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*> \brief \b CPTSV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition
* ==========
*
* SUBROUTINE CPTSV( N, NRHS, D, E, B, LDB, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
* REAL D( * )
* COMPLEX B( LDB, * ), E( * )
* ..
*
* Purpose
* =======
*
*>\details \b Purpose:
*>\verbatim
*>
*> CPTSV computes the solution to a complex system of linear equations
*> A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
*> matrix, and X and B are N-by-NRHS matrices.
*>
*> A is factored as A = L*D*L**H, and the factored form of A is then
*> used to solve the system of equations.
*>
*>\endverbatim
*
* Arguments
* =========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand sides, i.e., the number of columns
*> of the matrix B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> D is REAL array, dimension (N)
*> On entry, the n diagonal elements of the tridiagonal matrix
*> A. On exit, the n diagonal elements of the diagonal matrix
*> D from the factorization A = L*D*L**H.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*> E is COMPLEX array, dimension (N-1)
*> On entry, the (n-1) subdiagonal elements of the tridiagonal
*> matrix A. On exit, the (n-1) subdiagonal elements of the
*> unit bidiagonal factor L from the L*D*L**H factorization of
*> A. E can also be regarded as the superdiagonal of the unit
*> bidiagonal factor U from the U**H*D*U factorization of A.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX array, dimension (LDB,NRHS)
*> On entry, the N-by-NRHS right hand side matrix B.
*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the leading minor of order i is not
*> positive definite, and the solution has not been
*> computed. The factorization has not been completed
*> unless i = N.
*> \endverbatim
*>
*
* Authors
* =======
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complexOTHERcomputational
*
* =====================================================================
SUBROUTINE CPTSV( N, NRHS, D, E, B, LDB, INFO )
*
* -- LAPACK computational routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
REAL D( * )
COMPLEX B( LDB, * ), E( * )
* ..
*
* =====================================================================
*
* .. External Subroutines ..
EXTERNAL CPTTRF, CPTTRS, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( NRHS.LT.0 ) THEN
INFO = -2
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CPTSV ', -INFO )
RETURN
END IF
*
* Compute the L*D*L**H (or U**H*D*U) factorization of A.
*
CALL CPTTRF( N, D, E, INFO )
IF( INFO.EQ.0 ) THEN
*
* Solve the system A*X = B, overwriting B with X.
*
CALL CPTTRS( 'Lower', N, NRHS, D, E, B, LDB, INFO )
END IF
RETURN
*
* End of CPTSV
*
END
|
