*> \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 *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \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. * *> \date June 2016 * *> \ingroup complex16PTcomputational * * ===================================================================== SUBROUTINE ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. 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