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SUBROUTINE DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
*
* -- LAPACK auxiliary 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 ITRANS, LDB, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
* Purpose
* =======
*
* DGTTS2 solves one of the systems of equations
* A*X = B or A'*X = B,
* with a tridiagonal matrix A using the LU factorization computed
* by DGTTRF.
*
* Arguments
* =========
*
* ITRANS (input) INTEGER
* Specifies the form of the system of equations.
* = 0: A * X = B (No transpose)
* = 1: A'* X = B (Transpose)
* = 2: A'* X = B (Conjugate transpose = Transpose)
*
* N (input) INTEGER
* The order of the matrix A.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrix B. NRHS >= 0.
*
* DL (input) DOUBLE PRECISION array, dimension (N-1)
* The (n-1) multipliers that define the matrix L from the
* LU factorization of A.
*
* D (input) DOUBLE PRECISION array, dimension (N)
* The n diagonal elements of the upper triangular matrix U from
* the LU factorization of A.
*
* DU (input) DOUBLE PRECISION array, dimension (N-1)
* The (n-1) elements of the first super-diagonal of U.
*
* DU2 (input) DOUBLE PRECISION array, dimension (N-2)
* The (n-2) elements of the second super-diagonal of U.
*
* IPIV (input) 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.
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
* On entry, the matrix of right hand side vectors B.
* On exit, B is overwritten by the solution vectors X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, IP, J
DOUBLE PRECISION TEMP
* ..
* .. 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
IP = IPIV( I )
TEMP = B( I+1-IP+I, J ) - DL( I )*B( IP, J )
B( I, J ) = B( IP, J )
B( I+1, J ) = TEMP
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
*
* Solve A' * X = B.
*
IF( NRHS.LE.1 ) THEN
*
* Solve U'*x = b.
*
J = 1
70 CONTINUE
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'*x = b.
*
DO 90 I = N - 1, 1, -1
IP = IPIV( I )
TEMP = B( I, J ) - DL( I )*B( I+1, J )
B( I, J ) = B( IP, J )
B( IP, J ) = TEMP
90 CONTINUE
IF( J.LT.NRHS ) THEN
J = J + 1
GO TO 70
END IF
*
ELSE
DO 120 J = 1, NRHS
*
* Solve U'*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
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
END IF
*
* End of DGTTS2
*
END
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