diff options
Diffstat (limited to 'SRC/clags2.f')
| -rw-r--r-- | SRC/clags2.f | 50 |
1 files changed, 24 insertions, 26 deletions
diff --git a/SRC/clags2.f b/SRC/clags2.f index 508d3ea7..4b035d3f 100644 --- a/SRC/clags2.f +++ b/SRC/clags2.f @@ -18,28 +18,26 @@ * CLAGS2 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 ) +* U**H *A*Q = U**H *( A1 A2 )*Q = ( x 0 ) +* ( 0 A3 ) ( x x ) * and -* V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) -* ( 0 B3 ) ( x x ) +* V**H*B*Q = V**H *( 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 ) +* U**H *A*Q = U**H *( A1 0 )*Q = ( x x ) +* ( A2 A3 ) ( 0 x ) * and -* V'*B*Q = V'*( B1 0 )*Q = ( x x ) -* ( B2 B3 ) ( 0 x ) +* V**H *B*Q = V**H *( B1 0 )*Q = ( x x ) +* ( B2 B3 ) ( 0 x ) * where * -* U = ( CSU SNU ), V = ( CSV SNV ), -* ( -CONJG(SNU) CSU ) ( -CONJG(SNV) CSV ) +* U = ( CSU SNU ), V = ( CSV SNV ), +* ( -SNU**H CSU ) ( -SNV**H CSV ) * -* Q = ( CSQ SNQ ) -* ( -CONJG(SNQ) CSQ ) -* -* Z' denotes the conjugate transpose of Z. +* 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 @@ -135,8 +133,8 @@ 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 +145,7 @@ 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 CLARTG( -CMPLX( VB11R ), CONJG( VB12 ), CSQ, SNQ, @@ -171,8 +169,8 @@ * 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 = -CONJG( D1 )*SNL*A1 UA22 = -CONJG( D1 )*SNL*A2 + CSL*A3 @@ -183,7 +181,7 @@ 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 CLARTG( -CONJG( VB21 ), CONJG( VB22 ), CSQ, SNQ, R ) @@ -232,8 +230,8 @@ 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 @@ -244,7 +242,7 @@ 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 CLARTG( CMPLX( VB22R ), VB21, CSQ, SNQ, R ) @@ -264,8 +262,8 @@ * 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 + CONJG( D1 )*SNR*A2 UA12 = CONJG( D1 )*SNR*A3 @@ -276,7 +274,7 @@ 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 CLARTG( VB12, VB11, CSQ, SNQ, R ) |