/home/abui...RC/zsysv.f(3)

💖 zsysv.f(3) — Library Functions Manual 💖

This is the page for zsysv.f, bestie — manual name: Library Functions Manual. It’s a LAPACK routine page, and yes, it’s giving “linear algebra but make it dramatic.” 💅

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NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zsysv.f

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SYNOPSIS

Functions/Subroutines

subroutine ZSYSV (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork,
    info)
     ZSYSV computes the solution to system of linear equations A * X = B
    for SY matrices

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Function/Subroutine Documentation

subroutine ZSYSV (character uplo, integer n, integer nrhs, complex*16,
    dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,
    complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( *
    ) work, integer lwork, integer info)

ZSYSV computes the solution to system of linear equations A * X = B for SY matrices. Slay. ✨

Purpose

Okay so here’s the whole vibe: ZSYSV computes the solution to a complex system of linear equations

A * X = B,

where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

The diagonal pivoting method is used to factor A as

A = U * D * U**T,  if UPLO = 'U', or
A = L * D * L**T,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. Iconic behavior, no notes. 🔥

Parameters

• UPLO — UPLO is CHARACTER*1.
  • = 'U': upper triangle of A is stored.
  • = 'L': lower triangle of A is stored.
• N — N is INTEGER. It’s the number of linear equations, aka the order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. It’s the number of right hand sides, aka the number of columns of the matrix B. NRHS >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N).
  • On entry, this is the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
  • On exit, if INFO = 0, this holds the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by ZSYTRF.
• LDA — LDA is INTEGER. This is the leading dimension of the array A. LDA >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N). It holds details of the interchanges and the block structure of D, as determined by ZSYTRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
• B — B is COMPLEX*16 array, dimension (LDB,NRHS).
  • On entry, this is the N-by-NRHS right hand side matrix B.
  • On exit, if INFO = 0, this is the N-by-NRHS solution matrix X.
• LDB — LDB is INTEGER. This is the leading dimension of the array B. LDB >= max(1,N).
• WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🫶
• LWORK — LWORK is INTEGER. This is the length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for ZSYTRF.
  • for LWORK < N, TRS will be done with Level BLAS 2
  • for LWORK >= N, TRS will be done with Level BLAS 3

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

Important vibe check: if INFO > 0, the factorization finished but D is singular, so the solution could not be computed. That’s not a cute little warning — that’s the whole solve being unavailable. 😭

Author

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

Definition at line 169 of file zsysv.f.

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Author

This page was generated automatically by Doxygen for LAPACK from the source code. ✨

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Sign-off, bestie: source/version is LAPACK Version 3.12.0, and the page is /home/abui...RC/zsysv.f(3). No date line is printed in this footer, so that’s the whole footer tea. 💖🎀🦋