TESTING/LIN/zpst01.f(3)

🌸 NAME

Bestie, welcome to TESTING/LIN/zpst01.f(3) from the Library Functions Manual 💅✨. This page is literally all about the routine zpst01, and we are gonna keep every single detail, no cap.

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✨ SYNOPSIS

🎀 Functions/Subroutines

       subroutine zpst01 (uplo, n, a, lda, afac, ldafac, perm, ldperm, piv,
           rwork, resid, rank)
           ZPST01

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💖 Function/Subroutine Documentation

🌈 subroutine zpst01

Here's the full signature, character for character, because we do not play about exact details 🫶:

   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. Periodt 💅

💜 Parameters

• UPLO — UPLO is CHARACTER*1. It specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — N is INTEGER. The number of rows and columns of the matrix A. N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). The original Hermitian matrix A.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• AFAC — AFAC is COMPLEX*16 array, dimension (LDAFAC,N). The factor L or U from the L*L' or U'*U factorization of A.
• LDAFAC — LDAFAC is INTEGER. The leading dimension of the array AFAC. LDAFAC >= max(1,N).
• 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).
• LDPERM — LDPERM is INTEGER. The leading dimension of the array PERM. LDAPERM >= max(1,N).
• PIV — PIV is INTEGER array, dimension (N). PIV is such that the nonzero entries are P( PIV( K ), K ) = 1.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• 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 ).
• RANK — RANK is INTEGER. Number of nonzero singular values of A.

👑 Author

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

⭐ Definition at line

134 of file zpst01.f.

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💅 Author

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And that's the wrap, bestie 🫶💖: this page is from LAPACK Version 3.12.0, file TESTING/LIN/zpst01.f(3), and it was generated automatically by Doxygen for LAPACK from the source code. Byeee ✨🎀