GBTRF - 5.2 English - 68552

GBTRF computes the LU factorization of a general band matrix using the pivot

Purpose:

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

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

Parameters:

• M – [in]

  M is INTEGER

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

• N – [in]

  N is INTEGER

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

• KL – [in]

  KL is INTEGER

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

• KU – [in]

  KU is INTEGER

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

• AB – [inout]

  AB is REAL 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 fla_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 – [in]

  LDAB is INTEGER

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

• IPIV – [in]

  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 – [out]

  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.