SDISNA(3)

🌸 NAME 🌸

okay bestie, welcome to SDISNA(3) from the Library Functions Manual 🫶 — this is the page for the icon that is SDISNA, and the source file is:

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

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

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💖 Function/Subroutine Documentation 💖

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

🎀 Purpose 🎀

okay so here’s the tea ☕: 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 💅

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

🍓 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' and 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' and 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 at line 116 of file sdisna.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 — this page was served by LAPACK Version 3.12.0, file /home/abui...RC/sdisna.f(3). Date? not printed here, so we’re keeping it mysterious and timeless ✨💖