ZHET01_3(3)

💅 ZHET01_3(3) — Library Functions Manual 💅

okay so welcome to the ZHET01_3(3) manual page, Library Functions Manual energy and all. This is the one about checking a Hermitian indefinite matrix reconstruction, and yes bestie, we're keeping every single detail. 🫶

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zhet01_3.f

That's literally the NAME entry: a whole file path. Also known as ZHET01_3(3), iykyk. 💖

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine ZHET01_3 (uplo, n, a, lda, afac, ldafac, e, ipiv, c, ldc,
    rwork, resid)
    ZHET01_3

🦋 Function/Subroutine Documentation 🦋

subroutine ZHET01_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)
       ZHET01_3

💖 Purpose 💖

okay so ZHET01_3 reconstructs a Hermitian indefinite matrix A from its block L*D*L' or U*D*U' factorization computed by ZHETRF_RK (or ZHETRF_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 purpose. ✨

🎀 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

🦋 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)
• Diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK and ZHETRF_BK:
  • a) ONLY diagonal elements of the Hermitian 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*16 array, dimension (N)
• On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian 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 ZHETRF_RK (or ZHETRF_BK).

🌈 C 🌈

• C is COMPLEX*16 array, dimension (LDC,N)

💀 LDC 💀

• LDC is INTEGER
• The leading dimension of the array C. LDC >= max(1,N).

🎀 RWORK 🎀

• RWORK is DOUBLE PRECISION array, dimension (N)

🫶 RESID 🫶

• 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 📍

Definition at line 139 of file zhet01_3.f.

✨ Author (the generated-page one) ✨

Generated automatically by Doxygen for LAPACK from the source code.

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