version 1.3, 2010/08/06 15:28:56
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version 1.8, 2011/07/22 07:38:17
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SUBROUTINE ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, |
SUBROUTINE ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, |
$ SNV, CSQ, SNQ ) |
$ SNV, CSQ, SNQ ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.3.1) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* -- April 2011 -- |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
LOGICAL UPPER |
LOGICAL UPPER |
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* ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such |
* ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such |
* that if ( UPPER ) then |
* that if ( UPPER ) then |
* |
* |
* U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) |
* U**H *A*Q = U**H *( A1 A2 )*Q = ( x 0 ) |
* ( 0 A3 ) ( x x ) |
* ( 0 A3 ) ( x x ) |
* and |
* and |
* V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) |
* V**H*B*Q = V**H *( B1 B2 )*Q = ( x 0 ) |
* ( 0 B3 ) ( x x ) |
* ( 0 B3 ) ( x x ) |
* |
* |
* or if ( .NOT.UPPER ) then |
* or if ( .NOT.UPPER ) then |
* |
* |
* U'*A*Q = U'*( A1 0 )*Q = ( x x ) |
* U**H *A*Q = U**H *( A1 0 )*Q = ( x x ) |
* ( A2 A3 ) ( 0 x ) |
* ( A2 A3 ) ( 0 x ) |
* and |
* and |
* V'*B*Q = V'*( B1 0 )*Q = ( x x ) |
* V**H *B*Q = V**H *( B1 0 )*Q = ( x x ) |
* ( B2 B3 ) ( 0 x ) |
* ( B2 B3 ) ( 0 x ) |
* where |
* where |
* |
* |
* U = ( CSU SNU ), V = ( CSV SNV ), |
* U = ( CSU SNU ), V = ( CSV SNV ), |
* ( -CONJG(SNU) CSU ) ( -CONJG(SNV) CSV ) |
* ( -SNU**H CSU ) ( -SNV**H CSV ) |
* |
* |
* Q = ( CSQ SNQ ) |
* Q = ( CSQ SNQ ) |
* ( -CONJG(SNQ) CSQ ) |
* ( -SNQ**H CSQ ) |
* |
|
* Z' denotes the conjugate transpose of Z. |
|
* |
* |
* The rows of the transformed A and B are parallel. Moreover, if the |
* 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 |
* input 2-by-2 matrix A is not zero, then the transformed (1,1) entry |
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IF( ABS( CSL ).GE.ABS( SNL ) .OR. ABS( CSR ).GE.ABS( SNR ) ) |
IF( ABS( CSL ).GE.ABS( SNL ) .OR. ABS( CSR ).GE.ABS( SNR ) ) |
$ THEN |
$ THEN |
* |
* |
* Compute the (1,1) and (1,2) elements of U'*A and V'*B, |
* Compute the (1,1) and (1,2) elements of U**H *A and V**H *B, |
* and (1,2) element of |U|'*|A| and |V|'*|B|. |
* and (1,2) element of |U|**H *|A| and |V|**H *|B|. |
* |
* |
UA11R = CSL*A1 |
UA11R = CSL*A1 |
UA12 = CSL*A2 + D1*SNL*A3 |
UA12 = CSL*A2 + D1*SNL*A3 |
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AUA12 = ABS( CSL )*ABS1( A2 ) + ABS( SNL )*ABS( A3 ) |
AUA12 = ABS( CSL )*ABS1( A2 ) + ABS( SNL )*ABS( A3 ) |
AVB12 = ABS( CSR )*ABS1( B2 ) + ABS( SNR )*ABS( B3 ) |
AVB12 = ABS( CSR )*ABS1( B2 ) + ABS( SNR )*ABS( B3 ) |
* |
* |
* zero (1,2) elements of U'*A and V'*B |
* zero (1,2) elements of U**H *A and V**H *B |
* |
* |
IF( ( ABS( UA11R )+ABS1( UA12 ) ).EQ.ZERO ) THEN |
IF( ( ABS( UA11R )+ABS1( UA12 ) ).EQ.ZERO ) THEN |
CALL ZLARTG( -DCMPLX( VB11R ), DCONJG( VB12 ), CSQ, SNQ, |
CALL ZLARTG( -DCMPLX( VB11R ), DCONJG( VB12 ), CSQ, SNQ, |
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* |
* |
ELSE |
ELSE |
* |
* |
* Compute the (2,1) and (2,2) elements of U'*A and V'*B, |
* Compute the (2,1) and (2,2) elements of U**H *A and V**H *B, |
* and (2,2) element of |U|'*|A| and |V|'*|B|. |
* and (2,2) element of |U|**H *|A| and |V|**H *|B|. |
* |
* |
UA21 = -DCONJG( D1 )*SNL*A1 |
UA21 = -DCONJG( D1 )*SNL*A1 |
UA22 = -DCONJG( D1 )*SNL*A2 + CSL*A3 |
UA22 = -DCONJG( D1 )*SNL*A2 + CSL*A3 |
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AUA22 = ABS( SNL )*ABS1( A2 ) + ABS( CSL )*ABS( A3 ) |
AUA22 = ABS( SNL )*ABS1( A2 ) + ABS( CSL )*ABS( A3 ) |
AVB22 = ABS( SNR )*ABS1( B2 ) + ABS( CSR )*ABS( B3 ) |
AVB22 = ABS( SNR )*ABS1( B2 ) + ABS( CSR )*ABS( B3 ) |
* |
* |
* zero (2,2) elements of U'*A and V'*B, and then swap. |
* zero (2,2) elements of U**H *A and V**H *B, and then swap. |
* |
* |
IF( ( ABS1( UA21 )+ABS1( UA22 ) ).EQ.ZERO ) THEN |
IF( ( ABS1( UA21 )+ABS1( UA22 ) ).EQ.ZERO ) THEN |
CALL ZLARTG( -DCONJG( VB21 ), DCONJG( VB22 ), CSQ, SNQ, |
CALL ZLARTG( -DCONJG( VB21 ), DCONJG( VB22 ), CSQ, SNQ, |
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IF( ABS( CSR ).GE.ABS( SNR ) .OR. ABS( CSL ).GE.ABS( SNL ) ) |
IF( ABS( CSR ).GE.ABS( SNR ) .OR. ABS( CSL ).GE.ABS( SNL ) ) |
$ THEN |
$ THEN |
* |
* |
* Compute the (2,1) and (2,2) elements of U'*A and V'*B, |
* Compute the (2,1) and (2,2) elements of U**H *A and V**H *B, |
* and (2,1) element of |U|'*|A| and |V|'*|B|. |
* and (2,1) element of |U|**H *|A| and |V|**H *|B|. |
* |
* |
UA21 = -D1*SNR*A1 + CSR*A2 |
UA21 = -D1*SNR*A1 + CSR*A2 |
UA22R = CSR*A3 |
UA22R = CSR*A3 |
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AUA21 = ABS( SNR )*ABS( A1 ) + ABS( CSR )*ABS1( A2 ) |
AUA21 = ABS( SNR )*ABS( A1 ) + ABS( CSR )*ABS1( A2 ) |
AVB21 = ABS( SNL )*ABS( B1 ) + ABS( CSL )*ABS1( B2 ) |
AVB21 = ABS( SNL )*ABS( B1 ) + ABS( CSL )*ABS1( B2 ) |
* |
* |
* zero (2,1) elements of U'*A and V'*B. |
* zero (2,1) elements of U**H *A and V**H *B. |
* |
* |
IF( ( ABS1( UA21 )+ABS( UA22R ) ).EQ.ZERO ) THEN |
IF( ( ABS1( UA21 )+ABS( UA22R ) ).EQ.ZERO ) THEN |
CALL ZLARTG( DCMPLX( VB22R ), VB21, CSQ, SNQ, R ) |
CALL ZLARTG( DCMPLX( VB22R ), VB21, CSQ, SNQ, R ) |
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* |
* |
ELSE |
ELSE |
* |
* |
* Compute the (1,1) and (1,2) elements of U'*A and V'*B, |
* Compute the (1,1) and (1,2) elements of U**H *A and V**H *B, |
* and (1,1) element of |U|'*|A| and |V|'*|B|. |
* and (1,1) element of |U|**H *|A| and |V|**H *|B|. |
* |
* |
UA11 = CSR*A1 + DCONJG( D1 )*SNR*A2 |
UA11 = CSR*A1 + DCONJG( D1 )*SNR*A2 |
UA12 = DCONJG( D1 )*SNR*A3 |
UA12 = DCONJG( D1 )*SNR*A3 |
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AUA11 = ABS( CSR )*ABS( A1 ) + ABS( SNR )*ABS1( A2 ) |
AUA11 = ABS( CSR )*ABS( A1 ) + ABS( SNR )*ABS1( A2 ) |
AVB11 = ABS( CSL )*ABS( B1 ) + ABS( SNL )*ABS1( B2 ) |
AVB11 = ABS( CSL )*ABS( B1 ) + ABS( SNL )*ABS1( B2 ) |
* |
* |
* zero (1,1) elements of U'*A and V'*B, and then swap. |
* zero (1,1) elements of U**H *A and V**H *B, and then swap. |
* |
* |
IF( ( ABS1( UA11 )+ABS1( UA12 ) ).EQ.ZERO ) THEN |
IF( ( ABS1( UA11 )+ABS1( UA12 ) ).EQ.ZERO ) THEN |
CALL ZLARTG( VB12, VB11, CSQ, SNQ, R ) |
CALL ZLARTG( VB12, VB11, CSQ, SNQ, R ) |