LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ 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

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*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
integer function idamax(n, dx, incx)
IDAMAX
Definition idamax.f:71
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
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine drscl(n, sa, sx, incx)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition drscl.f:84
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