zgbsv.f(3)

NAME
zgbsv.f -

SYNOPSIS

  Functions/Subroutines

subroutine zgbsv (N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
ZGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver)

Function/Subroutine Documentation

  subroutine zgbsv (integerN, integerKL, integerKU, integerNRHS, complex*16, dimension( ldab, * )AB, integerLDAB, integer, dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, integerINFO)

ZGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver)

Purpose:

     ZGBSV computes the solution to a complex 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.

Parameters:
    N

              N is INTEGER
              The number of linear equations, i.e., the order of the
              matrix A.  N >= 0.

    KL

              KL is INTEGER
              The number of subdiagonals within the band of A.  KL >= 0.

    KU

              KU is INTEGER
              The number of superdiagonals within the band of A.  KU >= 0.

    NRHS

              NRHS is INTEGER
              The number of right hand sides, i.e., the number of columns
              of the matrix B.  NRHS >= 0.

    AB

              AB is COMPLEX*16 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

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

    IPIV

              IPIV is 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

              B is COMPLEX*16 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

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

    INFO

              INFO is 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.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

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.

Definition at line 163 of file zgbsv.f.

Author

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