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SUBROUTINE DDBTF2( M, N, KL, KU, AB, LDAB, INFO )
*
* Modified by Andrew J. Cleary in November, 96 from:
* -- LAPACK auxiliary routine (preliminary version) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* August 6, 1991
*
*
* .. Scalar Arguments ..
INTEGER INFO, KL, KU, LDAB, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AB( LDAB, * )
* ..
*
* Purpose
* =======
*
* Ddbtrf computes an LU factorization of a real m-by-n band matrix A
* without 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) DOUBLE PRECISION 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.
*
* 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:
*
* * 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 ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0 )
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER J, JP, JU, KM, KV
* ..
* .. External Functions ..
INTEGER ISAMAX
EXTERNAL ISAMAX
* ..
* .. External Subroutines ..
EXTERNAL DGER, DSCAL, DSWAP
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* KV is the number of superdiagonals in the factor U, allowing for
* fill-in.
*
KV = KU
*
* Test the input parameters.
*
INFO = 0
*ECA IF( M.LT.0 ) THEN
*ECA INFO = -1
*ECA ELSE IF( N.LT.0 ) THEN
*ECA INFO = -2
*ECA ELSE IF( KL.LT.0 ) THEN
*ECA INFO = -3
*ECA ELSE IF( KU.LT.0 ) THEN
*ECA INFO = -4
*ECA ELSE IF( LDAB.LT.KL+KV+1 ) THEN
*ECA INFO = -6
*ECA END IF
*ECA IF( INFO.NE.0 ) THEN
*ECA CALL XERBLA( 'DDBTF2', -INFO )
*ECA RETURN
*ECA END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 )
$ RETURN
*
* Gaussian elimination without partial pivoting
*
* 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 )
*
* Test for singularity. KM is the number of
* subdiagonal elements in the current column.
*
KM = MIN( KL, M-J )
JP = 1
IF( AB( KV+1, J ).NE.ZERO ) THEN
JU = MAX( JU, MIN( J+KU, N ) )
*
IF( KM.GT.0 ) THEN
*
* Compute multipliers.
*
CALL DSCAL( KM, ONE / AB( KU+1, J ), AB( KU+2, J ), 1 )
*
* Update trailing submatrix within the band.
*
IF( JU.GT.J ) THEN
CALL DGER( KM, JU-J, -ONE, AB( KU+2, J ), 1,
$ AB( KU, J+1 ), LDAB-1, AB( KU+1, J+1 ),
$ LDAB-1 )
END IF
END IF
ELSE
*
IF( INFO.EQ.0 )
$ INFO = J
END IF
40 CONTINUE
RETURN
*
* End of DDBTF2
*
END
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