TESTING/LIN/zlavsy.f(3)

🌸 NAME 🌸

okay bestie, this is the manual page for TESTING/LIN/zlavsy.f(3) — yes, the NAME really is just that path, and it's here to serve ZLAVSY main-character energy. 💅✨

✨ SYNOPSIS ✨

🧩 Functions/Subroutines

• subroutine zlavsy (uplo, trans, diag, n, nrhs, a, lda, ipiv, b, ldb, info) — ZLAVSY

🌟 Function/Subroutine Documentation 🌟

subroutine zlavsy (character uplo, character trans, character diag, integer
     n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda,
     integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer
     ldb, integer info)

ZLAVSY — she's the subroutine in question, and she's about to do some matrix-vector multiplication. 🎀

🎯 Purpose

okay so ZLAVSY performs one of these matrix-vector operations:

• x := A*x
• x := A'*x

where x is an N element vector and A is one of the factors from the block U*D*U' or L*D*L' factorization computed by ZSYTRF. 🦋

If TRANS = 'N', it multiplies by U or U * D (or L or L * D).

If TRANS = 'T', it multiplies by U' or D * U' (or L' or D * L').

🧾 Parameters

• UPLO is CHARACTER*1 — specifies whether the factor stored in A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS is CHARACTER*1 — specifies the operation to be performed:
  • = 'N': x := A*x
  • = 'T': x := A'*x
• DIAG is CHARACTER*1 — specifies whether or not the diagonal blocks are unit matrices. If the diagonal blocks are assumed to be unit, then A = U or A = L; otherwise A = U*D or A = L*D.
  • = 'U': Diagonal blocks are assumed to be unit matrices.
  • = 'N': Diagonal blocks are assumed to be non-unit matrices.
• N is INTEGER — the number of rows and columns of the matrix A. N >= 0.
• NRHS is INTEGER — the number of right hand sides, i.e., the number of vectors x to be multiplied by A. NRHS >= 0.
• A is COMPLEX*16 array, dimension (LDA,N) — the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF. Stored as a 2-D triangular matrix.
• LDA is INTEGER — the leading dimension of the array A. LDA >= max(1,N).
• IPIV is INTEGER array, dimension (N) — details of the interchanges and the block structure of D, as determined by ZSYTRF.
  • If UPLO = 'U':
    • 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 IPIV( k ) = k, no interchange was done).
    • If IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
  • If UPLO = 'L':
    • 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 IPIV( k ) = k, no interchange was done).
    • If IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
• B is COMPLEX*16 array, dimension (LDB,NRHS) — on entry, B contains NRHS vectors of length N. On exit, B is overwritten with the product A * B.
• LDB is INTEGER — the leading dimension of the array B. LDB >= max(1,N).
• INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -k, the k-th argument had an illegal value

👑 Author

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

Definition at line 151 of file zlavsy.f. 📍

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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signed, sealed, and shipped with LAPACK Version 3.12.0 — page TESTING/LIN/zlavsy.f(3) 💖🫶✨