LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zlaqsp()

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

ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

Purpose:
``` ZLAQSP equilibrates a symmetric 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,out] AP ``` AP is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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.```
Date
December 2016

Definition at line 128 of file zlaqsp.f.

128 *
129 * -- LAPACK auxiliary routine (version 3.7.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * December 2016
133 *
134 * .. Scalar Arguments ..
135  CHARACTER equed, uplo
136  INTEGER n
137  DOUBLE PRECISION amax, scond
138 * ..
139 * .. Array Arguments ..
140  DOUBLE PRECISION s( * )
141  COMPLEX*16 ap( * )
142 * ..
143 *
144 * =====================================================================
145 *
146 * .. Parameters ..
147  DOUBLE PRECISION one, thresh
148  parameter( one = 1.0d+0, thresh = 0.1d+0 )
149 * ..
150 * .. Local Scalars ..
151  INTEGER i, j, jc
152  DOUBLE PRECISION cj, large, small
153 * ..
154 * .. External Functions ..
155  LOGICAL lsame
156  DOUBLE PRECISION dlamch
157  EXTERNAL lsame, dlamch
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
190  ap( jc+i-1 ) = cj*s( i )*ap( jc+i-1 )
191  10 CONTINUE
192  jc = jc + j
193  20 CONTINUE
194  ELSE
195 *
196 * Lower triangle of A is stored.
197 *
198  jc = 1
199  DO 40 j = 1, n
200  cj = s( j )
201  DO 30 i = j, n
202  ap( jc+i-j ) = cj*s( i )*ap( jc+i-j )
203  30 CONTINUE
204  jc = jc + n - j + 1
205  40 CONTINUE
206  END IF
207  equed = 'Y'
208  END IF
209 *
210  RETURN
211 *
212 * End of ZLAQSP
213 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65