 LAPACK  3.9.1 LAPACK: Linear Algebra PACKage

## ◆ 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

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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)
XERBLA
Definition: xerbla.f:60
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