LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zunt03.f
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1 *> \brief \b ZUNT03
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE ZUNT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
12 * RWORK, RESULT, INFO )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER*( * ) RC
16 * INTEGER INFO, K, LDU, LDV, LWORK, MU, MV, N
17 * DOUBLE PRECISION RESULT
18 * ..
19 * .. Array Arguments ..
20 * DOUBLE PRECISION RWORK( * )
21 * COMPLEX*16 U( LDU, * ), V( LDV, * ), WORK( * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> ZUNT03 compares two unitary matrices U and V to see if their
31 *> corresponding rows or columns span the same spaces. The rows are
32 *> checked if RC = 'R', and the columns are checked if RC = 'C'.
33 *>
34 *> RESULT is the maximum of
35 *>
36 *> | V*V' - I | / ( MV ulp ), if RC = 'R', or
37 *>
38 *> | V'*V - I | / ( MV ulp ), if RC = 'C',
39 *>
40 *> and the maximum over rows (or columns) 1 to K of
41 *>
42 *> | U(i) - S*V(i) |/ ( N ulp )
43 *>
44 *> where abs(S) = 1 (chosen to minimize the expression), U(i) is the
45 *> i-th row (column) of U, and V(i) is the i-th row (column) of V.
46 *> \endverbatim
47 *
48 * Arguments:
49 * ==========
50 *
51 *> \param[in] RC
52 *> \verbatim
53 *> RC is CHARACTER*1
54 *> If RC = 'R' the rows of U and V are to be compared.
55 *> If RC = 'C' the columns of U and V are to be compared.
56 *> \endverbatim
57 *>
58 *> \param[in] MU
59 *> \verbatim
60 *> MU is INTEGER
61 *> The number of rows of U if RC = 'R', and the number of
62 *> columns if RC = 'C'. If MU = 0 ZUNT03 does nothing.
63 *> MU must be at least zero.
64 *> \endverbatim
65 *>
66 *> \param[in] MV
67 *> \verbatim
68 *> MV is INTEGER
69 *> The number of rows of V if RC = 'R', and the number of
70 *> columns if RC = 'C'. If MV = 0 ZUNT03 does nothing.
71 *> MV must be at least zero.
72 *> \endverbatim
73 *>
74 *> \param[in] N
75 *> \verbatim
76 *> N is INTEGER
77 *> If RC = 'R', the number of columns in the matrices U and V,
78 *> and if RC = 'C', the number of rows in U and V. If N = 0
79 *> ZUNT03 does nothing. N must be at least zero.
80 *> \endverbatim
81 *>
82 *> \param[in] K
83 *> \verbatim
84 *> K is INTEGER
85 *> The number of rows or columns of U and V to compare.
86 *> 0 <= K <= max(MU,MV).
87 *> \endverbatim
88 *>
89 *> \param[in] U
90 *> \verbatim
91 *> U is COMPLEX*16 array, dimension (LDU,N)
92 *> The first matrix to compare. If RC = 'R', U is MU by N, and
93 *> if RC = 'C', U is N by MU.
94 *> \endverbatim
95 *>
96 *> \param[in] LDU
97 *> \verbatim
98 *> LDU is INTEGER
99 *> The leading dimension of U. If RC = 'R', LDU >= max(1,MU),
100 *> and if RC = 'C', LDU >= max(1,N).
101 *> \endverbatim
102 *>
103 *> \param[in] V
104 *> \verbatim
105 *> V is COMPLEX*16 array, dimension (LDV,N)
106 *> The second matrix to compare. If RC = 'R', V is MV by N, and
107 *> if RC = 'C', V is N by MV.
108 *> \endverbatim
109 *>
110 *> \param[in] LDV
111 *> \verbatim
112 *> LDV is INTEGER
113 *> The leading dimension of V. If RC = 'R', LDV >= max(1,MV),
114 *> and if RC = 'C', LDV >= max(1,N).
115 *> \endverbatim
116 *>
117 *> \param[out] WORK
118 *> \verbatim
119 *> WORK is COMPLEX*16 array, dimension (LWORK)
120 *> \endverbatim
121 *>
122 *> \param[in] LWORK
123 *> \verbatim
124 *> LWORK is INTEGER
125 *> The length of the array WORK. For best performance, LWORK
126 *> should be at least N*N if RC = 'C' or M*M if RC = 'R', but
127 *> the tests will be done even if LWORK is 0.
128 *> \endverbatim
129 *>
130 *> \param[out] RWORK
131 *> \verbatim
132 *> RWORK is DOUBLE PRECISION array, dimension (max(MV,N))
133 *> \endverbatim
134 *>
135 *> \param[out] RESULT
136 *> \verbatim
137 *> RESULT is DOUBLE PRECISION
138 *> The value computed by the test described above. RESULT is
139 *> limited to 1/ulp to avoid overflow.
140 *> \endverbatim
141 *>
142 *> \param[out] INFO
143 *> \verbatim
144 *> INFO is INTEGER
145 *> 0 indicates a successful exit
146 *> -k indicates the k-th parameter had an illegal value
147 *> \endverbatim
148 *
149 * Authors:
150 * ========
151 *
152 *> \author Univ. of Tennessee
153 *> \author Univ. of California Berkeley
154 *> \author Univ. of Colorado Denver
155 *> \author NAG Ltd.
156 *
157 *> \ingroup complex16_eig
158 *
159 * =====================================================================
160  SUBROUTINE zunt03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
161  $ RWORK, RESULT, INFO )
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  DOUBLE PRECISION RESULT
171 * ..
172 * .. Array Arguments ..
173  DOUBLE PRECISION RWORK( * )
174  COMPLEX*16 U( LDU, * ), V( LDV, * ), WORK( * )
175 * ..
176 *
177 * =====================================================================
178 *
179 *
180 * .. Parameters ..
181  DOUBLE PRECISION ZERO, ONE
182  parameter( zero = 0.0d0, one = 1.0d0 )
183 * ..
184 * .. Local Scalars ..
185  INTEGER I, IRC, J, LMX
186  DOUBLE PRECISION RES1, RES2, ULP
187  COMPLEX*16 S, SU, SV
188 * ..
189 * .. External Functions ..
190  LOGICAL LSAME
191  INTEGER IZAMAX
192  DOUBLE PRECISION DLAMCH
193  EXTERNAL lsame, izamax, dlamch
194 * ..
195 * .. Intrinsic Functions ..
196  INTRINSIC abs, dble, dcmplx, max, min
197 * ..
198 * .. External Subroutines ..
199  EXTERNAL xerbla, zunt01
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( 'ZUNT03', -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 = dlamch( 'Precision' )
244 *
245  IF( irc.EQ.0 ) THEN
246 *
247 * Compare rows
248 *
249  res1 = zero
250  DO 20 i = 1, k
251  lmx = izamax( n, u( i, 1 ), ldu )
252  IF( v( i, lmx ).EQ.dcmplx( 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.dcmplx( 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 / ( dble( n )*ulp )
268 *
269 * Compute orthogonality of rows of V.
270 *
271  CALL zunt01( '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 = izamax( n, u( 1, i ), 1 )
280  IF( v( lmx, i ).EQ.dcmplx( 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.dcmplx( 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 / ( dble( n )*ulp )
296 *
297 * Compute orthogonality of columns of V.
298 *
299  CALL zunt01( '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 ZUNT03
307 *
308  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
ZUNT01
Definition: zunt01.f:126
subroutine zunt03(RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK, RWORK, RESULT, INFO)
ZUNT03
Definition: zunt03.f:162