 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zhet01()

 subroutine zhet01 ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex*16, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) RWORK, double precision RESID )

ZHET01

Purpose:
``` ZHET01 reconstructs a Hermitian indefinite matrix A from its
block L*D*L' or U*D*U' factorization and computes the residual
norm( C - A ) / ( N * norm(A) * EPS ),
where C is the reconstructed matrix, EPS is the machine epsilon,
L' is the conjugate transpose of L, and U' is the conjugate transpose
of U.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The number of rows and columns of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The original Hermitian matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)``` [in] AFAC ``` AFAC is COMPLEX*16 array, dimension (LDAFAC,N) The factored form of the matrix A. AFAC contains the block diagonal matrix D and the multipliers used to obtain the factor L or U from the block L*D*L' or U*D*U' factorization as computed by ZHETRF.``` [in] LDAFAC ``` LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,N).``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) The pivot indices from ZHETRF.``` [out] C ` C is COMPLEX*16 array, dimension (LDC,N)` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )```

Definition at line 124 of file zhet01.f.

126 *
127 * -- LAPACK test routine --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 *
131 * .. Scalar Arguments ..
132  CHARACTER UPLO
133  INTEGER LDA, LDAFAC, LDC, N
134  DOUBLE PRECISION RESID
135 * ..
136 * .. Array Arguments ..
137  INTEGER IPIV( * )
138  DOUBLE PRECISION RWORK( * )
139  COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  DOUBLE PRECISION ZERO, ONE
146  parameter( zero = 0.0d+0, one = 1.0d+0 )
147  COMPLEX*16 CZERO, CONE
148  parameter( czero = ( 0.0d+0, 0.0d+0 ),
149  \$ cone = ( 1.0d+0, 0.0d+0 ) )
150 * ..
151 * .. Local Scalars ..
152  INTEGER I, INFO, J
153  DOUBLE PRECISION ANORM, EPS
154 * ..
155 * .. External Functions ..
156  LOGICAL LSAME
157  DOUBLE PRECISION DLAMCH, ZLANHE
158  EXTERNAL lsame, dlamch, zlanhe
159 * ..
160 * .. External Subroutines ..
161  EXTERNAL zlaset, zlavhe
162 * ..
163 * .. Intrinsic Functions ..
164  INTRINSIC dble, dimag
165 * ..
166 * .. Executable Statements ..
167 *
168 * Quick exit if N = 0.
169 *
170  IF( n.LE.0 ) THEN
171  resid = zero
172  RETURN
173  END IF
174 *
175 * Determine EPS and the norm of A.
176 *
177  eps = dlamch( 'Epsilon' )
178  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
179 *
180 * Check the imaginary parts of the diagonal elements and return with
181 * an error code if any are nonzero.
182 *
183  DO 10 j = 1, n
184  IF( dimag( afac( j, j ) ).NE.zero ) THEN
185  resid = one / eps
186  RETURN
187  END IF
188  10 CONTINUE
189 *
190 * Initialize C to the identity matrix.
191 *
192  CALL zlaset( 'Full', n, n, czero, cone, c, ldc )
193 *
194 * Call ZLAVHE to form the product D * U' (or D * L' ).
195 *
196  CALL zlavhe( uplo, 'Conjugate', 'Non-unit', n, n, afac, ldafac,
197  \$ ipiv, c, ldc, info )
198 *
199 * Call ZLAVHE again to multiply by U (or L ).
200 *
201  CALL zlavhe( uplo, 'No transpose', 'Unit', n, n, afac, ldafac,
202  \$ ipiv, c, ldc, info )
203 *
204 * Compute the difference C - A .
205 *
206  IF( lsame( uplo, 'U' ) ) THEN
207  DO 30 j = 1, n
208  DO 20 i = 1, j - 1
209  c( i, j ) = c( i, j ) - a( i, j )
210  20 CONTINUE
211  c( j, j ) = c( j, j ) - dble( a( j, j ) )
212  30 CONTINUE
213  ELSE
214  DO 50 j = 1, n
215  c( j, j ) = c( j, j ) - dble( a( j, j ) )
216  DO 40 i = j + 1, n
217  c( i, j ) = c( i, j ) - a( i, j )
218  40 CONTINUE
219  50 CONTINUE
220  END IF
221 *
222 * Compute norm( C - A ) / ( N * norm(A) * EPS )
223 *
224  resid = zlanhe( '1', uplo, n, c, ldc, rwork )
225 *
226  IF( anorm.LE.zero ) THEN
227  IF( resid.NE.zero )
228  \$ resid = one / eps
229  ELSE
230  resid = ( ( resid / dble( n ) ) / anorm ) / eps
231  END IF
232 *
233  RETURN
234 *
235 * End of ZHET01
236 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zlavhe(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZLAVHE
Definition: zlavhe.f:153
double precision function zlanhe(NORM, UPLO, N, A, LDA, WORK)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanhe.f:124
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
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