SGBTF2 computes an LU factorization of a real m-by-n band matrix A


 using partial pivoting with row interchanges.


 This is the unblocked version of the algorithm, calling Level 2 BLAS.

M

          M is INTEGER


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

N

          N is INTEGER


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

KL

          KL is INTEGER


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

KU

          KU is INTEGER


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

AB

          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 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

          LDAB is INTEGER


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

IPIV

          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

          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.

December 2016

  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.