/* zlags2.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 zlags2_(logical *upper, doublereal *a1, doublecomplex *
a2, doublereal *a3, doublereal *b1, doublecomplex *b2, doublereal *b3,
doublereal *csu, doublecomplex *snu, doublereal *csv, doublecomplex *
snv, doublereal *csq, doublecomplex *snq)
{
/* System generated locals */
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8;
doublecomplex z__1, z__2, z__3, z__4, z__5;
/* Builtin functions */
double z_abs(doublecomplex *), d_imag(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
doublereal a;
doublecomplex b, c__;
doublereal d__;
doublecomplex r__, d1;
doublereal s1, s2, fb, fc;
doublecomplex ua11, ua12, ua21, ua22, vb11, vb12, vb21, vb22;
doublereal csl, csr, snl, snr, aua11, aua12, aua21, aua22, avb12, avb11,
avb21, avb22, ua11r, ua22r, vb11r, vb22r;
extern /* Subroutine */ int dlasv2_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *), zlartg_(doublecomplex *
, doublecomplex *, doublereal *, doublecomplex *, doublecomplex *)
;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such */
/* that if ( UPPER ) then */
/* U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) */
/* ( 0 A3 ) ( x x ) */
/* and */
/* V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) */
/* ( 0 B3 ) ( x x ) */
/* or if ( .NOT.UPPER ) then */
/* U'*A*Q = U'*( A1 0 )*Q = ( x x ) */
/* ( A2 A3 ) ( 0 x ) */
/* and */
/* V'*B*Q = V'*( B1 0 )*Q = ( x x ) */
/* ( B2 B3 ) ( 0 x ) */
/* where */
/* U = ( CSU SNU ), V = ( CSV SNV ), */
/* ( -CONJG(SNU) CSU ) ( -CONJG(SNV) CSV ) */
/* Q = ( CSQ SNQ ) */
/* ( -CONJG(SNQ) CSQ ) */
/* Z' denotes the conjugate transpose of Z. */
/* The rows of the transformed A and B are parallel. Moreover, if the */
/* input 2-by-2 matrix A is not zero, then the transformed (1,1) entry */
/* of A is not zero. If the input matrices A and B are both not zero, */
/* then the transformed (2,2) element of B is not zero, except when the */
/* first rows of input A and B are parallel and the second rows are */
/* zero. */
/* Arguments */
/* ========= */
/* UPPER (input) LOGICAL */
/* = .TRUE.: the input matrices A and B are upper triangular. */
/* = .FALSE.: the input matrices A and B are lower triangular. */
/* A1 (input) DOUBLE PRECISION */
/* A2 (input) COMPLEX*16 */
/* A3 (input) DOUBLE PRECISION */
/* On entry, A1, A2 and A3 are elements of the input 2-by-2 */
/* upper (lower) triangular matrix A. */
/* B1 (input) DOUBLE PRECISION */
/* B2 (input) COMPLEX*16 */
/* B3 (input) DOUBLE PRECISION */
/* On entry, B1, B2 and B3 are elements of the input 2-by-2 */
/* upper (lower) triangular matrix B. */
/* CSU (output) DOUBLE PRECISION */
/* SNU (output) COMPLEX*16 */
/* The desired unitary matrix U. */
/* CSV (output) DOUBLE PRECISION */
/* SNV (output) COMPLEX*16 */
/* The desired unitary matrix V. */
/* CSQ (output) DOUBLE PRECISION */
/* SNQ (output) COMPLEX*16 */
/* The desired unitary matrix Q. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
if (*upper) {
/* Input matrices A and B are upper triangular matrices */
/* Form matrix C = A*adj(B) = ( a b ) */
/* ( 0 d ) */
a = *a1 * *b3;
d__ = *a3 * *b1;
z__2.r = *b1 * a2->r, z__2.i = *b1 * a2->i;
z__3.r = *a1 * b2->r, z__3.i = *a1 * b2->i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
b.r = z__1.r, b.i = z__1.i;
fb = z_abs(&b);
/* Transform complex 2-by-2 matrix C to real matrix by unitary */
/* diagonal matrix diag(1,D1). */
d1.r = 1., d1.i = 0.;
if (fb != 0.) {
z__1.r = b.r / fb, z__1.i = b.i / fb;
d1.r = z__1.r, d1.i = z__1.i;
}
/* The SVD of real 2 by 2 triangular C */
/* ( CSL -SNL )*( A B )*( CSR SNR ) = ( R 0 ) */
/* ( SNL CSL ) ( 0 D ) ( -SNR CSR ) ( 0 T ) */
dlasv2_(&a, &fb, &d__, &s1, &s2, &snr, &csr, &snl, &csl);
if (abs(csl) >= abs(snl) || abs(csr) >= abs(snr)) {
/* Compute the (1,1) and (1,2) elements of U'*A and V'*B, */
/* and (1,2) element of |U|'*|A| and |V|'*|B|. */
ua11r = csl * *a1;
z__2.r = csl * a2->r, z__2.i = csl * a2->i;
z__4.r = snl * d1.r, z__4.i = snl * d1.i;
z__3.r = *a3 * z__4.r, z__3.i = *a3 * z__4.i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
ua12.r = z__1.r, ua12.i = z__1.i;
vb11r = csr * *b1;
z__2.r = csr * b2->r, z__2.i = csr * b2->i;
z__4.r = snr * d1.r, z__4.i = snr * d1.i;
z__3.r = *b3 * z__4.r, z__3.i = *b3 * z__4.i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
vb12.r = z__1.r, vb12.i = z__1.i;
aua12 = abs(csl) * ((d__1 = a2->r, abs(d__1)) + (d__2 = d_imag(a2)
, abs(d__2))) + abs(snl) * abs(*a3);
avb12 = abs(csr) * ((d__1 = b2->r, abs(d__1)) + (d__2 = d_imag(b2)
, abs(d__2))) + abs(snr) * abs(*b3);
/* zero (1,2) elements of U'*A and V'*B */
if (abs(ua11r) + ((d__1 = ua12.r, abs(d__1)) + (d__2 = d_imag(&
ua12), abs(d__2))) == 0.) {
z__2.r = vb11r, z__2.i = 0.;
z__1.r = -z__2.r, z__1.i = -z__2.i;
d_cnjg(&z__3, &vb12);
zlartg_(&z__1, &z__3, csq, snq, &r__);
} else if (abs(vb11r) + ((d__1 = vb12.r, abs(d__1)) + (d__2 =
d_imag(&vb12), abs(d__2))) == 0.) {
z__2.r = ua11r, z__2.i = 0.;
z__1.r = -z__2.r, z__1.i = -z__2.i;
d_cnjg(&z__3, &ua12);
zlartg_(&z__1, &z__3, csq, snq, &r__);
} else if (aua12 / (abs(ua11r) + ((d__1 = ua12.r, abs(d__1)) + (
d__2 = d_imag(&ua12), abs(d__2)))) <= avb12 / (abs(vb11r)
+ ((d__3 = vb12.r, abs(d__3)) + (d__4 = d_imag(&vb12),
abs(d__4))))) {
z__2.r = ua11r, z__2.i = 0.;
z__1.r = -z__2.r, z__1.i = -z__2.i;
d_cnjg(&z__3, &ua12);
zlartg_(&z__1, &z__3, csq, snq, &r__);
} else {
z__2.r = vb11r, z__2.i = 0.;
z__1.r = -z__2.r, z__1.i = -z__2.i;
d_cnjg(&z__3, &vb12);
zlartg_(&z__1, &z__3, csq, snq, &r__);
}
*csu = csl;
z__2.r = -d1.r, z__2.i = -d1.i;
z__1.r = snl * z__2.r, z__1.i = snl * z__2.i;
snu->r = z__1.r, snu->i = z__1.i;
*csv = csr;
z__2.r = -d1.r, z__2.i = -d1.i;
z__1.r = snr * z__2.r, z__1.i = snr * z__2.i;
snv->r = z__1.r, snv->i = z__1.i;
} else {
/* Compute the (2,1) and (2,2) elements of U'*A and V'*B, */
/* and (2,2) element of |U|'*|A| and |V|'*|B|. */
d_cnjg(&z__4, &d1);
z__3.r = -z__4.r, z__3.i = -z__4.i;
z__2.r = snl * z__3.r, z__2.i = snl * z__3.i;
z__1.r = *a1 * z__2.r, z__1.i = *a1 * z__2.i;
ua21.r = z__1.r, ua21.i = z__1.i;
d_cnjg(&z__5, &d1);
z__4.r = -z__5.r, z__4.i = -z__5.i;
z__3.r = snl * z__4.r, z__3.i = snl * z__4.i;
z__2.r = z__3.r * a2->r - z__3.i * a2->i, z__2.i = z__3.r * a2->i
+ z__3.i * a2->r;
d__1 = csl * *a3;
z__1.r = z__2.r + d__1, z__1.i = z__2.i;
ua22.r = z__1.r, ua22.i = z__1.i;
d_cnjg(&z__4, &d1);
z__3.r = -z__4.r, z__3.i = -z__4.i;
z__2.r = snr * z__3.r, z__2.i = snr * z__3.i;
z__1.r = *b1 * z__2.r, z__1.i = *b1 * z__2.i;
vb21.r = z__1.r, vb21.i = z__1.i;
d_cnjg(&z__5, &d1);
z__4.r = -z__5.r, z__4.i = -z__5.i;
z__3.r = snr * z__4.r, z__3.i = snr * z__4.i;
z__2.r = z__3.r * b2->r - z__3.i * b2->i, z__2.i = z__3.r * b2->i
+ z__3.i * b2->r;
d__1 = csr * *b3;
z__1.r = z__2.r + d__1, z__1.i = z__2.i;
vb22.r = z__1.r, vb22.i = z__1.i;
aua22 = abs(snl) * ((d__1 = a2->r, abs(d__1)) + (d__2 = d_imag(a2)
, abs(d__2))) + abs(csl) * abs(*a3);
avb22 = abs(snr) * ((d__1 = b2->r, abs(d__1)) + (d__2 = d_imag(b2)
, abs(d__2))) + abs(csr) * abs(*b3);
/* zero (2,2) elements of U'*A and V'*B, and then swap. */
if ((d__1 = ua21.r, abs(d__1)) + (d__2 = d_imag(&ua21), abs(d__2))
+ ((d__3 = ua22.r, abs(d__3)) + (d__4 = d_imag(&ua22),
abs(d__4))) == 0.) {
d_cnjg(&z__2, &vb21);
z__1.r = -z__2.r, z__1.i = -z__2.i;
d_cnjg(&z__3, &vb22);
zlartg_(&z__1, &z__3, csq, snq, &r__);
} else if ((d__1 = vb21.r, abs(d__1)) + (d__2 = d_imag(&vb21),
abs(d__2)) + z_abs(&vb22) == 0.) {
d_cnjg(&z__2, &ua21);
z__1.r = -z__2.r, z__1.i = -z__2.i;
d_cnjg(&z__3, &ua22);
zlartg_(&z__1, &z__3, csq, snq, &r__);
} else if (aua22 / ((d__1 = ua21.r, abs(d__1)) + (d__2 = d_imag(&
ua21), abs(d__2)) + ((d__3 = ua22.r, abs(d__3)) + (d__4 =
d_imag(&ua22), abs(d__4)))) <= avb22 / ((d__5 = vb21.r,
abs(d__5)) + (d__6 = d_imag(&vb21), abs(d__6)) + ((d__7 =
vb22.r, abs(d__7)) + (d__8 = d_imag(&vb22), abs(d__8)))))
{
d_cnjg(&z__2, &ua21);
z__1.r = -z__2.r, z__1.i = -z__2.i;
d_cnjg(&z__3, &ua22);
zlartg_(&z__1, &z__3, csq, snq, &r__);
} else {
d_cnjg(&z__2, &vb21);
z__1.r = -z__2.r, z__1.i = -z__2.i;
d_cnjg(&z__3, &vb22);
zlartg_(&z__1, &z__3, csq, snq, &r__);
}
*csu = snl;
z__1.r = csl * d1.r, z__1.i = csl * d1.i;
snu->r = z__1.r, snu->i = z__1.i;
*csv = snr;
z__1.r = csr * d1.r, z__1.i = csr * d1.i;
snv->r = z__1.r, snv->i = z__1.i;
}
} else {
/* Input matrices A and B are lower triangular matrices */
/* Form matrix C = A*adj(B) = ( a 0 ) */
/* ( c d ) */
a = *a1 * *b3;
d__ = *a3 * *b1;
z__2.r = *b3 * a2->r, z__2.i = *b3 * a2->i;
z__3.r = *a3 * b2->r, z__3.i = *a3 * b2->i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
c__.r = z__1.r, c__.i = z__1.i;
fc = z_abs(&c__);
/* Transform complex 2-by-2 matrix C to real matrix by unitary */
/* diagonal matrix diag(d1,1). */
d1.r = 1., d1.i = 0.;
if (fc != 0.) {
z__1.r = c__.r / fc, z__1.i = c__.i / fc;
d1.r = z__1.r, d1.i = z__1.i;
}
/* The SVD of real 2 by 2 triangular C */
/* ( CSL -SNL )*( A 0 )*( CSR SNR ) = ( R 0 ) */
/* ( SNL CSL ) ( C D ) ( -SNR CSR ) ( 0 T ) */
dlasv2_(&a, &fc, &d__, &s1, &s2, &snr, &csr, &snl, &csl);
if (abs(csr) >= abs(snr) || abs(csl) >= abs(snl)) {
/* Compute the (2,1) and (2,2) elements of U'*A and V'*B, */
/* and (2,1) element of |U|'*|A| and |V|'*|B|. */
z__4.r = -d1.r, z__4.i = -d1.i;
z__3.r = snr * z__4.r, z__3.i = snr * z__4.i;
z__2.r = *a1 * z__3.r, z__2.i = *a1 * z__3.i;
z__5.r = csr * a2->r, z__5.i = csr * a2->i;
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
ua21.r = z__1.r, ua21.i = z__1.i;
ua22r = csr * *a3;
z__4.r = -d1.r, z__4.i = -d1.i;
z__3.r = snl * z__4.r, z__3.i = snl * z__4.i;
z__2.r = *b1 * z__3.r, z__2.i = *b1 * z__3.i;
z__5.r = csl * b2->r, z__5.i = csl * b2->i;
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
vb21.r = z__1.r, vb21.i = z__1.i;
vb22r = csl * *b3;
aua21 = abs(snr) * abs(*a1) + abs(csr) * ((d__1 = a2->r, abs(d__1)
) + (d__2 = d_imag(a2), abs(d__2)));
avb21 = abs(snl) * abs(*b1) + abs(csl) * ((d__1 = b2->r, abs(d__1)
) + (d__2 = d_imag(b2), abs(d__2)));
/* zero (2,1) elements of U'*A and V'*B. */
if ((d__1 = ua21.r, abs(d__1)) + (d__2 = d_imag(&ua21), abs(d__2))
+ abs(ua22r) == 0.) {
z__1.r = vb22r, z__1.i = 0.;
zlartg_(&z__1, &vb21, csq, snq, &r__);
} else if ((d__1 = vb21.r, abs(d__1)) + (d__2 = d_imag(&vb21),
abs(d__2)) + abs(vb22r) == 0.) {
z__1.r = ua22r, z__1.i = 0.;
zlartg_(&z__1, &ua21, csq, snq, &r__);
} else if (aua21 / ((d__1 = ua21.r, abs(d__1)) + (d__2 = d_imag(&
ua21), abs(d__2)) + abs(ua22r)) <= avb21 / ((d__3 =
vb21.r, abs(d__3)) + (d__4 = d_imag(&vb21), abs(d__4)) +
abs(vb22r))) {
z__1.r = ua22r, z__1.i = 0.;
zlartg_(&z__1, &ua21, csq, snq, &r__);
} else {
z__1.r = vb22r, z__1.i = 0.;
zlartg_(&z__1, &vb21, csq, snq, &r__);
}
*csu = csr;
d_cnjg(&z__3, &d1);
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = snr * z__2.r, z__1.i = snr * z__2.i;
snu->r = z__1.r, snu->i = z__1.i;
*csv = csl;
d_cnjg(&z__3, &d1);
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = snl * z__2.r, z__1.i = snl * z__2.i;
snv->r = z__1.r, snv->i = z__1.i;
} else {
/* Compute the (1,1) and (1,2) elements of U'*A and V'*B, */
/* and (1,1) element of |U|'*|A| and |V|'*|B|. */
d__1 = csr * *a1;
d_cnjg(&z__4, &d1);
z__3.r = snr * z__4.r, z__3.i = snr * z__4.i;
z__2.r = z__3.r * a2->r - z__3.i * a2->i, z__2.i = z__3.r * a2->i
+ z__3.i * a2->r;
z__1.r = d__1 + z__2.r, z__1.i = z__2.i;
ua11.r = z__1.r, ua11.i = z__1.i;
d_cnjg(&z__3, &d1);
z__2.r = snr * z__3.r, z__2.i = snr * z__3.i;
z__1.r = *a3 * z__2.r, z__1.i = *a3 * z__2.i;
ua12.r = z__1.r, ua12.i = z__1.i;
d__1 = csl * *b1;
d_cnjg(&z__4, &d1);
z__3.r = snl * z__4.r, z__3.i = snl * z__4.i;
z__2.r = z__3.r * b2->r - z__3.i * b2->i, z__2.i = z__3.r * b2->i
+ z__3.i * b2->r;
z__1.r = d__1 + z__2.r, z__1.i = z__2.i;
vb11.r = z__1.r, vb11.i = z__1.i;
d_cnjg(&z__3, &d1);
z__2.r = snl * z__3.r, z__2.i = snl * z__3.i;
z__1.r = *b3 * z__2.r, z__1.i = *b3 * z__2.i;
vb12.r = z__1.r, vb12.i = z__1.i;
aua11 = abs(csr) * abs(*a1) + abs(snr) * ((d__1 = a2->r, abs(d__1)
) + (d__2 = d_imag(a2), abs(d__2)));
avb11 = abs(csl) * abs(*b1) + abs(snl) * ((d__1 = b2->r, abs(d__1)
) + (d__2 = d_imag(b2), abs(d__2)));
/* zero (1,1) elements of U'*A and V'*B, and then swap. */
if ((d__1 = ua11.r, abs(d__1)) + (d__2 = d_imag(&ua11), abs(d__2))
+ ((d__3 = ua12.r, abs(d__3)) + (d__4 = d_imag(&ua12),
abs(d__4))) == 0.) {
zlartg_(&vb12, &vb11, csq, snq, &r__);
} else if ((d__1 = vb11.r, abs(d__1)) + (d__2 = d_imag(&vb11),
abs(d__2)) + ((d__3 = vb12.r, abs(d__3)) + (d__4 = d_imag(
&vb12), abs(d__4))) == 0.) {
zlartg_(&ua12, &ua11, csq, snq, &r__);
} else if (aua11 / ((d__1 = ua11.r, abs(d__1)) + (d__2 = d_imag(&
ua11), abs(d__2)) + ((d__3 = ua12.r, abs(d__3)) + (d__4 =
d_imag(&ua12), abs(d__4)))) <= avb11 / ((d__5 = vb11.r,
abs(d__5)) + (d__6 = d_imag(&vb11), abs(d__6)) + ((d__7 =
vb12.r, abs(d__7)) + (d__8 = d_imag(&vb12), abs(d__8)))))
{
zlartg_(&ua12, &ua11, csq, snq, &r__);
} else {
zlartg_(&vb12, &vb11, csq, snq, &r__);
}
*csu = snr;
d_cnjg(&z__2, &d1);
z__1.r = csr * z__2.r, z__1.i = csr * z__2.i;
snu->r = z__1.r, snu->i = z__1.i;
*csv = snl;
d_cnjg(&z__2, &d1);
z__1.r = csl * z__2.r, z__1.i = csl * z__2.i;
snv->r = z__1.r, snv->i = z__1.i;
}
}
return 0;
/* End of ZLAGS2 */
} /* zlags2_ */