zgbtrf.f (3) - Linux Manuals


zgbtrf.f -



subroutine zgbtrf (M, N, KL, KU, AB, LDAB, IPIV, INFO)

Function/Subroutine Documentation

subroutine zgbtrf (integerM, integerN, integerKL, integerKU, complex*16, dimension( ldab, * )AB, integerLDAB, integer, dimension( * )IPIV, integerINFO)



 ZGBTRF computes an LU factorization of a complex m-by-n band matrix A
 using partial pivoting with row interchanges.

 This is the blocked version of the algorithm, calling Level 3 BLAS.




          M is INTEGER
          The number of rows of the matrix A.  M >= 0.


          N is INTEGER
          The number of columns of the matrix A.  N >= 0.


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


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


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


          IPIV is INTEGER array, dimension (min(M,N))
          The pivot indices; for 1 <= i <= min(M,N), row i of the
          matrix was interchanged with row IPIV(i).


          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 division by zero will occur if it is used
               to solve a system of equations.



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
  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 145 of file zgbtrf.f.


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