 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ ssycon()

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

SSYCON

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

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] A A is REAL array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF. [in] LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by SSYTRF. [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 128 of file ssycon.f.

130 *
131 * -- LAPACK computational routine --
132 * -- LAPACK is a software package provided by Univ. of Tennessee, --
133 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134 *
135 * .. Scalar Arguments ..
136  CHARACTER UPLO
137  INTEGER INFO, LDA, N
138  REAL ANORM, RCOND
139 * ..
140 * .. Array Arguments ..
141  INTEGER IPIV( * ), IWORK( * )
142  REAL A( LDA, * ), WORK( * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  REAL ONE, ZERO
149  parameter( one = 1.0e+0, zero = 0.0e+0 )
150 * ..
151 * .. Local Scalars ..
152  LOGICAL UPPER
153  INTEGER I, KASE
154  REAL AINVNM
155 * ..
156 * .. Local Arrays ..
157  INTEGER ISAVE( 3 )
158 * ..
159 * .. External Functions ..
160  LOGICAL LSAME
161  EXTERNAL lsame
162 * ..
163 * .. External Subroutines ..
164  EXTERNAL slacn2, ssytrs, xerbla
165 * ..
166 * .. Intrinsic Functions ..
167  INTRINSIC max
168 * ..
169 * .. Executable Statements ..
170 *
171 * Test the input parameters.
172 *
173  info = 0
174  upper = lsame( uplo, 'U' )
175  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
176  info = -1
177  ELSE IF( n.LT.0 ) THEN
178  info = -2
179  ELSE IF( lda.LT.max( 1, n ) ) THEN
180  info = -4
181  ELSE IF( anorm.LT.zero ) THEN
182  info = -6
183  END IF
184  IF( info.NE.0 ) THEN
185  CALL xerbla( 'SSYCON', -info )
186  RETURN
187  END IF
188 *
189 * Quick return if possible
190 *
191  rcond = zero
192  IF( n.EQ.0 ) THEN
193  rcond = one
194  RETURN
195  ELSE IF( anorm.LE.zero ) THEN
196  RETURN
197  END IF
198 *
199 * Check that the diagonal matrix D is nonsingular.
200 *
201  IF( upper ) THEN
202 *
203 * Upper triangular storage: examine D from bottom to top
204 *
205  DO 10 i = n, 1, -1
206  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
207  \$ RETURN
208  10 CONTINUE
209  ELSE
210 *
211 * Lower triangular storage: examine D from top to bottom.
212 *
213  DO 20 i = 1, n
214  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
215  \$ RETURN
216  20 CONTINUE
217  END IF
218 *
219 * Estimate the 1-norm of the inverse.
220 *
221  kase = 0
222  30 CONTINUE
223  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
224  IF( kase.NE.0 ) THEN
225 *
226 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
227 *
228  CALL ssytrs( uplo, n, 1, a, lda, ipiv, work, n, info )
229  GO TO 30
230  END IF
231 *
232 * Compute the estimate of the reciprocal condition number.
233 *
234  IF( ainvnm.NE.zero )
235  \$ rcond = ( one / ainvnm ) / anorm
236 *
237  RETURN
238 *
239 * End of SSYCON
240 *
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 ssytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SSYTRS
Definition: ssytrs.f:120
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