 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zhpcon()

 subroutine zhpcon ( character UPLO, integer N, complex*16, dimension( * ) AP, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, complex*16, dimension( * ) WORK, integer INFO )

ZHPCON

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Purpose:
``` ZHPCON estimates the reciprocal of the condition number of a complex
Hermitian packed matrix A using the factorization A = U*D*U**H or
A = L*D*L**H computed by ZHPTRF.

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 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**H; = 'L': Lower triangular, form is A = L*D*L**H.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] AP ``` AP is COMPLEX*16 array, dimension (N*(N+1)/2) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHPTRF, stored as a packed triangular matrix.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHPTRF.``` [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 an estimate of the 1-norm of inv(A) computed in this routine.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (2*N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Date
December 2016

Definition at line 120 of file zhpcon.f.

120 *
121 * -- LAPACK computational routine (version 3.7.0) --
122 * -- LAPACK is a software package provided by Univ. of Tennessee, --
123 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
124 * December 2016
125 *
126 * .. Scalar Arguments ..
127  CHARACTER uplo
128  INTEGER info, n
129  DOUBLE PRECISION anorm, rcond
130 * ..
131 * .. Array Arguments ..
132  INTEGER ipiv( * )
133  COMPLEX*16 ap( * ), 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  INTEGER i, ip, kase
145  DOUBLE PRECISION ainvnm
146 * ..
147 * .. Local Arrays ..
148  INTEGER isave( 3 )
149 * ..
150 * .. External Functions ..
151  LOGICAL lsame
152  EXTERNAL lsame
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL xerbla, zhptrs, zlacn2
156 * ..
157 * .. Executable Statements ..
158 *
159 * Test the input parameters.
160 *
161  info = 0
162  upper = lsame( uplo, 'U' )
163  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
164  info = -1
165  ELSE IF( n.LT.0 ) THEN
166  info = -2
167  ELSE IF( anorm.LT.zero ) THEN
168  info = -5
169  END IF
170  IF( info.NE.0 ) THEN
171  CALL xerbla( 'ZHPCON', -info )
172  RETURN
173  END IF
174 *
175 * Quick return if possible
176 *
177  rcond = zero
178  IF( n.EQ.0 ) THEN
179  rcond = one
180  RETURN
181  ELSE IF( anorm.LE.zero ) THEN
182  RETURN
183  END IF
184 *
185 * Check that the diagonal matrix D is nonsingular.
186 *
187  IF( upper ) THEN
188 *
189 * Upper triangular storage: examine D from bottom to top
190 *
191  ip = n*( n+1 ) / 2
192  DO 10 i = n, 1, -1
193  IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
194  \$ RETURN
195  ip = ip - i
196  10 CONTINUE
197  ELSE
198 *
199 * Lower triangular storage: examine D from top to bottom.
200 *
201  ip = 1
202  DO 20 i = 1, n
203  IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
204  \$ RETURN
205  ip = ip + n - i + 1
206  20 CONTINUE
207  END IF
208 *
209 * Estimate the 1-norm of the inverse.
210 *
211  kase = 0
212  30 CONTINUE
213  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
214  IF( kase.NE.0 ) THEN
215 *
216 * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
217 *
218  CALL zhptrs( uplo, n, 1, ap, ipiv, work, n, info )
219  GO TO 30
220  END IF
221 *
222 * Compute the estimate of the reciprocal condition number.
223 *
224  IF( ainvnm.NE.zero )
225  \$ rcond = ( one / ainvnm ) / anorm
226 *
227  RETURN
228 *
229 * End of ZHPCON
230 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine zlacn2(N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: zlacn2.f:135
subroutine zhptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
ZHPTRS
Definition: zhptrs.f:117
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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