ZSYT01_3(3)

🎀 NAME 🎀

okay so this page is zsyt01_3(3) from the Library Functions Manual, and the NAME section is literally this absolute path, bestie:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zsyt01_3.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

🌸 Function/Subroutine Documentation 🌸

here's the full signature, no cap:

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 🎯

okay so the purpose is giving reconstruction realness: 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. periodt.

🧸 Parameters 🧸

UPLO

UPLO is CHARACTER*1 and 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. Constraint: N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N) — the original symmetric matrix A. she's the original, your honor.

LDA

LDA is INTEGER — the leading dimension of the array A. Constraint: 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 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

LDAFAC is INTEGER — the leading dimension of the array AFAC. Constraint: LDAFAC >= max(1,N).

E

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

IPIV is INTEGER array, dimension (N) — the pivot indices from ZSYTRF_RK (or ZSYTRF_BK).

C

C is COMPLEX*16 array, dimension (LDC,N). that's the whole description, bestie — no extra lore.

LDC

LDC is INTEGER — the leading dimension of the array C. Constraint: 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 139 of file zsyt01_3.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

🫶 okay byeee, bestie — footer tea: LAPACK, Version 3.12.0, source /home/abui.../zsyt01_3.f(3), and no date listed, so we’re not inventing one. 💖