DSGT01(3)

💅 DSGT01 — like, the actual manual page, bestie

ok so real quick: this is the page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/dsgt01.f — yes that's the whole NAME, it's giving "my home address is my name" energy and honestly? iconic. It lives in the LAPACK Library Functions Manual and it's a subroutine page. Buckle up 🎀

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✨ SYNOPSIS ✨

Subroutines, bestie 🦋

subroutine DSGT01 (itype, uplo, n, m, a, lda, b, ldb, z, ldz, d, work,
    result)

DSGT01

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🌸 Function/Subroutine Documentation 🌸

Here's the whole vibe, literally every single argument, no cap:

subroutine DSGT01 (integer itype, character uplo, integer n, integer m,
    double precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( ldz, *
    ) z, integer ldz, double precision, dimension( * ) d, double precision,
    dimension( * ) work, double precision, dimension( * ) result)

DSGT01

🧚 Purpose 🧚

ok so DDGT01 checks a decomposition of the form

   A Z   =  B Z D or
   A B Z =  Z D or
   B A Z =  Z D

where A is a symmetric matrix, B is symmetric positive definite, Z is orthogonal, and D is diagonal. (yes it says DDGT01 in the Purpose block and DSGT01 everywhere else — that's just how the source is, don't come for me 🙈)

One of the following test ratios gets computed, and it's giving math girlie main character energy:

• ITYPE = 1: RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp )
• ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )
• ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )

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💖 Parameters 💖

• ITYPE — ITYPE is INTEGER. It's the form of the symmetric generalized eigenproblem, and the options are:
  • = 1: A*z = (lambda)*B*z
  • = 2: A*B*z = (lambda)*z
  • = 3: B*A*z = (lambda)*z
• UPLO — UPLO is CHARACTER*1. Tells you whether the upper or lower triangular part of the symmetric matrices A and B is stored. Pick your fighter:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — N is INTEGER. The order of the matrix A. Constraint: N >= 0.
• M — M is INTEGER. The number of eigenvalues found. Constraint: 0 <= M <= N.
• A — A is DOUBLE PRECISION array, dimension (LDA, N). The original symmetric matrix A. 💜
• LDA — LDA is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,N).
• B — B is DOUBLE PRECISION array, dimension (LDB, N). The original symmetric positive definite matrix B. (positive definite AND symmetric, we stan a well-behaved matrix 🫶)
• LDB — LDB is INTEGER. The leading dimension of the array B. Constraint: LDB >= max(1,N).
• Z — Z is DOUBLE PRECISION array, dimension (LDZ, M). The computed eigenvectors of the generalized eigenproblem. ⭐
• LDZ — LDZ is INTEGER. The leading dimension of the array Z. Constraint: LDZ >= max(1,N).
• D — D is DOUBLE PRECISION array, dimension (M). The computed eigenvalues of the generalized eigenproblem. 👑
• WORK — WORK is DOUBLE PRECISION array, dimension (N*N). That's the whole description, that's it, it's a workspace array, slay.
• RESULT — RESULT is DOUBLE PRECISION array, dimension (1). The test ratio as described above. One whole element of pure judgment. 🔥

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🎀 Author 🎀

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 144 of file dsgt01.f. 💀

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. Not me, not you, a robot did this. 🤖✨

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and that's the whole page bestie, we ate and left zero crumbs 🍓 — this was LAPACK, Version 3.12.0, brought to you from /home/abui...IG/dsgt01.f 💅💖