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SUBROUTINE <a name="DGBEQU.1"></a><a href="dgbequ.f.html#DGBEQU.1">DGBEQU</a>( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
$ AMAX, 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
DOUBLE PRECISION AMAX, COLCND, ROWCND
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
<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="DGBEQU.19"></a><a href="dgbequ.f.html#DGBEQU.1">DGBEQU</a> computes row and column scalings intended to equilibrate an
</span><span class="comment">*</span><span class="comment"> M-by-N band matrix A and reduce its condition number. R returns the
</span><span class="comment">*</span><span class="comment"> row scale factors and C the column scale factors, chosen to try to
</span><span class="comment">*</span><span class="comment"> make the largest element in each row and column of the matrix B with
</span><span class="comment">*</span><span class="comment"> elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> R(i) and C(j) are restricted to be between SMLNUM = smallest safe
</span><span class="comment">*</span><span class="comment"> number and BIGNUM = largest safe number. Use of these scaling
</span><span class="comment">*</span><span class="comment"> factors is not guaranteed to reduce the condition number of A but
</span><span class="comment">*</span><span class="comment"> works well in practice.
</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) DOUBLE PRECISION array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment"> The band matrix A, stored in rows 1 to KL+KU+1. The j-th
</span><span class="comment">*</span><span class="comment"> column of A is stored in the j-th column of the array AB as
</span><span class="comment">*</span><span class="comment"> follows:
</span><span class="comment">*</span><span class="comment"> AB(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"> LDAB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AB. LDAB >= KL+KU+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> R (output) DOUBLE PRECISION array, dimension (M)
</span><span class="comment">*</span><span class="comment"> If INFO = 0, or INFO > M, R contains the row scale factors
</span><span class="comment">*</span><span class="comment"> for A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C (output) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment"> If INFO = 0, C contains the column scale factors for A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ROWCND (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> If INFO = 0 or INFO > M, ROWCND contains the ratio of the
</span><span class="comment">*</span><span class="comment"> smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
</span><span class="comment">*</span><span class="comment"> AMAX is neither too large nor too small, it is not worth
</span><span class="comment">*</span><span class="comment"> scaling by R.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> COLCND (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> If INFO = 0, COLCND contains the ratio of the smallest
</span><span class="comment">*</span><span class="comment"> C(i) to the largest C(i). If COLCND >= 0.1, it is not
</span><span class="comment">*</span><span class="comment"> worth scaling by C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AMAX (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> Absolute value of largest matrix element. If AMAX is very
</span><span class="comment">*</span><span class="comment"> close to overflow or very close to underflow, the matrix
</span><span class="comment">*</span><span class="comment"> should be scaled.
</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, and i is
</span><span class="comment">*</span><span class="comment"> <= M: the i-th row of A is exactly zero
</span><span class="comment">*</span><span class="comment"> > M: the (i-M)-th column of A is exactly zero
</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 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER I, J, KD
DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> DOUBLE PRECISION <a name="DLAMCH.95"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
EXTERNAL <a name="DLAMCH.96"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="XERBLA.99"></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 ABS, 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"> 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
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