sgbsv.f

          SUBROUTINE SGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          REAL               AB( LDAB, * ), B( LDB, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SGBSV computes the solution to a real system of linear equations
    *  A * X = B, where A is a band matrix of order N with KL subdiagonals
    *  and KU superdiagonals, and X and B are N-by-NRHS matrices.
    *
    *  The LU decomposition with partial pivoting and row interchanges is
    *  used to factor A as A = L * U, where L is a product of permutation
    *  and unit lower triangular matrices with KL subdiagonals, and U is
    *  upper triangular with KL+KU superdiagonals.  The factored form of A
    *  is then used to solve the system of equations A * X = B.
    *
    *  Arguments
    *  =========
    *
    *  N       (input) INTEGER
    *          The number of linear equations, i.e., 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/output) REAL array, dimension (LDAB,N)
    *          On entry, the matrix A in band storage, in rows KL+1 to
    *          2*KL+KU+1; rows 1 to KL of the array need not be set.
    *          The j-th column of A is stored in the j-th column of the
    *          array AB as follows:
    *          AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
    *          On exit, details of the factorization: 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.
    *          See below for further details.
    *
    *  LDAB    (input) INTEGER
    *          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    *
    *  IPIV    (output) INTEGER array, dimension (N)
    *          The pivot indices that define the permutation matrix P;
    *          row i of the matrix was interchanged with row IPIV(i).
    *
    *  B       (input/output) REAL 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.  The factorization
    *                has been completed, but the factor U is exactly
    *                singular, and the solution has not been computed.
    *
    *  Further Details
    *  ===============
    *
    *  The band storage scheme is illustrated by the following example, when
    *  M = N = 6, KL = 2, KU = 1:
    *
    *  On entry:                       On exit:
    *
    *      *    *    *    +    +    +       *    *    *   u14  u25  u36
    *      *    *    +    +    +    +       *    *   u13  u24  u35  u46
    *      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
    *     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
    *     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
    *     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
    *
    *  Array elements marked * are not used by the routine; elements marked
    *  + need not be set on entry, but are required by the routine to store
    *  elements of U because of fill-in resulting from the row interchanges.
    *
    *  =====================================================================
    *
    *     .. External Subroutines ..
          EXTERNAL           SGBTRF, SGBTRS, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          IF( N.LT.0 ) THEN
             INFO = -1
          ELSE IF( KL.LT.0 ) THEN
             INFO = -2
          ELSE IF( KU.LT.0 ) THEN
             INFO = -3
          ELSE IF( NRHS.LT.0 ) THEN
             INFO = -4
          ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
             INFO = -6
          ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
             INFO = -9
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'SGBSV ', -INFO )
             RETURN
          END IF
    *
    *     Compute the LU factorization of the band matrix A.
    *
          CALL SGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO )
          IF( INFO.EQ.0 ) THEN
    *
    *        Solve the system A*X = B, overwriting B with X.
    *
             CALL SGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV,
         $                B, LDB, INFO )
          END IF
          RETURN
    *
    *     End of SGBSV
    *
          END