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

 subroutine spoequ ( integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info )

SPOEQU

Purpose:
``` SPOEQU 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 REAL 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 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.```

Definition at line 111 of file spoequ.f.

112*
113* -- LAPACK computational routine --
114* -- LAPACK is a software package provided by Univ. of Tennessee, --
115* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116*
117* .. Scalar Arguments ..
118 INTEGER INFO, LDA, N
119 REAL AMAX, SCOND
120* ..
121* .. Array Arguments ..
122 REAL A( LDA, * ), S( * )
123* ..
124*
125* =====================================================================
126*
127* .. Parameters ..
128 REAL ZERO, ONE
129 parameter( zero = 0.0e+0, one = 1.0e+0 )
130* ..
131* .. Local Scalars ..
132 INTEGER I
133 REAL SMIN
134* ..
135* .. External Subroutines ..
136 EXTERNAL xerbla
137* ..
138* .. Intrinsic Functions ..
139 INTRINSIC max, min, sqrt
140* ..
141* .. Executable Statements ..
142*
143* Test the input parameters.
144*
145 info = 0
146 IF( n.LT.0 ) THEN
147 info = -1
148 ELSE IF( lda.LT.max( 1, n ) ) THEN
149 info = -3
150 END IF
151 IF( info.NE.0 ) THEN
152 CALL xerbla( 'SPOEQU', -info )
153 RETURN
154 END IF
155*
156* Quick return if possible
157*
158 IF( n.EQ.0 ) THEN
159 scond = one
160 amax = zero
161 RETURN
162 END IF
163*
164* Find the minimum and maximum diagonal elements.
165*
166 s( 1 ) = a( 1, 1 )
167 smin = s( 1 )
168 amax = s( 1 )
169 DO 10 i = 2, n
170 s( i ) = a( i, i )
171 smin = min( smin, s( i ) )
172 amax = max( amax, s( i ) )
173 10 CONTINUE
174*
175 IF( smin.LE.zero ) THEN
176*
177* Find the first non-positive diagonal element and return.
178*
179 DO 20 i = 1, n
180 IF( s( i ).LE.zero ) THEN
181 info = i
182 RETURN
183 END IF
184 20 CONTINUE
185 ELSE
186*
187* Set the scale factors to the reciprocals
188* of the diagonal elements.
189*
190 DO 30 i = 1, n
191 s( i ) = one / sqrt( s( i ) )
192 30 CONTINUE
193*
194* Compute SCOND = min(S(I)) / max(S(I))
195*
196 scond = sqrt( smin ) / sqrt( amax )
197 END IF
198 RETURN
199*
200* End of SPOEQU
201*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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