SRC/sdisna.f(3)

💖 NAME 💖

SRC/sdisna.f — bestie, welcome to the SRC/sdisna.f(3) page in the Library Functions Manual. This is the one about SDISNA, and it is literally giving “reciprocal condition number” main character energy. 🫶✨

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine sdisna (job, m, n, d, sep, info) — the one and only SDISNA.

subroutine sdisna (job, m, n, d, sep, info)

🌸 Function/Subroutine Documentation 🌸

🎀 subroutine sdisna 🎀

subroutine sdisna (character job, integer m, integer n, real, dimension( * ) d, real, dimension( * ) sep, integer info)

SDISNA

🎀 Purpose 🎀

Okay so SDISNA computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix, or for the left or right singular vectors of a general m-by-n matrix. The reciprocal condition number is the “gap” between the corresponding eigenvalue or singular value and the nearest other one. 💅

The bound on the error, measured by angle in radians, in the I-th computed vector is given by:

SLAMCH( 'E' ) * ( ANORM / SEP( I ) )

where ANORM = 2-norm(A) = max( abs( D(j) ) ). SEP(I) is not allowed to be smaller than SLAMCH( 'E' )*ANORM in order to limit the size of the error bound. That part is important, bestie — it is the guardrail. 🛑

SDISNA may also be used to compute error bounds for eigenvectors of the generalized symmetric definite eigenproblem. Obsessed. ✨

🍓 Parameters 🍓

💜 JOB

JOB is CHARACTER*1. It specifies for which problem the reciprocal condition numbers should be computed:

• = 'E' — the eigenvectors of a symmetric/Hermitian matrix;
• = 'L' — the left singular vectors of a general matrix;
• = 'R' — the right singular vectors of a general matrix.

💜 M

M is INTEGER. It is the number of rows of the matrix. M >= 0.

💜 N

N is INTEGER. If JOB = 'L' or 'R', it is the number of columns of the matrix, in which case N >= 0. Ignored if JOB = 'E'.

💜 D

D is a REAL array:

• dimension (M) if JOB = 'E';
• dimension (min(M,N)) if JOB = 'L' or 'R'.

It holds the eigenvalues (if JOB = 'E') or singular values (if JOB = 'L' or 'R') of the matrix, in either increasing or decreasing order. If these are singular values, they must be non-negative. 🍓

💜 SEP

SEP is a REAL array:

• dimension (M) if JOB = 'E';
• dimension (min(M,N)) if JOB = 'L' or 'R'.

It holds the reciprocal condition numbers of the vectors.

💜 INFO

INFO is INTEGER:

• = 0 — successful exit.
• < 0 — if INFO = -i, the i-th argument had an illegal value. 😭

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 116 of file sdisna.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Sign-off, bestie: LAPACK Version 3.12.0, source SRC/sdisna.f(3). 💖✨