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/* dlags2.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 dlags2_(logical *upper, doublereal *a1, doublereal *a2,
doublereal *a3, doublereal *b1, doublereal *b2, doublereal *b3,
doublereal *csu, doublereal *snu, doublereal *csv, doublereal *snv,
doublereal *csq, doublereal *snq)
{
/* System generated locals */
doublereal d__1;
/* Local variables */
doublereal a, b, c__, d__, r__, s1, s2, ua11, ua12, ua21, ua22, vb11,
vb12, vb21, vb22, csl, csr, snl, snr, aua11, aua12, aua21, aua22,
avb11, avb12, avb21, avb22, ua11r, ua22r, vb11r, vb22r;
extern /* Subroutine */ int dlasv2_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *), dlartg_(doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAGS2 computes 2-by-2 orthogonal 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 ) */
/* The rows of the transformed A and B are parallel, where */
/* U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) */
/* ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) */
/* Z' denotes the transpose of Z. */
/* 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) DOUBLE PRECISION */
/* 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) DOUBLE PRECISION */
/* 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) DOUBLE PRECISION */
/* The desired orthogonal matrix U. */
/* CSV (output) DOUBLE PRECISION */
/* SNV (output) DOUBLE PRECISION */
/* The desired orthogonal matrix V. */
/* CSQ (output) DOUBLE PRECISION */
/* SNQ (output) DOUBLE PRECISION */
/* The desired orthogonal matrix Q. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. 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;
b = *a2 * *b1 - *a1 * *b2;
/* 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, &b, &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;
ua12 = csl * *a2 + snl * *a3;
vb11r = csr * *b1;
vb12 = csr * *b2 + snr * *b3;
aua12 = abs(csl) * abs(*a2) + abs(snl) * abs(*a3);
avb12 = abs(csr) * abs(*b2) + abs(snr) * abs(*b3);
/* zero (1,2) elements of U'*A and V'*B */
if (abs(ua11r) + abs(ua12) != 0.) {
if (aua12 / (abs(ua11r) + abs(ua12)) <= avb12 / (abs(vb11r) +
abs(vb12))) {
d__1 = -ua11r;
dlartg_(&d__1, &ua12, csq, snq, &r__);
} else {
d__1 = -vb11r;
dlartg_(&d__1, &vb12, csq, snq, &r__);
}
} else {
d__1 = -vb11r;
dlartg_(&d__1, &vb12, csq, snq, &r__);
}
*csu = csl;
*snu = -snl;
*csv = csr;
*snv = -snr;
} 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|. */
ua21 = -snl * *a1;
ua22 = -snl * *a2 + csl * *a3;
vb21 = -snr * *b1;
vb22 = -snr * *b2 + csr * *b3;
aua22 = abs(snl) * abs(*a2) + abs(csl) * abs(*a3);
avb22 = abs(snr) * abs(*b2) + abs(csr) * abs(*b3);
/* zero (2,2) elements of U'*A and V'*B, and then swap. */
if (abs(ua21) + abs(ua22) != 0.) {
if (aua22 / (abs(ua21) + abs(ua22)) <= avb22 / (abs(vb21) +
abs(vb22))) {
d__1 = -ua21;
dlartg_(&d__1, &ua22, csq, snq, &r__);
} else {
d__1 = -vb21;
dlartg_(&d__1, &vb22, csq, snq, &r__);
}
} else {
d__1 = -vb21;
dlartg_(&d__1, &vb22, csq, snq, &r__);
}
*csu = snl;
*snu = csl;
*csv = snr;
*snv = csr;
}
} 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;
c__ = *a2 * *b3 - *a3 * *b2;
/* 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, &c__, &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|. */
ua21 = -snr * *a1 + csr * *a2;
ua22r = csr * *a3;
vb21 = -snl * *b1 + csl * *b2;
vb22r = csl * *b3;
aua21 = abs(snr) * abs(*a1) + abs(csr) * abs(*a2);
avb21 = abs(snl) * abs(*b1) + abs(csl) * abs(*b2);
/* zero (2,1) elements of U'*A and V'*B. */
if (abs(ua21) + abs(ua22r) != 0.) {
if (aua21 / (abs(ua21) + abs(ua22r)) <= avb21 / (abs(vb21) +
abs(vb22r))) {
dlartg_(&ua22r, &ua21, csq, snq, &r__);
} else {
dlartg_(&vb22r, &vb21, csq, snq, &r__);
}
} else {
dlartg_(&vb22r, &vb21, csq, snq, &r__);
}
*csu = csr;
*snu = -snr;
*csv = csl;
*snv = -snl;
} 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|. */
ua11 = csr * *a1 + snr * *a2;
ua12 = snr * *a3;
vb11 = csl * *b1 + snl * *b2;
vb12 = snl * *b3;
aua11 = abs(csr) * abs(*a1) + abs(snr) * abs(*a2);
avb11 = abs(csl) * abs(*b1) + abs(snl) * abs(*b2);
/* zero (1,1) elements of U'*A and V'*B, and then swap. */
if (abs(ua11) + abs(ua12) != 0.) {
if (aua11 / (abs(ua11) + abs(ua12)) <= avb11 / (abs(vb11) +
abs(vb12))) {
dlartg_(&ua12, &ua11, csq, snq, &r__);
} else {
dlartg_(&vb12, &vb11, csq, snq, &r__);
}
} else {
dlartg_(&vb12, &vb11, csq, snq, &r__);
}
*csu = snr;
*snu = csr;
*csv = snl;
*snv = csl;
}
}
return 0;
/* End of DLAGS2 */
} /* dlags2_ */
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