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SUBROUTINE ZPTTS2( IUPLO, 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 IUPLO, LDB, N, NRHS
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * )
COMPLEX*16 B( LDB, * ), E( * )
* ..
*
* Purpose
* =======
*
* ZPTTS2 solves a tridiagonal system of the form
* A * X = B
* using the factorization A = U'*D*U or A = L*D*L' 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.
*
* Arguments
* =========
*
* IUPLO (input) 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'*D*U, E is the superdiagonal of U
* = 0: A = L*D*L', E is the subdiagonal of L
*
* 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) DOUBLE PRECISION array, dimension (N)
* The n diagonal elements of the diagonal matrix D from the
* factorization A = U'*D*U or A = L*D*L'.
*
* E (input) 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'*D*U.
* If IUPLO = 0, the (n-1) subdiagonal elements of the unit
* bidiagonal factor L from the factorization A = L*D*L'.
*
* B (input/output) DOUBLE PRECISION 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 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'*D*U,
* overwriting each right hand side vector with its solution.
*
IF( NRHS.LE.2 ) THEN
J = 1
10 CONTINUE
*
* Solve U' * 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' * 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',
* 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' * 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' * 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
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