ZSGT01(3)

💅 NAME 💅

okay so bestie, this is the manual page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zsgt01.f — like, that whole entire path, no cap. She's a Fortran file living her best life in the LAPACK testing directory, and this page is coming to you from the Library Functions Manual. Periodt.

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines

so here's the little angel herself:

subroutine ZSGT01 (itype, uplo, n, m, a, lda, b, ldb, z, ldz, d, work,
    rwork, result)

ZSGT01 — that's it, that's the name, iconic behavior honestly.

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🎀 Function/Subroutine Documentation 🎀

okay so here's the full signature in all her glory, every single argument, and yes we're listing all of them because she's thorough:

subroutine ZSGT01 (integer itype, character uplo, integer n, integer m,
    complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
    ldb, * ) b, integer ldb, complex*16, dimension( ldz, * ) z, integer ldz,
    double precision, dimension( * ) d, complex*16, dimension( * ) work,
    double precision, dimension( * ) rwork, double precision, dimension( * )
    result)

ZSGT01 💖

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🌸 Purpose 🌸

bestie, this is the whole point of her existence, and I'm quoting the vibe directly:

💜 CDGT01 checks a decomposition of the form text A Z = B Z D or A B Z = Z D or B A Z = Z D 💜 where A is a Hermitian matrix, B is Hermitian positive definite, Z is unitary, and D is diagonal. 💜 One of the following test ratios is computed: 💜 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 )

like, she literally just checks whether your eigenvectors and eigenvalues actually hold up. a vibe check for linear algebra. 💅

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🦋 Parameters 🦋

⭐ ITYPE

ITYPE is INTEGER The form of the Hermitian generalized eigenproblem. = 1: A*z = (lambda)*B*z = 2: A*B*z = (lambda)*z = 3: B*A*z = (lambda)*z

so like, which flavor of eigenproblem are we checking today? that's the whole assignment.

⭐ UPLO

UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrices A and B is stored. = 'U': Upper triangular = 'L': Lower triangular

upper girlie or lower girlie, pick your lane.

⭐ N

N is INTEGER The order of the matrix A. N >= 0.

the size of A. and yes, zero is allowed, she's not gonna gatekeep.

⭐ M

M is INTEGER The number of eigenvalues found. M >= 0.

how many eigenvalues you actually found. again, M >= 0, no pressure.

⭐ A

A is COMPLEX*16 array, dimension (LDA, N) The original Hermitian matrix A.

the main character matrix, honestly. 👑

⭐ LDA

LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

the leading dimension of A — don't fumble this one, LDA >= max(1,N).

⭐ B

B is COMPLEX*16 array, dimension (LDB, N) The original Hermitian positive definite matrix B.

the other matrix, except this one is Hermitian and positive definite. she's got standards.

⭐ LDB

LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

leading dimension of B. LDB >= max(1,N). write it down.

⭐ Z

Z is COMPLEX*16 array, dimension (LDZ, M) The computed eigenvectors of the generalized eigenproblem.

the eigenvectors you computed, looking cute in their array.

⭐ LDZ

LDZ is INTEGER The leading dimension of the array Z. LDZ >= max(1,N).

LDZ >= max(1,N), always, fr fr.

⭐ D

D is DOUBLE PRECISION array, dimension (M) The computed eigenvalues of the generalized eigenproblem.

the eigenvalues, double precision, dimension (M). slay.

⭐ WORK

WORK is COMPLEX*16 array, dimension (N*N)

just the workspace, doing her little behind-the-scenes thing. dimension (N*N). 🫶

⭐ RWORK

RWORK is DOUBLE PRECISION array, dimension (N)

real workspace, dimension (N). she's the sensible one.

⭐ RESULT

RESULT is DOUBLE PRECISION array, dimension (1) The test ratio as described above.

the moment of truth, bestie — dimension (1), and it holds the test ratio we described up in Purpose. this is where the verdict lives.

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👑 Author 👑

the absolute legends behind this:

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

academic royalty, all of them, no notes. 🌈

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💀 Definition at line 150 of file zsgt01.f.

yes, line 150, file zsgt01.f. that's the exact spot, iykyk.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. (not me, not you — Doxygen did that 💅)

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and that's the whole page, bestie!! 🎀✨ LAPACK, Version 3.12.0, dropping in from /home/abui...IG/zsgt01.f(3) — slay forever, mwah 💖🦋🌸