CLAVHE_ROOK(3)

okay bestie, welcome to TESTING/LI...avhe_rook.f(3) from the Library Functions Manual, section 3 — the source file is TESTING/LIN/clavhe_rook.f, and today's main character is CLAVHE_ROOK 💅🫶.

✨ NAME ✨

TESTING/LIN/clavhe_rook.f

🛠️ SYNOPSIS 🛠️

📦 Functions/Subroutines 📦

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

CLAVHE_ROOK — that's the icon, no cap 👑

💖 Function/Subroutine Documentation 💖

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

CLAVHE_ROOK

🎯 Purpose 🎯

Okay so CLAVHE_ROOK performs one of these matrix-vector operations:

x := A*x  or  x := A^H*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 CHETRF_ROOK.

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

🧩 Parameters 🧩

• UPLO — CHARACTER*1. Tells you whether the factor stored in A is upper or lower triangular. = 'U': Upper triangular. = 'L': Lower triangular.
• TRANS — CHARACTER*1. Specifies the operation to be performed. = 'N': x := A*x. = 'C': x := A^H*x.
• DIAG — 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 — INTEGER. The number of rows and columns of the matrix A. N >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of vectors x to be multiplied by A. NRHS >= 0.
• A — COMPLEX array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF_ROOK. Stored as a 2-D triangular matrix.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by CHETRF_ROOK.
  • If UPLO = 'U':
    • Only the last KB elements of IPIV are set.
    • 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) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged (yes, that's the spelling in the source 😭), D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
  • If UPLO = 'L':
    • Only the first KB elements of IPIV are set.
    • 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) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged (again, source spelling 💀), D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
• B — COMPLEX array, dimension (LDB,NRHS). On entry, B contains NRHS vectors of length N. On exit, B is overwritten with the product A * B.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• INFO — 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 154 of file clavhe_rook.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie — LAPACK Version 3.12.0, page TESTING/LI...avhe_rook.f(3), and the footer isn't showing a date so I'm not inventing one 🌈💖✨