From baba851215b44ac3b60b9248eb02bcce7eb76247 Mon Sep 17 00:00:00 2001 From: jason Date: Tue, 28 Oct 2008 01:38:50 +0000 Subject: Move LAPACK trunk into position. --- SRC/zlags2.f | 308 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 308 insertions(+) create mode 100644 SRC/zlags2.f (limited to 'SRC/zlags2.f') diff --git a/SRC/zlags2.f b/SRC/zlags2.f new file mode 100644 index 00000000..293f75e4 --- /dev/null +++ b/SRC/zlags2.f @@ -0,0 +1,308 @@ + SUBROUTINE ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, + $ SNV, CSQ, SNQ ) +* +* -- LAPACK auxiliary routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + LOGICAL UPPER + DOUBLE PRECISION A1, A3, B1, B3, CSQ, CSU, CSV + COMPLEX*16 A2, B2, SNQ, SNU, SNV +* .. +* +* 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 .. + DOUBLE PRECISION ZERO, ONE + PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION A, AUA11, AUA12, AUA21, AUA22, AVB12, AVB11, + $ AVB21, AVB22, CSL, CSR, D, FB, FC, S1, S2, + $ SNL, SNR, UA11R, UA22R, VB11R, VB22R + COMPLEX*16 B, C, D1, R, T, UA11, UA12, UA21, UA22, VB11, + $ VB12, VB21, VB22 +* .. +* .. External Subroutines .. + EXTERNAL DLASV2, ZLARTG +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG +* .. +* .. Statement Functions .. + DOUBLE PRECISION ABS1 +* .. +* .. Statement Function definitions .. + ABS1( T ) = ABS( DBLE( T ) ) + ABS( DIMAG( T ) ) +* .. +* .. Executable Statements .. +* + IF( UPPER ) THEN +* +* 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 + FB = ABS( B ) +* +* Transform complex 2-by-2 matrix C to real matrix by unitary +* diagonal matrix diag(1,D1). +* + D1 = ONE + IF( FB.NE.ZERO ) + $ D1 = B / FB +* +* 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 ) +* + CALL DLASV2( A, FB, D, S1, S2, SNR, CSR, SNL, CSL ) +* + IF( ABS( CSL ).GE.ABS( SNL ) .OR. ABS( CSR ).GE.ABS( SNR ) ) + $ THEN +* +* 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 + D1*SNL*A3 +* + VB11R = CSR*B1 + VB12 = CSR*B2 + D1*SNR*B3 +* + AUA12 = ABS( CSL )*ABS1( A2 ) + ABS( SNL )*ABS( A3 ) + AVB12 = ABS( CSR )*ABS1( B2 ) + ABS( SNR )*ABS( B3 ) +* +* zero (1,2) elements of U'*A and V'*B +* + IF( ( ABS( UA11R )+ABS1( UA12 ) ).EQ.ZERO ) THEN + CALL ZLARTG( -DCMPLX( VB11R ), DCONJG( VB12 ), CSQ, SNQ, + $ R ) + ELSE IF( ( ABS( VB11R )+ABS1( VB12 ) ).EQ.ZERO ) THEN + CALL ZLARTG( -DCMPLX( UA11R ), DCONJG( UA12 ), CSQ, SNQ, + $ R ) + ELSE IF( AUA12 / ( ABS( UA11R )+ABS1( UA12 ) ).LE.AVB12 / + $ ( ABS( VB11R )+ABS1( VB12 ) ) ) THEN + CALL ZLARTG( -DCMPLX( UA11R ), DCONJG( UA12 ), CSQ, SNQ, + $ R ) + ELSE + CALL ZLARTG( -DCMPLX( VB11R ), DCONJG( VB12 ), CSQ, SNQ, + $ R ) + END IF +* + CSU = CSL + SNU = -D1*SNL + CSV = CSR + SNV = -D1*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 = -DCONJG( D1 )*SNL*A1 + UA22 = -DCONJG( D1 )*SNL*A2 + CSL*A3 +* + VB21 = -DCONJG( D1 )*SNR*B1 + VB22 = -DCONJG( D1 )*SNR*B2 + CSR*B3 +* + AUA22 = ABS( SNL )*ABS1( A2 ) + ABS( CSL )*ABS( A3 ) + AVB22 = ABS( SNR )*ABS1( B2 ) + ABS( CSR )*ABS( B3 ) +* +* zero (2,2) elements of U'*A and V'*B, and then swap. +* + IF( ( ABS1( UA21 )+ABS1( UA22 ) ).EQ.ZERO ) THEN + CALL ZLARTG( -DCONJG( VB21 ), DCONJG( VB22 ), CSQ, SNQ, + $ R ) + ELSE IF( ( ABS1( VB21 )+ABS( VB22 ) ).EQ.ZERO ) THEN + CALL ZLARTG( -DCONJG( UA21 ), DCONJG( UA22 ), CSQ, SNQ, + $ R ) + ELSE IF( AUA22 / ( ABS1( UA21 )+ABS1( UA22 ) ).LE.AVB22 / + $ ( ABS1( VB21 )+ABS1( VB22 ) ) ) THEN + CALL ZLARTG( -DCONJG( UA21 ), DCONJG( UA22 ), CSQ, SNQ, + $ R ) + ELSE + CALL ZLARTG( -DCONJG( VB21 ), DCONJG( VB22 ), CSQ, SNQ, + $ R ) + END IF +* + CSU = SNL + SNU = D1*CSL + CSV = SNR + SNV = D1*CSR +* + END IF +* + 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 + FC = ABS( C ) +* +* Transform complex 2-by-2 matrix C to real matrix by unitary +* diagonal matrix diag(d1,1). +* + D1 = ONE + IF( FC.NE.ZERO ) + $ D1 = C / FC +* +* 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 ) +* + CALL DLASV2( A, FC, D, S1, S2, SNR, CSR, SNL, CSL ) +* + IF( ABS( CSR ).GE.ABS( SNR ) .OR. ABS( CSL ).GE.ABS( SNL ) ) + $ THEN +* +* 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 = -D1*SNR*A1 + CSR*A2 + UA22R = CSR*A3 +* + VB21 = -D1*SNL*B1 + CSL*B2 + VB22R = CSL*B3 +* + AUA21 = ABS( SNR )*ABS( A1 ) + ABS( CSR )*ABS1( A2 ) + AVB21 = ABS( SNL )*ABS( B1 ) + ABS( CSL )*ABS1( B2 ) +* +* zero (2,1) elements of U'*A and V'*B. +* + IF( ( ABS1( UA21 )+ABS( UA22R ) ).EQ.ZERO ) THEN + CALL ZLARTG( DCMPLX( VB22R ), VB21, CSQ, SNQ, R ) + ELSE IF( ( ABS1( VB21 )+ABS( VB22R ) ).EQ.ZERO ) THEN + CALL ZLARTG( DCMPLX( UA22R ), UA21, CSQ, SNQ, R ) + ELSE IF( AUA21 / ( ABS1( UA21 )+ABS( UA22R ) ).LE.AVB21 / + $ ( ABS1( VB21 )+ABS( VB22R ) ) ) THEN + CALL ZLARTG( DCMPLX( UA22R ), UA21, CSQ, SNQ, R ) + ELSE + CALL ZLARTG( DCMPLX( VB22R ), VB21, CSQ, SNQ, R ) + END IF +* + CSU = CSR + SNU = -DCONJG( D1 )*SNR + CSV = CSL + SNV = -DCONJG( D1 )*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 + DCONJG( D1 )*SNR*A2 + UA12 = DCONJG( D1 )*SNR*A3 +* + VB11 = CSL*B1 + DCONJG( D1 )*SNL*B2 + VB12 = DCONJG( D1 )*SNL*B3 +* + AUA11 = ABS( CSR )*ABS( A1 ) + ABS( SNR )*ABS1( A2 ) + AVB11 = ABS( CSL )*ABS( B1 ) + ABS( SNL )*ABS1( B2 ) +* +* zero (1,1) elements of U'*A and V'*B, and then swap. +* + IF( ( ABS1( UA11 )+ABS1( UA12 ) ).EQ.ZERO ) THEN + CALL ZLARTG( VB12, VB11, CSQ, SNQ, R ) + ELSE IF( ( ABS1( VB11 )+ABS1( VB12 ) ).EQ.ZERO ) THEN + CALL ZLARTG( UA12, UA11, CSQ, SNQ, R ) + ELSE IF( AUA11 / ( ABS1( UA11 )+ABS1( UA12 ) ).LE.AVB11 / + $ ( ABS1( VB11 )+ABS1( VB12 ) ) ) THEN + CALL ZLARTG( UA12, UA11, CSQ, SNQ, R ) + ELSE + CALL ZLARTG( VB12, VB11, CSQ, SNQ, R ) + END IF +* + CSU = SNR + SNU = DCONJG( D1 )*CSR + CSV = SNL + SNV = DCONJG( D1 )*CSL +* + END IF +* + END IF +* + RETURN +* +* End of ZLAGS2 +* + END -- cgit v1.2.3