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

 subroutine sspcon ( character UPLO, integer N, real, dimension( * ) AP, integer, dimension( * ) IPIV, real ANORM, real RCOND, real, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO )

SSPCON

Purpose:
``` SSPCON estimates the reciprocal of the condition number (in the
1-norm) of a real symmetric packed matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by SSPTRF.

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 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] AP ``` AP is REAL array, dimension (N*(N+1)/2) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSPTRF, stored as a packed triangular matrix.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by SSPTRF.``` [in] ANORM ``` ANORM is REAL The 1-norm of the original 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 (2*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 123 of file sspcon.f.

125*
126* -- LAPACK computational routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER UPLO
132 INTEGER INFO, N
133 REAL ANORM, RCOND
134* ..
135* .. Array Arguments ..
136 INTEGER IPIV( * ), IWORK( * )
137 REAL AP( * ), WORK( * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ONE, ZERO
144 parameter( one = 1.0e+0, zero = 0.0e+0 )
145* ..
146* .. Local Scalars ..
147 LOGICAL UPPER
148 INTEGER I, IP, KASE
149 REAL AINVNM
150* ..
151* .. Local Arrays ..
152 INTEGER ISAVE( 3 )
153* ..
154* .. External Functions ..
155 LOGICAL LSAME
156 EXTERNAL lsame
157* ..
158* .. External Subroutines ..
159 EXTERNAL slacn2, ssptrs, xerbla
160* ..
161* .. Executable Statements ..
162*
163* Test the input parameters.
164*
165 info = 0
166 upper = lsame( uplo, 'U' )
167 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
168 info = -1
169 ELSE IF( n.LT.0 ) THEN
170 info = -2
171 ELSE IF( anorm.LT.zero ) THEN
172 info = -5
173 END IF
174 IF( info.NE.0 ) THEN
175 CALL xerbla( 'SSPCON', -info )
176 RETURN
177 END IF
178*
179* Quick return if possible
180*
181 rcond = zero
182 IF( n.EQ.0 ) THEN
183 rcond = one
184 RETURN
185 ELSE IF( anorm.LE.zero ) THEN
186 RETURN
187 END IF
188*
189* Check that the diagonal matrix D is nonsingular.
190*
191 IF( upper ) THEN
192*
193* Upper triangular storage: examine D from bottom to top
194*
195 ip = n*( n+1 ) / 2
196 DO 10 i = n, 1, -1
197 IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
198 \$ RETURN
199 ip = ip - i
200 10 CONTINUE
201 ELSE
202*
203* Lower triangular storage: examine D from top to bottom.
204*
205 ip = 1
206 DO 20 i = 1, n
207 IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
208 \$ RETURN
209 ip = ip + n - i + 1
210 20 CONTINUE
211 END IF
212*
213* Estimate the 1-norm of the inverse.
214*
215 kase = 0
216 30 CONTINUE
217 CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
218 IF( kase.NE.0 ) THEN
219*
220* Multiply by inv(L*D*L**T) or inv(U*D*U**T).
221*
222 CALL ssptrs( uplo, n, 1, ap, ipiv, work, n, info )
223 GO TO 30
224 END IF
225*
226* Compute the estimate of the reciprocal condition number.
227*
228 IF( ainvnm.NE.zero )
229 \$ rcond = ( one / ainvnm ) / anorm
230*
231 RETURN
232*
233* End of SSPCON
234*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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 ssptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
SSPTRS
Definition: ssptrs.f:115
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