LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
schkq3.f
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1 *> \brief \b SCHKQ3
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 SCHKQ3( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
12 * THRESH, A, COPYA, S, TAU, WORK, IWORK,
13 * NOUT )
14 *
15 * .. Scalar Arguments ..
16 * INTEGER NM, NN, NNB, NOUT
17 * REAL THRESH
18 * ..
19 * .. Array Arguments ..
20 * LOGICAL DOTYPE( * )
21 * INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NVAL( * ),
22 * $ NXVAL( * )
23 * REAL A( * ), COPYA( * ), S( * ),
24 * $ TAU( * ), WORK( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> SCHKQ3 tests SGEQP3.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] DOTYPE
40 *> \verbatim
41 *> DOTYPE is LOGICAL array, dimension (NTYPES)
42 *> The matrix types to be used for testing. Matrices of type j
43 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
44 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
45 *> \endverbatim
46 *>
47 *> \param[in] NM
48 *> \verbatim
49 *> NM is INTEGER
50 *> The number of values of M contained in the vector MVAL.
51 *> \endverbatim
52 *>
53 *> \param[in] MVAL
54 *> \verbatim
55 *> MVAL is INTEGER array, dimension (NM)
56 *> The values of the matrix row dimension M.
57 *> \endverbatim
58 *>
59 *> \param[in] NN
60 *> \verbatim
61 *> NN is INTEGER
62 *> The number of values of N contained in the vector NVAL.
63 *> \endverbatim
64 *>
65 *> \param[in] NVAL
66 *> \verbatim
67 *> NVAL is INTEGER array, dimension (NN)
68 *> The values of the matrix column dimension N.
69 *> \endverbatim
70 *>
71 *> \param[in] NNB
72 *> \verbatim
73 *> NNB is INTEGER
74 *> The number of values of NB and NX contained in the
75 *> vectors NBVAL and NXVAL. The blocking parameters are used
76 *> in pairs (NB,NX).
77 *> \endverbatim
78 *>
79 *> \param[in] NBVAL
80 *> \verbatim
81 *> NBVAL is INTEGER array, dimension (NNB)
82 *> The values of the blocksize NB.
83 *> \endverbatim
84 *>
85 *> \param[in] NXVAL
86 *> \verbatim
87 *> NXVAL is INTEGER array, dimension (NNB)
88 *> The values of the crossover point NX.
89 *> \endverbatim
90 *>
91 *> \param[in] THRESH
92 *> \verbatim
93 *> THRESH is REAL
94 *> The threshold value for the test ratios. A result is
95 *> included in the output file if RESULT >= THRESH. To have
96 *> every test ratio printed, use THRESH = 0.
97 *> \endverbatim
98 *>
99 *> \param[out] A
100 *> \verbatim
101 *> A is REAL array, dimension (MMAX*NMAX)
102 *> where MMAX is the maximum value of M in MVAL and NMAX is the
103 *> maximum value of N in NVAL.
104 *> \endverbatim
105 *>
106 *> \param[out] COPYA
107 *> \verbatim
108 *> COPYA is REAL array, dimension (MMAX*NMAX)
109 *> \endverbatim
110 *>
111 *> \param[out] S
112 *> \verbatim
113 *> S is REAL array, dimension
114 *> (min(MMAX,NMAX))
115 *> \endverbatim
116 *>
117 *> \param[out] TAU
118 *> \verbatim
119 *> TAU is REAL array, dimension (MMAX)
120 *> \endverbatim
121 *>
122 *> \param[out] WORK
123 *> \verbatim
124 *> WORK is REAL array, dimension
125 *> (MMAX*NMAX + 4*NMAX + MMAX)
126 *> \endverbatim
127 *>
128 *> \param[out] IWORK
129 *> \verbatim
130 *> IWORK is INTEGER array, dimension (2*NMAX)
131 *> \endverbatim
132 *>
133 *> \param[in] NOUT
134 *> \verbatim
135 *> NOUT is INTEGER
136 *> The unit number for output.
137 *> \endverbatim
138 *
139 * Authors:
140 * ========
141 *
142 *> \author Univ. of Tennessee
143 *> \author Univ. of California Berkeley
144 *> \author Univ. of Colorado Denver
145 *> \author NAG Ltd.
146 *
147 *> \ingroup single_lin
148 *
149 * =====================================================================
150  SUBROUTINE schkq3( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
151  $ THRESH, A, COPYA, S, TAU, WORK, IWORK,
152  $ NOUT )
153 *
154 * -- LAPACK test routine --
155 * -- LAPACK is a software package provided by Univ. of Tennessee, --
156 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157 *
158 * .. Scalar Arguments ..
159  INTEGER NM, NN, NNB, NOUT
160  REAL THRESH
161 * ..
162 * .. Array Arguments ..
163  LOGICAL DOTYPE( * )
164  INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NVAL( * ),
165  $ nxval( * )
166  REAL A( * ), COPYA( * ), S( * ),
167  $ TAU( * ), WORK( * )
168 * ..
169 *
170 * =====================================================================
171 *
172 * .. Parameters ..
173  INTEGER NTYPES
174  PARAMETER ( NTYPES = 6 )
175  INTEGER NTESTS
176  parameter( ntests = 3 )
177  REAL ONE, ZERO
178  parameter( one = 1.0e0, zero = 0.0e0 )
179 * ..
180 * .. Local Scalars ..
181  CHARACTER*3 PATH
182  INTEGER I, IHIGH, ILOW, IM, IMODE, IN, INB, INFO,
183  $ istep, k, lda, lw, lwork, m, mnmin, mode, n,
184  $ nb, nerrs, nfail, nrun, nx
185  REAL EPS
186 * ..
187 * .. Local Arrays ..
188  INTEGER ISEED( 4 ), ISEEDY( 4 )
189  REAL RESULT( NTESTS )
190 * ..
191 * .. External Functions ..
192  REAL SLAMCH, SQPT01, SQRT11, SQRT12
193  EXTERNAL SLAMCH, SQPT01, SQRT11, SQRT12
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL alahd, alasum, icopy, sgeqp3, slacpy, slaord,
197  $ slaset, slatms, xlaenv
198 * ..
199 * .. Intrinsic Functions ..
200  INTRINSIC max, min
201 * ..
202 * .. Scalars in Common ..
203  LOGICAL LERR, OK
204  CHARACTER*32 SRNAMT
205  INTEGER INFOT, IOUNIT
206 * ..
207 * .. Common blocks ..
208  COMMON / infoc / infot, iounit, ok, lerr
209  COMMON / srnamc / srnamt
210 * ..
211 * .. Data statements ..
212  DATA iseedy / 1988, 1989, 1990, 1991 /
213 * ..
214 * .. Executable Statements ..
215 *
216 * Initialize constants and the random number seed.
217 *
218  path( 1: 1 ) = 'Single precision'
219  path( 2: 3 ) = 'Q3'
220  nrun = 0
221  nfail = 0
222  nerrs = 0
223  DO 10 i = 1, 4
224  iseed( i ) = iseedy( i )
225  10 CONTINUE
226  eps = slamch( 'Epsilon' )
227  infot = 0
228 *
229  DO 90 im = 1, nm
230 *
231 * Do for each value of M in MVAL.
232 *
233  m = mval( im )
234  lda = max( 1, m )
235 *
236  DO 80 in = 1, nn
237 *
238 * Do for each value of N in NVAL.
239 *
240  n = nval( in )
241  mnmin = min( m, n )
242  lwork = max( 1, m*max( m, n )+4*mnmin+max( m, n ),
243  $ m*n + 2*mnmin + 4*n )
244 *
245  DO 70 imode = 1, ntypes
246  IF( .NOT.dotype( imode ) )
247  $ GO TO 70
248 *
249 * Do for each type of matrix
250 * 1: zero matrix
251 * 2: one small singular value
252 * 3: geometric distribution of singular values
253 * 4: first n/2 columns fixed
254 * 5: last n/2 columns fixed
255 * 6: every second column fixed
256 *
257  mode = imode
258  IF( imode.GT.3 )
259  $ mode = 1
260 *
261 * Generate test matrix of size m by n using
262 * singular value distribution indicated by `mode'.
263 *
264  DO 20 i = 1, n
265  iwork( i ) = 0
266  20 CONTINUE
267  IF( imode.EQ.1 ) THEN
268  CALL slaset( 'Full', m, n, zero, zero, copya, lda )
269  DO 30 i = 1, mnmin
270  s( i ) = zero
271  30 CONTINUE
272  ELSE
273  CALL slatms( m, n, 'Uniform', iseed, 'Nonsymm', s,
274  $ mode, one / eps, one, m, n, 'No packing',
275  $ copya, lda, work, info )
276  IF( imode.GE.4 ) THEN
277  IF( imode.EQ.4 ) THEN
278  ilow = 1
279  istep = 1
280  ihigh = max( 1, n / 2 )
281  ELSE IF( imode.EQ.5 ) THEN
282  ilow = max( 1, n / 2 )
283  istep = 1
284  ihigh = n
285  ELSE IF( imode.EQ.6 ) THEN
286  ilow = 1
287  istep = 2
288  ihigh = n
289  END IF
290  DO 40 i = ilow, ihigh, istep
291  iwork( i ) = 1
292  40 CONTINUE
293  END IF
294  CALL slaord( 'Decreasing', mnmin, s, 1 )
295  END IF
296 *
297  DO 60 inb = 1, nnb
298 *
299 * Do for each pair of values (NB,NX) in NBVAL and NXVAL.
300 *
301  nb = nbval( inb )
302  CALL xlaenv( 1, nb )
303  nx = nxval( inb )
304  CALL xlaenv( 3, nx )
305 *
306 * Get a working copy of COPYA into A and a copy of
307 * vector IWORK.
308 *
309  CALL slacpy( 'All', m, n, copya, lda, a, lda )
310  CALL icopy( n, iwork( 1 ), 1, iwork( n+1 ), 1 )
311 *
312 * Compute the QR factorization with pivoting of A
313 *
314  lw = max( 1, 2*n+nb*( n+1 ) )
315 *
316 * Compute the QP3 factorization of A
317 *
318  srnamt = 'SGEQP3'
319  CALL sgeqp3( m, n, a, lda, iwork( n+1 ), tau, work,
320  $ lw, info )
321 *
322 * Compute norm(svd(a) - svd(r))
323 *
324  result( 1 ) = sqrt12( m, n, a, lda, s, work,
325  $ lwork )
326 *
327 * Compute norm( A*P - Q*R )
328 *
329  result( 2 ) = sqpt01( m, n, mnmin, copya, a, lda, tau,
330  $ iwork( n+1 ), work, lwork )
331 *
332 * Compute Q'*Q
333 *
334  result( 3 ) = sqrt11( m, mnmin, a, lda, tau, work,
335  $ lwork )
336 *
337 * Print information about the tests that did not pass
338 * the threshold.
339 *
340  DO 50 k = 1, ntests
341  IF( result( k ).GE.thresh ) THEN
342  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
343  $ CALL alahd( nout, path )
344  WRITE( nout, fmt = 9999 )'SGEQP3', m, n, nb,
345  $ imode, k, result( k )
346  nfail = nfail + 1
347  END IF
348  50 CONTINUE
349  nrun = nrun + ntests
350 *
351  60 CONTINUE
352  70 CONTINUE
353  80 CONTINUE
354  90 CONTINUE
355 *
356 * Print a summary of the results.
357 *
358  CALL alasum( path, nout, nfail, nrun, nerrs )
359 *
360  9999 FORMAT( 1x, a, ' M =', i5, ', N =', i5, ', NB =', i4, ', type ',
361  $ i2, ', test ', i2, ', ratio =', g12.5 )
362 *
363 * End of SCHKQ3
364 *
365  END
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:73
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:81
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
subroutine icopy(N, SX, INCX, SY, INCY)
ICOPY
Definition: icopy.f:75
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine sgeqp3(M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
SGEQP3
Definition: sgeqp3.f:151
subroutine slaord(JOB, N, X, INCX)
SLAORD
Definition: slaord.f:73
subroutine schkq3(DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, THRESH, A, COPYA, S, TAU, WORK, IWORK, NOUT)
SCHKQ3
Definition: schkq3.f:153