ZPST01(3)

💖 ZPST01 — like, the reconstruction queen of Hermitian positive semidefinite matrices 💖

okay bestie, so this page is from zpst01.f(3), one of the library functions in the LAPACK fam ✨ — buckle up, she's a Fortran test routine and she's serving.

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ZPST01 (uplo, n, a, lda, afac, ldafac, perm, ldperm, piv,
    rwork, resid, rank)

ZPST01 — that's her name, that's her whole brand 💅

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🎀 Function/Subroutine Documentation 🎀

subroutine ZPST01 (character uplo, integer n, complex*16, dimension( lda, *
    ) a, integer lda, complex*16, dimension( ldafac, * ) afac, integer
    ldafac, complex*16, dimension( ldperm, * ) perm, integer ldperm,
    integer, dimension( * ) piv, double precision, dimension( * ) rwork,
    double precision resid, integer rank)

ZPST01 🫶

✨ Purpose ✨

!> !> ZPST01 reconstructs an Hermitian positive semidefinite matrix A !> from its L or U factors and the permutation matrix P and computes !> the residual !> norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or !> norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ), !> where EPS is the machine epsilon, L' is the conjugate transpose of L, !> and U' is the conjugate transpose of U. !>

Like, she takes the pieces apart, puts them back together via the permutation matrix P, and then checks the residual to see how much of a mess she made 😭 iconic behaviour honestly.

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🦋 Parameters 🦋

• UPLO

!> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> Hermitian matrix A is stored: !> = 'U': Upper triangular !> = 'L': Lower triangular !>

so basically you pick a side: 'U' for upper triangular, 'L' for lower. main character choice, no cap.

• N

!> N is INTEGER !> The number of rows and columns of the matrix A. N >= 0. !>

rows and columns, both, same number, N >= 0 fr fr.

• A

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

the original Hermitian matrix herself 👑

• LDA

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

leading dimension of A, and she said LDA >= max(1,N), periodt.

• AFAC

!> AFAC is COMPLEX*16 array, dimension (LDAFAC,N) !> The factor L or U from the L*L' or U'*U !> factorization of A. !>

the factor L or U from the L*L' or U'*U factorization of A — the glow-up version, iykyk.

• LDAFAC

!> LDAFAC is INTEGER !> The leading dimension of the array AFAC. LDAFAC >= max(1,N). !>

leading dimension of AFAC. LDAFAC >= max(1,N). she's consistent bestie.

• PERM

!> PERM is COMPLEX*16 array, dimension (LDPERM,N) !> Overwritten with the reconstructed matrix, and then with the !> difference P*L*L'*P' - A (or P*U'*U*P' - A) !>

okay so this one gets overwritten twice — first with the reconstructed matrix, then with the difference P*L*L'*P' - A (or P*U'*U*P' - A). she's doing double duty, we stan a multitasker 💅

• LDPERM

!> LDPERM is INTEGER !> The leading dimension of the array PERM. !> LDAPERM >= max(1,N). !>

leading dimension of PERM. (and yes, the original really does say LDAPERM >= max(1,N). — not me, I'm just the messenger 🙈)

• PIV

!> PIV is INTEGER array, dimension (N) !> PIV is such that the nonzero entries are !> P( PIV( K ), K ) = 1. !>

this is the permutation lore: the nonzero entries are P( PIV( K ), K ) = 1. literally the whole pivot vibe check ✨

• RWORK

!> RWORK is DOUBLE PRECISION array, dimension (N) !>

double precision workspace, dimension (N). the little helper 🫶

• RESID

!> RESID is DOUBLE PRECISION !> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) !> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ) !>

double precision output, and the formula depends on which side you picked:

• If UPLO = 'L', it's norm(L*L' - A) / ( N * norm(A) * EPS )
• If UPLO = 'U', it's norm(U'*U - A) / ( N * norm(A) * EPS )

the residual!! the moment of truth!! 😭🔥

• RANK

!> RANK is INTEGER !> number of nonzero singular values of A. !>

integer, and she's literally just the number of nonzero singular values of A. slay.

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👑 Author 👑

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

the whole friend group contributed to this one 💜

Definition at line 134 of file zpst01.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

(not a human, just a robot doing her best 🧚)

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aaaand that's the page bestie!! 💖✨🎀🦋🌸

from the LAPACK source, Version 3.12.0, dated /home/abui...IN/zpst01.f(3) — see you in the group chat, mwah 😚💅🍓