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---
:name: zstein
:md5sum: e31fefcd280e4ed544d4a3d6fa703ad2
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: input
:dims:
- n
- e:
:type: doublereal
:intent: input
:dims:
- n-1
- m:
:type: integer
:intent: input
- w:
:type: doublereal
:intent: input
:dims:
- n
- iblock:
:type: integer
:intent: input
:dims:
- n
- isplit:
:type: integer
:intent: input
:dims:
- n
- z:
:type: doublecomplex
:intent: output
:dims:
- ldz
- m
- ldz:
:type: integer
:intent: input
- work:
:type: doublereal
:intent: workspace
:dims:
- 5*n
- iwork:
:type: integer
:intent: workspace
:dims:
- n
- ifail:
:type: integer
:intent: output
:dims:
- m
- info:
:type: integer
:intent: output
:substitutions:
ldz: MAX(1,n)
m: n
:fortran_help: " SUBROUTINE ZSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZSTEIN computes the eigenvectors of a real symmetric tridiagonal\n\
* matrix T corresponding to specified eigenvalues, using inverse\n\
* iteration.\n\
*\n\
* The maximum number of iterations allowed for each eigenvector is\n\
* specified by an internal parameter MAXITS (currently set to 5).\n\
*\n\
* Although the eigenvectors are real, they are stored in a complex\n\
* array, which may be passed to ZUNMTR or ZUPMTR for back\n\
* transformation to the eigenvectors of a complex Hermitian matrix\n\
* which was reduced to tridiagonal form.\n\
*\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix. N >= 0.\n\
*\n\
* D (input) DOUBLE PRECISION array, dimension (N)\n\
* The n diagonal elements of the tridiagonal matrix T.\n\
*\n\
* E (input) DOUBLE PRECISION array, dimension (N-1)\n\
* The (n-1) subdiagonal elements of the tridiagonal matrix\n\
* T, stored in elements 1 to N-1.\n\
*\n\
* M (input) INTEGER\n\
* The number of eigenvectors to be found. 0 <= M <= N.\n\
*\n\
* W (input) DOUBLE PRECISION array, dimension (N)\n\
* The first M elements of W contain the eigenvalues for\n\
* which eigenvectors are to be computed. The eigenvalues\n\
* should be grouped by split-off block and ordered from\n\
* smallest to largest within the block. ( The output array\n\
* W from DSTEBZ with ORDER = 'B' is expected here. )\n\
*\n\
* IBLOCK (input) INTEGER array, dimension (N)\n\
* The submatrix indices associated with the corresponding\n\
* eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to\n\
* the first submatrix from the top, =2 if W(i) belongs to\n\
* the second submatrix, etc. ( The output array IBLOCK\n\
* from DSTEBZ is expected here. )\n\
*\n\
* ISPLIT (input) INTEGER array, dimension (N)\n\
* The splitting points, at which T breaks up into submatrices.\n\
* The first submatrix consists of rows/columns 1 to\n\
* ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1\n\
* through ISPLIT( 2 ), etc.\n\
* ( The output array ISPLIT from DSTEBZ is expected here. )\n\
*\n\
* Z (output) COMPLEX*16 array, dimension (LDZ, M)\n\
* The computed eigenvectors. The eigenvector associated\n\
* with the eigenvalue W(i) is stored in the i-th column of\n\
* Z. Any vector which fails to converge is set to its current\n\
* iterate after MAXITS iterations.\n\
* The imaginary parts of the eigenvectors are set to zero.\n\
*\n\
* LDZ (input) INTEGER\n\
* The leading dimension of the array Z. LDZ >= max(1,N).\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (5*N)\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (N)\n\
*\n\
* IFAIL (output) INTEGER array, dimension (M)\n\
* On normal exit, all elements of IFAIL are zero.\n\
* If one or more eigenvectors fail to converge after\n\
* MAXITS iterations, then their indices are stored in\n\
* array IFAIL.\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, then i eigenvectors failed to converge\n\
* in MAXITS iterations. Their indices are stored in\n\
* array IFAIL.\n\
*\n\
* Internal Parameters\n\
* ===================\n\
*\n\
* MAXITS INTEGER, default = 5\n\
* The maximum number of iterations performed.\n\
*\n\
* EXTRA INTEGER, default = 2\n\
* The number of iterations performed after norm growth\n\
* criterion is satisfied, should be at least 1.\n\
*\n\n\
* =====================================================================\n\
*\n"
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