version 1.1, 2010/01/26 15:22:46
|
version 1.9, 2011/11/21 20:43:15
|
Line 1
|
Line 1
|
|
*> \brief \b ZLAGS2 |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download ZLAGS2 + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlags2.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlags2.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlags2.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, |
|
* SNV, CSQ, SNQ ) |
|
* |
|
* .. Scalar Arguments .. |
|
* LOGICAL UPPER |
|
* DOUBLE PRECISION A1, A3, B1, B3, CSQ, CSU, CSV |
|
* COMPLEX*16 A2, B2, SNQ, SNU, SNV |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such |
|
*> that if ( UPPER ) then |
|
*> |
|
*> U**H *A*Q = U**H *( A1 A2 )*Q = ( x 0 ) |
|
*> ( 0 A3 ) ( x x ) |
|
*> and |
|
*> V**H*B*Q = V**H *( B1 B2 )*Q = ( x 0 ) |
|
*> ( 0 B3 ) ( x x ) |
|
*> |
|
*> or if ( .NOT.UPPER ) then |
|
*> |
|
*> U**H *A*Q = U**H *( A1 0 )*Q = ( x x ) |
|
*> ( A2 A3 ) ( 0 x ) |
|
*> and |
|
*> V**H *B*Q = V**H *( B1 0 )*Q = ( x x ) |
|
*> ( B2 B3 ) ( 0 x ) |
|
*> where |
|
*> |
|
*> U = ( CSU SNU ), V = ( CSV SNV ), |
|
*> ( -SNU**H CSU ) ( -SNV**H CSV ) |
|
*> |
|
*> Q = ( CSQ SNQ ) |
|
*> ( -SNQ**H CSQ ) |
|
*> |
|
*> 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. |
|
*> \endverbatim |
|
* |
|
* Arguments: |
|
* ========== |
|
* |
|
*> \param[in] UPPER |
|
*> \verbatim |
|
*> UPPER is LOGICAL |
|
*> = .TRUE.: the input matrices A and B are upper triangular. |
|
*> = .FALSE.: the input matrices A and B are lower triangular. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] A1 |
|
*> \verbatim |
|
*> A1 is DOUBLE PRECISION |
|
*> \endverbatim |
|
*> |
|
*> \param[in] A2 |
|
*> \verbatim |
|
*> A2 is COMPLEX*16 |
|
*> \endverbatim |
|
*> |
|
*> \param[in] A3 |
|
*> \verbatim |
|
*> A3 is DOUBLE PRECISION |
|
*> On entry, A1, A2 and A3 are elements of the input 2-by-2 |
|
*> upper (lower) triangular matrix A. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] B1 |
|
*> \verbatim |
|
*> B1 is DOUBLE PRECISION |
|
*> \endverbatim |
|
*> |
|
*> \param[in] B2 |
|
*> \verbatim |
|
*> B2 is COMPLEX*16 |
|
*> \endverbatim |
|
*> |
|
*> \param[in] B3 |
|
*> \verbatim |
|
*> B3 is DOUBLE PRECISION |
|
*> On entry, B1, B2 and B3 are elements of the input 2-by-2 |
|
*> upper (lower) triangular matrix B. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] CSU |
|
*> \verbatim |
|
*> CSU is DOUBLE PRECISION |
|
*> \endverbatim |
|
*> |
|
*> \param[out] SNU |
|
*> \verbatim |
|
*> SNU is COMPLEX*16 |
|
*> The desired unitary matrix U. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] CSV |
|
*> \verbatim |
|
*> CSV is DOUBLE PRECISION |
|
*> \endverbatim |
|
*> |
|
*> \param[out] SNV |
|
*> \verbatim |
|
*> SNV is COMPLEX*16 |
|
*> The desired unitary matrix V. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] CSQ |
|
*> \verbatim |
|
*> CSQ is DOUBLE PRECISION |
|
*> \endverbatim |
|
*> |
|
*> \param[out] SNQ |
|
*> \verbatim |
|
*> SNQ is COMPLEX*16 |
|
*> The desired unitary matrix Q. |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \date November 2011 |
|
* |
|
*> \ingroup complex16OTHERauxiliary |
|
* |
|
* ===================================================================== |
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 3.4.0) -- |
* -- 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 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
LOGICAL UPPER |
LOGICAL UPPER |
Line 12
|
Line 169
|
COMPLEX*16 A2, B2, SNQ, SNU, SNV |
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 .. |
* .. Parameters .. |
Line 135
|
Line 225
|
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 |
Line 147
|
Line 237
|
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, |
Line 171
|
Line 261
|
* |
* |
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 |
Line 183
|
Line 273
|
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, |
Line 236
|
Line 326
|
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 |
Line 248
|
Line 338
|
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 ) |
Line 268
|
Line 358
|
* |
* |
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 |
Line 280
|
Line 370
|
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 ) |