DLAVSY_ROOK(3)

NAME

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SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

here's the full signature, literally exactly as the source has it 🫶

subroutine dlavsy_rook (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_ROOK

Purpose

okay so DLAVSY_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 DSYTRF_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. 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_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 DSYTRF_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 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 155 of file dlavsy_rook.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

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