SLAVSY_ROOK(3)

💅 SLAVSY_ROOK(3) 💅

okay so bestie, welcome to SLAVSY_ROOK(3) from the Library Functions Manual 💖 this is the whole page, and yes, every little technical crumb is still here. no cap.

✨ NAME ✨

TESTING/LIN/slavsy_rook.f

🫶 SYNOPSIS 🫶

🧚 Functions/Subroutines 🧚

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

SLAVSY_ROOK

🌸 Function/Subroutine Documentation 🌸

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

SLAVSY_ROOK

🎀 Purpose 🎀

SLAVSY_ROOK 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 SSYTRF_ROOK.

• 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 specifies whether the factor stored in A is upper or lower triangular.

• 'U': Upper triangular
• 'L': Lower triangular

🦋 TRANS 🦋

TRANS is CHARACTER*1. It specifies the operation to be performed.

• 'N': x := A*x
• 'T': x := A'*x
• 'C': x := A'*x

🌈 DIAG 🌈

DIAG is CHARACTER*1. It 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 ⭐

N is INTEGER. It is the number of rows and columns of the matrix A. N >= 0.

🍓 NRHS 🍓

NRHS is INTEGER. It is the number of right hand sides, i.e., the number of vectors x to be multiplied by A. NRHS >= 0.

👑 A 👑

A is REAL array, dimension (LDA,N). It holds the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF_ROOK. Stored as a 2-D triangular matrix.

💜 LDA 💜

LDA is INTEGER. It 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 SSYTRF_ROOK.

• 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) < 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 interchanged, and 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) < 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 interchanged, and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

🌸 B 🌸

B is REAL 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. It is 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 155 of file slavsy_rook.f. 📍

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole vibe, bestie 🫶 source/version: LAPACK Version 3.12.0; source page: TESTING/LI...avsy_rook.f(3); and the footer doesn’t list a date, so no fake date from me 💖✨