LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dpocon()

subroutine dpocon ( character  UPLO,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision  ANORM,
double precision  RCOND,
double precision, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

DPOCON

Download DPOCON + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DPOCON 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 DPOTRF.

 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 DOUBLE PRECISION 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 DPOTRF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]ANORM
          ANORM is DOUBLE PRECISION
          The 1-norm (or infinity-norm) of the symmetric matrix A.
[out]RCOND
          RCOND is DOUBLE PRECISION
          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 DOUBLE PRECISION 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 119 of file dpocon.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  DOUBLE PRECISION ANORM, RCOND
130 * ..
131 * .. Array Arguments ..
132  INTEGER IWORK( * )
133  DOUBLE PRECISION A( LDA, * ), WORK( * )
134 * ..
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139  DOUBLE PRECISION ONE, ZERO
140  parameter( one = 1.0d+0, zero = 0.0d+0 )
141 * ..
142 * .. Local Scalars ..
143  LOGICAL UPPER
144  CHARACTER NORMIN
145  INTEGER IX, KASE
146  DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
147 * ..
148 * .. Local Arrays ..
149  INTEGER ISAVE( 3 )
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAME
153  INTEGER IDAMAX
154  DOUBLE PRECISION DLAMCH
155  EXTERNAL lsame, idamax, dlamch
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL dlacn2, dlatrs, drscl, 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( 'DPOCON', -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 = dlamch( 'Safe minimum' )
194 *
195 * Estimate the 1-norm of inv(A).
196 *
197  kase = 0
198  normin = 'N'
199  10 CONTINUE
200  CALL dlacn2( 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 dlatrs( '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 dlatrs( '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 dlatrs( '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 dlatrs( '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 = idamax( n, work, 1 )
233  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
234  $ GO TO 20
235  CALL drscl( 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 DPOCON
249 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:84
subroutine dlacn2(N, V, X, ISGN, EST, KASE, ISAVE)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: dlacn2.f:136
subroutine dlatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
DLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition: dlatrs.f:238
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