SUBROUTINE CGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB ) * * -- LAPACK auxiliary routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER ITRANS, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) * .. * * Purpose * ======= * * CGTTS2 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 * ========= * * ITRANS (input) INTEGER * Specifies the form of the system of equations. * = 0: A * X = B (No transpose) * = 1: A**T * X = B (Transpose) * = 2: A**H * X = B (Conjugate 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) 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 super-diagonal of U. * * DU2 (input) COMPLEX 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) COMPLEX 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, J COMPLEX TEMP * .. * .. Intrinsic Functions .. INTRINSIC CONJG * .. * .. 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 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 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 IF( ITRANS.EQ.1 ) THEN * * Solve A**T * X = B. * IF( NRHS.LE.1 ) THEN J = 1 70 CONTINUE * * 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 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**T * x = b. * DO 90 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 90 CONTINUE IF( J.LT.NRHS ) THEN J = J + 1 GO TO 70 END IF ELSE DO 120 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 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 * * Solve L**T * x = b. * 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 ELSE * * Solve A**H * X = B. * IF( NRHS.LE.1 ) THEN J = 1 130 CONTINUE * * 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 140 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 ) ) 140 CONTINUE * * Solve L**H * x = b. * DO 150 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 150 CONTINUE IF( J.LT.NRHS ) THEN J = J + 1 GO TO 130 END IF ELSE DO 180 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 160 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 ) ) 160 CONTINUE * * Solve L**H * x = b. * DO 170 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 170 CONTINUE 180 CONTINUE END IF END IF * * End of CGTTS2 * END