.TH "SRC/ctgevc.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/ctgevc.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBctgevc\fP (side, howmny, select, n, s, lds, p, ldp, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)" .br .RI "\fBCTGEVC\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine ctgevc (character side, character howmny, logical, dimension( * ) select, integer n, complex, dimension( lds, * ) s, integer lds, complex, dimension( ldp, * ) p, integer ldp, complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)" .PP \fBCTGEVC\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CTGEVC computes some or all of the right and/or left eigenvectors of !> a pair of complex matrices (S,P), where S and P are upper triangular\&. !> Matrix pairs of this type are produced by the generalized Schur !> factorization of a complex matrix pair (A,B): !> !> A = Q*S*Z**H, B = Q*P*Z**H !> !> as computed by CGGHRD + CHGEQZ\&. !> !> The right eigenvector x and the left eigenvector y of (S,P) !> corresponding to an eigenvalue w are defined by: !> !> S*x = w*P*x, (y**H)*S = w*(y**H)*P, !> !> where y**H denotes the conjugate transpose of y\&. !> The eigenvalues are not input to this routine, but are computed !> directly from the diagonal elements of S and P\&. !> !> This routine returns the matrices X and/or Y of right and left !> eigenvectors of (S,P), or the products Z*X and/or Q*Y, !> where Z and Q are input matrices\&. !> If Q and Z are the unitary factors from the generalized Schur !> factorization of a matrix pair (A,B), then Z*X and Q*Y !> are the matrices of right and left eigenvectors of (A,B)\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fISIDE\fP .PP .nf !> SIDE is CHARACTER*1 !> = 'R': compute right eigenvectors only; !> = 'L': compute left eigenvectors only; !> = 'B': compute both right and left eigenvectors\&. !> .fi .PP .br \fIHOWMNY\fP .PP .nf !> HOWMNY is CHARACTER*1 !> = 'A': compute all right and/or left eigenvectors; !> = 'B': compute all right and/or left eigenvectors, !> backtransformed by the matrices in VR and/or VL; !> = 'S': compute selected right and/or left eigenvectors, !> specified by the logical array SELECT\&. !> .fi .PP .br \fISELECT\fP .PP .nf !> SELECT is LOGICAL array, dimension (N) !> If HOWMNY='S', SELECT specifies the eigenvectors to be !> computed\&. The eigenvector corresponding to the j-th !> eigenvalue is computed if SELECT(j) = \&.TRUE\&.\&. !> Not referenced if HOWMNY = 'A' or 'B'\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrices S and P\&. N >= 0\&. !> .fi .PP .br \fIS\fP .PP .nf !> S is COMPLEX array, dimension (LDS,N) !> The upper triangular matrix S from a generalized Schur !> factorization, as computed by CHGEQZ\&. !> .fi .PP .br \fILDS\fP .PP .nf !> LDS is INTEGER !> The leading dimension of array S\&. LDS >= max(1,N)\&. !> .fi .PP .br \fIP\fP .PP .nf !> P is COMPLEX array, dimension (LDP,N) !> The upper triangular matrix P from a generalized Schur !> factorization, as computed by CHGEQZ\&. P must have real !> diagonal elements\&. !> .fi .PP .br \fILDP\fP .PP .nf !> LDP is INTEGER !> The leading dimension of array P\&. LDP >= max(1,N)\&. !> .fi .PP .br \fIVL\fP .PP .nf !> VL is COMPLEX array, dimension (LDVL,MM) !> On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must !> contain an N-by-N matrix Q (usually the unitary matrix Q !> of left Schur vectors returned by CHGEQZ)\&. !> On exit, if SIDE = 'L' or 'B', VL contains: !> if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P); !> if HOWMNY = 'B', the matrix Q*Y; !> if HOWMNY = 'S', the left eigenvectors of (S,P) specified by !> SELECT, stored consecutively in the columns of !> VL, in the same order as their eigenvalues\&. !> Not referenced if SIDE = 'R'\&. !> .fi .PP .br \fILDVL\fP .PP .nf !> LDVL is INTEGER !> The leading dimension of array VL\&. LDVL >= 1, and if !> SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N\&. !> .fi .PP .br \fIVR\fP .PP .nf !> VR is COMPLEX array, dimension (LDVR,MM) !> On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must !> contain an N-by-N matrix Z (usually the unitary matrix Z !> of right Schur vectors returned by CHGEQZ)\&. !> On exit, if SIDE = 'R' or 'B', VR contains: !> if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); !> if HOWMNY = 'B', the matrix Z*X; !> if HOWMNY = 'S', the right eigenvectors of (S,P) specified by !> SELECT, stored consecutively in the columns of !> VR, in the same order as their eigenvalues\&. !> Not referenced if SIDE = 'L'\&. !> .fi .PP .br \fILDVR\fP .PP .nf !> LDVR is INTEGER !> The leading dimension of the array VR\&. LDVR >= 1, and if !> SIDE = 'R' or 'B', LDVR >= N\&. !> .fi .PP .br \fIMM\fP .PP .nf !> MM is INTEGER !> The number of columns in the arrays VL and/or VR\&. MM >= M\&. !> .fi .PP .br \fIM\fP .PP .nf !> M is INTEGER !> The number of columns in the arrays VL and/or VR actually !> used to store the eigenvectors\&. If HOWMNY = 'A' or 'B', M !> is set to N\&. Each selected eigenvector occupies one column\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX array, dimension (2*N) !> .fi .PP .br \fIRWORK\fP .PP .nf !> RWORK is REAL array, dimension (2*N) !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit\&. !> < 0: if INFO = -i, the i-th argument had an illegal value\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB217\fP of file \fBctgevc\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.