LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zpoequb ( integer N, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, integer INFO )

ZPOEQUB

Purpose:
``` ZPOEQUB computes row and column scalings intended to equilibrate a
symmetric 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 symmetric 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.```
Date
November 2011

Definition at line 115 of file zpoequb.f.

115 *
116 * -- LAPACK computational routine (version 3.4.0) --
117 * -- LAPACK is a software package provided by Univ. of Tennessee, --
118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119 * November 2011
120 *
121 * .. Scalar Arguments ..
122  INTEGER info, lda, n
123  DOUBLE PRECISION amax, scond
124 * ..
125 * .. Array Arguments ..
126  COMPLEX*16 a( lda, * )
127  DOUBLE PRECISION s( * )
128 * ..
129 *
130 * =====================================================================
131 *
132 * .. Parameters ..
133  DOUBLE PRECISION zero, one
134  parameter ( zero = 0.0d+0, one = 1.0d+0 )
135 * ..
136 * .. Local Scalars ..
137  INTEGER i
138  DOUBLE PRECISION smin, base, tmp
139 * ..
140 * .. External Functions ..
141  DOUBLE PRECISION dlamch
142  EXTERNAL dlamch
143 * ..
144 * .. External Subroutines ..
145  EXTERNAL xerbla
146 * ..
147 * .. Intrinsic Functions ..
148  INTRINSIC max, min, sqrt, log, int, REAL, dimag
149 * ..
150 * .. Executable Statements ..
151 *
152 * Test the input parameters.
153 *
154 * Positive definite only performs 1 pass of equilibration.
155 *
156  info = 0
157  IF( n.LT.0 ) THEN
158  info = -1
159  ELSE IF( lda.LT.max( 1, n ) ) THEN
160  info = -3
161  END IF
162  IF( info.NE.0 ) THEN
163  CALL xerbla( 'ZPOEQUB', -info )
164  RETURN
165  END IF
166 *
167 * Quick return if possible.
168 *
169  IF( n.EQ.0 ) THEN
170  scond = one
171  amax = zero
172  RETURN
173  END IF
174
175  base = dlamch( 'B' )
176  tmp = -0.5d+0 / log( base )
177 *
178 * Find the minimum and maximum diagonal elements.
179 *
180  s( 1 ) = a( 1, 1 )
181  smin = s( 1 )
182  amax = s( 1 )
183  DO 10 i = 2, n
184  s( i ) = a( i, i )
185  smin = min( smin, s( i ) )
186  amax = max( amax, s( i ) )
187  10 CONTINUE
188 *
189  IF( smin.LE.zero ) THEN
190 *
191 * Find the first non-positive diagonal element and return.
192 *
193  DO 20 i = 1, n
194  IF( s( i ).LE.zero ) THEN
195  info = i
196  RETURN
197  END IF
198  20 CONTINUE
199  ELSE
200 *
201 * Set the scale factors to the reciprocals
202 * of the diagonal elements.
203 *
204  DO 30 i = 1, n
205  s( i ) = base ** int( tmp * log( s( i ) ) )
206  30 CONTINUE
207 *
208 * Compute SCOND = min(S(I)) / max(S(I)).
209 *
210  scond = sqrt( smin ) / sqrt( amax )
211  END IF
212 *
213  RETURN
214 *
215 * End of ZPOEQUB
216 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62

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