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---
:name: sstegr
:md5sum: 992b1604b86ed979e0de63b7c057e36b
:category: :subroutine
:arguments:
- jobz:
:type: char
:intent: input
- range:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- d:
:type: real
:intent: input/output
:dims:
- n
- e:
:type: real
:intent: input/output
:dims:
- n
- vl:
:type: real
:intent: input
- vu:
:type: real
:intent: input
- il:
:type: integer
:intent: input
- iu:
:type: integer
:intent: input
- abstol:
:type: real
:intent: input
- m:
:type: integer
:intent: output
- w:
:type: real
:intent: output
:dims:
- n
- z:
:type: real
:intent: output
:dims:
- ldz
- MAX(1,m)
- ldz:
:type: integer
:intent: input
- isuppz:
:type: integer
:intent: output
:dims:
- 2*MAX(1,m)
- work:
:type: real
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: "lsame_(&jobz,\"V\") ? 18*n : lsame_(&jobz,\"N\") ? 12*n : 0"
- iwork:
:type: integer
:intent: output
:dims:
- MAX(1,liwork)
- liwork:
:type: integer
:intent: input
:option: true
:default: "lsame_(&jobz,\"V\") ? 10*n : lsame_(&jobz,\"N\") ? 8*n : 0"
- info:
:type: integer
:intent: output
:substitutions:
ldz: "lsame_(&jobz,\"V\") ? MAX(1,n) : 1"
m: "lsame_(&range,\"A\") ? n : lsame_(&range,\"I\") ? iu-il+1 : 0"
:fortran_help: " SUBROUTINE SSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SSTEGR computes selected eigenvalues and, optionally, eigenvectors\n\
* of a real symmetric tridiagonal matrix T. Any such unreduced matrix has\n\
* a well defined set of pairwise different real eigenvalues, the corresponding\n\
* real eigenvectors are pairwise orthogonal.\n\
*\n\
* The spectrum may be computed either completely or partially by specifying\n\
* either an interval (VL,VU] or a range of indices IL:IU for the desired\n\
* eigenvalues.\n\
*\n\
* SSTEGR is a compatibility wrapper around the improved SSTEMR routine.\n\
* See SSTEMR for further details.\n\
*\n\
* One important change is that the ABSTOL parameter no longer provides any\n\
* benefit and hence is no longer used.\n\
*\n\
* Note : SSTEGR and SSTEMR work only on machines which follow\n\
* IEEE-754 floating-point standard in their handling of infinities and\n\
* NaNs. Normal execution may create these exceptiona values and hence\n\
* may abort due to a floating point exception in environments which\n\
* do not conform to the IEEE-754 standard.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOBZ (input) CHARACTER*1\n\
* = 'N': Compute eigenvalues only;\n\
* = 'V': Compute eigenvalues and eigenvectors.\n\
*\n\
* RANGE (input) CHARACTER*1\n\
* = 'A': all eigenvalues will be found.\n\
* = 'V': all eigenvalues in the half-open interval (VL,VU]\n\
* will be found.\n\
* = 'I': the IL-th through IU-th eigenvalues will be found.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix. N >= 0.\n\
*\n\
* D (input/output) REAL array, dimension (N)\n\
* On entry, the N diagonal elements of the tridiagonal matrix\n\
* T. On exit, D is overwritten.\n\
*\n\
* E (input/output) REAL array, dimension (N)\n\
* On entry, the (N-1) subdiagonal elements of the tridiagonal\n\
* matrix T in elements 1 to N-1 of E. E(N) need not be set on\n\
* input, but is used internally as workspace.\n\
* On exit, E is overwritten.\n\
*\n\
* VL (input) REAL\n\
* VU (input) REAL\n\
* If RANGE='V', the lower and upper bounds of the interval to\n\
* be searched for eigenvalues. VL < VU.\n\
* Not referenced if RANGE = 'A' or 'I'.\n\
*\n\
* IL (input) INTEGER\n\
* IU (input) INTEGER\n\
* If RANGE='I', the indices (in ascending order) of the\n\
* smallest and largest eigenvalues to be returned.\n\
* 1 <= IL <= IU <= N, if N > 0.\n\
* Not referenced if RANGE = 'A' or 'V'.\n\
*\n\
* ABSTOL (input) REAL\n\
* Unused. Was the absolute error tolerance for the\n\
* eigenvalues/eigenvectors in previous versions.\n\
*\n\
* M (output) INTEGER\n\
* The total number of eigenvalues found. 0 <= M <= N.\n\
* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.\n\
*\n\
* W (output) REAL array, dimension (N)\n\
* The first M elements contain the selected eigenvalues in\n\
* ascending order.\n\
*\n\
* Z (output) REAL array, dimension (LDZ, max(1,M) )\n\
* If JOBZ = 'V', and if INFO = 0, then the first M columns of Z\n\
* contain the orthonormal eigenvectors of the matrix T\n\
* corresponding to the selected eigenvalues, with the i-th\n\
* column of Z holding the eigenvector associated with W(i).\n\
* If JOBZ = 'N', then Z is not referenced.\n\
* Note: the user must ensure that at least max(1,M) columns are\n\
* supplied in the array Z; if RANGE = 'V', the exact value of M\n\
* is not known in advance and an upper bound must be used.\n\
* Supplying N columns is always safe.\n\
*\n\
* LDZ (input) INTEGER\n\
* The leading dimension of the array Z. LDZ >= 1, and if\n\
* JOBZ = 'V', then LDZ >= max(1,N).\n\
*\n\
* ISUPPZ (output) INTEGER ARRAY, dimension ( 2*max(1,M) )\n\
* The support of the eigenvectors in Z, i.e., the indices\n\
* indicating the nonzero elements in Z. The i-th computed eigenvector\n\
* is nonzero only in elements ISUPPZ( 2*i-1 ) through\n\
* ISUPPZ( 2*i ). This is relevant in the case when the matrix\n\
* is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.\n\
*\n\
* WORK (workspace/output) REAL array, dimension (LWORK)\n\
* On exit, if INFO = 0, WORK(1) returns the optimal\n\
* (and minimal) LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK. LWORK >= max(1,18*N)\n\
* if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\n\
*\n\
* IWORK (workspace/output) INTEGER array, dimension (LIWORK)\n\
* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.\n\
*\n\
* LIWORK (input) INTEGER\n\
* The dimension of the array IWORK. LIWORK >= max(1,10*N)\n\
* if the eigenvectors are desired, and LIWORK >= max(1,8*N)\n\
* if only the eigenvalues are to be computed.\n\
* If LIWORK = -1, then a workspace query is assumed; the\n\
* routine only calculates the optimal size of the IWORK array,\n\
* returns this value as the first entry of the IWORK array, and\n\
* no error message related to LIWORK is issued by XERBLA.\n\
*\n\
* INFO (output) INTEGER\n\
* On exit, INFO\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
* > 0: if INFO = 1X, internal error in SLARRE,\n\
* if INFO = 2X, internal error in SLARRV.\n\
* Here, the digit X = ABS( IINFO ) < 10, where IINFO is\n\
* the nonzero error code returned by SLARRE or\n\
* SLARRV, respectively.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Inderjit Dhillon, IBM Almaden, USA\n\
* Osni Marques, LBNL/NERSC, USA\n\
* Christof Voemel, LBNL/NERSC, USA\n\
*\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL TRYRAC\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL SSTEMR\n\
* ..\n"
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