SRC/ddisna.f(3)

🦋 SRC/ddisna.f(3) — LAPACK Library Functions Manual 🦋

🌸 NAME 🌸

SRC/ddisna.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

• subroutine ddisna (job, m, n, d, sep, info) — DDISNA

💅 Function/Subroutine Documentation 💅

subroutine ddisna (character job, integer m, integer n, double precision, dimension( * ) d, double precision, dimension( * ) sep, integer info)

DDISNA — okay bestie, this is the whole subroutine.

🎀 Purpose 🎀

So DDISNA 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 literally the “gap” between the corresponding eigenvalue or singular value and the nearest other one. Slay.

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

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

...where ANORM = 2-norm(A) = max( abs( D(j) ) ). Caveat time: SEP(I) is not allowed to be smaller than DLAMCH( 'E' )*ANORM — that’s the rule that limits the size of the error bound. Not me explaining bounds with main character energy 😭.

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

🌈 Parameters 🌈

• JOB — CHARACTER*1. Tells you which problem the reciprocal condition numbers are for: = '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 — INTEGER. The number of rows of the matrix. M >= 0.
• N — INTEGER. If JOB = 'L' or 'R', the number of columns of the matrix, in which case N >= 0. Ignored if JOB = 'E'.
• D — DOUBLE PRECISION array, dimension (M) if JOB = 'E', dimension (min(M,N)) if JOB = 'L' or 'R'. The eigenvalues (if JOB = 'E') or singular values (if JOB = 'L' or 'R') of the matrix, in either increasing or decreasing order. If singular values, they must be non-negative.
• SEP — DOUBLE PRECISION array, dimension (M) if JOB = 'E', dimension (min(M,N)) if JOB = 'L' or 'R'. The reciprocal condition numbers of the vectors.
• INFO — 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 ddisna.f.

👑 Author 👑

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