 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ spocon()

 subroutine spocon ( character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, real ANORM, real RCOND, real, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO )

SPOCON

Purpose:
``` SPOCON estimates the reciprocal of the condition number (in the
1-norm) of a real symmetric positive definite matrix using the
Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is REAL array, dimension (LDA,N) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] ANORM ``` ANORM is REAL The 1-norm (or infinity-norm) of the symmetric matrix A.``` [out] RCOND ``` RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.``` [out] WORK ` WORK is REAL array, dimension (3*N)` [out] IWORK ` IWORK is INTEGER array, dimension (N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 119 of file spocon.f.

121*
122* -- LAPACK computational routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 CHARACTER UPLO
128 INTEGER INFO, LDA, N
129 REAL ANORM, RCOND
130* ..
131* .. Array Arguments ..
132 INTEGER IWORK( * )
133 REAL A( LDA, * ), WORK( * )
134* ..
135*
136* =====================================================================
137*
138* .. Parameters ..
139 REAL ONE, ZERO
140 parameter( one = 1.0e+0, zero = 0.0e+0 )
141* ..
142* .. Local Scalars ..
143 LOGICAL UPPER
144 CHARACTER NORMIN
145 INTEGER IX, KASE
146 REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
147* ..
148* .. Local Arrays ..
149 INTEGER ISAVE( 3 )
150* ..
151* .. External Functions ..
152 LOGICAL LSAME
153 INTEGER ISAMAX
154 REAL SLAMCH
155 EXTERNAL lsame, isamax, slamch
156* ..
157* .. External Subroutines ..
158 EXTERNAL slacn2, slatrs, srscl, xerbla
159* ..
160* .. Intrinsic Functions ..
161 INTRINSIC abs, max
162* ..
163* .. Executable Statements ..
164*
165* Test the input parameters.
166*
167 info = 0
168 upper = lsame( uplo, 'U' )
169 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
170 info = -1
171 ELSE IF( n.LT.0 ) THEN
172 info = -2
173 ELSE IF( lda.LT.max( 1, n ) ) THEN
174 info = -4
175 ELSE IF( anorm.LT.zero ) THEN
176 info = -5
177 END IF
178 IF( info.NE.0 ) THEN
179 CALL xerbla( 'SPOCON', -info )
180 RETURN
181 END IF
182*
183* Quick return if possible
184*
185 rcond = zero
186 IF( n.EQ.0 ) THEN
187 rcond = one
188 RETURN
189 ELSE IF( anorm.EQ.zero ) THEN
190 RETURN
191 END IF
192*
193 smlnum = slamch( 'Safe minimum' )
194*
195* Estimate the 1-norm of inv(A).
196*
197 kase = 0
198 normin = 'N'
199 10 CONTINUE
200 CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
201 IF( kase.NE.0 ) THEN
202 IF( upper ) THEN
203*
204* Multiply by inv(U**T).
205*
206 CALL slatrs( 'Upper', 'Transpose', 'Non-unit', normin, n, a,
207 \$ lda, work, scalel, work( 2*n+1 ), info )
208 normin = 'Y'
209*
210* Multiply by inv(U).
211*
212 CALL slatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
213 \$ a, lda, work, scaleu, work( 2*n+1 ), info )
214 ELSE
215*
216* Multiply by inv(L).
217*
218 CALL slatrs( 'Lower', 'No transpose', 'Non-unit', normin, n,
219 \$ a, lda, work, scalel, work( 2*n+1 ), info )
220 normin = 'Y'
221*
222* Multiply by inv(L**T).
223*
224 CALL slatrs( 'Lower', 'Transpose', 'Non-unit', normin, n, a,
225 \$ lda, work, scaleu, work( 2*n+1 ), info )
226 END IF
227*
228* Multiply by 1/SCALE if doing so will not cause overflow.
229*
230 scale = scalel*scaleu
231 IF( scale.NE.one ) THEN
232 ix = isamax( n, work, 1 )
233 IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
234 \$ GO TO 20
235 CALL srscl( n, scale, work, 1 )
236 END IF
237 GO TO 10
238 END IF
239*
240* Compute the estimate of the reciprocal condition number.
241*
242 IF( ainvnm.NE.zero )
243 \$ rcond = ( one / ainvnm ) / anorm
244*
245 20 CONTINUE
246 RETURN
247*
248* End of SPOCON
249*
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:71
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine slatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
SLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition: slatrs.f:238
subroutine slacn2(N, V, X, ISGN, EST, KASE, ISAVE)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: slacn2.f:136
subroutine srscl(N, SA, SX, INCX)
SRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: srscl.f:84
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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