zlavhe_rook.f - Man Page

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

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.