SUBROUTINE CGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, $ INFO ) * * -- LAPACK routine (version 2.0) -- * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., * Courant Institute, Argonne National Lab, and Rice University * September 30, 1994 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) * .. * * Purpose * ======= * * CGTTRS solves one of the systems of equations * A * X = B, A**T * X = B, or A**H * X = B, * with a tridiagonal matrix A using the LU factorization computed * by CGTTRF. * * Arguments * ========= * * 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. * * DU2 (input) COMPLEX array, dimension (N-2) * The (n-2) elements of the second superdiagonal 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) 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 NOTRAN INTEGER I, J COMPLEX TEMP * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG, MAX * .. * .. Executable Statements .. * INFO = 0 NOTRAN = LSAME( TRANS, 'N' ) IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. $ LSAME( TRANS, 'C' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( NRHS.LT.0 ) THEN INFO = -3 ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CGTTRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) $ RETURN * IF( NOTRAN ) THEN * * Solve A*X = B using the LU factorization of A, * overwriting each right hand side vector with its solution. * DO 30 J = 1, NRHS * * Solve L*x = b. * DO 10 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 10 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 20 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 ) 20 CONTINUE 30 CONTINUE ELSE IF( LSAME( TRANS, 'T' ) ) THEN * * Solve A**T * X = B. * DO 60 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 )-DU2( I-2 )* $ B( I-2, J ) ) / D( I ) 40 CONTINUE * * Solve L**T * x = b. * DO 50 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 50 CONTINUE 60 CONTINUE ELSE * * Solve A**H * X = B. * DO 90 J = 1, NRHS * * Solve U**H * x = b. * B( 1, J ) = B( 1, J ) / CONJG( D( 1 ) ) IF( N.GT.1 ) $ B( 2, J ) = ( B( 2, J )-CONJG( DU( 1 ) )*B( 1, J ) ) / $ CONJG( D( 2 ) ) DO 70 I = 3, N B( I, J ) = ( B( I, J )-CONJG( DU( I-1 ) )*B( I-1, J )- $ CONJG( DU2( I-2 ) )*B( I-2, J ) ) / $ CONJG( D( I ) ) 70 CONTINUE * * Solve L**H * x = b. * DO 80 I = N - 1, 1, -1 IF( IPIV( I ).EQ.I ) THEN B( I, J ) = B( I, J ) - CONJG( DL( I ) )*B( I+1, J ) ELSE TEMP = B( I+1, J ) B( I+1, J ) = B( I, J ) - CONJG( DL( I ) )*TEMP B( I, J ) = TEMP END IF 80 CONTINUE 90 CONTINUE END IF * * End of CGTTRS * END