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SUBROUTINE <a name="DGBTRF.1"></a><a href="dgbtrf.f.html#DGBTRF.1">DGBTRF</a>( M, N, KL, KU, AB, LDAB, IPIV, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> INTEGER INFO, KL, KU, LDAB, M, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IPIV( * )
DOUBLE PRECISION AB( LDAB, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DGBTRF.18"></a><a href="dgbtrf.f.html#DGBTRF.1">DGBTRF</a> computes an LU factorization of a real m-by-n band matrix A
</span><span class="comment">*</span><span class="comment"> using partial pivoting with row interchanges.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> This is the blocked version of the algorithm, calling Level 3 BLAS.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> M (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of rows of the matrix A. M >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of columns of the matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KL (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of subdiagonals within the band of A. KL >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KU (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of superdiagonals within the band of A. KU >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment"> On entry, the matrix A in band storage, in rows KL+1 to
</span><span class="comment">*</span><span class="comment"> 2*KL+KU+1; rows 1 to KL of the array need not be set.
</span><span class="comment">*</span><span class="comment"> The j-th column of A is stored in the j-th column of the
</span><span class="comment">*</span><span class="comment"> array AB as follows:
</span><span class="comment">*</span><span class="comment"> AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, details of the factorization: U is stored as an
</span><span class="comment">*</span><span class="comment"> upper triangular band matrix with KL+KU superdiagonals in
</span><span class="comment">*</span><span class="comment"> rows 1 to KL+KU+1, and the multipliers used during the
</span><span class="comment">*</span><span class="comment"> factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
</span><span class="comment">*</span><span class="comment"> See below for further details.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDAB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IPIV (output) INTEGER array, dimension (min(M,N))
</span><span class="comment">*</span><span class="comment"> The pivot indices; for 1 <= i <= min(M,N), row i of the
</span><span class="comment">*</span><span class="comment"> matrix was interchanged with row IPIV(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment"> > 0: if INFO = +i, U(i,i) is exactly zero. The factorization
</span><span class="comment">*</span><span class="comment"> has been completed, but the factor U is exactly
</span><span class="comment">*</span><span class="comment"> singular, and division by zero will occur if it is used
</span><span class="comment">*</span><span class="comment"> to solve a system of equations.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The band storage scheme is illustrated by the following example, when
</span><span class="comment">*</span><span class="comment"> M = N = 6, KL = 2, KU = 1:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On entry: On exit:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> * * * + + + * * * u14 u25 u36
</span><span class="comment">*</span><span class="comment"> * * + + + + * * u13 u24 u35 u46
</span><span class="comment">*</span><span class="comment"> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
</span><span class="comment">*</span><span class="comment"> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
</span><span class="comment">*</span><span class="comment"> a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
</span><span class="comment">*</span><span class="comment"> a31 a42 a53 a64 * * m31 m42 m53 m64 * *
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Array elements marked * are not used by the routine; elements marked
</span><span class="comment">*</span><span class="comment"> + need not be set on entry, but are required by the routine to store
</span><span class="comment">*</span><span class="comment"> elements of U because of fill-in resulting from the row interchanges.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
INTEGER NBMAX, LDWORK
PARAMETER ( NBMAX = 64, LDWORK = NBMAX+1 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER I, I2, I3, II, IP, J, J2, J3, JB, JJ, JM, JP,
$ JU, K2, KM, KV, NB, NW
DOUBLE PRECISION TEMP
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Arrays ..
</span> DOUBLE PRECISION WORK13( LDWORK, NBMAX ),
$ WORK31( LDWORK, NBMAX )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> INTEGER IDAMAX, <a name="ILAENV.103"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
EXTERNAL IDAMAX, <a name="ILAENV.104"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL DCOPY, <a name="DGBTF2.107"></a><a href="dgbtf2.f.html#DGBTF2.1">DGBTF2</a>, DGEMM, DGER, <a name="DLASWP.107"></a><a href="dlaswp.f.html#DLASWP.1">DLASWP</a>, DSCAL,
$ DSWAP, DTRSM, <a name="XERBLA.108"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX, MIN
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KV is the number of superdiagonals in the factor U, allowing for
</span><span class="comment">*</span><span class="comment"> fill-in
</span><span class="comment">*</span><span class="comment">
</span> KV = KU + KL
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span> 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 <a name="XERBLA.135"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DGBTRF.135"></a><a href="dgbtrf.f.html#DGBTRF.1">DGBTRF</a>'</span>, -INFO )
RETURN
END IF
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