LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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