disna(3)

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version 3.12.1 · 9 versions
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✨ disna(3) ✨

okay bestie, this is the Library Functions Manual page for disna — literally disna: eig condition numbers, and she is giving very specific linear-algebra main character energy. Not a command-line tool, just two Fortran routines: ddisna and sdisna. 💖

🌸 NAME 🌸

disna - disna: eig condition numbers

✨ SYNOPSIS ✨

okay so here’s the function lineup, no cap:

🎀 Functions 🎀

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

🦋 Detailed Description 🦋

so the Detailed Description section is lowkey just a placeholder here — the real tea is in Function Documentation below. No extra prose, no hidden lore, just the two routines. 🫶

👑 Function Documentation 👑

💅 ddisna / DDISNA 💅

Signature, exactly:

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

DDISNA

💖 Purpose 💖

okay 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 the 'gap' between the corresponding eigenvalue or singular value and the nearest other one. That’s the whole point, and she ate. 💅

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

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

where ANORM = 2-norm(A) = max( abs( D(j) ) ). And SEP(I) is not allowed to be smaller than DLAMCH( 'E' )*ANORM in order to limit the size of the error bound. Important caveat, bestie: do not let SEP(I) drop below that, or the error bound gets huge. 😭

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

🎀 Parameters 🎀

  • JOB — JOB is CHARACTER*1. 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. The number of rows of the matrix. M >= 0.
  • N — N is INTEGER. If JOB = 'L' or 'R', the number of columns of the matrix, in which case N >= 0. Ignored if JOB = 'E'.
  • D — D is 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 — SEP is 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 — 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 ⭐

Definition at line 116 of file ddisna.f.

💅 sdisna / SDISNA 💅

Signature, exactly:

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

SDISNA

💖 Purpose 💖

same energy, single-precision edition: 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. iconic, honestly. ✨

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) ) ). And SEP(I) is not allowed to be smaller than SLAMCH( 'E' )*ANORM in order to limit the size of the error bound. Same warning, bestie: respect the floor. 🫶

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

🎀 Parameters 🎀

  • JOB — JOB is CHARACTER*1. 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. The number of rows of the matrix. M >= 0.
  • N — N is INTEGER. If JOB = 'L' or 'R', the number of columns of the matrix, in which case N >= 0. Ignored if JOB = 'E'.
  • D — D is REAL 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 — SEP is REAL array, dimension (M) if JOB = 'E', dimension (min(M,N)) if JOB = 'L' or 'R'. 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 ⭐

Definition at line 116 of file sdisna.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

and that’s the whole page, bestie! the footer gives me LAPACK Version 3.12.0 and disna(3) — and there’s no date printed on this one, so I’m not gonna invent one. mwah 💋✨

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