TESTING/LIN/zsyt01_3.f(3)

🌸 NAME 🌸

Okay so bestie, welcome to the TESTING/LIN/zsyt01_3.f page from the Library Functions Manual — it’s a LAPACK thing, and it’s all about the zsyt01_3 subroutine. 💖

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

       subroutine zsyt01_3 (uplo, n, a, lda, afac, ldafac, e, ipiv, c, ldc,
           rwork, resid)
           ZSYT01_3

🧚 Function/Subroutine Documentation 🧚

   subroutine zsyt01_3 (character uplo, integer n, complex*16, dimension( lda,
       * ) a, integer lda, complex*16, dimension( ldafac, * ) afac, integer
       ldafac, complex*16, dimension( * ) e, integer, dimension( * ) ipiv,
       complex*16, dimension( ldc, * ) c, integer ldc, double precision,
       dimension( * ) rwork, double precision resid)
       ZSYT01_3

🎯 Purpose 🎯

ZSYT01_3 reconstructs a symmetric indefinite matrix A from its block L*D*L' or U*D*U' factorization computed by ZSYTRF_RK (or ZSYTRF_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, that’s the whole job. 💫

🌈 Parameters 🌈

• UPLO — is CHARACTER*1; it specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — is INTEGER; the number of rows and columns of the matrix A. N >= 0. 🫶
• A — is COMPLEX*16 array, dimension (LDA,N); the original symmetric matrix A.
• LDA — is INTEGER; the leading dimension of the array A. LDA >= max(1,N)
• AFAC — is COMPLEX*16 array, dimension (LDAFAC,N); diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and ZSYTRF_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 — is INTEGER; the leading dimension of the array AFAC. LDAFAC >= max(1,N).
• E — is COMPLEX*16 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 — is INTEGER array, dimension (N); the pivot indices from ZSYTRF_RK (or ZSYTRF_BK).
• C — is COMPLEX*16 array, dimension (LDC,N).
• LDC — is INTEGER; the leading dimension of the array C. LDC >= max(1,N).
• RWORK — is DOUBLE PRECISION array, dimension (N).
• RESID — is DOUBLE PRECISION; 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 zsyt01_3.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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Okay bestie, that’s the whole page. Footer source/version + date check: LAPACK Version 3.12.0, page TESTING/LIN/zsyt01_3.f(3) — and the footer date slot isn’t filled on this page, so no invented date, periodt. 💅✨