 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ cpot01()

 subroutine cpot01 ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, real, dimension( * ) RWORK, real RESID )

CPOT01

Purpose:
``` CPOT01 reconstructs a Hermitian positive definite matrix  A  from
its L*L' or U'*U factorization and computes the residual
norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS ),
where 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 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,out] AFAC ``` AFAC is COMPLEX array, dimension (LDAFAC,N) On entry, the factor L or U from the L * L**H or U**H * U factorization of A. Overwritten with the reconstructed matrix, and then with the difference L * L**H - A (or U**H * U - A).``` [in] LDAFAC ``` LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,N).``` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RESID ``` RESID is REAL If UPLO = 'L', norm(L * L**H - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U**H * U - A) / ( N * norm(A) * EPS )```

Definition at line 105 of file cpot01.f.

106 *
107 * -- LAPACK test routine --
108 * -- LAPACK is a software package provided by Univ. of Tennessee, --
109 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
110 *
111 * .. Scalar Arguments ..
112  CHARACTER UPLO
113  INTEGER LDA, LDAFAC, N
114  REAL RESID
115 * ..
116 * .. Array Arguments ..
117  REAL RWORK( * )
118  COMPLEX A( LDA, * ), AFAC( LDAFAC, * )
119 * ..
120 *
121 * =====================================================================
122 *
123 * .. Parameters ..
124  REAL ZERO, ONE
125  parameter( zero = 0.0e+0, one = 1.0e+0 )
126 * ..
127 * .. Local Scalars ..
128  INTEGER I, J, K
129  REAL ANORM, EPS, TR
130  COMPLEX TC
131 * ..
132 * .. External Functions ..
133  LOGICAL LSAME
134  REAL CLANHE, SLAMCH
135  COMPLEX CDOTC
136  EXTERNAL lsame, clanhe, slamch, cdotc
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL cher, cscal, ctrmv
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC aimag, real
143 * ..
144 * .. Executable Statements ..
145 *
146 * Quick exit if N = 0.
147 *
148  IF( n.LE.0 ) THEN
149  resid = zero
150  RETURN
151  END IF
152 *
153 * Exit with RESID = 1/EPS if ANORM = 0.
154 *
155  eps = slamch( 'Epsilon' )
156  anorm = clanhe( '1', uplo, n, a, lda, rwork )
157  IF( anorm.LE.zero ) THEN
158  resid = one / eps
159  RETURN
160  END IF
161 *
162 * Check the imaginary parts of the diagonal elements and return with
163 * an error code if any are nonzero.
164 *
165  DO 10 j = 1, n
166  IF( aimag( afac( j, j ) ).NE.zero ) THEN
167  resid = one / eps
168  RETURN
169  END IF
170  10 CONTINUE
171 *
172 * Compute the product U**H * U, overwriting U.
173 *
174  IF( lsame( uplo, 'U' ) ) THEN
175  DO 20 k = n, 1, -1
176 *
177 * Compute the (K,K) element of the result.
178 *
179  tr = cdotc( k, afac( 1, k ), 1, afac( 1, k ), 1 )
180  afac( k, k ) = tr
181 *
182 * Compute the rest of column K.
183 *
184  CALL ctrmv( 'Upper', 'Conjugate', 'Non-unit', k-1, afac,
185  \$ ldafac, afac( 1, k ), 1 )
186 *
187  20 CONTINUE
188 *
189 * Compute the product L * L**H, overwriting L.
190 *
191  ELSE
192  DO 30 k = n, 1, -1
193 *
194 * Add a multiple of column K of the factor L to each of
195 * columns K+1 through N.
196 *
197  IF( k+1.LE.n )
198  \$ CALL cher( 'Lower', n-k, one, afac( k+1, k ), 1,
199  \$ afac( k+1, k+1 ), ldafac )
200 *
201 * Scale column K by the diagonal element.
202 *
203  tc = afac( k, k )
204  CALL cscal( n-k+1, tc, afac( k, k ), 1 )
205 *
206  30 CONTINUE
207  END IF
208 *
209 * Compute the difference L * L**H - A (or U**H * U - A).
210 *
211  IF( lsame( uplo, 'U' ) ) THEN
212  DO 50 j = 1, n
213  DO 40 i = 1, j - 1
214  afac( i, j ) = afac( i, j ) - a( i, j )
215  40 CONTINUE
216  afac( j, j ) = afac( j, j ) - real( a( j, j ) )
217  50 CONTINUE
218  ELSE
219  DO 70 j = 1, n
220  afac( j, j ) = afac( j, j ) - real( a( j, j ) )
221  DO 60 i = j + 1, n
222  afac( i, j ) = afac( i, j ) - a( i, j )
223  60 CONTINUE
224  70 CONTINUE
225  END IF
226 *
227 * Compute norm(L*U - A) / ( N * norm(A) * EPS )
228 *
229  resid = clanhe( '1', uplo, n, afac, ldafac, rwork )
230 *
231  resid = ( ( resid / real( n ) ) / anorm ) / eps
232 *
233  RETURN
234 *
235 * End of CPOT01
236 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
complex function cdotc(N, CX, INCX, CY, INCY)
CDOTC
Definition: cdotc.f:83
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine ctrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
CTRMV
Definition: ctrmv.f:147
subroutine cher(UPLO, N, ALPHA, X, INCX, A, LDA)
CHER
Definition: cher.f:135
real function clanhe(NORM, UPLO, N, A, LDA, WORK)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clanhe.f:124
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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