LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dppcon()

subroutine dppcon ( character  UPLO,
integer  N,
double precision, dimension( * )  AP,
double precision  ANORM,
double precision  RCOND,
double precision, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

DPPCON

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

 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]AP
          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The triangular factor U or L from the Cholesky factorization
          A = U**T*U or A = L*L**T, packed columnwise in a linear
          array.  The j-th column of U or L is stored in the array AP
          as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=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.
Date
December 2016

Definition at line 120 of file dppcon.f.

120 *
121 * -- LAPACK computational routine (version 3.7.0) --
122 * -- LAPACK is a software package provided by Univ. of Tennessee, --
123 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
124 * December 2016
125 *
126 * .. Scalar Arguments ..
127  CHARACTER uplo
128  INTEGER info, n
129  DOUBLE PRECISION anorm, rcond
130 * ..
131 * .. Array Arguments ..
132  INTEGER iwork( * )
133  DOUBLE PRECISION ap( * ), 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, dlatps, drscl, xerbla
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC abs
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( anorm.LT.zero ) THEN
174  info = -4
175  END IF
176  IF( info.NE.0 ) THEN
177  CALL xerbla( 'DPPCON', -info )
178  RETURN
179  END IF
180 *
181 * Quick return if possible
182 *
183  rcond = zero
184  IF( n.EQ.0 ) THEN
185  rcond = one
186  RETURN
187  ELSE IF( anorm.EQ.zero ) THEN
188  RETURN
189  END IF
190 *
191  smlnum = dlamch( 'Safe minimum' )
192 *
193 * Estimate the 1-norm of the inverse.
194 *
195  kase = 0
196  normin = 'N'
197  10 CONTINUE
198  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
199  IF( kase.NE.0 ) THEN
200  IF( upper ) THEN
201 *
202 * Multiply by inv(U**T).
203 *
204  CALL dlatps( 'Upper', 'Transpose', 'Non-unit', normin, n,
205  $ ap, work, scalel, work( 2*n+1 ), info )
206  normin = 'Y'
207 *
208 * Multiply by inv(U).
209 *
210  CALL dlatps( 'Upper', 'No transpose', 'Non-unit', normin, n,
211  $ ap, work, scaleu, work( 2*n+1 ), info )
212  ELSE
213 *
214 * Multiply by inv(L).
215 *
216  CALL dlatps( 'Lower', 'No transpose', 'Non-unit', normin, n,
217  $ ap, work, scalel, work( 2*n+1 ), info )
218  normin = 'Y'
219 *
220 * Multiply by inv(L**T).
221 *
222  CALL dlatps( 'Lower', 'Transpose', 'Non-unit', normin, n,
223  $ ap, work, scaleu, work( 2*n+1 ), info )
224  END IF
225 *
226 * Multiply by 1/SCALE if doing so will not cause overflow.
227 *
228  scale = scalel*scaleu
229  IF( scale.NE.one ) THEN
230  ix = idamax( n, work, 1 )
231  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
232  $ GO TO 20
233  CALL drscl( n, scale, work, 1 )
234  END IF
235  GO TO 10
236  END IF
237 *
238 * Compute the estimate of the reciprocal condition number.
239 *
240  IF( ainvnm.NE.zero )
241  $ rcond = ( one / ainvnm ) / anorm
242 *
243  20 CONTINUE
244  RETURN
245 *
246 * End of DPPCON
247 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:73
subroutine dlatps(UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE, CNORM, INFO)
DLATPS solves a triangular system of equations with the matrix held in packed storage.
Definition: dlatps.f:231
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:138
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:86
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