# zlavhe_rook.f - Man Page

TESTING/LIN/zlavhe_rook.f

## Synopsis

### Functions/Subroutines

subroutine **zlavhe_rook** (uplo, trans, diag, n, nrhs, a, lda, ipiv, b, ldb, info)**ZLAVHE_ROOK**

## Function/Subroutine Documentation

### subroutine zlavhe_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)

**ZLAVHE_ROOK**

**Purpose:**ZLAVHE_ROOK performs one of the 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 ZHETRF_ROOK.

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

**Parameters***UPLO*UPLO is CHARACTER*1 Specifies whether the factor stored in A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular

*TRANS*TRANS is CHARACTER*1 Specifies the operation to be performed: = 'N': x := A*x = 'C': x := A^H*x

*DIAG*DIAG is 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*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 ZHETRF_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 ZHETRF_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, 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, 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.

*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 **151** of file **zlavhe_rook.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlavhe_rook(3) is an alias of zlavhe_rook.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK