SRC/zstegr.f(3)

💖 SRC/zstegr.f(3) — Library Functions Manual 💖

okay bestie, welcome to the SRC/zstegr.f(3) page — manual name: Library Functions Manual. This is your ZSTEGR era, and yes, we’re keeping every single detail. 💅

🌸 NAME 🌸

SRC/zstegr.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

   subroutine zstegr (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w,
       z, ldz, isuppz, work, lwork, iwork, liwork, info)

ZSTEGR

🎀 Function/Subroutine Documentation 🎀

   subroutine zstegr (character jobz, character range, integer n, double
       precision, dimension( * ) d, double precision, dimension( * ) e, double
       precision vl, double precision vu, integer il, integer iu, double
       precision abstol, integer m, double precision, dimension( * ) w,
       complex*16, dimension( ldz, * ) z, integer ldz, integer, dimension( * )
       isuppz, double precision, dimension( * ) work, integer lwork, integer,
       dimension( * ) iwork, integer liwork, integer info)

ZSTEGR

🦋 Purpose 🦋

okay so ZSTEGR computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T. Any such unreduced matrix has a well defined set of pairwise different real eigenvalues, and the corresponding real eigenvectors are pairwise orthogonal. 🌈

The spectrum may be computed either completely or partially by specifying either an interval (VL,VU] or a range of indices IL:IU for the desired eigenvalues. ✨

ZSTEGR is a compatibility wrapper around the improved ZSTEMR routine. See ZSTEMR for further details. 🫶

One important change is that the ABSTOL parameter no longer provides any benefit and hence is no longer used. 💅

Note: ZSTEGR and ZSTEMR work only on machines which follow IEEE-754 floating-point standard in their handling of infinities and NaNs. Normal execution may create these exceptional values and hence may abort due to a floating point exception in environments which do not conform to the IEEE-754 standard. 😭

💅 Parameters 💅

• JOBZ — JOBZ is CHARACTER*1
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• RANGE — RANGE is CHARACTER*1
  • = 'A': all eigenvalues will be found.
  • = 'V': all eigenvalues in the half-open interval (VL,VU] will be found.
  • = 'I': the IL-th through IU-th eigenvalues will be found.
• N — N is INTEGER. The order of the matrix. N >= 0.
• D — D is DOUBLE PRECISION array, dimension (N). On entry, the N diagonal elements of the tridiagonal matrix T. On exit, D is overwritten.
• E — E is DOUBLE PRECISION array, dimension (N). On entry, the (N-1) subdiagonal elements of the tridiagonal matrix T in elements 1 to N-1 of E. E(N) need not be set on input, but is used internally as workspace. On exit, E is overwritten.
• VL — VL is DOUBLE PRECISION. If RANGE='V', the lower bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.
• VU — VU is DOUBLE PRECISION. If RANGE='V', the upper bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.
• IL — IL is INTEGER. If RANGE='I', the index of the smallest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0. Not referenced if RANGE = 'A' or 'V'.
• IU — IU is INTEGER. If RANGE='I', the index of the largest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0. Not referenced if RANGE = 'A' or 'V'.
• ABSTOL — ABSTOL is DOUBLE PRECISION. Unused. Was the absolute error tolerance for the eigenvalues/eigenvectors in previous versions.
• M — M is INTEGER. The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
• W — W is DOUBLE PRECISION array, dimension (N). The first M elements contain the selected eigenvalues in ascending order.
• Z — Z is COMPLEX*16 array, dimension (LDZ, max(1,M) ). If JOBZ = 'V', and if INFO = 0, then the first M columns of Z contain the orthonormal eigenvectors of the matrix T corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used. Supplying N columns is always safe.
• LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', then LDZ >= max(1,N).
• ISUPPZ — ISUPPZ is INTEGER array, dimension ( 2*max(1,M) ). The support of the eigenvectors in Z, i.e., the indices indicating the nonzero elements in Z. The i-th computed eigenvector is nonzero only in elements ISUPPZ( 2*i-1 ) through ISUPPZ( 2*i ). This is relevant in the case when the matrix is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK). On exit, if INFO = 0, WORK(1) returns the optimal (and minimal) LWORK.
• LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= max(1,18*N) if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
• IWORK — IWORK is INTEGER array, dimension (LIWORK). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
• LIWORK — LIWORK is INTEGER. The dimension of the array IWORK. LIWORK >= max(1,10*N) if the eigenvectors are desired, and LIWORK >= max(1,8*N) if only the eigenvalues are to be computed. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA.
• INFO — INFO is INTEGER. On exit, INFO
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = 1X, internal error in DLARRE, if INFO = 2X, internal error in ZLARRV. Here, the digit X = ABS( IINFO ) < 10, where IINFO is the nonzero error code returned by DLARRE or ZLARRV, respectively.

🌟 Author 🌟

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

💖 Contributors: 💖

• Inderjit Dhillon, IBM Almaden, USA
• Osni Marques, LBNL/NERSC, USA
• Christof Voemel, LBNL/NERSC, USA

Definition at line 262 of file zstegr.f.

🌟 Author 🌟

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