LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  chsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO) 
CHSEIN 
subroutine chsein  (  character  SIDE, 
character  EIGSRC,  
character  INITV,  
logical, dimension( * )  SELECT,  
integer  N,  
complex, dimension( ldh, * )  H,  
integer  LDH,  
complex, dimension( * )  W,  
complex, dimension( ldvl, * )  VL,  
integer  LDVL,  
complex, dimension( ldvr, * )  VR,  
integer  LDVR,  
integer  MM,  
integer  M,  
complex, dimension( * )  WORK,  
real, dimension( * )  RWORK,  
integer, dimension( * )  IFAILL,  
integer, dimension( * )  IFAILR,  
integer  INFO  
) 
CHSEIN
Download CHSEIN + dependencies [TGZ] [ZIP] [TXT]CHSEIN uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H. The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by: H * x = w * x, y**h * H = w * y**h where y**h denotes the conjugate transpose of the vector y.
[in]  SIDE  SIDE is CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors. 
[in]  EIGSRC  EIGSRC is CHARACTER*1 Specifies the source of eigenvalues supplied in W: = 'Q': the eigenvalues were found using CHSEQR; thus, if H has zero subdiagonal elements, and so is blocktriangular, then the jth eigenvalue can be assumed to be an eigenvalue of the block containing the jth row/column. This property allows CHSEIN to perform inverse iteration on just one diagonal block. = 'N': no assumptions are made on the correspondence between eigenvalues and diagonal blocks. In this case, CHSEIN must always perform inverse iteration using the whole matrix H. 
[in]  INITV  INITV is CHARACTER*1 = 'N': no initial vectors are supplied; = 'U': usersupplied initial vectors are stored in the arrays VL and/or VR. 
[in]  SELECT  SELECT is LOGICAL array, dimension (N) Specifies the eigenvectors to be computed. To select the eigenvector corresponding to the eigenvalue W(j), SELECT(j) must be set to .TRUE.. 
[in]  N  N is INTEGER The order of the matrix H. N >= 0. 
[in]  H  H is COMPLEX array, dimension (LDH,N) The upper Hessenberg matrix H. 
[in]  LDH  LDH is INTEGER The leading dimension of the array H. LDH >= max(1,N). 
[in,out]  W  W is COMPLEX array, dimension (N) On entry, the eigenvalues of H. On exit, the real parts of W may have been altered since close eigenvalues are perturbed slightly in searching for independent eigenvectors. 
[in,out]  VL  VL is COMPLEX array, dimension (LDVL,MM) On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must contain starting vectors for the inverse iteration for the left eigenvectors; the starting vector for each eigenvector must be in the same column in which the eigenvector will be stored. On exit, if SIDE = 'L' or 'B', the left eigenvectors specified by SELECT will be stored consecutively in the columns of VL, in the same order as their eigenvalues. If SIDE = 'R', VL is not referenced. 
[in]  LDVL  LDVL is INTEGER The leading dimension of the array VL. LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise. 
[in,out]  VR  VR is COMPLEX array, dimension (LDVR,MM) On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must contain starting vectors for the inverse iteration for the right eigenvectors; the starting vector for each eigenvector must be in the same column in which the eigenvector will be stored. On exit, if SIDE = 'R' or 'B', the right eigenvectors specified by SELECT will be stored consecutively in the columns of VR, in the same order as their eigenvalues. If SIDE = 'L', VR is not referenced. 
[in]  LDVR  LDVR is INTEGER The leading dimension of the array VR. LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise. 
[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 required to store the eigenvectors (= the number of .TRUE. elements in SELECT). 
[out]  WORK  WORK is COMPLEX array, dimension (N*N) 
[out]  RWORK  RWORK is REAL array, dimension (N) 
[out]  IFAILL  IFAILL is INTEGER array, dimension (MM) If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left eigenvector in the ith column of VL (corresponding to the eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the eigenvector converged satisfactorily. If SIDE = 'R', IFAILL is not referenced. 
[out]  IFAILR  IFAILR is INTEGER array, dimension (MM) If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right eigenvector in the ith column of VR (corresponding to the eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the eigenvector converged satisfactorily. If SIDE = 'L', IFAILR is not referenced. 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, i is the number of eigenvectors which failed to converge; see IFAILL and IFAILR for further details. 
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 243 of file chsein.f.