LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  shsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI, VL, LDVL, VR, LDVR, MM, M, WORK, IFAILL, IFAILR, INFO) 
SHSEIN 
subroutine shsein  (  character  SIDE, 
character  EIGSRC,  
character  INITV,  
logical, dimension( * )  SELECT,  
integer  N,  
real, dimension( ldh, * )  H,  
integer  LDH,  
real, dimension( * )  WR,  
real, dimension( * )  WI,  
real, dimension( ldvl, * )  VL,  
integer  LDVL,  
real, dimension( ldvr, * )  VR,  
integer  LDVR,  
integer  MM,  
integer  M,  
real, dimension( * )  WORK,  
integer, dimension( * )  IFAILL,  
integer, dimension( * )  IFAILR,  
integer  INFO  
) 
SHSEIN
Download SHSEIN + dependencies [TGZ] [ZIP] [TXT]SHSEIN uses inverse iteration to find specified right and/or left eigenvectors of a real 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 (WR,WI): = 'Q': the eigenvalues were found using SHSEQR; 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 SHSEIN 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, SHSEIN 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,out]  SELECT  SELECT is LOGICAL array, dimension (N) Specifies the eigenvectors to be computed. To select the real eigenvector corresponding to a real eigenvalue WR(j), SELECT(j) must be set to .TRUE.. To select the complex eigenvector corresponding to a complex eigenvalue (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)), either SELECT(j) or SELECT(j+1) or both must be set to .TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is .FALSE.. 
[in]  N  N is INTEGER The order of the matrix H. N >= 0. 
[in]  H  H is REAL 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]  WR  WR is REAL array, dimension (N) 
[in]  WI  WI is REAL array, dimension (N) On entry, the real and imaginary parts of the eigenvalues of H; a complex conjugate pair of eigenvalues must be stored in consecutive elements of WR and WI. On exit, WR may have been altered since close eigenvalues are perturbed slightly in searching for independent eigenvectors. 
[in,out]  VL  VL is REAL 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(s) 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. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part. 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 REAL 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(s) 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. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part. 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; each selected real eigenvector occupies one column and each selected complex eigenvector occupies two columns. 
[out]  WORK  WORK is REAL array, dimension ((N+2)*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 the ith and (i+1)th columns of VL hold a complex eigenvector, then IFAILL(i) and IFAILL(i+1) are set to the same value. 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 the ith and (i+1)th columns of VR hold a complex eigenvector, then IFAILR(i) and IFAILR(i+1) are set to the same value. 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 261 of file shsein.f.