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---
:name: chsein
:md5sum: 47f76f0ff879b1035b2920625919b141
:category: :subroutine
:arguments:
- side:
:type: char
:intent: input
- eigsrc:
:type: char
:intent: input
- initv:
:type: char
:intent: input
- select:
:type: logical
:intent: input
:dims:
- n
- n:
:type: integer
:intent: input
- h:
:type: complex
:intent: input
:dims:
- ldh
- n
- ldh:
:type: integer
:intent: input
- w:
:type: complex
:intent: input/output
:dims:
- n
- vl:
:type: complex
:intent: input/output
:dims:
- ldvl
- mm
- ldvl:
:type: integer
:intent: input
- vr:
:type: complex
:intent: input/output
:dims:
- ldvr
- mm
- ldvr:
:type: integer
:intent: input
- mm:
:type: integer
:intent: input
- m:
:type: integer
:intent: output
- work:
:type: complex
:intent: workspace
:dims:
- n*n
- rwork:
:type: real
:intent: workspace
:dims:
- n
- ifaill:
:type: integer
:intent: output
:dims:
- mm
- ifailr:
:type: integer
:intent: output
:dims:
- mm
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CHSEIN uses inverse iteration to find specified right and/or left\n\
* eigenvectors of a complex upper Hessenberg matrix H.\n\
*\n\
* The right eigenvector x and the left eigenvector y of the matrix H\n\
* corresponding to an eigenvalue w are defined by:\n\
*\n\
* H * x = w * x, y**h * H = w * y**h\n\
*\n\
* where y**h denotes the conjugate transpose of the vector y.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* SIDE (input) CHARACTER*1\n\
* = 'R': compute right eigenvectors only;\n\
* = 'L': compute left eigenvectors only;\n\
* = 'B': compute both right and left eigenvectors.\n\
*\n\
* EIGSRC (input) CHARACTER*1\n\
* Specifies the source of eigenvalues supplied in W:\n\
* = 'Q': the eigenvalues were found using CHSEQR; thus, if\n\
* H has zero subdiagonal elements, and so is\n\
* block-triangular, then the j-th eigenvalue can be\n\
* assumed to be an eigenvalue of the block containing\n\
* the j-th row/column. This property allows CHSEIN to\n\
* perform inverse iteration on just one diagonal block.\n\
* = 'N': no assumptions are made on the correspondence\n\
* between eigenvalues and diagonal blocks. In this\n\
* case, CHSEIN must always perform inverse iteration\n\
* using the whole matrix H.\n\
*\n\
* INITV (input) CHARACTER*1\n\
* = 'N': no initial vectors are supplied;\n\
* = 'U': user-supplied initial vectors are stored in the arrays\n\
* VL and/or VR.\n\
*\n\
* SELECT (input) LOGICAL array, dimension (N)\n\
* Specifies the eigenvectors to be computed. To select the\n\
* eigenvector corresponding to the eigenvalue W(j),\n\
* SELECT(j) must be set to .TRUE..\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix H. N >= 0.\n\
*\n\
* H (input) COMPLEX array, dimension (LDH,N)\n\
* The upper Hessenberg matrix H.\n\
*\n\
* LDH (input) INTEGER\n\
* The leading dimension of the array H. LDH >= max(1,N).\n\
*\n\
* W (input/output) COMPLEX array, dimension (N)\n\
* On entry, the eigenvalues of H.\n\
* On exit, the real parts of W may have been altered since\n\
* close eigenvalues are perturbed slightly in searching for\n\
* independent eigenvectors.\n\
*\n\
* VL (input/output) COMPLEX array, dimension (LDVL,MM)\n\
* On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must\n\
* contain starting vectors for the inverse iteration for the\n\
* left eigenvectors; the starting vector for each eigenvector\n\
* must be in the same column in which the eigenvector will be\n\
* stored.\n\
* On exit, if SIDE = 'L' or 'B', the left eigenvectors\n\
* specified by SELECT will be stored consecutively in the\n\
* columns of VL, in the same order as their eigenvalues.\n\
* If SIDE = 'R', VL is not referenced.\n\
*\n\
* LDVL (input) INTEGER\n\
* The leading dimension of the array VL.\n\
* LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.\n\
*\n\
* VR (input/output) COMPLEX array, dimension (LDVR,MM)\n\
* On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must\n\
* contain starting vectors for the inverse iteration for the\n\
* right eigenvectors; the starting vector for each eigenvector\n\
* must be in the same column in which the eigenvector will be\n\
* stored.\n\
* On exit, if SIDE = 'R' or 'B', the right eigenvectors\n\
* specified by SELECT will be stored consecutively in the\n\
* columns of VR, in the same order as their eigenvalues.\n\
* If SIDE = 'L', VR is not referenced.\n\
*\n\
* LDVR (input) INTEGER\n\
* The leading dimension of the array VR.\n\
* LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.\n\
*\n\
* MM (input) INTEGER\n\
* The number of columns in the arrays VL and/or VR. MM >= M.\n\
*\n\
* M (output) INTEGER\n\
* The number of columns in the arrays VL and/or VR required to\n\
* store the eigenvectors (= the number of .TRUE. elements in\n\
* SELECT).\n\
*\n\
* WORK (workspace) COMPLEX array, dimension (N*N)\n\
*\n\
* RWORK (workspace) REAL array, dimension (N)\n\
*\n\
* IFAILL (output) INTEGER array, dimension (MM)\n\
* If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left\n\
* eigenvector in the i-th column of VL (corresponding to the\n\
* eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the\n\
* eigenvector converged satisfactorily.\n\
* If SIDE = 'R', IFAILL is not referenced.\n\
*\n\
* IFAILR (output) INTEGER array, dimension (MM)\n\
* If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right\n\
* eigenvector in the i-th column of VR (corresponding to the\n\
* eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the\n\
* eigenvector converged satisfactorily.\n\
* If SIDE = 'L', IFAILR is not referenced.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
* > 0: if INFO = i, i is the number of eigenvectors which\n\
* failed to converge; see IFAILL and IFAILR for further\n\
* details.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Each eigenvector is normalized so that the element of largest\n\
* magnitude has magnitude 1; here the magnitude of a complex number\n\
* (x,y) is taken to be |x|+|y|.\n\
*\n\
* =====================================================================\n\
*\n"
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