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|
/* clags2.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 clags2_(logical *upper, real *a1, complex *a2, real *a3,
real *b1, complex *b2, real *b3, real *csu, complex *snu, real *csv,
complex *snv, real *csq, complex *snq)
{
/* System generated locals */
real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8;
complex q__1, q__2, q__3, q__4, q__5;
/* Builtin functions */
double c_abs(complex *), r_imag(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
real a;
complex b, c__;
real d__;
complex r__, d1;
real s1, s2, fb, fc;
complex ua11, ua12, ua21, ua22, vb11, vb12, vb21, vb22;
real csl, csr, snl, snr, aua11, aua12, aua21, aua22, avb11, avb12, avb21,
avb22, ua11r, ua22r, vb11r, vb22r;
extern /* Subroutine */ int slasv2_(real *, real *, real *, real *, real *
, real *, real *, real *, real *), clartg_(complex *, complex *,
real *, complex *, complex *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLAGS2 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) REAL */
/* A2 (input) COMPLEX */
/* A3 (input) REAL */
/* On entry, A1, A2 and A3 are elements of the input 2-by-2 */
/* upper (lower) triangular matrix A. */
/* B1 (input) REAL */
/* B2 (input) COMPLEX */
/* B3 (input) REAL */
/* On entry, B1, B2 and B3 are elements of the input 2-by-2 */
/* upper (lower) triangular matrix B. */
/* CSU (output) REAL */
/* SNU (output) COMPLEX */
/* The desired unitary matrix U. */
/* CSV (output) REAL */
/* SNV (output) COMPLEX */
/* The desired unitary matrix V. */
/* CSQ (output) REAL */
/* SNQ (output) COMPLEX */
/* 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;
q__2.r = *b1 * a2->r, q__2.i = *b1 * a2->i;
q__3.r = *a1 * b2->r, q__3.i = *a1 * b2->i;
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
b.r = q__1.r, b.i = q__1.i;
fb = c_abs(&b);
/* Transform complex 2-by-2 matrix C to real matrix by unitary */
/* diagonal matrix diag(1,D1). */
d1.r = 1.f, d1.i = 0.f;
if (fb != 0.f) {
q__1.r = b.r / fb, q__1.i = b.i / fb;
d1.r = q__1.r, d1.i = q__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 ) */
slasv2_(&a, &fb, &d__, &s1, &s2, &snr, &csr, &snl, &csl);
if (dabs(csl) >= dabs(snl) || dabs(csr) >= dabs(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;
q__2.r = csl * a2->r, q__2.i = csl * a2->i;
q__4.r = snl * d1.r, q__4.i = snl * d1.i;
q__3.r = *a3 * q__4.r, q__3.i = *a3 * q__4.i;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
ua12.r = q__1.r, ua12.i = q__1.i;
vb11r = csr * *b1;
q__2.r = csr * b2->r, q__2.i = csr * b2->i;
q__4.r = snr * d1.r, q__4.i = snr * d1.i;
q__3.r = *b3 * q__4.r, q__3.i = *b3 * q__4.i;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
vb12.r = q__1.r, vb12.i = q__1.i;
aua12 = dabs(csl) * ((r__1 = a2->r, dabs(r__1)) + (r__2 = r_imag(
a2), dabs(r__2))) + dabs(snl) * dabs(*a3);
avb12 = dabs(csr) * ((r__1 = b2->r, dabs(r__1)) + (r__2 = r_imag(
b2), dabs(r__2))) + dabs(snr) * dabs(*b3);
/* zero (1,2) elements of U'*A and V'*B */
if (dabs(ua11r) + ((r__1 = ua12.r, dabs(r__1)) + (r__2 = r_imag(&
ua12), dabs(r__2))) == 0.f) {
q__2.r = vb11r, q__2.i = 0.f;
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &vb12);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else if (dabs(vb11r) + ((r__1 = vb12.r, dabs(r__1)) + (r__2 =
r_imag(&vb12), dabs(r__2))) == 0.f) {
q__2.r = ua11r, q__2.i = 0.f;
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &ua12);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else if (aua12 / (dabs(ua11r) + ((r__1 = ua12.r, dabs(r__1)) + (
r__2 = r_imag(&ua12), dabs(r__2)))) <= avb12 / (dabs(
vb11r) + ((r__3 = vb12.r, dabs(r__3)) + (r__4 = r_imag(&
vb12), dabs(r__4))))) {
q__2.r = ua11r, q__2.i = 0.f;
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &ua12);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else {
q__2.r = vb11r, q__2.i = 0.f;
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &vb12);
clartg_(&q__1, &q__3, csq, snq, &r__);
}
*csu = csl;
q__2.r = -d1.r, q__2.i = -d1.i;
q__1.r = snl * q__2.r, q__1.i = snl * q__2.i;
snu->r = q__1.r, snu->i = q__1.i;
*csv = csr;
q__2.r = -d1.r, q__2.i = -d1.i;
q__1.r = snr * q__2.r, q__1.i = snr * q__2.i;
snv->r = q__1.r, snv->i = q__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|. */
r_cnjg(&q__4, &d1);
q__3.r = -q__4.r, q__3.i = -q__4.i;
q__2.r = snl * q__3.r, q__2.i = snl * q__3.i;
q__1.r = *a1 * q__2.r, q__1.i = *a1 * q__2.i;
ua21.r = q__1.r, ua21.i = q__1.i;
r_cnjg(&q__5, &d1);
q__4.r = -q__5.r, q__4.i = -q__5.i;
q__3.r = snl * q__4.r, q__3.i = snl * q__4.i;
q__2.r = q__3.r * a2->r - q__3.i * a2->i, q__2.i = q__3.r * a2->i
+ q__3.i * a2->r;
r__1 = csl * *a3;
q__1.r = q__2.r + r__1, q__1.i = q__2.i;
ua22.r = q__1.r, ua22.i = q__1.i;
r_cnjg(&q__4, &d1);
q__3.r = -q__4.r, q__3.i = -q__4.i;
q__2.r = snr * q__3.r, q__2.i = snr * q__3.i;
q__1.r = *b1 * q__2.r, q__1.i = *b1 * q__2.i;
vb21.r = q__1.r, vb21.i = q__1.i;
r_cnjg(&q__5, &d1);
q__4.r = -q__5.r, q__4.i = -q__5.i;
q__3.r = snr * q__4.r, q__3.i = snr * q__4.i;
q__2.r = q__3.r * b2->r - q__3.i * b2->i, q__2.i = q__3.r * b2->i
+ q__3.i * b2->r;
r__1 = csr * *b3;
q__1.r = q__2.r + r__1, q__1.i = q__2.i;
vb22.r = q__1.r, vb22.i = q__1.i;
aua22 = dabs(snl) * ((r__1 = a2->r, dabs(r__1)) + (r__2 = r_imag(
a2), dabs(r__2))) + dabs(csl) * dabs(*a3);
avb22 = dabs(snr) * ((r__1 = b2->r, dabs(r__1)) + (r__2 = r_imag(
b2), dabs(r__2))) + dabs(csr) * dabs(*b3);
/* zero (2,2) elements of U'*A and V'*B, and then swap. */
if ((r__1 = ua21.r, dabs(r__1)) + (r__2 = r_imag(&ua21), dabs(
r__2)) + ((r__3 = ua22.r, dabs(r__3)) + (r__4 = r_imag(&
ua22), dabs(r__4))) == 0.f) {
r_cnjg(&q__2, &vb21);
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &vb22);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else if ((r__1 = vb21.r, dabs(r__1)) + (r__2 = r_imag(&vb21),
dabs(r__2)) + c_abs(&vb22) == 0.f) {
r_cnjg(&q__2, &ua21);
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &ua22);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else if (aua22 / ((r__1 = ua21.r, dabs(r__1)) + (r__2 = r_imag(&
ua21), dabs(r__2)) + ((r__3 = ua22.r, dabs(r__3)) + (r__4
= r_imag(&ua22), dabs(r__4)))) <= avb22 / ((r__5 = vb21.r,
dabs(r__5)) + (r__6 = r_imag(&vb21), dabs(r__6)) + ((
r__7 = vb22.r, dabs(r__7)) + (r__8 = r_imag(&vb22), dabs(
r__8))))) {
r_cnjg(&q__2, &ua21);
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &ua22);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else {
r_cnjg(&q__2, &vb21);
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &vb22);
clartg_(&q__1, &q__3, csq, snq, &r__);
}
*csu = snl;
q__1.r = csl * d1.r, q__1.i = csl * d1.i;
snu->r = q__1.r, snu->i = q__1.i;
*csv = snr;
q__1.r = csr * d1.r, q__1.i = csr * d1.i;
snv->r = q__1.r, snv->i = q__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;
q__2.r = *b3 * a2->r, q__2.i = *b3 * a2->i;
q__3.r = *a3 * b2->r, q__3.i = *a3 * b2->i;
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
c__.r = q__1.r, c__.i = q__1.i;
fc = c_abs(&c__);
/* Transform complex 2-by-2 matrix C to real matrix by unitary */
/* diagonal matrix diag(d1,1). */
d1.r = 1.f, d1.i = 0.f;
if (fc != 0.f) {
q__1.r = c__.r / fc, q__1.i = c__.i / fc;
d1.r = q__1.r, d1.i = q__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 ) */
slasv2_(&a, &fc, &d__, &s1, &s2, &snr, &csr, &snl, &csl);
if (dabs(csr) >= dabs(snr) || dabs(csl) >= dabs(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|. */
q__4.r = -d1.r, q__4.i = -d1.i;
q__3.r = snr * q__4.r, q__3.i = snr * q__4.i;
q__2.r = *a1 * q__3.r, q__2.i = *a1 * q__3.i;
q__5.r = csr * a2->r, q__5.i = csr * a2->i;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
ua21.r = q__1.r, ua21.i = q__1.i;
ua22r = csr * *a3;
q__4.r = -d1.r, q__4.i = -d1.i;
q__3.r = snl * q__4.r, q__3.i = snl * q__4.i;
q__2.r = *b1 * q__3.r, q__2.i = *b1 * q__3.i;
q__5.r = csl * b2->r, q__5.i = csl * b2->i;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
vb21.r = q__1.r, vb21.i = q__1.i;
vb22r = csl * *b3;
aua21 = dabs(snr) * dabs(*a1) + dabs(csr) * ((r__1 = a2->r, dabs(
r__1)) + (r__2 = r_imag(a2), dabs(r__2)));
avb21 = dabs(snl) * dabs(*b1) + dabs(csl) * ((r__1 = b2->r, dabs(
r__1)) + (r__2 = r_imag(b2), dabs(r__2)));
/* zero (2,1) elements of U'*A and V'*B. */
if ((r__1 = ua21.r, dabs(r__1)) + (r__2 = r_imag(&ua21), dabs(
r__2)) + dabs(ua22r) == 0.f) {
q__1.r = vb22r, q__1.i = 0.f;
clartg_(&q__1, &vb21, csq, snq, &r__);
} else if ((r__1 = vb21.r, dabs(r__1)) + (r__2 = r_imag(&vb21),
dabs(r__2)) + dabs(vb22r) == 0.f) {
q__1.r = ua22r, q__1.i = 0.f;
clartg_(&q__1, &ua21, csq, snq, &r__);
} else if (aua21 / ((r__1 = ua21.r, dabs(r__1)) + (r__2 = r_imag(&
ua21), dabs(r__2)) + dabs(ua22r)) <= avb21 / ((r__3 =
vb21.r, dabs(r__3)) + (r__4 = r_imag(&vb21), dabs(r__4))
+ dabs(vb22r))) {
q__1.r = ua22r, q__1.i = 0.f;
clartg_(&q__1, &ua21, csq, snq, &r__);
} else {
q__1.r = vb22r, q__1.i = 0.f;
clartg_(&q__1, &vb21, csq, snq, &r__);
}
*csu = csr;
r_cnjg(&q__3, &d1);
q__2.r = -q__3.r, q__2.i = -q__3.i;
q__1.r = snr * q__2.r, q__1.i = snr * q__2.i;
snu->r = q__1.r, snu->i = q__1.i;
*csv = csl;
r_cnjg(&q__3, &d1);
q__2.r = -q__3.r, q__2.i = -q__3.i;
q__1.r = snl * q__2.r, q__1.i = snl * q__2.i;
snv->r = q__1.r, snv->i = q__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|. */
r__1 = csr * *a1;
r_cnjg(&q__4, &d1);
q__3.r = snr * q__4.r, q__3.i = snr * q__4.i;
q__2.r = q__3.r * a2->r - q__3.i * a2->i, q__2.i = q__3.r * a2->i
+ q__3.i * a2->r;
q__1.r = r__1 + q__2.r, q__1.i = q__2.i;
ua11.r = q__1.r, ua11.i = q__1.i;
r_cnjg(&q__3, &d1);
q__2.r = snr * q__3.r, q__2.i = snr * q__3.i;
q__1.r = *a3 * q__2.r, q__1.i = *a3 * q__2.i;
ua12.r = q__1.r, ua12.i = q__1.i;
r__1 = csl * *b1;
r_cnjg(&q__4, &d1);
q__3.r = snl * q__4.r, q__3.i = snl * q__4.i;
q__2.r = q__3.r * b2->r - q__3.i * b2->i, q__2.i = q__3.r * b2->i
+ q__3.i * b2->r;
q__1.r = r__1 + q__2.r, q__1.i = q__2.i;
vb11.r = q__1.r, vb11.i = q__1.i;
r_cnjg(&q__3, &d1);
q__2.r = snl * q__3.r, q__2.i = snl * q__3.i;
q__1.r = *b3 * q__2.r, q__1.i = *b3 * q__2.i;
vb12.r = q__1.r, vb12.i = q__1.i;
aua11 = dabs(csr) * dabs(*a1) + dabs(snr) * ((r__1 = a2->r, dabs(
r__1)) + (r__2 = r_imag(a2), dabs(r__2)));
avb11 = dabs(csl) * dabs(*b1) + dabs(snl) * ((r__1 = b2->r, dabs(
r__1)) + (r__2 = r_imag(b2), dabs(r__2)));
/* zero (1,1) elements of U'*A and V'*B, and then swap. */
if ((r__1 = ua11.r, dabs(r__1)) + (r__2 = r_imag(&ua11), dabs(
r__2)) + ((r__3 = ua12.r, dabs(r__3)) + (r__4 = r_imag(&
ua12), dabs(r__4))) == 0.f) {
clartg_(&vb12, &vb11, csq, snq, &r__);
} else if ((r__1 = vb11.r, dabs(r__1)) + (r__2 = r_imag(&vb11),
dabs(r__2)) + ((r__3 = vb12.r, dabs(r__3)) + (r__4 =
r_imag(&vb12), dabs(r__4))) == 0.f) {
clartg_(&ua12, &ua11, csq, snq, &r__);
} else if (aua11 / ((r__1 = ua11.r, dabs(r__1)) + (r__2 = r_imag(&
ua11), dabs(r__2)) + ((r__3 = ua12.r, dabs(r__3)) + (r__4
= r_imag(&ua12), dabs(r__4)))) <= avb11 / ((r__5 = vb11.r,
dabs(r__5)) + (r__6 = r_imag(&vb11), dabs(r__6)) + ((
r__7 = vb12.r, dabs(r__7)) + (r__8 = r_imag(&vb12), dabs(
r__8))))) {
clartg_(&ua12, &ua11, csq, snq, &r__);
} else {
clartg_(&vb12, &vb11, csq, snq, &r__);
}
*csu = snr;
r_cnjg(&q__2, &d1);
q__1.r = csr * q__2.r, q__1.i = csr * q__2.i;
snu->r = q__1.r, snu->i = q__1.i;
*csv = snl;
r_cnjg(&q__2, &d1);
q__1.r = csl * q__2.r, q__1.i = csl * q__2.i;
snv->r = q__1.r, snv->i = q__1.i;
}
}
return 0;
/* End of CLAGS2 */
} /* clags2_ */
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