LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ sppcon()

subroutine sppcon ( character  uplo,
integer  n,
real, dimension( * )  ap,
real  anorm,
real  rcond,
real, dimension( * )  work,
integer, dimension( * )  iwork,
integer  info 
)

SPPCON

Download SPPCON + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SPPCON 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
 SPPTRF.

 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 REAL 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 REAL
          The 1-norm (or infinity-norm) of the symmetric matrix A.
[out]RCOND
          RCOND is REAL
          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 REAL 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 117 of file sppcon.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 REAL ANORM, RCOND
127* ..
128* .. Array Arguments ..
129 INTEGER IWORK( * )
130 REAL AP( * ), WORK( * )
131* ..
132*
133* =====================================================================
134*
135* .. Parameters ..
136 REAL ONE, ZERO
137 parameter( one = 1.0e+0, zero = 0.0e+0 )
138* ..
139* .. Local Scalars ..
140 LOGICAL UPPER
141 CHARACTER NORMIN
142 INTEGER IX, KASE
143 REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
144* ..
145* .. Local Arrays ..
146 INTEGER ISAVE( 3 )
147* ..
148* .. External Functions ..
149 LOGICAL LSAME
150 INTEGER ISAMAX
151 REAL SLAMCH
152 EXTERNAL lsame, isamax, slamch
153* ..
154* .. External Subroutines ..
155 EXTERNAL slacn2, slatps, srscl, 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( 'SPPCON', -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 = slamch( 'Safe minimum' )
189*
190* Estimate the 1-norm of the inverse.
191*
192 kase = 0
193 normin = 'N'
194 10 CONTINUE
195 CALL slacn2( 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 slatps( '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 slatps( '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 slatps( '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 slatps( '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 = isamax( n, work, 1 )
228 IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
229 $ GO TO 20
230 CALL srscl( 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 SPPCON
244*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
integer function isamax(n, sx, incx)
ISAMAX
Definition isamax.f:71
subroutine slacn2(n, v, x, isgn, est, kase, isave)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition slacn2.f:136
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
subroutine slatps(uplo, trans, diag, normin, n, ap, x, scale, cnorm, info)
SLATPS solves a triangular system of equations with the matrix held in packed storage.
Definition slatps.f:229
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine srscl(n, sa, sx, incx)
SRSCL multiplies a vector by the reciprocal of a real scalar.
Definition srscl.f:84
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