 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zpbt01()

 subroutine zpbt01 ( character UPLO, integer N, integer KD, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldafac, * ) AFAC, integer LDAFAC, double precision, dimension( * ) RWORK, double precision RESID )

ZPBT01

Purpose:
``` ZPBT01 reconstructs a Hermitian positive definite band 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] KD ``` KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The original Hermitian band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See ZPBTRF for further details.``` [in] LDA ``` LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).``` [in] AFAC ``` AFAC is COMPLEX*16 array, dimension (LDAFAC,N) The factored form of the matrix A. AFAC contains the factor L or U from the L*L' or U'*U factorization in band storage format, as computed by ZPBTRF.``` [in] LDAFAC ``` LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,KD+1).``` [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 )```
Date
December 2016

Definition at line 122 of file zpbt01.f.

122 *
123 * -- LAPACK test routine (version 3.7.0) --
124 * -- LAPACK is a software package provided by Univ. of Tennessee, --
125 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126 * December 2016
127 *
128 * .. Scalar Arguments ..
129  CHARACTER uplo
130  INTEGER kd, lda, ldafac, n
131  DOUBLE PRECISION resid
132 * ..
133 * .. Array Arguments ..
134  DOUBLE PRECISION rwork( * )
135  COMPLEX*16 a( lda, * ), afac( ldafac, * )
136 * ..
137 *
138 * =====================================================================
139 *
140 *
141 * .. Parameters ..
142  DOUBLE PRECISION zero, one
143  parameter( zero = 0.0d+0, one = 1.0d+0 )
144 * ..
145 * .. Local Scalars ..
146  INTEGER i, j, k, kc, klen, ml, mu
147  DOUBLE PRECISION akk, anorm, eps
148 * ..
149 * .. External Functions ..
150  LOGICAL lsame
151  DOUBLE PRECISION dlamch, zlanhb
152  COMPLEX*16 zdotc
153  EXTERNAL lsame, dlamch, zlanhb, zdotc
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL zdscal, zher, ztrmv
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC dble, dimag, max, min
160 * ..
161 * .. Executable Statements ..
162 *
163 * Quick exit if N = 0.
164 *
165  IF( n.LE.0 ) THEN
166  resid = zero
167  RETURN
168  END IF
169 *
170 * Exit with RESID = 1/EPS if ANORM = 0.
171 *
172  eps = dlamch( 'Epsilon' )
173  anorm = zlanhb( '1', uplo, n, kd, a, lda, rwork )
174  IF( anorm.LE.zero ) THEN
175  resid = one / eps
176  RETURN
177  END IF
178 *
179 * Check the imaginary parts of the diagonal elements and return with
180 * an error code if any are nonzero.
181 *
182  IF( lsame( uplo, 'U' ) ) THEN
183  DO 10 j = 1, n
184  IF( dimag( afac( kd+1, j ) ).NE.zero ) THEN
185  resid = one / eps
186  RETURN
187  END IF
188  10 CONTINUE
189  ELSE
190  DO 20 j = 1, n
191  IF( dimag( afac( 1, j ) ).NE.zero ) THEN
192  resid = one / eps
193  RETURN
194  END IF
195  20 CONTINUE
196  END IF
197 *
198 * Compute the product U'*U, overwriting U.
199 *
200  IF( lsame( uplo, 'U' ) ) THEN
201  DO 30 k = n, 1, -1
202  kc = max( 1, kd+2-k )
203  klen = kd + 1 - kc
204 *
205 * Compute the (K,K) element of the result.
206 *
207  akk = zdotc( klen+1, afac( kc, k ), 1, afac( kc, k ), 1 )
208  afac( kd+1, k ) = akk
209 *
210 * Compute the rest of column K.
211 *
212  IF( klen.GT.0 )
213  \$ CALL ztrmv( 'Upper', 'Conjugate', 'Non-unit', klen,
214  \$ afac( kd+1, k-klen ), ldafac-1,
215  \$ afac( kc, k ), 1 )
216 *
217  30 CONTINUE
218 *
219 * UPLO = 'L': Compute the product L*L', overwriting L.
220 *
221  ELSE
222  DO 40 k = n, 1, -1
223  klen = min( kd, n-k )
224 *
225 * Add a multiple of column K of the factor L to each of
226 * columns K+1 through N.
227 *
228  IF( klen.GT.0 )
229  \$ CALL zher( 'Lower', klen, one, afac( 2, k ), 1,
230  \$ afac( 1, k+1 ), ldafac-1 )
231 *
232 * Scale column K by the diagonal element.
233 *
234  akk = afac( 1, k )
235  CALL zdscal( klen+1, akk, afac( 1, k ), 1 )
236 *
237  40 CONTINUE
238  END IF
239 *
240 * Compute the difference L*L' - A or U'*U - A.
241 *
242  IF( lsame( uplo, 'U' ) ) THEN
243  DO 60 j = 1, n
244  mu = max( 1, kd+2-j )
245  DO 50 i = mu, kd + 1
246  afac( i, j ) = afac( i, j ) - a( i, j )
247  50 CONTINUE
248  60 CONTINUE
249  ELSE
250  DO 80 j = 1, n
251  ml = min( kd+1, n-j+1 )
252  DO 70 i = 1, ml
253  afac( i, j ) = afac( i, j ) - a( i, j )
254  70 CONTINUE
255  80 CONTINUE
256  END IF
257 *
258 * Compute norm( L*L' - A ) / ( N * norm(A) * EPS )
259 *
260  resid = zlanhb( '1', uplo, n, kd, afac, ldafac, rwork )
261 *
262  resid = ( ( resid / dble( n ) ) / anorm ) / eps
263 *
264  RETURN
265 *
266 * End of ZPBT01
267 *
subroutine zher(UPLO, N, ALPHA, X, INCX, A, LDA)
ZHER
Definition: zher.f:137
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine ztrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRMV
Definition: ztrmv.f:149
complex *16 function zdotc(N, ZX, INCX, ZY, INCY)
ZDOTC
Definition: zdotc.f:85
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:80
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
double precision function zlanhb(NORM, UPLO, N, K, AB, LDAB, WORK)
ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.
Definition: zlanhb.f:134
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