LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zunt01()

 subroutine zunt01 ( character ROWCOL, integer M, integer N, complex*16, dimension( ldu, * ) U, integer LDU, complex*16, dimension( * ) WORK, integer LWORK, double precision, dimension( * ) RWORK, double precision RESID )

ZUNT01

Purpose:
``` ZUNT01 checks that the matrix U is unitary by computing the ratio

RESID = norm( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
or
RESID = norm( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.

Alternatively, if there isn't sufficient workspace to form
I - U*U' or I - U'*U, the ratio is computed as

RESID = abs( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
or
RESID = abs( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.

where EPS is the machine precision.  ROWCOL is used only if m = n;
if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
assumed to be 'R'.```
Parameters
 [in] ROWCOL ``` ROWCOL is CHARACTER Specifies whether the rows or columns of U should be checked for orthogonality. Used only if M = N. = 'R': Check for orthogonal rows of U = 'C': Check for orthogonal columns of U``` [in] M ``` M is INTEGER The number of rows of the matrix U.``` [in] N ``` N is INTEGER The number of columns of the matrix U.``` [in] U ``` U is COMPLEX*16 array, dimension (LDU,N) The unitary matrix U. U is checked for orthogonal columns if m > n or if m = n and ROWCOL = 'C'. U is checked for orthogonal rows if m < n or if m = n and ROWCOL = 'R'.``` [in] LDU ``` LDU is INTEGER The leading dimension of the array U. LDU >= max(1,M).``` [out] WORK ` WORK is COMPLEX*16 array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. For best performance, LWORK should be at least N*N if ROWCOL = 'C' or M*M if ROWCOL = 'R', but the test will be done even if LWORK is 0.``` [out] RWORK ``` RWORK is DOUBLE PRECISION array, dimension (min(M,N)) Used only if LWORK is large enough to use the Level 3 BLAS code.``` [out] RESID ``` RESID is DOUBLE PRECISION RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'.```

Definition at line 124 of file zunt01.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 ROWCOL
133  INTEGER LDU, LWORK, M, N
134  DOUBLE PRECISION RESID
135 * ..
136 * .. Array Arguments ..
137  DOUBLE PRECISION RWORK( * )
138  COMPLEX*16 U( LDU, * ), WORK( * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  DOUBLE PRECISION ZERO, ONE
145  parameter( zero = 0.0d+0, one = 1.0d+0 )
146 * ..
147 * .. Local Scalars ..
148  CHARACTER TRANSU
149  INTEGER I, J, K, LDWORK, MNMIN
150  DOUBLE PRECISION EPS
151  COMPLEX*16 TMP, ZDUM
152 * ..
153 * .. External Functions ..
154  LOGICAL LSAME
155  DOUBLE PRECISION DLAMCH, ZLANSY
156  COMPLEX*16 ZDOTC
157  EXTERNAL lsame, dlamch, zlansy, zdotc
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL zherk, zlaset
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC abs, dble, dcmplx, dimag, max, min
164 * ..
165 * .. Statement Functions ..
166  DOUBLE PRECISION CABS1
167 * ..
168 * .. Statement Function definitions ..
169  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
170 * ..
171 * .. Executable Statements ..
172 *
173  resid = zero
174 *
175 * Quick return if possible
176 *
177  IF( m.LE.0 .OR. n.LE.0 )
178  \$ RETURN
179 *
180  eps = dlamch( 'Precision' )
181  IF( m.LT.n .OR. ( m.EQ.n .AND. lsame( rowcol, 'R' ) ) ) THEN
182  transu = 'N'
183  k = n
184  ELSE
185  transu = 'C'
186  k = m
187  END IF
188  mnmin = min( m, n )
189 *
190  IF( ( mnmin+1 )*mnmin.LE.lwork ) THEN
191  ldwork = mnmin
192  ELSE
193  ldwork = 0
194  END IF
195  IF( ldwork.GT.0 ) THEN
196 *
197 * Compute I - U*U' or I - U'*U.
198 *
199  CALL zlaset( 'Upper', mnmin, mnmin, dcmplx( zero ),
200  \$ dcmplx( one ), work, ldwork )
201  CALL zherk( 'Upper', transu, mnmin, k, -one, u, ldu, one, work,
202  \$ ldwork )
203 *
204 * Compute norm( I - U*U' ) / ( K * EPS ) .
205 *
206  resid = zlansy( '1', 'Upper', mnmin, work, ldwork, rwork )
207  resid = ( resid / dble( k ) ) / eps
208  ELSE IF( transu.EQ.'C' ) THEN
209 *
210 * Find the maximum element in abs( I - U'*U ) / ( m * EPS )
211 *
212  DO 20 j = 1, n
213  DO 10 i = 1, j
214  IF( i.NE.j ) THEN
215  tmp = zero
216  ELSE
217  tmp = one
218  END IF
219  tmp = tmp - zdotc( m, u( 1, i ), 1, u( 1, j ), 1 )
220  resid = max( resid, cabs1( tmp ) )
221  10 CONTINUE
222  20 CONTINUE
223  resid = ( resid / dble( m ) ) / eps
224  ELSE
225 *
226 * Find the maximum element in abs( I - U*U' ) / ( n * EPS )
227 *
228  DO 40 j = 1, m
229  DO 30 i = 1, j
230  IF( i.NE.j ) THEN
231  tmp = zero
232  ELSE
233  tmp = one
234  END IF
235  tmp = tmp - zdotc( n, u( j, 1 ), ldu, u( i, 1 ), ldu )
236  resid = max( resid, cabs1( tmp ) )
237  30 CONTINUE
238  40 CONTINUE
239  resid = ( resid / dble( n ) ) / eps
240  END IF
241  RETURN
242 *
243 * End of ZUNT01
244 *
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 zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:173
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
double precision function zlansy(NORM, UPLO, N, A, LDA, WORK)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansy.f:123
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