 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zhecon_rook()

 subroutine zhecon_rook ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, complex*16, dimension( * ) WORK, integer INFO )

ZHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)

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

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] A ``` A is COMPLEX*16 array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF_ROOK.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHETRF_ROOK.``` [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```
Contributors:
```  June 2017,  Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester```

Definition at line 137 of file zhecon_rook.f.

139 *
140 * -- LAPACK computational routine --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 *
144 * .. Scalar Arguments ..
145  CHARACTER UPLO
146  INTEGER INFO, LDA, N
147  DOUBLE PRECISION ANORM, RCOND
148 * ..
149 * .. Array Arguments ..
150  INTEGER IPIV( * )
151  COMPLEX*16 A( LDA, * ), WORK( * )
152 * ..
153 *
154 * =====================================================================
155 *
156 * .. Parameters ..
157  DOUBLE PRECISION ONE, ZERO
158  parameter( one = 1.0d+0, zero = 0.0d+0 )
159 * ..
160 * .. Local Scalars ..
161  LOGICAL UPPER
162  INTEGER I, KASE
163  DOUBLE PRECISION AINVNM
164 * ..
165 * .. Local Arrays ..
166  INTEGER ISAVE( 3 )
167 * ..
168 * .. External Functions ..
169  LOGICAL LSAME
170  EXTERNAL lsame
171 * ..
172 * .. External Subroutines ..
173  EXTERNAL zhetrs_rook, zlacn2, xerbla
174 * ..
175 * .. Intrinsic Functions ..
176  INTRINSIC max
177 * ..
178 * .. Executable Statements ..
179 *
180 * Test the input parameters.
181 *
182  info = 0
183  upper = lsame( uplo, 'U' )
184  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
185  info = -1
186  ELSE IF( n.LT.0 ) THEN
187  info = -2
188  ELSE IF( lda.LT.max( 1, n ) ) THEN
189  info = -4
190  ELSE IF( anorm.LT.zero ) THEN
191  info = -6
192  END IF
193  IF( info.NE.0 ) THEN
194  CALL xerbla( 'ZHECON_ROOK', -info )
195  RETURN
196  END IF
197 *
198 * Quick return if possible
199 *
200  rcond = zero
201  IF( n.EQ.0 ) THEN
202  rcond = one
203  RETURN
204  ELSE IF( anorm.LE.zero ) THEN
205  RETURN
206  END IF
207 *
208 * Check that the diagonal matrix D is nonsingular.
209 *
210  IF( upper ) THEN
211 *
212 * Upper triangular storage: examine D from bottom to top
213 *
214  DO 10 i = n, 1, -1
215  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
216  \$ RETURN
217  10 CONTINUE
218  ELSE
219 *
220 * Lower triangular storage: examine D from top to bottom.
221 *
222  DO 20 i = 1, n
223  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
224  \$ RETURN
225  20 CONTINUE
226  END IF
227 *
228 * Estimate the 1-norm of the inverse.
229 *
230  kase = 0
231  30 CONTINUE
232  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
233  IF( kase.NE.0 ) THEN
234 *
235 * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
236 *
237  CALL zhetrs_rook( uplo, n, 1, a, lda, ipiv, work, n, info )
238  GO TO 30
239  END IF
240 *
241 * Compute the estimate of the reciprocal condition number.
242 *
243  IF( ainvnm.NE.zero )
244  \$ rcond = ( one / ainvnm ) / anorm
245 *
246  RETURN
247 *
248 * End of ZHECON_ROOK
249 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zhetrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using fac...
Definition: zhetrs_rook.f:136
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
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