 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

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```

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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