LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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