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SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
* * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ) * .. * * 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**H *X = B may be solved by interchanging the * order of the arguments DU and DL. * * Arguments * ========= * * N (input) INTEGER * The order of the 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. * * DL (input/output) 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). * * D (input/output) 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. * * DU (input/output) 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. * * B (input/output) 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. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * INFO (output) 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. * * ===================================================================== * * .. 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 * END |