LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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)
XERBLA
Definition: xerbla.f:60
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