TESTING/LIN/dlavsy.f(3)

🌸 NAME 🌸

okay bestie, welcome to the Library Functions Manual page for TESTING/LIN/dlavsy.f(3) — the NAME line is TESTING/LIN/dlavsy.f, and yes, we're keeping both because details are sacred. 💖 This one is literally the dlavsy routine, and it's giving “block factorization realness” in the best way. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine dlavsy (uplo, trans, diag, n, nrhs, a, lda, ipiv, b, ldb, info)
DLAVSY

🦋 Function/Subroutine Documentation 🦋

subroutine dlavsy (character uplo, character trans, character diag, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DLAVSY

🎯 Purpose

Okay so DLAVSY performs one of the matrix-vector operations

x := A*x  or  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 DSYTRF.

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

🧩 Parameters

• UPLO — UPLO is CHARACTER*1. It says whether the factor stored in A is upper or lower triangular. Values: = 'U': upper triangular; = 'L': lower triangular. ✨
• TRANS — TRANS is CHARACTER*1. It picks the operation: = 'N': x := A*x; = 'T': x := A'*x; = 'C': x := A'*x. 💫
• DIAG — DIAG is CHARACTER*1. It says 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. Values: = 'U': diagonal blocks are assumed to be unit matrices; = 'N': diagonal blocks are assumed to be non-unit matrices.
• N — N is INTEGER. The number of rows and columns of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of vectors x to be multiplied by A. NRHS >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF. Stored as a 2-D triangular matrix.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by DSYTRF.
  • 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 — B is DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, B contains NRHS vectors of length N. On exit, B is overwritten with the product A * B.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• INFO — 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 153 of file dlavsy.f.

👑 Author

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kisses and sparkles, bestie — LAPACK Version 3.12.0, source TESTING/LIN/dlavsy.f(3) 💜