zgbtf2.f

          SUBROUTINE ZGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, KL, KU, LDAB, M, N
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX*16         AB( LDAB, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZGBTF2 computes an LU factorization of a complex m-by-n band matrix
    *  A using partial pivoting with row interchanges.
    *
    *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
    *
    *  Arguments
    *  =========
    *
    *  M       (input) INTEGER
    *          The number of rows of the matrix A.  M >= 0.
    *
    *  N       (input) INTEGER
    *          The number of columns of the matrix A.  N >= 0.
    *
    *  KL      (input) INTEGER
    *          The number of subdiagonals within the band of A.  KL >= 0.
    *
    *  KU      (input) INTEGER
    *          The number of superdiagonals within the band of A.  KU >= 0.
    *
    *  AB      (input/output) 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    (input) INTEGER
    *          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    *
    *  IPIV    (output) 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    (output) 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.
    *
    *  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.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX*16         ONE, ZERO
          PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
         $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, J, JP, JU, KM, KV
    *     ..
    *     .. External Functions ..
          INTEGER            IZAMAX
          EXTERNAL           IZAMAX
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZGERU, ZSCAL, ZSWAP
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN
    *     ..
    *     .. Executable Statements ..
    *
    *     KV is the number of superdiagonals in the factor U, allowing for
    *     fill-in.
    *
          KV = KU + KL
    *
    *     Test the input parameters.
    *
          INFO = 0
          IF( M.LT.0 ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( KL.LT.0 ) THEN
             INFO = -3
          ELSE IF( KU.LT.0 ) THEN
             INFO = -4
          ELSE IF( LDAB.LT.KL+KV+1 ) THEN
             INFO = -6
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZGBTF2', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( M.EQ.0 .OR. N.EQ.0 )
         $   RETURN
    *
    *     Gaussian elimination with partial pivoting
    *
    *     Set fill-in elements in columns KU+2 to KV to zero.
    *
          DO 20 J = KU + 2, MIN( KV, N )
             DO 10 I = KV - J + 2, KL
                AB( I, J ) = ZERO
       10    CONTINUE
       20 CONTINUE
    *
    *     JU is the index of the last column affected by the current stage
    *     of the factorization.
    *
          JU = 1
    *
          DO 40 J = 1, MIN( M, N )
    *
    *        Set fill-in elements in column J+KV to zero.
    *
             IF( J+KV.LE.N ) THEN
                DO 30 I = 1, KL
                   AB( I, J+KV ) = ZERO
       30       CONTINUE
             END IF
    *
    *        Find pivot and test for singularity. KM is the number of
    *        subdiagonal elements in the current column.
    *
             KM = MIN( KL, M-J )
             JP = IZAMAX( KM+1, AB( KV+1, J ), 1 )
             IPIV( J ) = JP + J - 1
             IF( AB( KV+JP, J ).NE.ZERO ) THEN
                JU = MAX( JU, MIN( J+KU+JP-1, N ) )
    *
    *           Apply interchange to columns J to JU.
    *
                IF( JP.NE.1 )
         $         CALL ZSWAP( JU-J+1, AB( KV+JP, J ), LDAB-1,
         $                     AB( KV+1, J ), LDAB-1 )
                IF( KM.GT.0 ) THEN
    *
    *              Compute multipliers.
    *
                   CALL ZSCAL( KM, ONE / AB( KV+1, J ), AB( KV+2, J ), 1 )
    *
    *              Update trailing submatrix within the band.
    *
                   IF( JU.GT.J )
         $            CALL ZGERU( KM, JU-J, -ONE, AB( KV+2, J ), 1,
         $                        AB( KV, J+1 ), LDAB-1, AB( KV+1, J+1 ),
         $                        LDAB-1 )
                END IF
             ELSE
    *
    *           If pivot is zero, set INFO to the index of the pivot
    *           unless a zero pivot has already been found.
    *
                IF( INFO.EQ.0 )
         $         INFO = J
             END IF
       40 CONTINUE
          RETURN
    *
    *     End of ZGBTF2
    *
          END