CLAVSY_ROOK(3)

🌸 NAME 🌸

TESTING/LIN/clavsy_rook.f — okay bestie, this is the file this page is all about. The header also shows it as TESTING/LI...avsy_rook.f(3) from the Library Functions Manual, and it is very much giving “LAPACK Fortran subroutine documentation” energy. ✨

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

💅 FUNCTION/SUBROUTINE DOCUMENTATION 💅

🎀 CLAVSY_ROOK 🎀

Here’s the full signature so you can see every type, dimension and argument name exactly as written:

   subroutine clavsy_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)
       CLAVSY_ROOK

🦋 PURPOSE 🦋

Bestie, CLAVSY_ROOK performs one of these matrix-vector operations — and yes, that apostrophe means transpose:

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 CSYTRF_ROOK. Iconic linear algebra behavior.

• 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')

🌸 PARAMETERS 🌸

UPLO

UPLO is CHARACTER*1. It specifies whether the factor stored in A is upper or lower triangular. One character, big job.

• = '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. It’s the number of rows and columns of the matrix A. Constraint: N >= 0. Respect the constraint, bestie.

NRHS

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

A

A is COMPLEX array, dimension (LDA,N). It’s the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF_ROOK. Stored as a 2-D triangular matrix. We love a structured storage moment.

LDA

LDA is INTEGER. It’s the leading dimension of the array A. Constraint: 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 CSYTRF_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. Yep, “inerchaged” is the source’s spelling — I’m keeping it exactly.

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 array, dimension (LDB,NRHS). On entry, B contains NRHS vectors of length N. On exit, B is overwritten with the product A * B. The math ate and left no crumbs.

LDB

LDB is INTEGER. It’s the leading dimension of the array B. Constraint: 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 📌

Definition at line 153 of file clavsy_rook.f.

🌈 AUTHOR 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That’s the whole page, bestie. Source/version situation: LAPACK Version 3.12.0, footer page TESTING/LI...avsy_rook.f(3). The footer didn’t print a date, so I’m not inventing one — no cap, just facts. 🎀✨