CSYT01_3(3)

💅 CSYT01_3(3) 💅

Okay bestie, this is the Library Functions Manual entry for CSYT01_3(3), and it's lowkey iconic. It's a LAPACK testing subroutine that reconstructs a symmetric indefinite matrix and checks the residual — very "trust but verify" of it. 💖

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🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/csyt01_3.f

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🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

subroutine CSYT01_3 (uplo, n, a, lda, afac, ldafac, e, ipiv, c, ldc, rwork, resid)

And yes, the main character is CSYT01_3. 💅

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🦋 Function/Subroutine Documentation 🦋

Here's the full signature, character-for-character:

subroutine CSYT01_3 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldafac, * ) afac, integer ldafac, complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( ldc, * ) c, integer ldc, real, dimension( * ) rwork, real resid)

Yup: CSYT01_3. 🌟

🎯 Purpose 🎯

CSYT01_3 reconstructs a symmetric indefinite matrix A from its block L*D*L' or U*D*U' factorization computed by CSYTRF_RK (or CSYTRF_BK) and computes the residual

norm( C - A ) / ( N * norm(A) * EPS ),

where C is the reconstructed matrix and EPS is the machine epsilon. Slay, math. ✨

💖 Parameters 💖

• UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric 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 array, dimension (LDA,N). The original symmetric matrix A.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N)
• AFAC — AFAC is COMPLEX array, dimension (LDAFAC,N). Diagonal of the block diagonal matrix D and factors U or L as computed by CSYTRF_RK and CSYTRF_BK:
  • a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and
  • b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.
• LDAFAC — LDAFAC is INTEGER. The leading dimension of the array AFAC. LDAFAC >= max(1,N).
• E — E is COMPLEX array, dimension (N). On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where
  • If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
  • If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
• IPIV — IPIV is INTEGER array, dimension (N). The pivot indices from CSYTRF_RK (or CSYTRF_BK).
• C — C is COMPLEX array, dimension (LDC,N).
• LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,N).
• RWORK — RWORK is REAL array, dimension (N).
• RESID — RESID is REAL.
  • If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
  • If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )

👑 Author 👑

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

Definition at line 139 of file csyt01_3.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo bestie 💖 — this page is from LAPACK, Version 3.12.0, at /home/abui.../csyt01_3.f(3). Go off, queen. 👑✨