 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dort03()

 subroutine dort03 ( character*( * ) RC, integer MU, integer MV, integer N, integer K, double precision, dimension( ldu, * ) U, integer LDU, double precision, dimension( ldv, * ) V, integer LDV, double precision, dimension( * ) WORK, integer LWORK, double precision RESULT, integer INFO )

DORT03

Purpose:
``` DORT03 compares two orthogonal 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 S is +-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 DORT03 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 DORT03 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 DORT03 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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] RESULT ``` RESULT is DOUBLE PRECISION 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 154 of file dort03.f.

156 *
157 * -- LAPACK test routine --
158 * -- LAPACK is a software package provided by Univ. of Tennessee, --
159 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
160 *
161 * .. Scalar Arguments ..
162  CHARACTER*( * ) RC
163  INTEGER INFO, K, LDU, LDV, LWORK, MU, MV, N
164  DOUBLE PRECISION RESULT
165 * ..
166 * .. Array Arguments ..
167  DOUBLE PRECISION U( LDU, * ), V( LDV, * ), WORK( * )
168 * ..
169 *
170 * =====================================================================
171 *
172 * .. Parameters ..
173  DOUBLE PRECISION ZERO, ONE
174  parameter( zero = 0.0d0, one = 1.0d0 )
175 * ..
176 * .. Local Scalars ..
177  INTEGER I, IRC, J, LMX
178  DOUBLE PRECISION RES1, RES2, S, ULP
179 * ..
180 * .. External Functions ..
181  LOGICAL LSAME
182  INTEGER IDAMAX
183  DOUBLE PRECISION DLAMCH
184  EXTERNAL lsame, idamax, dlamch
185 * ..
186 * .. Intrinsic Functions ..
187  INTRINSIC abs, dble, max, min, sign
188 * ..
189 * .. External Subroutines ..
190  EXTERNAL dort01, xerbla
191 * ..
192 * .. Executable Statements ..
193 *
194 * Check inputs
195 *
196  info = 0
197  IF( lsame( rc, 'R' ) ) THEN
198  irc = 0
199  ELSE IF( lsame( rc, 'C' ) ) THEN
200  irc = 1
201  ELSE
202  irc = -1
203  END IF
204  IF( irc.EQ.-1 ) THEN
205  info = -1
206  ELSE IF( mu.LT.0 ) THEN
207  info = -2
208  ELSE IF( mv.LT.0 ) THEN
209  info = -3
210  ELSE IF( n.LT.0 ) THEN
211  info = -4
212  ELSE IF( k.LT.0 .OR. k.GT.max( mu, mv ) ) THEN
213  info = -5
214  ELSE IF( ( irc.EQ.0 .AND. ldu.LT.max( 1, mu ) ) .OR.
215  \$ ( irc.EQ.1 .AND. ldu.LT.max( 1, n ) ) ) THEN
216  info = -7
217  ELSE IF( ( irc.EQ.0 .AND. ldv.LT.max( 1, mv ) ) .OR.
218  \$ ( irc.EQ.1 .AND. ldv.LT.max( 1, n ) ) ) THEN
219  info = -9
220  END IF
221  IF( info.NE.0 ) THEN
222  CALL xerbla( 'DORT03', -info )
223  RETURN
224  END IF
225 *
226 * Initialize result
227 *
228  result = zero
229  IF( mu.EQ.0 .OR. mv.EQ.0 .OR. n.EQ.0 )
230  \$ RETURN
231 *
232 * Machine constants
233 *
234  ulp = dlamch( 'Precision' )
235 *
236  IF( irc.EQ.0 ) THEN
237 *
238 * Compare rows
239 *
240  res1 = zero
241  DO 20 i = 1, k
242  lmx = idamax( n, u( i, 1 ), ldu )
243  s = sign( one, u( i, lmx ) )*sign( one, v( i, lmx ) )
244  DO 10 j = 1, n
245  res1 = max( res1, abs( u( i, j )-s*v( i, j ) ) )
246  10 CONTINUE
247  20 CONTINUE
248  res1 = res1 / ( dble( n )*ulp )
249 *
250 * Compute orthogonality of rows of V.
251 *
252  CALL dort01( 'Rows', mv, n, v, ldv, work, lwork, res2 )
253 *
254  ELSE
255 *
256 * Compare columns
257 *
258  res1 = zero
259  DO 40 i = 1, k
260  lmx = idamax( n, u( 1, i ), 1 )
261  s = sign( one, u( lmx, i ) )*sign( one, v( lmx, i ) )
262  DO 30 j = 1, n
263  res1 = max( res1, abs( u( j, i )-s*v( j, i ) ) )
264  30 CONTINUE
265  40 CONTINUE
266  res1 = res1 / ( dble( n )*ulp )
267 *
268 * Compute orthogonality of columns of V.
269 *
270  CALL dort01( 'Columns', n, mv, v, ldv, work, lwork, res2 )
271  END IF
272 *
273  result = min( max( res1, res2 ), one / ulp )
274  RETURN
275 *
276 * End of DORT03
277 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dort01(ROWCOL, M, N, U, LDU, WORK, LWORK, RESID)
DORT01
Definition: dort01.f:116
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