 LAPACK  3.10.1 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```

Definition at line 117 of file zhpcon.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 IPIV( * )
130  COMPLEX*16 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  INTEGER I, IP, KASE
142  DOUBLE PRECISION AINVNM
143 * ..
144 * .. Local Arrays ..
145  INTEGER ISAVE( 3 )
146 * ..
147 * .. External Functions ..
148  LOGICAL LSAME
149  EXTERNAL lsame
150 * ..
151 * .. External Subroutines ..
152  EXTERNAL xerbla, zhptrs, zlacn2
153 * ..
154 * .. Executable Statements ..
155 *
156 * Test the input parameters.
157 *
158  info = 0
159  upper = lsame( uplo, 'U' )
160  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
161  info = -1
162  ELSE IF( n.LT.0 ) THEN
163  info = -2
164  ELSE IF( anorm.LT.zero ) THEN
165  info = -5
166  END IF
167  IF( info.NE.0 ) THEN
168  CALL xerbla( 'ZHPCON', -info )
169  RETURN
170  END IF
171 *
172 * Quick return if possible
173 *
174  rcond = zero
175  IF( n.EQ.0 ) THEN
176  rcond = one
177  RETURN
178  ELSE IF( anorm.LE.zero ) THEN
179  RETURN
180  END IF
181 *
182 * Check that the diagonal matrix D is nonsingular.
183 *
184  IF( upper ) THEN
185 *
186 * Upper triangular storage: examine D from bottom to top
187 *
188  ip = n*( n+1 ) / 2
189  DO 10 i = n, 1, -1
190  IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
191  \$ RETURN
192  ip = ip - i
193  10 CONTINUE
194  ELSE
195 *
196 * Lower triangular storage: examine D from top to bottom.
197 *
198  ip = 1
199  DO 20 i = 1, n
200  IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
201  \$ RETURN
202  ip = ip + n - i + 1
203  20 CONTINUE
204  END IF
205 *
206 * Estimate the 1-norm of the inverse.
207 *
208  kase = 0
209  30 CONTINUE
210  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
211  IF( kase.NE.0 ) THEN
212 *
213 * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
214 *
215  CALL zhptrs( uplo, n, 1, ap, ipiv, work, n, info )
216  GO TO 30
217  END IF
218 *
219 * Compute the estimate of the reciprocal condition number.
220 *
221  IF( ainvnm.NE.zero )
222  \$ rcond = ( one / ainvnm ) / anorm
223 *
224  RETURN
225 *
226 * End of ZHPCON
227 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:133
subroutine zhptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
ZHPTRS
Definition: zhptrs.f:115
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