TESTING/LIN/dsyt01_3.f(3)

💖 NAME 💖

okay so bestie, this is the manual page for TESTING/LIN/dsyt01_3.f, straight out of the Library Functions Manual. It's all about the Fortran subroutine dsyt01_3, and she is lowkey iconic in a linear-algebra-testing way 💅✨

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✨ SYNOPSIS ✨

🌀 Functions/Subroutines 🌀

subroutine dsyt01_3 (uplo, n, a, lda, afac, ldafac, e, ipiv, c, ldc,
    rwork, resid)
    DSYT01_3

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🦋 Function/Subroutine Documentation 🦋

subroutine dsyt01_3 (character uplo, integer n, double precision, dimension(
    lda, * ) a, integer lda, double precision, dimension( ldafac, * ) afac,
    integer ldafac, double precision, dimension( * ) e, integer, dimension(
    * ) ipiv, double precision, dimension( ldc, * ) c, integer ldc, double
    precision, dimension( * ) rwork, double precision resid)

DSYT01_3

🎯 Purpose 🎯

DSYT01_3 reconstructs a symmetric indefinite matrix A from its block L*D*L' or U*D*U' factorization computed by DSYTRF_RK (or DSYTRF_BK) and computes the residual

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

where C is the reconstructed matrix and EPS is the machine epsilon. no cap, that's the whole purpose and she's serving it 💖

🧾 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDAFAC,N)

Diagonal of the block diagonal matrix D and factors U or L as computed by DSYTRF_RK and DSYTRF_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 DOUBLE PRECISION 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 DSYTRF_RK (or DSYTRF_BK).

C

C is DOUBLE PRECISION 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 138 of file dsyt01_3.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. she's literally generated, bestie 💫

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okay that's the whole page, mwah 💋 the footer/source energy is LAPACK, Version 3.12.0, and this page is TESTING/LIN/dsyt01_3.f(3). iconic, automatic, periodt ✨🫶