SUBROUTINE CGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, \$ INFO ) * * -- LAPACK routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX AB( LDAB, * ), B( LDB, * ) * .. * * Purpose * ======= * * CGBTRS solves a system of linear equations * A * X = B, A**T * X = B, or A**H * X = B * with a general band matrix A using the LU factorization computed * by CGBTRF. * * Arguments * ========= * * TRANS (input) CHARACTER*1 * 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. * * KL (input) INTEGER * The number of subdiagonals within the band of A. KL >= 0. * * KU (input) INTEGER * The number of superdiagonals within the band of A. KU >= 0. * * NRHS (input) INTEGER * The number of right hand sides, i.e., the number of columns * of the matrix B. NRHS >= 0. * * AB (input) COMPLEX array, dimension (LDAB,N) * Details of the LU factorization of the band matrix A, as * computed by CGBTRF. U is stored as an upper triangular band * matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and * the multipliers used during the factorization are stored in * rows KL+KU+2 to 2*KL+KU+1. * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= 2*KL+KU+1. * * IPIV (input) INTEGER array, dimension (N) * The pivot indices; for 1 <= i <= N, row i of the matrix was * interchanged with row IPIV(i). * * B (input/output) COMPLEX array, dimension (LDB,NRHS) * On entry, the right hand side matrix B. * On exit, 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 * * ===================================================================== * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL LNOTI, NOTRAN INTEGER I, J, KD, L, LM * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL CGEMV, CGERU, CLACGV, CSWAP, CTBSV, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * 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( KL.LT.0 ) THEN INFO = -3 ELSE IF( KU.LT.0 ) THEN INFO = -4 ELSE IF( NRHS.LT.0 ) THEN INFO = -5 ELSE IF( LDAB.LT.( 2*KL+KU+1 ) ) THEN INFO = -7 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CGBTRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) \$ RETURN * KD = KU + KL + 1 LNOTI = KL.GT.0 * IF( NOTRAN ) THEN * * Solve A*X = B. * * Solve L*X = B, overwriting B with X. * * L is represented as a product of permutations and unit lower * triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1), * where each transformation L(i) is a rank-one modification of * the identity matrix. * IF( LNOTI ) THEN DO 10 J = 1, N - 1 LM = MIN( KL, N-J ) L = IPIV( J ) IF( L.NE.J ) \$ CALL CSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB ) CALL CGERU( LM, NRHS, -ONE, AB( KD+1, J ), 1, B( J, 1 ), \$ LDB, B( J+1, 1 ), LDB ) 10 CONTINUE END IF * DO 20 I = 1, NRHS * * Solve U*X = B, overwriting B with X. * CALL CTBSV( 'Upper', 'No transpose', 'Non-unit', N, KL+KU, \$ AB, LDAB, B( 1, I ), 1 ) 20 CONTINUE * ELSE IF( LSAME( TRANS, 'T' ) ) THEN * * Solve A**T * X = B. * DO 30 I = 1, NRHS * * Solve U**T * X = B, overwriting B with X. * CALL CTBSV( 'Upper', 'Transpose', 'Non-unit', N, KL+KU, AB, \$ LDAB, B( 1, I ), 1 ) 30 CONTINUE * * Solve L**T * X = B, overwriting B with X. * IF( LNOTI ) THEN DO 40 J = N - 1, 1, -1 LM = MIN( KL, N-J ) CALL CGEMV( 'Transpose', LM, NRHS, -ONE, B( J+1, 1 ), \$ LDB, AB( KD+1, J ), 1, ONE, B( J, 1 ), LDB ) L = IPIV( J ) IF( L.NE.J ) \$ CALL CSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB ) 40 CONTINUE END IF * ELSE * * Solve A**H * X = B. * DO 50 I = 1, NRHS * * Solve U**H * X = B, overwriting B with X. * CALL CTBSV( 'Upper', 'Conjugate transpose', 'Non-unit', N, \$ KL+KU, AB, LDAB, B( 1, I ), 1 ) 50 CONTINUE * * Solve L**H * X = B, overwriting B with X. * IF( LNOTI ) THEN DO 60 J = N - 1, 1, -1 LM = MIN( KL, N-J ) CALL CLACGV( NRHS, B( J, 1 ), LDB ) CALL CGEMV( 'Conjugate transpose', LM, NRHS, -ONE, \$ B( J+1, 1 ), LDB, AB( KD+1, J ), 1, ONE, \$ B( J, 1 ), LDB ) CALL CLACGV( NRHS, B( J, 1 ), LDB ) L = IPIV( J ) IF( L.NE.J ) \$ CALL CSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB ) 60 CONTINUE END IF END IF RETURN * * End of CGBTRS * END