SRC/dstevx.f(3)

💖 SRC/dstevx.f 💖

okay bestie, welcome to SRC/dstevx.f(3) from the Library Functions Manual 💖 This is the LAPACK tea: DSTEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A — and it can pick them by value range or index range. Iconic. ✨

🌸 NAME 🌸

SRC/dstevx.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

   subroutine dstevx (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w,
       z, ldz, work, iwork, ifail, info)

DSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 🫶

🦋 Function/Subroutine Documentation 🦋

   subroutine dstevx (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, double
       precision, dimension( ldz, * ) z, integer ldz, double precision,
       dimension( * ) work, integer, dimension( * ) iwork, integer, dimension(
       * ) ifail, integer info)

DSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. (Yes, it's giving "I contain multitudes" 😭 but that's what the page says.)

🎀 Purpose 🎀

DSTEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A. You can select eigenvalues and eigenvectors by specifying either a range of values or a range of indices for the desired eigenvalues. No cap. 🔥

💅 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 A. On exit, D may be multiplied by a constant factor chosen to avoid over/underflow in computing the eigenvalues.
• E — E is DOUBLE PRECISION array, dimension (max(1,N-1)). On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A in elements 1 to N-1 of E. On exit, E may be multiplied by a constant factor chosen to avoid over/underflow in computing the eigenvalues.
• 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; IL = 1 and IU = 0 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; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.
• ABSTOL — ABSTOL is DOUBLE PRECISION. The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ) , where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix.

Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('S').

See by Demmel and Kahan, LAPACK Working Note #3.

• 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 DOUBLE PRECISION array, dimension (LDZ, max(1,M) ). If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge (INFO > 0), then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. 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. 🚨
• LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — WORK is DOUBLE PRECISION array, dimension (5*N).
• IWORK — IWORK is INTEGER array, dimension (5*N).
• IFAIL — IFAIL is INTEGER array, dimension (N). If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced.
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, then i eigenvectors failed to converge. Their indices are stored in array IFAIL.

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 225 of file dstevx.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 💖 The cute little footer says LAPACK, Version 3.12.0, for SRC/dstevx.f(3) — no date on this one, just vibes and versioning. Slay. 🎀✨