#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int slags2_(logical *upper, real *a1, real *a2, real *a3, real *b1, real *b2, real *b3, real *csu, real *snu, real *csv, real * snv, real *csq, real *snq) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SLAGS2 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) REAL A2 (input) REAL 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) REAL 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) REAL The desired orthogonal matrix U. CSV (output) REAL SNV (output) REAL The desired orthogonal matrix V. CSQ (output) REAL SNQ (output) REAL The desired orthogonal matrix Q. ===================================================================== */ /* System generated locals */ real r__1; /* Local variables */ static real 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 slasv2_(real *, real *, real *, real *, real * , real *, real *, real *, real *), slartg_(real *, real *, real *, real *, real *); 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 ) */ slasv2_(&a, &b, &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; ua12 = csl * *a2 + snl * *a3; vb11r = csr * *b1; vb12 = csr * *b2 + snr * *b3; aua12 = dabs(csl) * dabs(*a2) + dabs(snl) * dabs(*a3); avb12 = dabs(csr) * dabs(*b2) + dabs(snr) * dabs(*b3); /* zero (1,2) elements of U'*A and V'*B */ if (dabs(ua11r) + dabs(ua12) != 0.f) { if (aua12 / (dabs(ua11r) + dabs(ua12)) <= avb12 / (dabs(vb11r) + dabs(vb12))) { r__1 = -ua11r; slartg_(&r__1, &ua12, csq, snq, &r__); } else { r__1 = -vb11r; slartg_(&r__1, &vb12, csq, snq, &r__); } } else { r__1 = -vb11r; slartg_(&r__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 = dabs(snl) * dabs(*a2) + dabs(csl) * dabs(*a3); avb22 = dabs(snr) * dabs(*b2) + dabs(csr) * dabs(*b3); /* zero (2,2) elements of U'*A and V'*B, and then swap. */ if (dabs(ua21) + dabs(ua22) != 0.f) { if (aua22 / (dabs(ua21) + dabs(ua22)) <= avb22 / (dabs(vb21) + dabs(vb22))) { r__1 = -ua21; slartg_(&r__1, &ua22, csq, snq, &r__); } else { r__1 = -vb21; slartg_(&r__1, &vb22, csq, snq, &r__); } } else { r__1 = -vb21; slartg_(&r__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 ) */ slasv2_(&a, &c__, &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|. */ ua21 = -snr * *a1 + csr * *a2; ua22r = csr * *a3; vb21 = -snl * *b1 + csl * *b2; vb22r = csl * *b3; aua21 = dabs(snr) * dabs(*a1) + dabs(csr) * dabs(*a2); avb21 = dabs(snl) * dabs(*b1) + dabs(csl) * dabs(*b2); /* zero (2,1) elements of U'*A and V'*B. */ if (dabs(ua21) + dabs(ua22r) != 0.f) { if (aua21 / (dabs(ua21) + dabs(ua22r)) <= avb21 / (dabs(vb21) + dabs(vb22r))) { slartg_(&ua22r, &ua21, csq, snq, &r__); } else { slartg_(&vb22r, &vb21, csq, snq, &r__); } } else { slartg_(&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 = dabs(csr) * dabs(*a1) + dabs(snr) * dabs(*a2); avb11 = dabs(csl) * dabs(*b1) + dabs(snl) * dabs(*b2); /* zero (1,1) elements of U'*A and V'*B, and then swap. */ if (dabs(ua11) + dabs(ua12) != 0.f) { if (aua11 / (dabs(ua11) + dabs(ua12)) <= avb11 / (dabs(vb11) + dabs(vb12))) { slartg_(&ua12, &ua11, csq, snq, &r__); } else { slartg_(&vb12, &vb11, csq, snq, &r__); } } else { slartg_(&vb12, &vb11, csq, snq, &r__); } *csu = snr; *snu = csr; *csv = snl; *snv = csl; } } return 0; /* End of SLAGS2 */ } /* slags2_ */