LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cunt03()

 subroutine cunt03 ( character*( * ) RC, integer MU, integer MV, integer N, integer K, complex, dimension( ldu, * ) U, integer LDU, complex, dimension( ldv, * ) V, integer LDV, complex, dimension( * ) WORK, integer LWORK, real, dimension( * ) RWORK, real RESULT, integer INFO )

CUNT03

Purpose:
``` CUNT03 compares two unitary matrices U and V to see if their
corresponding rows or columns span the same spaces.  The rows are
checked if RC = 'R', and the columns are checked if RC = 'C'.

RESULT is the maximum of

| V*V' - I | / ( MV ulp ), if RC = 'R', or

| V'*V - I | / ( MV ulp ), if RC = 'C',

and the maximum over rows (or columns) 1 to K of

| U(i) - S*V(i) |/ ( N ulp )

where abs(S) = 1 (chosen to minimize the expression), U(i) is the
i-th row (column) of U, and V(i) is the i-th row (column) of V.```
Parameters
 [in] RC ``` RC is CHARACTER*1 If RC = 'R' the rows of U and V are to be compared. If RC = 'C' the columns of U and V are to be compared.``` [in] MU ``` MU is INTEGER The number of rows of U if RC = 'R', and the number of columns if RC = 'C'. If MU = 0 CUNT03 does nothing. MU must be at least zero.``` [in] MV ``` MV is INTEGER The number of rows of V if RC = 'R', and the number of columns if RC = 'C'. If MV = 0 CUNT03 does nothing. MV must be at least zero.``` [in] N ``` N is INTEGER If RC = 'R', the number of columns in the matrices U and V, and if RC = 'C', the number of rows in U and V. If N = 0 CUNT03 does nothing. N must be at least zero.``` [in] K ``` K is INTEGER The number of rows or columns of U and V to compare. 0 <= K <= max(MU,MV).``` [in] U ``` U is COMPLEX array, dimension (LDU,N) The first matrix to compare. If RC = 'R', U is MU by N, and if RC = 'C', U is N by MU.``` [in] LDU ``` LDU is INTEGER The leading dimension of U. If RC = 'R', LDU >= max(1,MU), and if RC = 'C', LDU >= max(1,N).``` [in] V ``` V is COMPLEX array, dimension (LDV,N) The second matrix to compare. If RC = 'R', V is MV by N, and if RC = 'C', V is N by MV.``` [in] LDV ``` LDV is INTEGER The leading dimension of V. If RC = 'R', LDV >= max(1,MV), and if RC = 'C', LDV >= max(1,N).``` [out] WORK ` WORK is COMPLEX 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 RC = 'C' or M*M if RC = 'R', but the tests will be done even if LWORK is 0.``` [out] RWORK ` RWORK is REAL array, dimension (max(MV,N))` [out] RESULT ``` RESULT is REAL The value computed by the test described above. RESULT is limited to 1/ulp to avoid overflow.``` [out] INFO ``` INFO is INTEGER 0 indicates a successful exit -k indicates the k-th parameter had an illegal value```

Definition at line 160 of file cunt03.f.

162*
163* -- LAPACK test routine --
164* -- LAPACK is a software package provided by Univ. of Tennessee, --
165* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166*
167* .. Scalar Arguments ..
168 CHARACTER*( * ) RC
169 INTEGER INFO, K, LDU, LDV, LWORK, MU, MV, N
170 REAL RESULT
171* ..
172* .. Array Arguments ..
173 REAL RWORK( * )
174 COMPLEX U( LDU, * ), V( LDV, * ), WORK( * )
175* ..
176*
177* =====================================================================
178*
179*
180* .. Parameters ..
181 REAL ZERO, ONE
182 parameter( zero = 0.0e0, one = 1.0e0 )
183* ..
184* .. Local Scalars ..
185 INTEGER I, IRC, J, LMX
186 REAL RES1, RES2, ULP
187 COMPLEX S, SU, SV
188* ..
189* .. External Functions ..
190 LOGICAL LSAME
191 INTEGER ICAMAX
192 REAL SLAMCH
193 EXTERNAL lsame, icamax, slamch
194* ..
195* .. Intrinsic Functions ..
196 INTRINSIC abs, cmplx, max, min, real
197* ..
198* .. External Subroutines ..
199 EXTERNAL cunt01, xerbla
200* ..
201* .. Executable Statements ..
202*
203* Check inputs
204*
205 info = 0
206 IF( lsame( rc, 'R' ) ) THEN
207 irc = 0
208 ELSE IF( lsame( rc, 'C' ) ) THEN
209 irc = 1
210 ELSE
211 irc = -1
212 END IF
213 IF( irc.EQ.-1 ) THEN
214 info = -1
215 ELSE IF( mu.LT.0 ) THEN
216 info = -2
217 ELSE IF( mv.LT.0 ) THEN
218 info = -3
219 ELSE IF( n.LT.0 ) THEN
220 info = -4
221 ELSE IF( k.LT.0 .OR. k.GT.max( mu, mv ) ) THEN
222 info = -5
223 ELSE IF( ( irc.EQ.0 .AND. ldu.LT.max( 1, mu ) ) .OR.
224 \$ ( irc.EQ.1 .AND. ldu.LT.max( 1, n ) ) ) THEN
225 info = -7
226 ELSE IF( ( irc.EQ.0 .AND. ldv.LT.max( 1, mv ) ) .OR.
227 \$ ( irc.EQ.1 .AND. ldv.LT.max( 1, n ) ) ) THEN
228 info = -9
229 END IF
230 IF( info.NE.0 ) THEN
231 CALL xerbla( 'CUNT03', -info )
232 RETURN
233 END IF
234*
235* Initialize result
236*
237 result = zero
238 IF( mu.EQ.0 .OR. mv.EQ.0 .OR. n.EQ.0 )
239 \$ RETURN
240*
241* Machine constants
242*
243 ulp = slamch( 'Precision' )
244*
245 IF( irc.EQ.0 ) THEN
246*
247* Compare rows
248*
249 res1 = zero
250 DO 20 i = 1, k
251 lmx = icamax( n, u( i, 1 ), ldu )
252 IF( v( i, lmx ).EQ.cmplx( zero ) ) THEN
253 sv = one
254 ELSE
255 sv = abs( v( i, lmx ) ) / v( i, lmx )
256 END IF
257 IF( u( i, lmx ).EQ.cmplx( zero ) ) THEN
258 su = one
259 ELSE
260 su = abs( u( i, lmx ) ) / u( i, lmx )
261 END IF
262 s = sv / su
263 DO 10 j = 1, n
264 res1 = max( res1, abs( u( i, j )-s*v( i, j ) ) )
265 10 CONTINUE
266 20 CONTINUE
267 res1 = res1 / ( real( n )*ulp )
268*
269* Compute orthogonality of rows of V.
270*
271 CALL cunt01( 'Rows', mv, n, v, ldv, work, lwork, rwork, res2 )
272*
273 ELSE
274*
275* Compare columns
276*
277 res1 = zero
278 DO 40 i = 1, k
279 lmx = icamax( n, u( 1, i ), 1 )
280 IF( v( lmx, i ).EQ.cmplx( zero ) ) THEN
281 sv = one
282 ELSE
283 sv = abs( v( lmx, i ) ) / v( lmx, i )
284 END IF
285 IF( u( lmx, i ).EQ.cmplx( zero ) ) THEN
286 su = one
287 ELSE
288 su = abs( u( lmx, i ) ) / u( lmx, i )
289 END IF
290 s = sv / su
291 DO 30 j = 1, n
292 res1 = max( res1, abs( u( j, i )-s*v( j, i ) ) )
293 30 CONTINUE
294 40 CONTINUE
295 res1 = res1 / ( real( n )*ulp )
296*
297* Compute orthogonality of columns of V.
298*
299 CALL cunt01( 'Columns', n, mv, v, ldv, work, lwork, rwork,
300 \$ res2 )
301 END IF
302*
303 result = min( max( res1, res2 ), one / ulp )
304 RETURN
305*
306* End of CUNT03
307*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
CUNT01
Definition: cunt01.f:126
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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