LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ zhecon_3()

 subroutine zhecon_3 ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, complex*16, dimension( * ) WORK, integer INFO )

ZHECON_3

Download ZHECON_3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
``` ZHECON_3 estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian matrix A using the factorization
computed by ZHETRF_RK or ZHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**H (or L**H) is the conjugate of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is Hermitian and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This routine uses BLAS3 solver ZHETRS_3.```
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 = P*U*D*(U**H)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**H)*(P**T).``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK and ZHETRF_BK: a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] E ``` E is COMPLEX*16 array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK.``` [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 164 of file zhecon_3.f.

166 *
167 * -- LAPACK computational routine --
168 * -- LAPACK is a software package provided by Univ. of Tennessee, --
169 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
170 *
171 * .. Scalar Arguments ..
172  CHARACTER UPLO
173  INTEGER INFO, LDA, N
174  DOUBLE PRECISION ANORM, RCOND
175 * ..
176 * .. Array Arguments ..
177  INTEGER IPIV( * )
178  COMPLEX*16 A( LDA, * ), E( * ), WORK( * )
179 * ..
180 *
181 * =====================================================================
182 *
183 * .. Parameters ..
184  DOUBLE PRECISION ONE, ZERO
185  parameter( one = 1.0d+0, zero = 0.0d+0 )
186 * ..
187 * .. Local Scalars ..
188  LOGICAL UPPER
189  INTEGER I, KASE
190  DOUBLE PRECISION AINVNM
191 * ..
192 * .. Local Arrays ..
193  INTEGER ISAVE( 3 )
194 * ..
195 * .. External Functions ..
196  LOGICAL LSAME
197  EXTERNAL lsame
198 * ..
199 * .. External Subroutines ..
200  EXTERNAL zhetrs_3, zlacn2, xerbla
201 * ..
202 * .. Intrinsic Functions ..
203  INTRINSIC max
204 * ..
205 * .. Executable Statements ..
206 *
207 * Test the input parameters.
208 *
209  info = 0
210  upper = lsame( uplo, 'U' )
211  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
212  info = -1
213  ELSE IF( n.LT.0 ) THEN
214  info = -2
215  ELSE IF( lda.LT.max( 1, n ) ) THEN
216  info = -4
217  ELSE IF( anorm.LT.zero ) THEN
218  info = -7
219  END IF
220  IF( info.NE.0 ) THEN
221  CALL xerbla( 'ZHECON_3', -info )
222  RETURN
223  END IF
224 *
225 * Quick return if possible
226 *
227  rcond = zero
228  IF( n.EQ.0 ) THEN
229  rcond = one
230  RETURN
231  ELSE IF( anorm.LE.zero ) THEN
232  RETURN
233  END IF
234 *
235 * Check that the diagonal matrix D is nonsingular.
236 *
237  IF( upper ) THEN
238 *
239 * Upper triangular storage: examine D from bottom to top
240 *
241  DO i = n, 1, -1
242  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
243  \$ RETURN
244  END DO
245  ELSE
246 *
247 * Lower triangular storage: examine D from top to bottom.
248 *
249  DO i = 1, n
250  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
251  \$ RETURN
252  END DO
253  END IF
254 *
255 * Estimate the 1-norm of the inverse.
256 *
257  kase = 0
258  30 CONTINUE
259  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
260  IF( kase.NE.0 ) THEN
261 *
262 * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
263 *
264  CALL zhetrs_3( uplo, n, 1, a, lda, e, ipiv, work, n, info )
265  GO TO 30
266  END IF
267 *
268 * Compute the estimate of the reciprocal condition number.
269 *
270  IF( ainvnm.NE.zero )
271  \$ rcond = ( one / ainvnm ) / anorm
272 *
273  RETURN
274 *
275 * End of ZHECON_3
276 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zhetrs_3(UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, INFO)
ZHETRS_3
Definition: zhetrs_3.f:165
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
Here is the call graph for this function:
Here is the caller graph for this function: