 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zlaqhp()

 subroutine zlaqhp ( character UPLO, integer N, complex*16, dimension( * ) AP, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, character EQUED )

ZLAQHP scales a Hermitian matrix stored in packed form.

Purpose:
``` ZLAQHP 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*16 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 DOUBLE PRECISION array, dimension (N) The scale factors for A.``` [in] SCOND ``` SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i).``` [in] AMAX ``` AMAX is DOUBLE PRECISION 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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 zlaqhp.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  DOUBLE PRECISION AMAX, SCOND
135 * ..
136 * .. Array Arguments ..
137  DOUBLE PRECISION S( * )
138  COMPLEX*16 AP( * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  DOUBLE PRECISION ONE, THRESH
145  parameter( one = 1.0d+0, thresh = 0.1d+0 )
146 * ..
147 * .. Local Scalars ..
148  INTEGER I, J, JC
149  DOUBLE PRECISION CJ, LARGE, SMALL
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAME
153  DOUBLE PRECISION DLAMCH
154  EXTERNAL lsame, dlamch
155 * ..
156 * .. Intrinsic Functions ..
157  INTRINSIC dble
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 = dlamch( 'Safe minimum' ) / dlamch( '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*dble( 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*dble( 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 ZLAQHP
215 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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