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SUBROUTINE SPTTS2( N, NRHS, D, E, B, LDB )
*
* -- LAPACK routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2006
*
* .. Scalar Arguments ..
INTEGER LDB, N, NRHS
* ..
* .. Array Arguments ..
REAL B( LDB, * ), D( * ), E( * )
* ..
*
* Purpose
* =======
*
* SPTTS2 solves a tridiagonal system of the form
* A * X = B
* using the L*D*L**T factorization of A computed by SPTTRF. D is a
* diagonal matrix specified in the vector D, L is a unit bidiagonal
* matrix whose subdiagonal is specified in the vector E, and X and B
* are N by NRHS matrices.
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the tridiagonal matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrix B. NRHS >= 0.
*
* D (input) REAL array, dimension (N)
* The n diagonal elements of the diagonal matrix D from the
* L*D*L**T factorization of A.
*
* E (input) REAL array, dimension (N-1)
* The (n-1) subdiagonal elements of the unit bidiagonal factor
* L from the L*D*L**T factorization of A. E can also be regarded
* as the superdiagonal of the unit bidiagonal factor U from the
* factorization A = U**T*D*U.
*
* B (input/output) REAL array, dimension (LDB,NRHS)
* On entry, the right hand side vectors B for the system of
* linear equations.
* On exit, the solution vectors, X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, J
* ..
* .. External Subroutines ..
EXTERNAL SSCAL
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.1 ) THEN
IF( N.EQ.1 )
$ CALL SSCAL( NRHS, 1. / D( 1 ), B, LDB )
RETURN
END IF
*
* Solve A * X = B using the factorization A = L*D*L**T,
* overwriting each right hand side vector with its solution.
*
DO 30 J = 1, NRHS
*
* Solve L * x = b.
*
DO 10 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
10 CONTINUE
*
* Solve D * L**T * x = b.
*
B( N, J ) = B( N, J ) / D( N )
DO 20 I = N - 1, 1, -1
B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
20 CONTINUE
30 CONTINUE
*
RETURN
*
* End of SPTTS2
*
END
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