#include "blaswrap.h" #include "f2c.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) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 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. ===================================================================== */ /* System generated locals */ doublereal d__1; /* Local variables */ static 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 *); 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_ */