 LAPACK  3.10.1 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```

Definition at line 117 of file dppcon.f.

118 *
119 * -- LAPACK computational routine --
120 * -- LAPACK is a software package provided by Univ. of Tennessee, --
121 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
122 *
123 * .. Scalar Arguments ..
124  CHARACTER UPLO
125  INTEGER INFO, N
126  DOUBLE PRECISION ANORM, RCOND
127 * ..
128 * .. Array Arguments ..
129  INTEGER IWORK( * )
130  DOUBLE PRECISION AP( * ), WORK( * )
131 * ..
132 *
133 * =====================================================================
134 *
135 * .. Parameters ..
136  DOUBLE PRECISION ONE, ZERO
137  parameter( one = 1.0d+0, zero = 0.0d+0 )
138 * ..
139 * .. Local Scalars ..
140  LOGICAL UPPER
141  CHARACTER NORMIN
142  INTEGER IX, KASE
143  DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
144 * ..
145 * .. Local Arrays ..
146  INTEGER ISAVE( 3 )
147 * ..
148 * .. External Functions ..
149  LOGICAL LSAME
150  INTEGER IDAMAX
151  DOUBLE PRECISION DLAMCH
152  EXTERNAL lsame, idamax, dlamch
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL dlacn2, dlatps, drscl, xerbla
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC abs
159 * ..
160 * .. Executable Statements ..
161 *
162 * Test the input parameters.
163 *
164  info = 0
165  upper = lsame( uplo, 'U' )
166  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
167  info = -1
168  ELSE IF( n.LT.0 ) THEN
169  info = -2
170  ELSE IF( anorm.LT.zero ) THEN
171  info = -4
172  END IF
173  IF( info.NE.0 ) THEN
174  CALL xerbla( 'DPPCON', -info )
175  RETURN
176  END IF
177 *
178 * Quick return if possible
179 *
180  rcond = zero
181  IF( n.EQ.0 ) THEN
182  rcond = one
183  RETURN
184  ELSE IF( anorm.EQ.zero ) THEN
185  RETURN
186  END IF
187 *
188  smlnum = dlamch( 'Safe minimum' )
189 *
190 * Estimate the 1-norm of the inverse.
191 *
192  kase = 0
193  normin = 'N'
194  10 CONTINUE
195  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
196  IF( kase.NE.0 ) THEN
197  IF( upper ) THEN
198 *
199 * Multiply by inv(U**T).
200 *
201  CALL dlatps( 'Upper', 'Transpose', 'Non-unit', normin, n,
202  \$ ap, work, scalel, work( 2*n+1 ), info )
203  normin = 'Y'
204 *
205 * Multiply by inv(U).
206 *
207  CALL dlatps( 'Upper', 'No transpose', 'Non-unit', normin, n,
208  \$ ap, work, scaleu, work( 2*n+1 ), info )
209  ELSE
210 *
211 * Multiply by inv(L).
212 *
213  CALL dlatps( 'Lower', 'No transpose', 'Non-unit', normin, n,
214  \$ ap, work, scalel, work( 2*n+1 ), info )
215  normin = 'Y'
216 *
217 * Multiply by inv(L**T).
218 *
219  CALL dlatps( 'Lower', 'Transpose', 'Non-unit', normin, n,
220  \$ ap, work, scaleu, work( 2*n+1 ), info )
221  END IF
222 *
223 * Multiply by 1/SCALE if doing so will not cause overflow.
224 *
225  scale = scalel*scaleu
226  IF( scale.NE.one ) THEN
227  ix = idamax( n, work, 1 )
228  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
229  \$ GO TO 20
230  CALL drscl( n, scale, work, 1 )
231  END IF
232  GO TO 10
233  END IF
234 *
235 * Compute the estimate of the reciprocal condition number.
236 *
237  IF( ainvnm.NE.zero )
238  \$ rcond = ( one / ainvnm ) / anorm
239 *
240  20 CONTINUE
241  RETURN
242 *
243 * End of DPPCON
244 *
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 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:229
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
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