LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ cpoequb()

subroutine cpoequb ( integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
real, dimension( * )  S,
real  SCOND,
real  AMAX,
integer  INFO 
)

CPOEQUB

Download CPOEQUB + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CPOEQUB 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.

 This routine differs from CPOEQU 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
 between sqrt(radix) and 1/sqrt(radix).
Parameters
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]A
          A is COMPLEX 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 REAL array, dimension (N)
          If INFO = 0, S contains the scale factors for A.
[out]SCOND
          SCOND is REAL
          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 REAL
          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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 118 of file cpoequb.f.

119*
120* -- LAPACK computational routine --
121* -- LAPACK is a software package provided by Univ. of Tennessee, --
122* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
123*
124* .. Scalar Arguments ..
125 INTEGER INFO, LDA, N
126 REAL AMAX, SCOND
127* ..
128* .. Array Arguments ..
129 COMPLEX A( LDA, * )
130 REAL S( * )
131* ..
132*
133* =====================================================================
134*
135* .. Parameters ..
136 REAL ZERO, ONE
137 parameter( zero = 0.0e+0, one = 1.0e+0 )
138* ..
139* .. Local Scalars ..
140 INTEGER I
141 REAL SMIN, BASE, TMP
142* ..
143* .. External Functions ..
144 REAL SLAMCH
145 EXTERNAL slamch
146* ..
147* .. External Subroutines ..
148 EXTERNAL xerbla
149* ..
150* .. Intrinsic Functions ..
151 INTRINSIC max, min, sqrt, log, int
152* ..
153* .. Executable Statements ..
154*
155* Test the input parameters.
156*
157* Positive definite only performs 1 pass of equilibration.
158*
159 info = 0
160 IF( n.LT.0 ) THEN
161 info = -1
162 ELSE IF( lda.LT.max( 1, n ) ) THEN
163 info = -3
164 END IF
165 IF( info.NE.0 ) THEN
166 CALL xerbla( 'CPOEQUB', -info )
167 RETURN
168 END IF
169*
170* Quick return if possible.
171*
172 IF( n.EQ.0 ) THEN
173 scond = one
174 amax = zero
175 RETURN
176 END IF
177
178 base = slamch( 'B' )
179 tmp = -0.5 / log( base )
180*
181* Find the minimum and maximum diagonal elements.
182*
183 s( 1 ) = real( a( 1, 1 ) )
184 smin = s( 1 )
185 amax = s( 1 )
186 DO 10 i = 2, n
187 s( i ) = real( a( i, i ) )
188 smin = min( smin, s( i ) )
189 amax = max( amax, s( i ) )
190 10 CONTINUE
191*
192 IF( smin.LE.zero ) THEN
193*
194* Find the first non-positive diagonal element and return.
195*
196 DO 20 i = 1, n
197 IF( s( i ).LE.zero ) THEN
198 info = i
199 RETURN
200 END IF
201 20 CONTINUE
202 ELSE
203*
204* Set the scale factors to the reciprocals
205* of the diagonal elements.
206*
207 DO 30 i = 1, n
208 s( i ) = base ** int( tmp * log( s( i ) ) )
209 30 CONTINUE
210*
211* Compute SCOND = min(S(I)) / max(S(I)).
212*
213 scond = sqrt( smin ) / sqrt( amax )
214 END IF
215*
216 RETURN
217*
218* End of CPOEQUB
219*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
Here is the call graph for this function:
Here is the caller graph for this function: