LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ dpoequb()

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

DPOEQUB

Purpose:
``` DPOEQUB 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.

This routine differs from DPOEQU by restricting the scaling factors
to a power of the radix.  Barring over- and underflow, scaling by
these factors introduces no additional rounding errors.  However, the
scaled diagonal entries are no longer approximately 1 but lie
Parameters
 [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is DOUBLE PRECISION 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.```

Definition at line 117 of file dpoequb.f.

118*
119* -- LAPACK computational routine --
120* -- LAPACK is a software package provided by Univ. of Tennessee, --
121* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
122*
123* .. Scalar Arguments ..
124 INTEGER INFO, LDA, N
125 DOUBLE PRECISION AMAX, SCOND
126* ..
127* .. Array Arguments ..
128 DOUBLE PRECISION A( LDA, * ), S( * )
129* ..
130*
131* =====================================================================
132*
133* .. Parameters ..
134 DOUBLE PRECISION ZERO, ONE
135 parameter( zero = 0.0d+0, one = 1.0d+0 )
136* ..
137* .. Local Scalars ..
138 INTEGER I
139 DOUBLE PRECISION SMIN, BASE, TMP
140* ..
141* .. External Functions ..
142 DOUBLE PRECISION DLAMCH
143 EXTERNAL dlamch
144* ..
145* .. External Subroutines ..
146 EXTERNAL xerbla
147* ..
148* .. Intrinsic Functions ..
149 INTRINSIC max, min, sqrt, log, int
150* ..
151* .. Executable Statements ..
152*
153* Test the input parameters.
154*
155* Positive definite only performs 1 pass of equilibration.
156*
157 info = 0
158 IF( n.LT.0 ) THEN
159 info = -1
160 ELSE IF( lda.LT.max( 1, n ) ) THEN
161 info = -3
162 END IF
163 IF( info.NE.0 ) THEN
164 CALL xerbla( 'DPOEQUB', -info )
165 RETURN
166 END IF
167*
168* Quick return if possible.
169*
170 IF( n.EQ.0 ) THEN
171 scond = one
172 amax = zero
173 RETURN
174 END IF
175
176 base = dlamch( 'B' )
177 tmp = -0.5d+0 / log( base )
178*
179* Find the minimum and maximum diagonal elements.
180*
181 s( 1 ) = a( 1, 1 )
182 smin = s( 1 )
183 amax = s( 1 )
184 DO 10 i = 2, n
185 s( i ) = a( i, i )
186 smin = min( smin, s( i ) )
187 amax = max( amax, s( i ) )
188 10 CONTINUE
189*
190 IF( smin.LE.zero ) THEN
191*
192* Find the first non-positive diagonal element and return.
193*
194 DO 20 i = 1, n
195 IF( s( i ).LE.zero ) THEN
196 info = i
197 RETURN
198 END IF
199 20 CONTINUE
200 ELSE
201*
202* Set the scale factors to the reciprocals
203* of the diagonal elements.
204*
205 DO 30 i = 1, n
206 s( i ) = base ** int( tmp * log( s( i ) ) )
207 30 CONTINUE
208*
209* Compute SCOND = min(S(I)) / max(S(I)).
210*
211 scond = sqrt( smin ) / sqrt( amax )
212 END IF
213*
214 RETURN
215*
216* End of DPOEQUB
217*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
Here is the call graph for this function:
Here is the caller graph for this function: