LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zptcon()

 subroutine zptcon ( integer N, double precision, dimension( * ) D, complex*16, dimension( * ) E, double precision ANORM, double precision RCOND, double precision, dimension( * ) RWORK, integer INFO )

ZPTCON

Purpose:
ZPTCON computes the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite tridiagonal matrix
using the factorization A = L*D*L**H or A = U**H*D*U computed by
ZPTTRF.

Norm(inv(A)) is computed by a direct method, and the reciprocal of
the condition number is computed as
RCOND = 1 / (ANORM * norm(inv(A))).
Parameters
 [in] N N is INTEGER The order of the matrix A. N >= 0. [in] D D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by ZPTTRF. [in] E E is COMPLEX*16 array, dimension (N-1) The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by ZPTTRF. [in] ANORM ANORM is DOUBLE PRECISION The 1-norm of the original 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 the 1-norm of inv(A) computed in this routine. [out] RWORK RWORK is DOUBLE PRECISION array, dimension (N) [out] INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Further Details:
The method used is described in Nicholas J. Higham, "Efficient
Algorithms for Computing the Condition Number of a Tridiagonal
Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.

Definition at line 118 of file zptcon.f.

119*
120* -- LAPACK computational routine --
121* -- LAPACK is a software package provided by Univ. of Tennessee, --
122* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
123*
124* .. Scalar Arguments ..
125 INTEGER INFO, N
126 DOUBLE PRECISION ANORM, RCOND
127* ..
128* .. Array Arguments ..
129 DOUBLE PRECISION D( * ), RWORK( * )
130 COMPLEX*16 E( * )
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 INTEGER I, IX
141 DOUBLE PRECISION AINVNM
142* ..
143* .. External Functions ..
144 INTEGER IDAMAX
145 EXTERNAL idamax
146* ..
147* .. External Subroutines ..
148 EXTERNAL xerbla
149* ..
150* .. Intrinsic Functions ..
151 INTRINSIC abs
152* ..
153* .. Executable Statements ..
154*
155* Test the input arguments.
156*
157 info = 0
158 IF( n.LT.0 ) THEN
159 info = -1
160 ELSE IF( anorm.LT.zero ) THEN
161 info = -4
162 END IF
163 IF( info.NE.0 ) THEN
164 CALL xerbla( 'ZPTCON', -info )
165 RETURN
166 END IF
167*
168* Quick return if possible
169*
170 rcond = zero
171 IF( n.EQ.0 ) THEN
172 rcond = one
173 RETURN
174 ELSE IF( anorm.EQ.zero ) THEN
175 RETURN
176 END IF
177*
178* Check that D(1:N) is positive.
179*
180 DO 10 i = 1, n
181 IF( d( i ).LE.zero )
182 \$ RETURN
183 10 CONTINUE
184*
185* Solve M(A) * x = e, where M(A) = (m(i,j)) is given by
186*
187* m(i,j) = abs(A(i,j)), i = j,
188* m(i,j) = -abs(A(i,j)), i .ne. j,
189*
190* and e = [ 1, 1, ..., 1 ]**T. Note M(A) = M(L)*D*M(L)**H.
191*
192* Solve M(L) * x = e.
193*
194 rwork( 1 ) = one
195 DO 20 i = 2, n
196 rwork( i ) = one + rwork( i-1 )*abs( e( i-1 ) )
197 20 CONTINUE
198*
199* Solve D * M(L)**H * x = b.
200*
201 rwork( n ) = rwork( n ) / d( n )
202 DO 30 i = n - 1, 1, -1
203 rwork( i ) = rwork( i ) / d( i ) + rwork( i+1 )*abs( e( i ) )
204 30 CONTINUE
205*
206* Compute AINVNM = max(x(i)), 1<=i<=n.
207*
208 ix = idamax( n, rwork, 1 )
209 ainvnm = abs( rwork( ix ) )
210*
211* Compute the reciprocal condition number.
212*
213 IF( ainvnm.NE.zero )
214 \$ rcond = ( one / ainvnm ) / anorm
215*
216 RETURN
217*
218* End of ZPTCON
219*
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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