--- rpl/lapack/lapack/ztgsy2.f 2010/12/21 13:53:57 1.7 +++ rpl/lapack/lapack/ztgsy2.f 2011/07/22 07:38:21 1.8 @@ -2,10 +2,10 @@ $ LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL, $ INFO ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- LAPACK auxiliary routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* -- April 2011 -- * * .. Scalar Arguments .. CHARACTER TRANS @@ -22,7 +22,7 @@ * * ZTGSY2 solves the generalized Sylvester equation * -* A * R - L * B = scale * C (1) +* A * R - L * B = scale * C (1) * D * R - L * E = scale * F * * using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices, @@ -36,17 +36,17 @@ * In matrix notation solving equation (1) corresponds to solve * Zx = scale * b, where Z is defined as * -* Z = [ kron(In, A) -kron(B', Im) ] (2) -* [ kron(In, D) -kron(E', Im) ], +* Z = [ kron(In, A) -kron(B**H, Im) ] (2) +* [ kron(In, D) -kron(E**H, Im) ], * -* Ik is the identity matrix of size k and X' is the transpose of X. +* Ik is the identity matrix of size k and X**H is the conjuguate transpose of X. * kron(X, Y) is the Kronecker product between the matrices X and Y. * -* If TRANS = 'C', y in the conjugate transposed system Z'y = scale*b +* If TRANS = 'C', y in the conjugate transposed system Z**H*y = scale*b * is solved for, which is equivalent to solve for R and L in * -* A' * R + D' * L = scale * C (3) -* R * B' + L * E' = scale * -F +* A**H * R + D**H * L = scale * C (3) +* R * B**H + L * E**H = scale * -F * * This case is used to compute an estimate of Dif[(A, D), (B, E)] = * = sigma_min(Z) using reverse communicaton with ZLACON. @@ -298,7 +298,7 @@ ELSE * * Solve transposed (I, J) - system: -* A(I, I)' * R(I, J) + D(I, I)' * L(J, J) = C(I, J) +* A(I, I)**H * R(I, J) + D(I, I)**H * L(J, J) = C(I, J) * R(I, I) * B(J, J) + L(I, J) * E(J, J) = -F(I, J) * for I = 1, 2, ..., M, J = N, N - 1, ..., 1 * @@ -307,7 +307,7 @@ DO 80 I = 1, M DO 70 J = N, 1, -1 * -* Build 2 by 2 system Z' +* Build 2 by 2 system Z**H * Z( 1, 1 ) = DCONJG( A( I, I ) ) Z( 2, 1 ) = -DCONJG( B( J, J ) ) @@ -320,7 +320,7 @@ RHS( 1 ) = C( I, J ) RHS( 2 ) = F( I, J ) * -* Solve Z' * x = RHS +* Solve Z**H * x = RHS * CALL ZGETC2( LDZ, Z, LDZ, IPIV, JPIV, IERR ) IF( IERR.GT.0 )