LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
sorhr_col01.f
Go to the documentation of this file.
1 *> \brief \b SORHR_COL01
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 SORHR_COL01( M, N, MB1, NB1, NB2, RESULT )
12 *
13 * .. Scalar Arguments ..
14 * INTEGER M, N, MB1, NB1, NB2
15 * .. Return values ..
16 * REAL RESULT(6)
17 *
18 *
19 *> \par Purpose:
20 * =============
21 *>
22 *> \verbatim
23 *>
24 *> SORHR_COL01 tests SORGTSQR and SORHR_COL using SLATSQR, SGEMQRT.
25 *> Therefore, SLATSQR (part of SGEQR), SGEMQRT (part of SGEMQR)
26 *> have to be tested before this test.
27 *>
28 *> \endverbatim
29 *
30 * Arguments:
31 * ==========
32 *
33 *> \param[in] M
34 *> \verbatim
35 *> M is INTEGER
36 *> Number of rows in test matrix.
37 *> \endverbatim
38 *> \param[in] N
39 *> \verbatim
40 *> N is INTEGER
41 *> Number of columns in test matrix.
42 *> \endverbatim
43 *> \param[in] MB1
44 *> \verbatim
45 *> MB1 is INTEGER
46 *> Number of row in row block in an input test matrix.
47 *> \endverbatim
48 *>
49 *> \param[in] NB1
50 *> \verbatim
51 *> NB1 is INTEGER
52 *> Number of columns in column block an input test matrix.
53 *> \endverbatim
54 *>
55 *> \param[in] NB2
56 *> \verbatim
57 *> NB2 is INTEGER
58 *> Number of columns in column block in an output test matrix.
59 *> \endverbatim
60 *>
61 *> \param[out] RESULT
62 *> \verbatim
63 *> RESULT is REAL array, dimension (6)
64 *> Results of each of the six tests below.
65 *>
66 *> A is a m-by-n test input matrix to be factored.
67 *> so that A = Q_gr * ( R )
68 *> ( 0 ),
69 *>
70 *> Q_qr is an implicit m-by-m orthogonal Q matrix, the result
71 *> of factorization in blocked WY-representation,
72 *> stored in SGEQRT output format.
73 *>
74 *> R is a n-by-n upper-triangular matrix,
75 *>
76 *> 0 is a (m-n)-by-n zero matrix,
77 *>
78 *> Q is an explicit m-by-m orthogonal matrix Q = Q_gr * I
79 *>
80 *> C is an m-by-n random matrix,
81 *>
82 *> D is an n-by-m random matrix.
83 *>
84 *> The six tests are:
85 *>
86 *> RESULT(1) = |R - (Q**H) * A| / ( eps * m * |A| )
87 *> is equivalent to test for | A - Q * R | / (eps * m * |A|),
88 *>
89 *> RESULT(2) = |I - (Q**H) * Q| / ( eps * m ),
90 *>
91 *> RESULT(3) = | Q_qr * C - Q * C | / (eps * m * |C|),
92 *>
93 *> RESULT(4) = | (Q_gr**H) * C - (Q**H) * C | / (eps * m * |C|)
94 *>
95 *> RESULT(5) = | D * Q_qr - D * Q | / (eps * m * |D|)
96 *>
97 *> RESULT(6) = | D * (Q_qr**H) - D * (Q**H) | / (eps * m * |D|),
98 *>
99 *> where:
100 *> Q_qr * C, (Q_gr**H) * C, D * Q_qr, D * (Q_qr**H) are
101 *> computed using SGEMQRT,
102 *>
103 *> Q * C, (Q**H) * C, D * Q, D * (Q**H) are
104 *> computed using SGEMM.
105 *> \endverbatim
106 *
107 * Authors:
108 * ========
109 *
110 *> \author Univ. of Tennessee
111 *> \author Univ. of California Berkeley
112 *> \author Univ. of Colorado Denver
113 *> \author NAG Ltd.
114 *
115 *> \ingroup single_lin
116 *
117 * =====================================================================
118  SUBROUTINE sorhr_col01( M, N, MB1, NB1, NB2, RESULT )
119  IMPLICIT NONE
120 *
121 * -- LAPACK test routine --
122 * -- LAPACK is a software package provided by Univ. of Tennessee, --
123 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
124 *
125 * .. Scalar Arguments ..
126  INTEGER M, N, MB1, NB1, NB2
127 * .. Return values ..
128  REAL RESULT(6)
129 *
130 * =====================================================================
131 *
132 * ..
133 * .. Local allocatable arrays
134  REAL , ALLOCATABLE :: A(:,:), AF(:,:), Q(:,:), R(:,:),
135  \$ RWORK(:), WORK( : ), T1(:,:), T2(:,:), DIAG(:),
136  \$ C(:,:), CF(:,:), D(:,:), DF(:,:)
137 *
138 * .. Parameters ..
139  REAL ONE, ZERO
140  parameter( zero = 0.0e+0, one = 1.0e+0 )
141 * ..
142 * .. Local Scalars ..
143  LOGICAL TESTZEROS
144  INTEGER INFO, I, J, K, L, LWORK, NB1_UB, NB2_UB, NRB
145  REAL ANORM, EPS, RESID, CNORM, DNORM
146 * ..
147 * .. Local Arrays ..
148  INTEGER ISEED( 4 )
149  REAL WORKQUERY( 1 )
150 * ..
151 * .. External Functions ..
152  REAL SLAMCH, SLANGE, SLANSY
153  EXTERNAL slamch, slange, slansy
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL slacpy, slarnv, slaset, slatsqr, sorhr_col,
158 * ..
159 * .. Intrinsic Functions ..
160  INTRINSIC ceiling, real, max, min
161 * ..
162 * .. Scalars in Common ..
163  CHARACTER(LEN=32) SRNAMT
164 * ..
165 * .. Common blocks ..
166  COMMON / srmnamc / srnamt
167 * ..
168 * .. Data statements ..
169  DATA iseed / 1988, 1989, 1990, 1991 /
170 *
171 * TEST MATRICES WITH HALF OF MATRIX BEING ZEROS
172 *
173  testzeros = .false.
174 *
175  eps = slamch( 'Epsilon' )
176  k = min( m, n )
177  l = max( m, n, 1)
178 *
179 * Dynamically allocate local arrays
180 *
181  ALLOCATE ( a(m,n), af(m,n), q(l,l), r(m,l), rwork(l),
182  \$ c(m,n), cf(m,n),
183  \$ d(n,m), df(n,m) )
184 *
185 * Put random numbers into A and copy to AF
186 *
187  DO j = 1, n
188  CALL slarnv( 2, iseed, m, a( 1, j ) )
189  END DO
190  IF( testzeros ) THEN
191  IF( m.GE.4 ) THEN
192  DO j = 1, n
193  CALL slarnv( 2, iseed, m/2, a( m/4, j ) )
194  END DO
195  END IF
196  END IF
197  CALL slacpy( 'Full', m, n, a, m, af, m )
198 *
199 * Number of row blocks in SLATSQR
200 *
201  nrb = max( 1, ceiling( real( m - n ) / real( mb1 - n ) ) )
202 *
203  ALLOCATE ( t1( nb1, n * nrb ) )
204  ALLOCATE ( t2( nb2, n ) )
205  ALLOCATE ( diag( n ) )
206 *
207 * Begin determine LWORK for the array WORK and allocate memory.
208 *
209 * SLATSQR requires NB1 to be bounded by N.
210 *
211  nb1_ub = min( nb1, n)
212 *
213 * SGEMQRT requires NB2 to be bounded by N.
214 *
215  nb2_ub = min( nb2, n)
216 *
217  CALL slatsqr( m, n, mb1, nb1_ub, af, m, t1, nb1,
218  \$ workquery, -1, info )
219  lwork = int( workquery( 1 ) )
220  CALL sorgtsqr( m, n, mb1, nb1, af, m, t1, nb1, workquery, -1,
221  \$ info )
222
223  lwork = max( lwork, int( workquery( 1 ) ) )
224 *
225 * In SGEMQRT, WORK is N*NB2_UB if SIDE = 'L',
226 * or M*NB2_UB if SIDE = 'R'.
227 *
228  lwork = max( lwork, nb2_ub * n, nb2_ub * m )
229 *
230  ALLOCATE ( work( lwork ) )
231 *
232 * End allocate memory for WORK.
233 *
234 *
235 * Begin Householder reconstruction routines
236 *
237 * Factor the matrix A in the array AF.
238 *
239  srnamt = 'SLATSQR'
240  CALL slatsqr( m, n, mb1, nb1_ub, af, m, t1, nb1, work, lwork,
241  \$ info )
242 *
243 * Copy the factor R into the array R.
244 *
245  srnamt = 'SLACPY'
246  CALL slacpy( 'U', n, n, af, m, r, m )
247 *
248 * Reconstruct the orthogonal matrix Q.
249 *
250  srnamt = 'SORGTSQR'
251  CALL sorgtsqr( m, n, mb1, nb1, af, m, t1, nb1, work, lwork,
252  \$ info )
253 *
254 * Perform the Householder reconstruction, the result is stored
255 * the arrays AF and T2.
256 *
257  srnamt = 'SORHR_COL'
258  CALL sorhr_col( m, n, nb2, af, m, t2, nb2, diag, info )
259 *
260 * Compute the factor R_hr corresponding to the Householder
261 * reconstructed Q_hr and place it in the upper triangle of AF to
262 * match the Q storage format in SGEQRT. R_hr = R_tsqr * S,
263 * this means changing the sign of I-th row of the matrix R_tsqr
264 * according to sign of of I-th diagonal element DIAG(I) of the
265 * matrix S.
266 *
267  srnamt = 'SLACPY'
268  CALL slacpy( 'U', n, n, r, m, af, m )
269 *
270  DO i = 1, n
271  IF( diag( i ).EQ.-one ) THEN
272  CALL sscal( n+1-i, -one, af( i, i ), m )
273  END IF
274  END DO
275 *
276 * End Householder reconstruction routines.
277 *
278 *
279 * Generate the m-by-m matrix Q
280 *
281  CALL slaset( 'Full', m, m, zero, one, q, m )
282 *
283  srnamt = 'SGEMQRT'
284  CALL sgemqrt( 'L', 'N', m, m, k, nb2_ub, af, m, t2, nb2, q, m,
285  \$ work, info )
286 *
287 * Copy R
288 *
289  CALL slaset( 'Full', m, n, zero, zero, r, m )
290 *
291  CALL slacpy( 'Upper', m, n, af, m, r, m )
292 *
293 * TEST 1
294 * Compute |R - (Q**T)*A| / ( eps * m * |A| ) and store in RESULT(1)
295 *
296  CALL sgemm( 'T', 'N', m, n, m, -one, q, m, a, m, one, r, m )
297 *
298  anorm = slange( '1', m, n, a, m, rwork )
299  resid = slange( '1', m, n, r, m, rwork )
300  IF( anorm.GT.zero ) THEN
301  result( 1 ) = resid / ( eps * max( 1, m ) * anorm )
302  ELSE
303  result( 1 ) = zero
304  END IF
305 *
306 * TEST 2
307 * Compute |I - (Q**T)*Q| / ( eps * m ) and store in RESULT(2)
308 *
309  CALL slaset( 'Full', m, m, zero, one, r, m )
310  CALL ssyrk( 'U', 'T', m, m, -one, q, m, one, r, m )
311  resid = slansy( '1', 'Upper', m, r, m, rwork )
312  result( 2 ) = resid / ( eps * max( 1, m ) )
313 *
314 * Generate random m-by-n matrix C
315 *
316  DO j = 1, n
317  CALL slarnv( 2, iseed, m, c( 1, j ) )
318  END DO
319  cnorm = slange( '1', m, n, c, m, rwork )
320  CALL slacpy( 'Full', m, n, c, m, cf, m )
321 *
322 * Apply Q to C as Q*C = CF
323 *
324  srnamt = 'SGEMQRT'
325  CALL sgemqrt( 'L', 'N', m, n, k, nb2_ub, af, m, t2, nb2, cf, m,
326  \$ work, info )
327 *
328 * TEST 3
329 * Compute |CF - Q*C| / ( eps * m * |C| )
330 *
331  CALL sgemm( 'N', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
332  resid = slange( '1', m, n, cf, m, rwork )
333  IF( cnorm.GT.zero ) THEN
334  result( 3 ) = resid / ( eps * max( 1, m ) * cnorm )
335  ELSE
336  result( 3 ) = zero
337  END IF
338 *
339 * Copy C into CF again
340 *
341  CALL slacpy( 'Full', m, n, c, m, cf, m )
342 *
343 * Apply Q to C as (Q**T)*C = CF
344 *
345  srnamt = 'SGEMQRT'
346  CALL sgemqrt( 'L', 'T', m, n, k, nb2_ub, af, m, t2, nb2, cf, m,
347  \$ work, info )
348 *
349 * TEST 4
350 * Compute |CF - (Q**T)*C| / ( eps * m * |C|)
351 *
352  CALL sgemm( 'T', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
353  resid = slange( '1', m, n, cf, m, rwork )
354  IF( cnorm.GT.zero ) THEN
355  result( 4 ) = resid / ( eps * max( 1, m ) * cnorm )
356  ELSE
357  result( 4 ) = zero
358  END IF
359 *
360 * Generate random n-by-m matrix D and a copy DF
361 *
362  DO j = 1, m
363  CALL slarnv( 2, iseed, n, d( 1, j ) )
364  END DO
365  dnorm = slange( '1', n, m, d, n, rwork )
366  CALL slacpy( 'Full', n, m, d, n, df, n )
367 *
368 * Apply Q to D as D*Q = DF
369 *
370  srnamt = 'SGEMQRT'
371  CALL sgemqrt( 'R', 'N', n, m, k, nb2_ub, af, m, t2, nb2, df, n,
372  \$ work, info )
373 *
374 * TEST 5
375 * Compute |DF - D*Q| / ( eps * m * |D| )
376 *
377  CALL sgemm( 'N', 'N', n, m, m, -one, d, n, q, m, one, df, n )
378  resid = slange( '1', n, m, df, n, rwork )
379  IF( dnorm.GT.zero ) THEN
380  result( 5 ) = resid / ( eps * max( 1, m ) * dnorm )
381  ELSE
382  result( 5 ) = zero
383  END IF
384 *
385 * Copy D into DF again
386 *
387  CALL slacpy( 'Full', n, m, d, n, df, n )
388 *
389 * Apply Q to D as D*QT = DF
390 *
391  srnamt = 'SGEMQRT'
392  CALL sgemqrt( 'R', 'T', n, m, k, nb2_ub, af, m, t2, nb2, df, n,
393  \$ work, info )
394 *
395 * TEST 6
396 * Compute |DF - D*(Q**T)| / ( eps * m * |D| )
397 *
398  CALL sgemm( 'N', 'T', n, m, m, -one, d, n, q, m, one, df, n )
399  resid = slange( '1', n, m, df, n, rwork )
400  IF( dnorm.GT.zero ) THEN
401  result( 6 ) = resid / ( eps * max( 1, m ) * dnorm )
402  ELSE
403  result( 6 ) = zero
404  END IF
405 *
406 * Deallocate all arrays
407 *
408  DEALLOCATE ( a, af, q, r, rwork, work, t1, t2, diag,
409  \$ c, d, cf, df )
410 *
411  RETURN
412 *
413 * End of SORHR_COL01
414 *
415  END
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: slarnv.f:97
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 sgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
SGEMQRT
Definition: sgemqrt.f:168
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:169
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
subroutine sorhr_col01(M, N, MB1, NB1, NB2, RESULT)
SORHR_COL01
Definition: sorhr_col01.f:119
subroutine slatsqr(M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, INFO)
SLATSQR
Definition: slatsqr.f:166
subroutine sorgtsqr(M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, INFO)
SORGTSQR
Definition: sorgtsqr.f:175
subroutine sorhr_col(M, N, NB, A, LDA, T, LDT, D, INFO)
SORHR_COL
Definition: sorhr_col.f:259