--- rpl/lapack/lapack/zlags2.f 2010/04/21 13:45:33 1.2
+++ rpl/lapack/lapack/zlags2.f 2011/11/21 22:19:51 1.10
@@ -1,10 +1,167 @@
+*> \brief \b ZLAGS2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZLAGS2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \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,
$ 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, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* November 2011
*
* .. Scalar Arguments ..
LOGICAL UPPER
@@ -12,73 +169,6 @@
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 ..
@@ -135,8 +225,8 @@
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|.
+* Compute the (1,1) and (1,2) elements of U**H *A and V**H *B,
+* and (1,2) element of |U|**H *|A| and |V|**H *|B|.
*
UA11R = CSL*A1
UA12 = CSL*A2 + D1*SNL*A3
@@ -147,7 +237,7 @@
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
+* zero (1,2) elements of U**H *A and V**H *B
*
IF( ( ABS( UA11R )+ABS1( UA12 ) ).EQ.ZERO ) THEN
CALL ZLARTG( -DCMPLX( VB11R ), DCONJG( VB12 ), CSQ, SNQ,
@@ -171,8 +261,8 @@
*
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|.
+* Compute the (2,1) and (2,2) elements of U**H *A and V**H *B,
+* and (2,2) element of |U|**H *|A| and |V|**H *|B|.
*
UA21 = -DCONJG( D1 )*SNL*A1
UA22 = -DCONJG( D1 )*SNL*A2 + CSL*A3
@@ -183,7 +273,7 @@
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.
+* zero (2,2) elements of U**H *A and V**H *B, and then swap.
*
IF( ( ABS1( UA21 )+ABS1( UA22 ) ).EQ.ZERO ) THEN
CALL ZLARTG( -DCONJG( VB21 ), DCONJG( VB22 ), CSQ, SNQ,
@@ -236,8 +326,8 @@
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|.
+* Compute the (2,1) and (2,2) elements of U**H *A and V**H *B,
+* and (2,1) element of |U|**H *|A| and |V|**H *|B|.
*
UA21 = -D1*SNR*A1 + CSR*A2
UA22R = CSR*A3
@@ -248,7 +338,7 @@
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.
+* zero (2,1) elements of U**H *A and V**H *B.
*
IF( ( ABS1( UA21 )+ABS( UA22R ) ).EQ.ZERO ) THEN
CALL ZLARTG( DCMPLX( VB22R ), VB21, CSQ, SNQ, R )
@@ -268,8 +358,8 @@
*
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|.
+* Compute the (1,1) and (1,2) elements of U**H *A and V**H *B,
+* and (1,1) element of |U|**H *|A| and |V|**H *|B|.
*
UA11 = CSR*A1 + DCONJG( D1 )*SNR*A2
UA12 = DCONJG( D1 )*SNR*A3
@@ -280,7 +370,7 @@
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.
+* zero (1,1) elements of U**H *A and V**H *B, and then swap.
*
IF( ( ABS1( UA11 )+ABS1( UA12 ) ).EQ.ZERO ) THEN
CALL ZLARTG( VB12, VB11, CSQ, SNQ, R )