DSTEVX(3)

✨ DSTEVX(3) ✨

okay bestie, this is the DSTEVX(3) page from the Library Functions Manual, and it is literally about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dstevx.f. It’s giving “LAPACK 3.12.0 era, but make it tridiagonal.” Buckle up 💖

💖 NAME 💖

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

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

The icon herself:

       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 🎀

   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

💜 Purpose 💜

DSTEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A. You can pick which eigenvalues and eigenvectors you want by specifying either a range of values or a range of indices for the desired eigenvalues. Very choose-your-own-adventure, honestly ✨

✨ Parameters ✨

• JOBZ — is CHARACTER*1. = 'N': compute eigenvalues only; = 'V': compute eigenvalues and eigenvectors.
• 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 — is INTEGER. The order of the matrix. N >= 0.
• 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 — 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 — 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 — 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 — 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 — 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 — 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'). No cap, that’s the move 🫶

Also the source has this reference line: See by Demmel and Kahan, LAPACK Working Note #3. — yes, with the double space, bestie 💀

• 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 — is DOUBLE PRECISION array, dimension (N). The first M elements contain the selected eigenvalues in ascending order.
• 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. That’s the “bring extra columns just in case” vibe 🌈

• LDZ — is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — is DOUBLE PRECISION array, dimension (5*N).
• IWORK — is INTEGER array, dimension (5*N).
• 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 — 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.

---

periodt 💅 Cute sign-off time: this one’s from the Library Functions Manual, footer vibes are LAPACK Version 3.12.0 and /home/abui...RC/dstevx.f(3). No explicit date line in the source, so I’m not inventing one — you’re welcome, bestie 🎀✨