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## cpbsv()

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

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

Download CPBSV + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> CPBSV 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

  [in]

  UPLO

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

  [in]

  N

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

  [in]

  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.
      !>

  [in]

  NRHS

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

  [in,out]

  AB

      !>          AB is COMPLEX 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.
      !>

  [in]

  LDAB

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

  [in,out]

  B

      !>          B is COMPLEX 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.
      !>

  [in]

  LDB

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

  [out]

  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.
      !>