 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zppt01()

 subroutine zppt01 ( character UPLO, integer N, complex*16, dimension( * ) A, complex*16, dimension( * ) AFAC, double precision, dimension( * ) RWORK, double precision RESID )

ZPPT01

Purpose:
``` ZPPT01 reconstructs a Hermitian positive definite packed 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*16 array, dimension (N*(N+1)/2) The original Hermitian matrix A, stored as a packed triangular matrix.``` [in,out] AFAC ``` AFAC is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the factor L or U from the L*L' or U'*U factorization of A, stored as a packed triangular matrix. Overwritten with the reconstructed matrix, and then with the difference L*L' - A (or U'*U - A).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )```

Definition at line 94 of file zppt01.f.

95 *
96 * -- LAPACK test routine --
97 * -- LAPACK is a software package provided by Univ. of Tennessee, --
98 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
99 *
100 * .. Scalar Arguments ..
101  CHARACTER UPLO
102  INTEGER N
103  DOUBLE PRECISION RESID
104 * ..
105 * .. Array Arguments ..
106  DOUBLE PRECISION RWORK( * )
107  COMPLEX*16 A( * ), AFAC( * )
108 * ..
109 *
110 * =====================================================================
111 *
112 * .. Parameters ..
113  DOUBLE PRECISION ZERO, ONE
114  parameter( zero = 0.0d+0, one = 1.0d+0 )
115 * ..
116 * .. Local Scalars ..
117  INTEGER I, K, KC
118  DOUBLE PRECISION ANORM, EPS, TR
119  COMPLEX*16 TC
120 * ..
121 * .. External Functions ..
122  LOGICAL LSAME
123  DOUBLE PRECISION DLAMCH, ZLANHP
124  COMPLEX*16 ZDOTC
125  EXTERNAL lsame, dlamch, zlanhp, zdotc
126 * ..
127 * .. External Subroutines ..
128  EXTERNAL zhpr, zscal, ztpmv
129 * ..
130 * .. Intrinsic Functions ..
131  INTRINSIC dble, dimag
132 * ..
133 * .. Executable Statements ..
134 *
135 * Quick exit if N = 0
136 *
137  IF( n.LE.0 ) THEN
138  resid = zero
139  RETURN
140  END IF
141 *
142 * Exit with RESID = 1/EPS if ANORM = 0.
143 *
144  eps = dlamch( 'Epsilon' )
145  anorm = zlanhp( '1', uplo, n, a, rwork )
146  IF( anorm.LE.zero ) THEN
147  resid = one / eps
148  RETURN
149  END IF
150 *
151 * Check the imaginary parts of the diagonal elements and return with
152 * an error code if any are nonzero.
153 *
154  kc = 1
155  IF( lsame( uplo, 'U' ) ) THEN
156  DO 10 k = 1, n
157  IF( dimag( afac( kc ) ).NE.zero ) THEN
158  resid = one / eps
159  RETURN
160  END IF
161  kc = kc + k + 1
162  10 CONTINUE
163  ELSE
164  DO 20 k = 1, n
165  IF( dimag( afac( kc ) ).NE.zero ) THEN
166  resid = one / eps
167  RETURN
168  END IF
169  kc = kc + n - k + 1
170  20 CONTINUE
171  END IF
172 *
173 * Compute the product U'*U, overwriting U.
174 *
175  IF( lsame( uplo, 'U' ) ) THEN
176  kc = ( n*( n-1 ) ) / 2 + 1
177  DO 30 k = n, 1, -1
178 *
179 * Compute the (K,K) element of the result.
180 *
181  tr = zdotc( k, afac( kc ), 1, afac( kc ), 1 )
182  afac( kc+k-1 ) = tr
183 *
184 * Compute the rest of column K.
185 *
186  IF( k.GT.1 ) THEN
187  CALL ztpmv( 'Upper', 'Conjugate', 'Non-unit', k-1, afac,
188  \$ afac( kc ), 1 )
189  kc = kc - ( k-1 )
190  END IF
191  30 CONTINUE
192 *
193 * Compute the difference L*L' - A
194 *
195  kc = 1
196  DO 50 k = 1, n
197  DO 40 i = 1, k - 1
198  afac( kc+i-1 ) = afac( kc+i-1 ) - a( kc+i-1 )
199  40 CONTINUE
200  afac( kc+k-1 ) = afac( kc+k-1 ) - dble( a( kc+k-1 ) )
201  kc = kc + k
202  50 CONTINUE
203 *
204 * Compute the product L*L', overwriting L.
205 *
206  ELSE
207  kc = ( n*( n+1 ) ) / 2
208  DO 60 k = n, 1, -1
209 *
210 * Add a multiple of column K of the factor L to each of
211 * columns K+1 through N.
212 *
213  IF( k.LT.n )
214  \$ CALL zhpr( 'Lower', n-k, one, afac( kc+1 ), 1,
215  \$ afac( kc+n-k+1 ) )
216 *
217 * Scale column K by the diagonal element.
218 *
219  tc = afac( kc )
220  CALL zscal( n-k+1, tc, afac( kc ), 1 )
221 *
222  kc = kc - ( n-k+2 )
223  60 CONTINUE
224 *
225 * Compute the difference U'*U - A
226 *
227  kc = 1
228  DO 80 k = 1, n
229  afac( kc ) = afac( kc ) - dble( a( kc ) )
230  DO 70 i = k + 1, n
231  afac( kc+i-k ) = afac( kc+i-k ) - a( kc+i-k )
232  70 CONTINUE
233  kc = kc + n - k + 1
234  80 CONTINUE
235  END IF
236 *
237 * Compute norm( L*U - A ) / ( N * norm(A) * EPS )
238 *
239  resid = zlanhp( '1', uplo, n, afac, rwork )
240 *
241  resid = ( ( resid / dble( n ) ) / anorm ) / eps
242 *
243  RETURN
244 *
245 * End of ZPPT01
246 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
complex *16 function zdotc(N, ZX, INCX, ZY, INCY)
ZDOTC
Definition: zdotc.f:83
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:78
subroutine zhpr(UPLO, N, ALPHA, X, INCX, AP)
ZHPR
Definition: zhpr.f:130
subroutine ztpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV
Definition: ztpmv.f:142
double precision function zlanhp(NORM, UPLO, N, AP, WORK)
ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanhp.f:117
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