numeric-linalg

Educational material on the SciPy implementation of numerical linear algebra algorithms

Name	Size	Mode
..
lapack/SRC/cpttrs.f	5661B	-rw-r--r--

*> \brief \b CPTTRS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CPTTRS + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cpttrs.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cpttrs.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cpttrs.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE CPTTRS( UPLO, N, NRHS, D, E, B, LDB, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDB, N, NRHS
*       ..
*       .. Array Arguments ..
*       REAL               D( * )
*       COMPLEX            B( LDB, * ), E( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CPTTRS solves a tridiagonal system of the form
*>    A * X = B
*> using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF.
*> D is a diagonal matrix specified in the vector D, U (or L) is a unit
*> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
*> the vector E, and X and B are N by NRHS matrices.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies the form of the factorization and whether the
*>          vector E is the superdiagonal of the upper bidiagonal factor
*>          U or the subdiagonal of the lower bidiagonal factor L.
*>          = 'U':  A = U**H*D*U, E is the superdiagonal of U
*>          = 'L':  A = L*D*L**H, E is the subdiagonal of L
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the tridiagonal 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] D
*> \verbatim
*>          D is REAL array, dimension (N)
*>          The n diagonal elements of the diagonal matrix D from the
*>          factorization A = U**H*D*U or A = L*D*L**H.
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*>          E is COMPLEX array, dimension (N-1)
*>          If UPLO = 'U', the (n-1) superdiagonal elements of the unit
*>          bidiagonal factor U from the factorization A = U**H*D*U.
*>          If UPLO = 'L', the (n-1) subdiagonal elements of the unit
*>          bidiagonal factor L from the factorization A = L*D*L**H.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is COMPLEX array, dimension (LDB,NRHS)
*>          On entry, the right hand side vectors B for the system of
*>          linear equations.
*>          On exit, the solution vectors, 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 = -k, the k-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup pttrs
*
*  =====================================================================
      SUBROUTINE CPTTRS( UPLO, N, NRHS, D, E, B, LDB, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      REAL               D( * )
      COMPLEX            B( LDB, * ), E( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            IUPLO, J, JB, NB
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ILAENV
*     ..
*     .. External Subroutines ..
      EXTERNAL           CPTTS2, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments.
*
      INFO = 0
      UPPER = ( UPLO.EQ.'U' .OR. UPLO.EQ.'u' )
      IF( .NOT.UPPER .AND. .NOT.( UPLO.EQ.'L' .OR. UPLO.EQ.'l' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -7
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CPTTRS', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 .OR. NRHS.EQ.0 )
     $   RETURN
*
*     Determine the number of right-hand sides to solve at a time.
*
      IF( NRHS.EQ.1 ) THEN
         NB = 1
      ELSE
         NB = MAX( 1, ILAENV( 1, 'CPTTRS', UPLO, N, NRHS, -1, -1 ) )
      END IF
*
*     Decode UPLO
*
      IF( UPPER ) THEN
         IUPLO = 1
      ELSE
         IUPLO = 0
      END IF
*
      IF( NB.GE.NRHS ) THEN
         CALL CPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
      ELSE
         DO 10 J = 1, NRHS, NB
            JB = MIN( NRHS-J+1, NB )
            CALL CPTTS2( IUPLO, N, JB, D, E, B( 1, J ), LDB )
   10    CONTINUE
      END IF
*
      RETURN
*
*     End of CPTTRS
*
      END