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

 subroutine zpoequ ( integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, integer info )

ZPOEQU

Purpose:
``` ZPOEQU computes row and column scalings intended to equilibrate a
Hermitian positive definite matrix A and reduce its condition number
(with respect to the two-norm).  S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
choice of S puts the condition number of B within a factor N of the
smallest possible condition number over all possible diagonal
scalings.```
Parameters
 [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The N-by-N Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] S ``` S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A.``` [out] SCOND ``` SCOND is DOUBLE PRECISION If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.``` [out] AMAX ``` AMAX is DOUBLE PRECISION Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive.```

Definition at line 112 of file zpoequ.f.

113*
114* -- LAPACK computational routine --
115* -- LAPACK is a software package provided by Univ. of Tennessee, --
116* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117*
118* .. Scalar Arguments ..
119 INTEGER INFO, LDA, N
120 DOUBLE PRECISION AMAX, SCOND
121* ..
122* .. Array Arguments ..
123 DOUBLE PRECISION S( * )
124 COMPLEX*16 A( LDA, * )
125* ..
126*
127* =====================================================================
128*
129* .. Parameters ..
130 DOUBLE PRECISION ZERO, ONE
131 parameter( zero = 0.0d+0, one = 1.0d+0 )
132* ..
133* .. Local Scalars ..
134 INTEGER I
135 DOUBLE PRECISION SMIN
136* ..
137* .. External Subroutines ..
138 EXTERNAL xerbla
139* ..
140* .. Intrinsic Functions ..
141 INTRINSIC dble, max, min, sqrt
142* ..
143* .. Executable Statements ..
144*
145* Test the input parameters.
146*
147 info = 0
148 IF( n.LT.0 ) THEN
149 info = -1
150 ELSE IF( lda.LT.max( 1, n ) ) THEN
151 info = -3
152 END IF
153 IF( info.NE.0 ) THEN
154 CALL xerbla( 'ZPOEQU', -info )
155 RETURN
156 END IF
157*
158* Quick return if possible
159*
160 IF( n.EQ.0 ) THEN
161 scond = one
162 amax = zero
163 RETURN
164 END IF
165*
166* Find the minimum and maximum diagonal elements.
167*
168 s( 1 ) = dble( a( 1, 1 ) )
169 smin = s( 1 )
170 amax = s( 1 )
171 DO 10 i = 2, n
172 s( i ) = dble( a( i, i ) )
173 smin = min( smin, s( i ) )
174 amax = max( amax, s( i ) )
175 10 CONTINUE
176*
177 IF( smin.LE.zero ) THEN
178*
179* Find the first non-positive diagonal element and return.
180*
181 DO 20 i = 1, n
182 IF( s( i ).LE.zero ) THEN
183 info = i
184 RETURN
185 END IF
186 20 CONTINUE
187 ELSE
188*
189* Set the scale factors to the reciprocals
190* of the diagonal elements.
191*
192 DO 30 i = 1, n
193 s( i ) = one / sqrt( s( i ) )
194 30 CONTINUE
195*
196* Compute SCOND = min(S(I)) / max(S(I))
197*
198 scond = sqrt( smin ) / sqrt( amax )
199 END IF
200 RETURN
201*
202* End of ZPOEQU
203*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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