SRC/zpbsv.f(3)

NAME
SRC/zpbsv.f

SYNOPSIS

  Functions/Subroutines
subroutine zpbsv (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
ZPBSV computes the solution to system of linear equations A * X = B for OTHER matrices

Function/Subroutine Documentation

  subroutine zpbsv (character uplo, integer n, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZPBSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

     ZPBSV computes the solution to a complex system of linear equations
        A * X = B,
     where A is an N-by-N Hermitian positive definite band matrix and X
     and B are N-by-NRHS matrices.
     The Cholesky decomposition is used to factor A as
        A = U**H * U,  if UPLO = 'U', or
        A = L * L**H,  if UPLO = 'L',
     where U is an upper triangular band matrix, and L is a lower
     triangular band matrix, with the same number of superdiagonals or
     subdiagonals as A.  The factored form of A is then used to solve the
     system of equations A * X = B.

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

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

    KD

              KD is INTEGER
              The number of superdiagonals of the matrix A if UPLO = 'U',
              or the number of subdiagonals if UPLO = 'L'.  KD >= 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 upper or lower triangle of the Hermitian band
              matrix A, stored in the first KD+1 rows of the array.  The
              j-th column of A is stored in the j-th column of the array AB
              as follows:
              if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
              if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(N,j+KD).
              See below for further details.
              On exit, if INFO = 0, the triangular factor U or L from the
              Cholesky factorization A = U**H *U or A = L*L**H of the band
              matrix A, in the same storage format as A.

    LDAB

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KD+1.

    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, the leading principal minor of order i
                    of A is not positive, so the factorization could not
                    be completed, and the solution has not been computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      The band storage scheme is illustrated by the following example, when
      N = 6, KD = 2, and UPLO = 'U':
      On entry:                       On exit:
          *    *   a13  a24  a35  a46      *    *   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
      Similarly, if UPLO = 'L' the format of A is as follows:
      On entry:                       On exit:
         a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
         a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
         a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
      Array elements marked * are not used by the routine.

Definition at line 163 of file zpbsv.f.

Author

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