LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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

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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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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