LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
schktz.f
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1 *> \brief \b SCHKTZ
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 SCHKTZ( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A,
12 * COPYA, S, TAU, WORK, NOUT )
13 *
14 * .. Scalar Arguments ..
15 * LOGICAL TSTERR
16 * INTEGER NM, NN, NOUT
17 * REAL THRESH
18 * ..
19 * .. Array Arguments ..
20 * LOGICAL DOTYPE( * )
21 * INTEGER MVAL( * ), NVAL( * )
22 * REAL A( * ), COPYA( * ), S( * ),
23 * $ TAU( * ), WORK( * )
24 * ..
25 *
26 *
27 *> \par Purpose:
28 * =============
29 *>
30 *> \verbatim
31 *>
32 *> SCHKTZ tests STZRZF.
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] DOTYPE
39 *> \verbatim
40 *> DOTYPE is LOGICAL array, dimension (NTYPES)
41 *> The matrix types to be used for testing. Matrices of type j
42 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
43 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
44 *> \endverbatim
45 *>
46 *> \param[in] NM
47 *> \verbatim
48 *> NM is INTEGER
49 *> The number of values of M contained in the vector MVAL.
50 *> \endverbatim
51 *>
52 *> \param[in] MVAL
53 *> \verbatim
54 *> MVAL is INTEGER array, dimension (NM)
55 *> The values of the matrix row dimension M.
56 *> \endverbatim
57 *>
58 *> \param[in] NN
59 *> \verbatim
60 *> NN is INTEGER
61 *> The number of values of N contained in the vector NVAL.
62 *> \endverbatim
63 *>
64 *> \param[in] NVAL
65 *> \verbatim
66 *> NVAL is INTEGER array, dimension (NN)
67 *> The values of the matrix column dimension N.
68 *> \endverbatim
69 *>
70 *> \param[in] THRESH
71 *> \verbatim
72 *> THRESH is REAL
73 *> The threshold value for the test ratios. A result is
74 *> included in the output file if RESULT >= THRESH. To have
75 *> every test ratio printed, use THRESH = 0.
76 *> \endverbatim
77 *>
78 *> \param[in] TSTERR
79 *> \verbatim
80 *> TSTERR is LOGICAL
81 *> Flag that indicates whether error exits are to be tested.
82 *> \endverbatim
83 *>
84 *> \param[out] A
85 *> \verbatim
86 *> A is REAL array, dimension (MMAX*NMAX)
87 *> where MMAX is the maximum value of M in MVAL and NMAX is the
88 *> maximum value of N in NVAL.
89 *> \endverbatim
90 *>
91 *> \param[out] COPYA
92 *> \verbatim
93 *> COPYA is REAL array, dimension (MMAX*NMAX)
94 *> \endverbatim
95 *>
96 *> \param[out] S
97 *> \verbatim
98 *> S is REAL array, dimension
99 *> (min(MMAX,NMAX))
100 *> \endverbatim
101 *>
102 *> \param[out] TAU
103 *> \verbatim
104 *> TAU is REAL array, dimension (MMAX)
105 *> \endverbatim
106 *>
107 *> \param[out] WORK
108 *> \verbatim
109 *> WORK is REAL array, dimension
110 *> (MMAX*NMAX + 4*NMAX + MMAX)
111 *> \endverbatim
112 *>
113 *> \param[in] NOUT
114 *> \verbatim
115 *> NOUT is INTEGER
116 *> The unit number for output.
117 *> \endverbatim
118 *
119 * Authors:
120 * ========
121 *
122 *> \author Univ. of Tennessee
123 *> \author Univ. of California Berkeley
124 *> \author Univ. of Colorado Denver
125 *> \author NAG Ltd.
126 *
127 *> \date December 2016
128 *
129 *> \ingroup single_lin
130 *
131 * =====================================================================
132  SUBROUTINE schktz( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A,
133  $ COPYA, S, TAU, WORK, NOUT )
134 *
135 * -- LAPACK test routine (version 3.7.0) --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 * December 2016
139 *
140 * .. Scalar Arguments ..
141  LOGICAL TSTERR
142  INTEGER NM, NN, NOUT
143  REAL THRESH
144 * ..
145 * .. Array Arguments ..
146  LOGICAL DOTYPE( * )
147  INTEGER MVAL( * ), NVAL( * )
148  REAL A( * ), COPYA( * ), S( * ),
149  $ tau( * ), work( * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  INTEGER NTYPES
156  parameter( ntypes = 3 )
157  INTEGER NTESTS
158  parameter( ntests = 3 )
159  REAL ONE, ZERO
160  parameter( one = 1.0e0, zero = 0.0e0 )
161 * ..
162 * .. Local Scalars ..
163  CHARACTER*3 PATH
164  INTEGER I, IM, IMODE, IN, INFO, K, LDA, LWORK, M,
165  $ mnmin, mode, n, nerrs, nfail, nrun
166  REAL EPS
167 * ..
168 * .. Local Arrays ..
169  INTEGER ISEED( 4 ), ISEEDY( 4 )
170  REAL RESULT( ntests )
171 * ..
172 * .. External Functions ..
173  REAL SLAMCH, SQRT12, SRZT01, SRZT02
174  EXTERNAL slamch, sqrt12, srzt01, srzt02
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL alahd, alasum, serrtz, sgeqr2, slacpy, slaord,
178  $ slaset, slatms, stzrzf
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC max, min
182 * ..
183 * .. Scalars in Common ..
184  LOGICAL LERR, OK
185  CHARACTER*32 SRNAMT
186  INTEGER INFOT, IOUNIT
187 * ..
188 * .. Common blocks ..
189  COMMON / infoc / infot, iounit, ok, lerr
190  COMMON / srnamc / srnamt
191 * ..
192 * .. Data statements ..
193  DATA iseedy / 1988, 1989, 1990, 1991 /
194 * ..
195 * .. Executable Statements ..
196 *
197 * Initialize constants and the random number seed.
198 *
199  path( 1: 1 ) = 'Single precision'
200  path( 2: 3 ) = 'TZ'
201  nrun = 0
202  nfail = 0
203  nerrs = 0
204  DO 10 i = 1, 4
205  iseed( i ) = iseedy( i )
206  10 CONTINUE
207  eps = slamch( 'Epsilon' )
208 *
209 * Test the error exits
210 *
211  IF( tsterr )
212  $ CALL serrtz( path, nout )
213  infot = 0
214 *
215  DO 70 im = 1, nm
216 *
217 * Do for each value of M in MVAL.
218 *
219  m = mval( im )
220  lda = max( 1, m )
221 *
222  DO 60 in = 1, nn
223 *
224 * Do for each value of N in NVAL for which M .LE. N.
225 *
226  n = nval( in )
227  mnmin = min( m, n )
228  lwork = max( 1, n*n+4*m+n, m*n+2*mnmin+4*n )
229 *
230  IF( m.LE.n ) THEN
231  DO 50 imode = 1, ntypes
232  IF( .NOT.dotype( imode ) )
233  $ GO TO 50
234 *
235 * Do for each type of singular value distribution.
236 * 0: zero matrix
237 * 1: one small singular value
238 * 2: exponential distribution
239 *
240  mode = imode - 1
241 *
242 * Test STZRQF
243 *
244 * Generate test matrix of size m by n using
245 * singular value distribution indicated by `mode'.
246 *
247  IF( mode.EQ.0 ) THEN
248  CALL slaset( 'Full', m, n, zero, zero, a, lda )
249  DO 30 i = 1, mnmin
250  s( i ) = zero
251  30 CONTINUE
252  ELSE
253  CALL slatms( m, n, 'Uniform', iseed,
254  $ 'Nonsymmetric', s, imode,
255  $ one / eps, one, m, n, 'No packing', a,
256  $ lda, work, info )
257  CALL sgeqr2( m, n, a, lda, work, work( mnmin+1 ),
258  $ info )
259  CALL slaset( 'Lower', m-1, n, zero, zero, a( 2 ),
260  $ lda )
261  CALL slaord( 'Decreasing', mnmin, s, 1 )
262  END IF
263 *
264 * Save A and its singular values
265 *
266  CALL slacpy( 'All', m, n, a, lda, copya, lda )
267 *
268 * Call STZRZF to reduce the upper trapezoidal matrix to
269 * upper triangular form.
270 *
271  srnamt = 'STZRZF'
272  CALL stzrzf( m, n, a, lda, tau, work, lwork, info )
273 *
274 * Compute norm(svd(a) - svd(r))
275 *
276  result( 1 ) = sqrt12( m, m, a, lda, s, work,
277  $ lwork )
278 *
279 * Compute norm( A - R*Q )
280 *
281  result( 2 ) = srzt01( m, n, copya, a, lda, tau, work,
282  $ lwork )
283 *
284 * Compute norm(Q'*Q - I).
285 *
286  result( 3 ) = srzt02( m, n, a, lda, tau, work, lwork )
287 *
288 * Print information about the tests that did not pass
289 * the threshold.
290 *
291  DO 40 k = 1, ntests
292  IF( result( k ).GE.thresh ) THEN
293  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
294  $ CALL alahd( nout, path )
295  WRITE( nout, fmt = 9999 )m, n, imode, k,
296  $ result( k )
297  nfail = nfail + 1
298  END IF
299  40 CONTINUE
300  nrun = nrun + 3
301  50 CONTINUE
302  END IF
303  60 CONTINUE
304  70 CONTINUE
305 *
306 * Print a summary of the results.
307 *
308  CALL alasum( path, nout, nfail, nrun, nerrs )
309 *
310  9999 FORMAT( ' M =', i5, ', N =', i5, ', type ', i2, ', test ', i2,
311  $ ', ratio =', g12.5 )
312 *
313 * End if SCHKTZ
314 *
315  END
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
subroutine schktz(DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, COPYA, S, TAU, WORK, NOUT)
SCHKTZ
Definition: schktz.f:134
subroutine sgeqr2(M, N, A, LDA, TAU, WORK, INFO)
SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm...
Definition: sgeqr2.f:123
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
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:112
subroutine stzrzf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
STZRZF
Definition: stzrzf.f:153
subroutine slaord(JOB, N, X, INCX)
SLAORD
Definition: slaord.f:75
subroutine serrtz(PATH, NUNIT)
SERRTZ
Definition: serrtz.f:56
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:105
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75