LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ slaqsb()

 subroutine slaqsb ( character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real amax, character equed )

SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:
``` SLAQSB equilibrates a symmetric band matrix A using the scaling
factors in the vector S.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] KD ``` KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.``` [in,out] AB ``` AB is REAL array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, in the same storage format as A.``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.``` [in] S ``` S is REAL array, dimension (N) The scale factors for A.``` [in] SCOND ``` SCOND is REAL Ratio of the smallest S(i) to the largest S(i).``` [in] AMAX ``` AMAX is REAL Absolute value of largest matrix entry.``` [out] EQUED ``` EQUED is CHARACTER*1 Specifies whether or not equilibration was done. = 'N': No equilibration. = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```
Internal Parameters:
```  THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors.  If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.```

Definition at line 139 of file slaqsb.f.

140*
141* -- LAPACK auxiliary routine --
142* -- LAPACK is a software package provided by Univ. of Tennessee, --
143* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144*
145* .. Scalar Arguments ..
146 CHARACTER EQUED, UPLO
147 INTEGER KD, LDAB, N
148 REAL AMAX, SCOND
149* ..
150* .. Array Arguments ..
151 REAL AB( LDAB, * ), S( * )
152* ..
153*
154* =====================================================================
155*
156* .. Parameters ..
157 REAL ONE, THRESH
158 parameter( one = 1.0e+0, thresh = 0.1e+0 )
159* ..
160* .. Local Scalars ..
161 INTEGER I, J
162 REAL CJ, LARGE, SMALL
163* ..
164* .. External Functions ..
165 LOGICAL LSAME
166 REAL SLAMCH
167 EXTERNAL lsame, slamch
168* ..
169* .. Intrinsic Functions ..
170 INTRINSIC max, min
171* ..
172* .. Executable Statements ..
173*
174* Quick return if possible
175*
176 IF( n.LE.0 ) THEN
177 equed = 'N'
178 RETURN
179 END IF
180*
181* Initialize LARGE and SMALL.
182*
183 small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
184 large = one / small
185*
186 IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
187*
188* No equilibration
189*
190 equed = 'N'
191 ELSE
192*
193* Replace A by diag(S) * A * diag(S).
194*
195 IF( lsame( uplo, 'U' ) ) THEN
196*
197* Upper triangle of A is stored in band format.
198*
199 DO 20 j = 1, n
200 cj = s( j )
201 DO 10 i = max( 1, j-kd ), j
202 ab( kd+1+i-j, j ) = cj*s( i )*ab( kd+1+i-j, j )
203 10 CONTINUE
204 20 CONTINUE
205 ELSE
206*
207* Lower triangle of A is stored.
208*
209 DO 40 j = 1, n
210 cj = s( j )
211 DO 30 i = j, min( n, j+kd )
212 ab( 1+i-j, j ) = cj*s( i )*ab( 1+i-j, j )
213 30 CONTINUE
214 40 CONTINUE
215 END IF
216 equed = 'Y'
217 END IF
218*
219 RETURN
220*
221* End of SLAQSB
222*
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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