LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ claqhp()

 subroutine claqhp ( character UPLO, integer N, complex, dimension( * ) AP, real, dimension( * ) S, real SCOND, real AMAX, character EQUED )

CLAQHP scales a Hermitian matrix stored in packed form.

Purpose:
``` CLAQHP equilibrates a Hermitian 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 Hermitian matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] AP ``` AP is COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A.``` [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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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 125 of file claqhp.f.

126*
127* -- LAPACK auxiliary routine --
128* -- LAPACK is a software package provided by Univ. of Tennessee, --
129* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*
131* .. Scalar Arguments ..
132 CHARACTER EQUED, UPLO
133 INTEGER N
134 REAL AMAX, SCOND
135* ..
136* .. Array Arguments ..
137 REAL S( * )
138 COMPLEX AP( * )
139* ..
140*
141* =====================================================================
142*
143* .. Parameters ..
144 REAL ONE, THRESH
145 parameter( one = 1.0e+0, thresh = 0.1e+0 )
146* ..
147* .. Local Scalars ..
148 INTEGER I, J, JC
149 REAL CJ, LARGE, SMALL
150* ..
151* .. External Functions ..
152 LOGICAL LSAME
153 REAL SLAMCH
154 EXTERNAL lsame, slamch
155* ..
156* .. Intrinsic Functions ..
157 INTRINSIC real
158* ..
159* .. Executable Statements ..
160*
161* Quick return if possible
162*
163 IF( n.LE.0 ) THEN
164 equed = 'N'
165 RETURN
166 END IF
167*
168* Initialize LARGE and SMALL.
169*
170 small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
171 large = one / small
172*
173 IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
174*
175* No equilibration
176*
177 equed = 'N'
178 ELSE
179*
180* Replace A by diag(S) * A * diag(S).
181*
182 IF( lsame( uplo, 'U' ) ) THEN
183*
184* Upper triangle of A is stored.
185*
186 jc = 1
187 DO 20 j = 1, n
188 cj = s( j )
189 DO 10 i = 1, j - 1
190 ap( jc+i-1 ) = cj*s( i )*ap( jc+i-1 )
191 10 CONTINUE
192 ap( jc+j-1 ) = cj*cj*real( ap( jc+j-1 ) )
193 jc = jc + j
194 20 CONTINUE
195 ELSE
196*
197* Lower triangle of A is stored.
198*
199 jc = 1
200 DO 40 j = 1, n
201 cj = s( j )
202 ap( jc ) = cj*cj*real( ap( jc ) )
203 DO 30 i = j + 1, n
204 ap( jc+i-j ) = cj*s( i )*ap( jc+i-j )
205 30 CONTINUE
206 jc = jc + n - j + 1
207 40 CONTINUE
208 END IF
209 equed = 'Y'
210 END IF
211*
212 RETURN
213*
214* End of CLAQHP
215*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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