shsein (3)  Linux Manuals
NAME
shsein.f 
SYNOPSIS
Functions/Subroutines
subroutine shsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI, VL, LDVL, VR, LDVR, MM, M, WORK, IFAILL, IFAILR, INFO)
SHSEIN
Function/Subroutine Documentation
subroutine shsein (characterSIDE, characterEIGSRC, characterINITV, logical, dimension( * )SELECT, integerN, real, dimension( ldh, * )H, integerLDH, real, dimension( * )WR, real, dimension( * )WI, real, dimension( ldvl, * )VL, integerLDVL, real, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, real, dimension( * )WORK, integer, dimension( * )IFAILL, integer, dimension( * )IFAILR, integerINFO)
SHSEIN
Purpose:

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.
Parameters:

SIDE
SIDE is CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors.
EIGSRCEIGSRC 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.
INITVINITV is CHARACTER*1 = 'N': no initial vectors are supplied; = 'U': usersupplied initial vectors are stored in the arrays VL and/or VR.
SELECTSELECT 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..
NN is INTEGER The order of the matrix H. N >= 0.
HH is REAL array, dimension (LDH,N) The upper Hessenberg matrix H. If a NaN is detected in H, the routine will return with INFO=6.
LDHLDH is INTEGER The leading dimension of the array H. LDH >= max(1,N).
WRWR is REAL array, dimension (N)
WIWI 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.
VLVL 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.
LDVLLDVL is INTEGER The leading dimension of the array VL. LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
VRVR 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.
LDVRLDVR is INTEGER The leading dimension of the array VR. LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
MMMM is INTEGER The number of columns in the arrays VL and/or VR. MM >= M.
MM 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.
WORKWORK is REAL array, dimension ((N+2)*N)
IFAILLIFAILL 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.
IFAILRIFAILR 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.
INFOINFO 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.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2013
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 262 of file shsein.f.
Author
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