zpbsv.f man page

zpbsv.f —



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 (characterUPLO, integerN, integerKD, integerNRHS, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldb, * )B, integerLDB, integerINFO)

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


 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.


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


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


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


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


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


          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, the leading minor of order i of A is not
                positive definite, so the factorization could not be
                completed, and the solution has not been computed.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.


November 2011

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 165 of file zpbsv.f.


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Referenced By

zpbsv(3) is an alias of zpbsv.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK