zgtsv()

subroutine zgtsv	(	integer	n,
		integer	nrhs,
		complex*16, dimension( * )	dl,
		complex*16, dimension( * )	d,
		complex*16, dimension( * )	du,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		integer	info
	)

ZGTSV computes the solution to system of linear equations A * X = B for GT matrices

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Purpose:

 ZGTSV  solves the equation

    A*X = B,

 where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
 partial pivoting.

 Note that the equation  A**T *X = B  may be solved by interchanging the
 order of the arguments DU and DL.

Parameters

[in]	N	N is INTEGER The order of the 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,out]	DL	DL is COMPLEX*16 array, dimension (N-1) On entry, DL must contain the (n-1) subdiagonal elements of A. On exit, DL is overwritten by the (n-2) elements of the second superdiagonal of the upper triangular matrix U from the LU factorization of A, in DL(1), ..., DL(n-2).
[in,out]	D	D is COMPLEX*16 array, dimension (N) On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of U.
[in,out]	DU	DU is COMPLEX*16 array, dimension (N-1) On entry, DU must contain the (n-1) superdiagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first superdiagonal of U.
[in,out]	B	B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = N.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 123 of file zgtsv.f.

*
*  -- LAPACK driver 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            INFO, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      COMPLEX*16         B( LDB, * ), D( * ), DL( * ), DU( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      parameter( zero = ( 0.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            J, K
      COMPLEX*16         MULT, TEMP, ZDUM
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, dble, dimag, max
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla
*     ..
*     .. Statement Functions ..
      DOUBLE PRECISION   CABS1
*     ..
*     .. Statement Function definitions ..
      cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
*     ..
*     .. Executable Statements ..
*
      info = 0
      IF( n.LT.0 ) THEN
         info = -1
      ELSE IF( nrhs.LT.0 ) THEN
         info = -2
      ELSE IF( ldb.LT.max( 1, n ) ) THEN
         info = -7
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZGTSV ', -info )
         RETURN
      END IF
*
      IF( n.EQ.0 )
     $   RETURN
*
      DO 30 k = 1, n - 1
         IF( dl( k ).EQ.zero ) THEN
*
*           Subdiagonal is zero, no elimination is required.
*
            IF( d( k ).EQ.zero ) THEN
*
*              Diagonal is zero: set INFO = K and return; a unique
*              solution can not be found.
*
               info = k
               RETURN
            END IF
         ELSE IF( cabs1( d( k ) ).GE.cabs1( dl( k ) ) ) THEN
*
*           No row interchange required
*
            mult = dl( k ) / d( k )
            d( k+1 ) = d( k+1 ) - mult*du( k )
            DO 10 j = 1, nrhs
               b( k+1, j ) = b( k+1, j ) - mult*b( k, j )
   10       CONTINUE
            IF( k.LT.( n-1 ) )
     $         dl( k ) = zero
         ELSE
*
*           Interchange rows K and K+1
*
            mult = d( k ) / dl( k )
            d( k ) = dl( k )
            temp = d( k+1 )
            d( k+1 ) = du( k ) - mult*temp
            IF( k.LT.( n-1 ) ) THEN
               dl( k ) = du( k+1 )
               du( k+1 ) = -mult*dl( k )
            END IF
            du( k ) = temp
            DO 20 j = 1, nrhs
               temp = b( k, j )
               b( k, j ) = b( k+1, j )
               b( k+1, j ) = temp - mult*b( k+1, j )
   20       CONTINUE
         END IF
   30 CONTINUE
      IF( d( n ).EQ.zero ) THEN
         info = n
         RETURN
      END IF
*
*     Back solve with the matrix U from the factorization.
*
      DO 50 j = 1, nrhs
         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 40 k = n - 2, 1, -1
            b( k, j ) = ( b( k, j )-du( k )*b( k+1, j )-dl( k )*
     $                  b( k+2, j ) ) / d( k )
   40    CONTINUE
   50 CONTINUE
*
      RETURN
*
*     End of ZGTSV
*

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