LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ 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
Here is the call graph for this function:
Here is the caller graph for this function: