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|
*> \brief \b CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CGTTS2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgtts2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgtts2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgtts2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
*
* .. Scalar Arguments ..
* INTEGER ITRANS, LDB, N, NRHS
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CGTTS2 solves one of the systems of equations
*> A * X = B, A**T * X = B, or A**H * X = B,
*> with a tridiagonal matrix A using the LU factorization computed
*> by CGTTRF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] ITRANS
*> \verbatim
*> ITRANS is INTEGER
*> Specifies the form of the system of equations.
*> = 0: A * X = B (No transpose)
*> = 1: A**T * X = B (Transpose)
*> = 2: A**H * X = B (Conjugate transpose)
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A.
*> \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] DL
*> \verbatim
*> DL is COMPLEX array, dimension (N-1)
*> The (n-1) multipliers that define the matrix L from the
*> LU factorization of A.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is COMPLEX array, dimension (N)
*> The n diagonal elements of the upper triangular matrix U from
*> the LU factorization of A.
*> \endverbatim
*>
*> \param[in] DU
*> \verbatim
*> DU is COMPLEX array, dimension (N-1)
*> The (n-1) elements of the first super-diagonal of U.
*> \endverbatim
*>
*> \param[in] DU2
*> \verbatim
*> DU2 is COMPLEX array, dimension (N-2)
*> The (n-2) elements of the second super-diagonal of U.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices; for 1 <= i <= n, row i of the matrix was
*> interchanged with row IPIV(i). IPIV(i) will always be either
*> i or i+1; IPIV(i) = i indicates a row interchange was not
*> required.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX array, dimension (LDB,NRHS)
*> On entry, the matrix of right hand side vectors B.
*> On exit, B is overwritten by 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 December 2016
*
*> \ingroup complexGTcomputational
*
* =====================================================================
SUBROUTINE CGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, 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..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER ITRANS, LDB, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, J
COMPLEX TEMP
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 )
$ RETURN
*
IF( ITRANS.EQ.0 ) THEN
*
* Solve A*X = B using the LU factorization of A,
* overwriting each right hand side vector with its solution.
*
IF( NRHS.LE.1 ) THEN
J = 1
10 CONTINUE
*
* Solve L*x = b.
*
DO 20 I = 1, N - 1
IF( IPIV( I ).EQ.I ) THEN
B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
ELSE
TEMP = B( I, J )
B( I, J ) = B( I+1, J )
B( I+1, J ) = TEMP - DL( I )*B( I, J )
END IF
20 CONTINUE
*
* Solve U*x = b.
*
B( N, J ) = B( N, J ) / D( N )
IF( N.GT.1 )
$ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
$ D( N-1 )
DO 30 I = N - 2, 1, -1
B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
$ B( I+2, J ) ) / D( I )
30 CONTINUE
IF( J.LT.NRHS ) THEN
J = J + 1
GO TO 10
END IF
ELSE
DO 60 J = 1, NRHS
*
* Solve L*x = b.
*
DO 40 I = 1, N - 1
IF( IPIV( I ).EQ.I ) THEN
B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
ELSE
TEMP = B( I, J )
B( I, J ) = B( I+1, J )
B( I+1, J ) = TEMP - DL( I )*B( I, J )
END IF
40 CONTINUE
*
* Solve U*x = b.
*
B( N, J ) = B( N, J ) / D( N )
IF( N.GT.1 )
$ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
$ D( N-1 )
DO 50 I = N - 2, 1, -1
B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
$ B( I+2, J ) ) / D( I )
50 CONTINUE
60 CONTINUE
END IF
ELSE IF( ITRANS.EQ.1 ) THEN
*
* Solve A**T * X = B.
*
IF( NRHS.LE.1 ) THEN
J = 1
70 CONTINUE
*
* Solve U**T * x = b.
*
B( 1, J ) = B( 1, J ) / D( 1 )
IF( N.GT.1 )
$ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
DO 80 I = 3, N
B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )*
$ B( I-2, J ) ) / D( I )
80 CONTINUE
*
* Solve L**T * x = b.
*
DO 90 I = N - 1, 1, -1
IF( IPIV( I ).EQ.I ) THEN
B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
ELSE
TEMP = B( I+1, J )
B( I+1, J ) = B( I, J ) - DL( I )*TEMP
B( I, J ) = TEMP
END IF
90 CONTINUE
IF( J.LT.NRHS ) THEN
J = J + 1
GO TO 70
END IF
ELSE
DO 120 J = 1, NRHS
*
* Solve U**T * x = b.
*
B( 1, J ) = B( 1, J ) / D( 1 )
IF( N.GT.1 )
$ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
DO 100 I = 3, N
B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-
$ DU2( I-2 )*B( I-2, J ) ) / D( I )
100 CONTINUE
*
* Solve L**T * x = b.
*
DO 110 I = N - 1, 1, -1
IF( IPIV( I ).EQ.I ) THEN
B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
ELSE
TEMP = B( I+1, J )
B( I+1, J ) = B( I, J ) - DL( I )*TEMP
B( I, J ) = TEMP
END IF
110 CONTINUE
120 CONTINUE
END IF
ELSE
*
* Solve A**H * X = B.
*
IF( NRHS.LE.1 ) THEN
J = 1
130 CONTINUE
*
* Solve U**H * x = b.
*
B( 1, J ) = B( 1, J ) / CONJG( D( 1 ) )
IF( N.GT.1 )
$ B( 2, J ) = ( B( 2, J )-CONJG( DU( 1 ) )*B( 1, J ) ) /
$ CONJG( D( 2 ) )
DO 140 I = 3, N
B( I, J ) = ( B( I, J )-CONJG( DU( I-1 ) )*B( I-1, J )-
$ CONJG( DU2( I-2 ) )*B( I-2, J ) ) /
$ CONJG( D( I ) )
140 CONTINUE
*
* Solve L**H * x = b.
*
DO 150 I = N - 1, 1, -1
IF( IPIV( I ).EQ.I ) THEN
B( I, J ) = B( I, J ) - CONJG( DL( I ) )*B( I+1, J )
ELSE
TEMP = B( I+1, J )
B( I+1, J ) = B( I, J ) - CONJG( DL( I ) )*TEMP
B( I, J ) = TEMP
END IF
150 CONTINUE
IF( J.LT.NRHS ) THEN
J = J + 1
GO TO 130
END IF
ELSE
DO 180 J = 1, NRHS
*
* Solve U**H * x = b.
*
B( 1, J ) = B( 1, J ) / CONJG( D( 1 ) )
IF( N.GT.1 )
$ B( 2, J ) = ( B( 2, J )-CONJG( DU( 1 ) )*B( 1, J ) ) /
$ CONJG( D( 2 ) )
DO 160 I = 3, N
B( I, J ) = ( B( I, J )-CONJG( DU( I-1 ) )*
$ B( I-1, J )-CONJG( DU2( I-2 ) )*
$ B( I-2, J ) ) / CONJG( D( I ) )
160 CONTINUE
*
* Solve L**H * x = b.
*
DO 170 I = N - 1, 1, -1
IF( IPIV( I ).EQ.I ) THEN
B( I, J ) = B( I, J ) - CONJG( DL( I ) )*
$ B( I+1, J )
ELSE
TEMP = B( I+1, J )
B( I+1, J ) = B( I, J ) - CONJG( DL( I ) )*TEMP
B( I, J ) = TEMP
END IF
170 CONTINUE
180 CONTINUE
END IF
END IF
*
* End of CGTTS2
*
END
|
