of */
/* (sA - wB) */
/*< CALL DLARTG( H3, SCALE1*A( 2, 1 ), CSR, SNR, T ) >*/
d__1 = scale1 * a[a_dim1 + 2];
dlartg_(&h3, &d__1, csr, snr, &t);
/*< END IF >*/
}
/*< SNR = -SNR >*/
*snr = -(*snr);
/*< CALL DROT( 2, A( 1, 1 ), 1, A( 1, 2 ), 1, CSR, SNR ) >*/
drot_(&c__2, &a[a_dim1 + 1], &c__1, &a[(a_dim1 << 1) + 1], &c__1,
csr, snr);
/*< CALL DROT( 2, B( 1, 1 ), 1, B( 1, 2 ), 1, CSR, SNR ) >*/
drot_(&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 */
d__5 = (d__1 = a[a_dim1 + 1], abs(d__1)) + (d__2 = a[(a_dim1 << 1)
+ 1], abs(d__2)), d__6 = (d__3 = a[a_dim1 + 2], abs(d__3)
) + (d__4 = a[(a_dim1 << 1) + 2], abs(d__4));
h1 = max(d__5,d__6);
/*< >*/
/* Computing MAX */
d__5 = (d__1 = b[b_dim1 + 1], abs(d__1)) + (d__2 = b[(b_dim1 << 1)
+ 1], abs(d__2)), d__6 = (d__3 = b[b_dim1 + 2], abs(d__3)
) + (d__4 = b[(b_dim1 << 1) + 2], abs(d__4));
h2 = max(d__5,d__6);
/*< IF( ( SCALE1*H1 ).GE.ABS( WR1 )*H2 ) THEN >*/
if (scale1 * h1 >= abs(wr1) * h2) {
/* find left rotation matrix Q to zero out B(2,1) */
/*< CALL DLARTG( B( 1, 1 ), B( 2, 1 ), CSL, SNL, R ) >*/
dlartg_(&b[b_dim1 + 1], &b[b_dim1 + 2], csl, snl, &r__);
/*< ELSE >*/
} else {
/* find left rotation matrix Q to zero out A(2,1) */
/*< CALL DLARTG( A( 1, 1 ), A( 2, 1 ), CSL, SNL, R ) >*/
dlartg_(&a[a_dim1 + 1], &a[a_dim1 + 2], csl, snl, &r__);
/*< END IF >*/
}
/*< CALL DROT( 2, A( 1, 1 ), LDA, A( 2, 1 ), LDA, CSL, SNL ) >*/
drot_(&c__2, &a[a_dim1 + 1], lda, &a[a_dim1 + 2], lda, csl, snl);
/*< CALL DROT( 2, B( 1, 1 ), LDB, B( 2, 1 ), LDB, CSL, SNL ) >*/
drot_(&c__2, &b[b_dim1 + 1], ldb, &b[b_dim1 + 2], ldb, csl, snl);
/*< A( 2, 1 ) = ZERO >*/
a[a_dim1 + 2] = 0.;
/*< B( 2, 1 ) = ZERO >*/
b[b_dim1 + 2] = 0.;
/*< ELSE >*/
} else {
/* a pair of complex conjugate eigenvalues */
/* first compute the SVD of the matrix B */
/*< >*/
dlasv2_(&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 DLASV2 */
/*< CALL DROT( 2, A( 1, 1 ), LDA, A( 2, 1 ), LDA, CSL, SNL ) >*/
drot_(&c__2, &a[a_dim1 + 1], lda, &a[a_dim1 + 2], lda, csl, snl);
/*< CALL DROT( 2, B( 1, 1 ), LDB, B( 2, 1 ), LDB, CSL, SNL ) >*/
drot_(&c__2, &b[b_dim1 + 1], ldb, &b[b_dim1 + 2], ldb, csl, snl);
/*< CALL DROT( 2, A( 1, 1 ), 1, A( 1, 2 ), 1, CSR, SNR ) >*/
drot_(&c__2, &a[a_dim1 + 1], &c__1, &a[(a_dim1 << 1) + 1], &c__1,
csr, snr);
/*< CALL DROT( 2, B( 1, 1 ), 1, B( 1, 2 ), 1, CSR, SNR ) >*/
drot_(&c__2, &b[b_dim1 + 1], &c__1, &b[(b_dim1 << 1) + 1], &c__1,
csr, snr);
/*< B( 2, 1 ) = ZERO >*/
b[b_dim1 + 2] = 0.;
/*< B( 1, 2 ) = ZERO >*/
b[(b_dim1 << 1) + 1] = 0.;
/*< END IF >*/
}
/*< END IF >*/
}
/* Unscaling */
/*< A( 1, 1 ) = ANORM*A( 1, 1 ) >*/
a[a_dim1 + 1] = anorm * a[a_dim1 + 1];
/*< A( 2, 1 ) = ANORM*A( 2, 1 ) >*/
a[a_dim1 + 2] = anorm * a[a_dim1 + 2];
/*< A( 1, 2 ) = ANORM*A( 1, 2 ) >*/
a[(a_dim1 << 1) + 1] = anorm * a[(a_dim1 << 1) + 1];
/*< A( 2, 2 ) = ANORM*A( 2, 2 ) >*/
a[(a_dim1 << 1) + 2] = anorm * a[(a_dim1 << 1) + 2];
/*< B( 1, 1 ) = BNORM*B( 1, 1 ) >*/
b[b_dim1 + 1] = bnorm * b[b_dim1 + 1];
/*< B( 2, 1 ) = BNORM*B( 2, 1 ) >*/
b[b_dim1 + 2] = bnorm * b[b_dim1 + 2];
/*< B( 1, 2 ) = BNORM*B( 1, 2 ) >*/
b[(b_dim1 << 1) + 1] = bnorm * b[(b_dim1 << 1) + 1];
/*< B( 2, 2 ) = BNORM*B( 2, 2 ) >*/
b[(b_dim1 << 1) + 2] = bnorm * b[(b_dim1 << 1) + 2];
/*< IF( WI.EQ.ZERO ) THEN >*/
if (wi == 0.) {
/*< ALPHAR( 1 ) = A( 1, 1 ) >*/
alphar[1] = a[a_dim1 + 1];
/*< ALPHAR( 2 ) = A( 2, 2 ) >*/
alphar[2] = a[(a_dim1 << 1) + 2];
/*< ALPHAI( 1 ) = ZERO >*/
alphai[1] = 0.;
/*< ALPHAI( 2 ) = ZERO >*/
alphai[2] = 0.;
/*< BETA( 1 ) = B( 1, 1 ) >*/
beta[1] = b[b_dim1 + 1];
/*< BETA( 2 ) = B( 2, 2 ) >*/
beta[2] = b[(b_dim1 << 1) + 2];
/*< ELSE >*/
} else {
/*< ALPHAR( 1 ) = ANORM*WR1 / SCALE1 / BNORM >*/
alphar[1] = anorm * wr1 / scale1 / bnorm;
/*< ALPHAI( 1 ) = ANORM*WI / SCALE1 / BNORM >*/
alphai[1] = anorm * wi / scale1 / bnorm;
/*< ALPHAR( 2 ) = ALPHAR( 1 ) >*/
alphar[2] = alphar[1];
/*< ALPHAI( 2 ) = -ALPHAI( 1 ) >*/
alphai[2] = -alphai[1];
/*< BETA( 1 ) = ONE >*/
beta[1] = 1.;
/*< BETA( 2 ) = ONE >*/
beta[2] = 1.;
/*< END IF >*/
}
/*< 10 CONTINUE >*/
/* L10: */
/*< RETURN >*/
return 0;
/* End of DLAGV2 */
/*< END >*/
} /* dlagv2_ */
#ifdef __cplusplus
}
#endif
|
