# 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

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