SUBROUTINE ZDTTRSV( UPLO, TRANS, N, NRHS, DL, D, DU, $ B, LDB, INFO ) * * Written by Andrew J. Cleary, University of Tennessee. * August, 1996. * Modified from ZGTTRS: * -- LAPACK routine (preliminary version) -- * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., * Courant Institute, Argonne National Lab, and Rice University * * .. Scalar Arguments .. CHARACTER UPLO, TRANS INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ) * .. * * Purpose * ======= * * ZDTTRSV solves one of the systems of equations * L * X = B, L**T * X = B, or L**H * X = B, * U * X = B, U**T * X = B, or U**H * X = B, * with factors of the tridiagonal matrix A from the LU factorization * computed by ZDTTRF. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * Specifies whether to solve with L or U. * * TRANS (input) CHARACTER * Specifies the form of the system of equations: * = 'N': A * X = B (No transpose) * = 'T': A**T * X = B (Transpose) * = 'C': A**H * X = B (Conjugate transpose) * * 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) COMPLEX array, dimension (N-1) * The (n-1) multipliers that define the matrix L from the * LU factorization of A. * * D (input) COMPLEX array, dimension (N) * The n diagonal elements of the upper triangular matrix U from * the LU factorization of A. * * DU (input) COMPLEX array, dimension (N-1) * The (n-1) elements of the first superdiagonal of U. * * B (input/output) COMPLEX array, dimension (LDB,NRHS) * On entry, the right hand side matrix B. * On exit, B is overwritten by the 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 * * ===================================================================== * * .. Local Scalars .. LOGICAL LOWER, NOTRAN INTEGER I, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG, MAX * .. * .. Executable Statements .. * INFO = 0 NOTRAN = LSAME( TRANS, 'N' ) LOWER = LSAME( UPLO, 'L' ) IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. $ LSAME( TRANS, 'C' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( NRHS.LT.0 ) THEN INFO = -4 ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN INFO = -9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZDTTRSV', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) $ RETURN * IF( NOTRAN ) THEN * IF( LOWER ) THEN * Solve L*X = B, overwriting B with X. * DO 35 J = 1, NRHS * * Solve L*x = b. * DO 10 I = 1, N - 1 B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J ) 10 CONTINUE 35 CONTINUE * ELSE * Solve U*x = b. * DO 30 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 20 I = N - 2, 1, -1 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J ) ) / D( I ) 20 CONTINUE 30 CONTINUE * ENDIF * ELSE IF( LSAME( TRANS, 'T' ) ) THEN * IF( .NOT. LOWER ) THEN * Solve U**T * X = B, overwriting B with X. * DO 65 J = 1, NRHS * * Solve U**T * 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 40 I = 3, N B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J ) ) / D( I ) 40 CONTINUE 65 CONTINUE * ELSE * * Solve L**T * X = B, overwriting B with X. DO 60 J = 1, NRHS * * Solve L**T * x = b. * DO 50 I = N - 1, 1, -1 B( I, J ) = B( I, J ) - DL( I )*B( I+1, J ) 50 CONTINUE 60 CONTINUE ENDIF ELSE * IF( .NOT. LOWER ) THEN * Solve U**H * X = B, overwriting B with X. * DO 95 J = 1, NRHS * * Solve U**H * x = b. * B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) ) IF( N.GT.1 ) $ B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) ) / $ DCONJG( D( 2 ) ) DO 70 I = 3, N B( I, J ) = ( B( I, J ) $ -DCONJG( DU( I-1 ) )*B( I-1, J ) ) / $ DCONJG( D( I ) ) 70 CONTINUE 95 CONTINUE * ELSE * * Solve L**H * X = B, overwriting B with X. DO 90 J = 1, NRHS * * Solve L**H * x = b. * DO 80 I = N - 1, 1, -1 B( I, J ) = B( I, J ) - DCONJG( DL( I ) )*B( I+1, J ) 80 CONTINUE 90 CONTINUE ENDIF END IF * * End of ZDTTRSV * END