sptts2()

subroutine sptts2	(	integer	n,
		integer	nrhs,
		real, dimension( * )	d,
		real, dimension( * )	e,
		real, dimension( ldb, * )	b,
		integer	ldb
	)

SPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.

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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.

Parameters

[in]	N	N is INTEGER The order of the tridiagonal matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	D	D is REAL array, dimension (N) The n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A.
[in]	E	E is 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.
[in,out]	B	B is 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.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 101 of file sptts2.f.

*
*  -- 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            LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      REAL               B( LDB, * ), D( * ), E( * )
*     ..
*
*  =====================================================================
*
*     .. 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
*

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