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*> \brief \b ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZPTTS2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zptts2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zptts2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zptts2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
*
* .. Scalar Arguments ..
* INTEGER IUPLO, LDB, N, NRHS
* ..
* .. Array Arguments ..
* DOUBLE PRECISION D( * )
* COMPLEX*16 B( LDB, * ), E( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZPTTS2 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 ZPTTRF.
*> 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] IUPLO
*> \verbatim
*> IUPLO is INTEGER
*> 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.
*> = 1: A = U**H *D*U, E is the superdiagonal of U
*> = 0: 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 DOUBLE PRECISION 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*16 array, dimension (N-1)
*> If IUPLO = 1, the (n-1) superdiagonal elements of the unit
*> bidiagonal factor U from the factorization A = U**H*D*U.
*> If IUPLO = 0, 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*16 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
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup ptts2
*
* =====================================================================
SUBROUTINE ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
*
* -- 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 ..
INTEGER IUPLO, LDB, N, NRHS
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * )
COMPLEX*16 B( LDB, * ), E( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, J
* ..
* .. External Subroutines ..
EXTERNAL ZDSCAL
* ..
* .. Intrinsic Functions ..
INTRINSIC DCONJG
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.1 ) THEN
IF( N.EQ.1 )
$ CALL ZDSCAL( NRHS, 1.D0 / D( 1 ), B, LDB )
RETURN
END IF
*
IF( IUPLO.EQ.1 ) THEN
*
* Solve A * X = B using the factorization A = U**H *D*U,
* overwriting each right hand side vector with its solution.
*
IF( NRHS.LE.2 ) THEN
J = 1
10 CONTINUE
*
* Solve U**H * x = b.
*
DO 20 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) )
20 CONTINUE
*
* Solve D * U * x = b.
*
DO 30 I = 1, N
B( I, J ) = B( I, J ) / D( I )
30 CONTINUE
DO 40 I = N - 1, 1, -1
B( I, J ) = B( I, J ) - B( I+1, J )*E( I )
40 CONTINUE
IF( J.LT.NRHS ) THEN
J = J + 1
GO TO 10
END IF
ELSE
DO 70 J = 1, NRHS
*
* Solve U**H * x = b.
*
DO 50 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) )
50 CONTINUE
*
* Solve D * U * x = b.
*
B( N, J ) = B( N, J ) / D( N )
DO 60 I = N - 1, 1, -1
B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
60 CONTINUE
70 CONTINUE
END IF
ELSE
*
* Solve A * X = B using the factorization A = L*D*L**H,
* overwriting each right hand side vector with its solution.
*
IF( NRHS.LE.2 ) THEN
J = 1
80 CONTINUE
*
* Solve L * x = b.
*
DO 90 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
90 CONTINUE
*
* Solve D * L**H * x = b.
*
DO 100 I = 1, N
B( I, J ) = B( I, J ) / D( I )
100 CONTINUE
DO 110 I = N - 1, 1, -1
B( I, J ) = B( I, J ) - B( I+1, J )*DCONJG( E( I ) )
110 CONTINUE
IF( J.LT.NRHS ) THEN
J = J + 1
GO TO 80
END IF
ELSE
DO 140 J = 1, NRHS
*
* Solve L * x = b.
*
DO 120 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
120 CONTINUE
*
* Solve D * L**H * x = b.
*
B( N, J ) = B( N, J ) / D( N )
DO 130 I = N - 1, 1, -1
B( I, J ) = B( I, J ) / D( I ) -
$ B( I+1, J )*DCONJG( E( I ) )
130 CONTINUE
140 CONTINUE
END IF
END IF
*
RETURN
*
* End of ZPTTS2
*
END
|
