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SUBROUTINE <a name="ZGBTF2.1"></a><a href="zgbtf2.f.html#ZGBTF2.1">ZGBTF2</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( * )
COMPLEX*16 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="ZGBTF2.18"></a><a href="zgbtf2.f.html#ZGBTF2.1">ZGBTF2</a> computes an LU factorization of a complex m-by-n band matrix
</span><span class="comment">*</span><span class="comment"> A 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 unblocked version of the algorithm, calling Level 2 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) COMPLEX*16 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
</span><span class="comment">*</span><span class="comment"> 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> COMPLEX*16 ONE, ZERO
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
$ ZERO = ( 0.0D+0, 0.0D+0 ) )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER I, J, JP, JU, KM, KV
<span class="comment">*</span><span class="comment"> ..
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