LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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subroutine ztrevc3 | ( | character | side, |
character | howmny, | ||
logical, dimension( * ) | select, | ||
integer | n, | ||
complex*16, dimension( ldt, * ) | t, | ||
integer | ldt, | ||
complex*16, dimension( ldvl, * ) | vl, | ||
integer | ldvl, | ||
complex*16, dimension( ldvr, * ) | vr, | ||
integer | ldvr, | ||
integer | mm, | ||
integer | m, | ||
complex*16, dimension( * ) | work, | ||
integer | lwork, | ||
double precision, dimension( * ) | rwork, | ||
integer | lrwork, | ||
integer | info ) |
ZTREVC3
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!> !> ZTREVC3 computes some or all of the right and/or left eigenvectors of !> a complex upper triangular matrix T. !> Matrices of this type are produced by the Schur factorization of !> a complex general matrix: A = Q*T*Q**H, as computed by ZHSEQR. !> !> The right eigenvector x and the left eigenvector y of T corresponding !> to an eigenvalue w are defined by: !> !> T*x = w*x, (y**H)*T = w*(y**H) !> !> where y**H denotes the conjugate transpose of the vector y. !> The eigenvalues are not input to this routine, but are read directly !> from the diagonal of T. !> !> This routine returns the matrices X and/or Y of right and left !> eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an !> input matrix. If Q is the unitary factor that reduces a matrix A to !> Schur form T, then Q*X and Q*Y are the matrices of right and left !> eigenvectors of A. !> !> This uses a Level 3 BLAS version of the back transformation. !>
[in] | SIDE | !> SIDE is CHARACTER*1 !> = 'R': compute right eigenvectors only; !> = 'L': compute left eigenvectors only; !> = 'B': compute both right and left eigenvectors. !> |
[in] | HOWMNY | !> HOWMNY is CHARACTER*1 !> = 'A': compute all right and/or left eigenvectors; !> = 'B': compute all right and/or left eigenvectors, !> backtransformed using the matrices supplied in !> VR and/or VL; !> = 'S': compute selected right and/or left eigenvectors, !> as indicated by the logical array SELECT. !> |
[in] | SELECT | !> 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'. !> |
[in] | N | !> N is INTEGER !> The order of the matrix T. N >= 0. !> |
[in,out] | T | !> T is COMPLEX*16 array, dimension (LDT,N) !> The upper triangular matrix T. T is modified, but restored !> on exit. !> |
[in] | LDT | !> LDT is INTEGER !> The leading dimension of the array T. LDT >= max(1,N). !> |
[in,out] | VL | !> VL is COMPLEX*16 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 !> Schur vectors returned by ZHSEQR). !> On exit, if SIDE = 'L' or 'B', VL contains: !> if HOWMNY = 'A', the matrix Y of left eigenvectors of T; !> if HOWMNY = 'B', the matrix Q*Y; !> if HOWMNY = 'S', the left eigenvectors of T specified by !> SELECT, stored consecutively in the columns !> of VL, in the same order as their !> eigenvalues. !> Not referenced if SIDE = 'R'. !> |
[in] | LDVL | !> LDVL is INTEGER !> The leading dimension of the array VL. !> LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N. !> |
[in,out] | VR | !> VR is COMPLEX*16 array, dimension (LDVR,MM) !> On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must !> contain an N-by-N matrix Q (usually the unitary matrix Q of !> Schur vectors returned by ZHSEQR). !> On exit, if SIDE = 'R' or 'B', VR contains: !> if HOWMNY = 'A', the matrix X of right eigenvectors of T; !> if HOWMNY = 'B', the matrix Q*X; !> if HOWMNY = 'S', the right eigenvectors of T specified by !> SELECT, stored consecutively in the columns !> of VR, in the same order as their !> eigenvalues. !> Not referenced if SIDE = 'L'. !> |
[in] | LDVR | !> LDVR is INTEGER !> The leading dimension of the array VR. !> LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N. !> |
[in] | MM | !> MM is INTEGER !> The number of columns in the arrays VL and/or VR. MM >= M. !> |
[out] | M | !> 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. !> |
[out] | WORK | !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> |
[in] | LWORK | !> LWORK is INTEGER !> The dimension of array WORK. LWORK >= max(1,2*N). !> For optimum performance, LWORK >= N + 2*N*NB, where NB is !> the optimal blocksize. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> |
[out] | RWORK | !> RWORK is DOUBLE PRECISION array, dimension (LRWORK) !> |
[in] | LRWORK | !> LRWORK is INTEGER !> The dimension of array RWORK. LRWORK >= max(1,N). !> !> If LRWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the RWORK array, returns !> this value as the first entry of the RWORK array, and no error !> message related to LRWORK is issued by XERBLA. !> |
[out] | INFO | !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> |
!> !> The algorithm used in this program is basically backward (forward) !> substitution, with scaling to make the the code robust against !> possible overflow. !> !> Each eigenvector is normalized so that the element of largest !> magnitude has magnitude 1; here the magnitude of a complex number !> (x,y) is taken to be |x| + |y|. !>
Definition at line 240 of file ztrevc3.f.