ZLAVSY_ROOK.F(3)

💅 NAME 💅

TESTING/LIN/zlavsy_rook.f — okay so this is the manual page for that file, and the manual name is Library Functions Manual. Header vibe is TESTING/LI...avsy_rook.f(3), so yes bestie, you're in the right place for ZLAVSY_ROOK tea. 🫶

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine zlavsy_rook — the short call, literally:

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

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🦋 Function/Subroutine Documentation 🦋

🌸 zlavsy_rook 🌸

Here's the full signature, no cap:

subroutine zlavsy_rook (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_ROOK — that's the whole main character right there. 👑

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🎀 Purpose 🎀

Okay so ZLAVSY_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 ZSYTRF_ROOK. This is the factorization lore, iykyk. 🧚

• 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').

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🍓 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

🌸 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. 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 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_ROOK. 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 ZSYTRF_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 inerchaged, 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 inerchaged, 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, 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

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🌟 Author 🌟

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

⭐ Definition at line 153 of file zlavsy_rook.f. ⭐

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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🌈 That's the whole page, bestie. Source/version sign-off: LAPACK Version 3.12.0, footer tag TESTING/LI...avsy_rook.f(3). The footer doesn't give a date, so I'm not making one up — periodt. 💖