ZSTEGR(3)

💅 ZSTEGR(3) — like, the manual page, bestie

okay so this is ZSTEGR, and it lives in the Library Functions Manual (section 3, iykyk). Buckle up, because we're about to read the whole thing together and honestly? it ate. 🦋

The whole thing comes from this file, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zstegr.f

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zstegr.f — that's the file, that's the name, that's the whole vibe 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

okay so there's exactly one subroutine here and she's the main character:

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

ZSTEGR 🫶

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👑 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 — yes bestie, again, that's her name ✨

🎀 Purpose 🎀

text !> !> 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, 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. !>

so like, she computes selected eigenvalues and (if you want) eigenvectors of a real symmetric tridiagonal matrix T 💜 and literally any such unreduced matrix has a well defined set of pairwise different real eigenvalues, and the corresponding real eigenvectors are pairwise orthogonal. iconic behavior, honestly.

you can get the spectrum fully or partially — your choice, main character energy — by specifying either an interval (VL,VU] or a range of indices IL:IU for the eigenvalues you want 🔥

ZSTEGR is a compatibility wrapper around the improved ZSTEMR routine — see ZSTEMR for further details 👀

one important change, bestie: the ABSTOL parameter no longer provides any benefit and hence is no longer used. it's giving retired queen 💀

⚠️ Note, and this is serious: 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. so like, check your machine, fr fr 😭

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⭐ Parameters ⭐

okay this is the long part, but we're getting through all of them together, no skipping 🫶

JOBZ

text !> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors.

JOBZ is CHARACTER*1. 'N' means compute eigenvalues only; 'V' means compute eigenvalues and eigenvectors 💅

RANGE

text !> 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.

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

text !> N is INTEGER !> The order of the matrix. N >= 0.

N is INTEGER — the order of the matrix. N >= 0 ✨

D

text !> D is DOUBLE PRECISION array, dimension (N) !> On entry, the N diagonal elements of the tridiagonal matrix !> T. On exit, D is overwritten.

D is a DOUBLE PRECISION array, dimension (N). on entry: the N diagonal elements of the tridiagonal matrix T. on exit: D is overwritten 🫶

E

text !> 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.

E is a 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

text !> 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'.

VL is DOUBLE PRECISION. if RANGE='V', it's the lower bound of the interval to be searched for eigenvalues. VL < VU. not referenced if RANGE = 'A' or 'I' 🙈

VU

text !> 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'.

VU is DOUBLE PRECISION. if RANGE='V', it's the upper bound of the interval to be searched for eigenvalues. VL < VU. not referenced if RANGE = 'A' or 'I' 🦋

IL

text !> 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'.

IL is INTEGER. if RANGE='I', it's the index of the smallest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0. not referenced if RANGE = 'A' or 'V' ✨

IU

text !> 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'.

IU is INTEGER. if RANGE='I', it's the index of the largest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0. not referenced if RANGE = 'A' or 'V' 💜

ABSTOL

text !> ABSTOL is DOUBLE PRECISION !> Unused. Was the absolute error tolerance for the !> eigenvalues/eigenvectors in previous versions.

ABSTOL is DOUBLE PRECISION. Unused. she was the absolute error tolerance for the eigenvalues/eigenvectors in previous versions. past her prime, but we respect her 🎀

M

text !> 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.

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

text !> W is DOUBLE PRECISION array, dimension (N) !> The first M elements contain the selected eigenvalues in !> ascending order.

W is a DOUBLE PRECISION array, dimension (N). the first M elements contain the selected eigenvalues in ascending order 🔥

Z

text !> 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.

Z is a 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. always safe, bestie, remember that 💅

LDZ

text !> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= 1, and if !> JOBZ = 'V', then LDZ >= max(1,N).

LDZ is INTEGER — the leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', then LDZ >= max(1,N) ✨

ISUPPZ

text !> 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.

ISUPPZ is an INTEGER array, dimension ( 2*max(1,M) ). it's 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

text !> WORK is DOUBLE PRECISION array, dimension (LWORK) !> On exit, if INFO = 0, WORK(1) returns the optimal !> (and minimal) LWORK.

WORK is a DOUBLE PRECISION array, dimension (LWORK). on exit, if INFO = 0, WORK(1) returns the optimal (and minimal) LWORK 👑

LWORK

text !> 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.

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

text !> IWORK is INTEGER array, dimension (LIWORK) !> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

IWORK is an INTEGER array, dimension (LIWORK). on exit, if INFO = 0, IWORK(1) returns the optimal LIWORK 💜

LIWORK

text !> 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.

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

text !> 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.

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 💀

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🧚 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

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💫 Definition 💫

Definition at line 262 of file zstegr.f 📍

Author (the doxygen one)

Generated automatically by Doxygen for LAPACK from the source code 🤖

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aaand that's the whole page, bestie, you ate that reading session 🍓

LAPACK · Version 3.12.0 · /home/abui...RC/zstegr.f(3) — mwah, that's the sign-off, mwah 💋 🎀✨