clavsp()

subroutine clavsp	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		complex, dimension( * )	A,
		integer, dimension( * )	IPIV,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		integer	INFO
	)

CLAVSP

Purpose:

    CLAVSP  performs one of the matrix-vector operations
       x := A*x  or  x := A^T*x,
    where x is an N element vector and  A is one of the factors
    from the symmetric factorization computed by CSPTRF.
    CSPTRF produces a factorization of the form
         U * D * U^T     or     L * D * L^T,
    where U (or L) is a product of permutation and unit upper (lower)
    triangular matrices, U^T (or L^T) is the transpose of
    U (or L), and D is symmetric and block diagonal with 1 x 1 and
    2 x 2 diagonal blocks.  The multipliers for the transformations
    and the upper or lower triangular parts of the diagonal blocks
    are stored columnwise in packed format in the linear array A.

    If TRANS = 'N' or 'n', CLAVSP multiplies either by U or U * D
    (or L or L * D).
    If TRANS = 'C' or 'c', CLAVSP multiplies either by U^T or D * U^T
    (or L^T or D * L^T ).

  UPLO   - CHARACTER*1
           On entry, UPLO specifies whether the triangular matrix
           stored in A is upper or lower triangular.
              UPLO = 'U' or 'u'   The matrix is upper triangular.
              UPLO = 'L' or 'l'   The matrix is lower triangular.
           Unchanged on exit.

  TRANS  - CHARACTER*1
           On entry, TRANS specifies the operation to be performed as
           follows:
              TRANS = 'N' or 'n'   x := A*x.
              TRANS = 'T' or 't'   x := A^T*x.
           Unchanged on exit.

  DIAG   - CHARACTER*1
           On entry, DIAG specifies whether the diagonal blocks are
           assumed to be unit matrices, as follows:
              DIAG = 'U' or 'u'   Diagonal blocks are unit matrices.
              DIAG = 'N' or 'n'   Diagonal blocks are non-unit.
           Unchanged on exit.

  N      - INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  NRHS   - INTEGER
           On entry, NRHS specifies the number of right hand sides,
           i.e., the number of vectors x to be multiplied by A.
           NRHS must be at least zero.
           Unchanged on exit.

  A      - COMPLEX array, dimension( N*(N+1)/2 )
           On entry, A contains a block diagonal matrix and the
           multipliers of the transformations used to obtain it,
           stored as a packed triangular matrix.
           Unchanged on exit.

  IPIV   - INTEGER array, dimension( N )
           On entry, IPIV contains the vector of pivot indices as
           determined by CSPTRF.
           If IPIV( K ) = K, no interchange was done.
           If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter-
           changed with row IPIV( K ) and a 1 x 1 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.

  B      - 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    - INTEGER
           On entry, LDB contains the leading dimension of B as
           declared in the calling program.  LDB must be at least
           max( 1, N ).
           Unchanged on exit.

  INFO   - INTEGER
           INFO is the error flag.
           On exit, a value of 0 indicates a successful exit.
           A negative value, say -K, indicates that the K-th argument
           has an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.