LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zunhr_col02.f
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1 *> \brief \b ZUNHR_COL02
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 ZUNHR_COL02( M, N, MB1, NB1, NB2, RESULT )
12 *
13 * .. Scalar Arguments ..
14 * INTEGER M, N, MB1, NB1, NB2
15 * .. Return values ..
16 * DOUBLE PRECISION RESULT(6)
17 *
18 *
19 *> \par Purpose:
20 * =============
21 *>
22 *> \verbatim
23 *>
24 *> ZUNHR_COL02 tests ZUNGTSQR_ROW and ZUNHR_COL inside ZGETSQRHRT
25 *> (which calls ZLATSQR, ZUNGTSQR_ROW and ZUNHR_COL) using ZGEMQRT.
26 *> Therefore, ZLATSQR (part of ZGEQR), ZGEMQRT (part of ZGEMQR)
27 *> have to be tested before this test.
28 *>
29 *> \endverbatim
30 *
31 * Arguments:
32 * ==========
33 *
34 *> \param[in] M
35 *> \verbatim
36 *> M is INTEGER
37 *> Number of rows in test matrix.
38 *> \endverbatim
39 *> \param[in] N
40 *> \verbatim
41 *> N is INTEGER
42 *> Number of columns in test matrix.
43 *> \endverbatim
44 *> \param[in] MB1
45 *> \verbatim
46 *> MB1 is INTEGER
47 *> Number of row in row block in an input test matrix.
48 *> \endverbatim
49 *>
50 *> \param[in] NB1
51 *> \verbatim
52 *> NB1 is INTEGER
53 *> Number of columns in column block an input test matrix.
54 *> \endverbatim
55 *>
56 *> \param[in] NB2
57 *> \verbatim
58 *> NB2 is INTEGER
59 *> Number of columns in column block in an output test matrix.
60 *> \endverbatim
61 *>
62 *> \param[out] RESULT
63 *> \verbatim
64 *> RESULT is DOUBLE PRECISION array, dimension (6)
65 *> Results of each of the six tests below.
66 *>
67 *> A is a m-by-n test input matrix to be factored.
68 *> so that A = Q_gr * ( R )
69 *> ( 0 ),
70 *>
71 *> Q_qr is an implicit m-by-m unitary Q matrix, the result
72 *> of factorization in blocked WY-representation,
73 *> stored in ZGEQRT output format.
74 *>
75 *> R is a n-by-n upper-triangular matrix,
76 *>
77 *> 0 is a (m-n)-by-n zero matrix,
78 *>
79 *> Q is an explicit m-by-m unitary matrix Q = Q_gr * I
80 *>
81 *> C is an m-by-n random matrix,
82 *>
83 *> D is an n-by-m random matrix.
84 *>
85 *> The six tests are:
86 *>
87 *> RESULT(1) = |R - (Q**H) * A| / ( eps * m * |A| )
88 *> is equivalent to test for | A - Q * R | / (eps * m * |A|),
89 *>
90 *> RESULT(2) = |I - (Q**H) * Q| / ( eps * m ),
91 *>
92 *> RESULT(3) = | Q_qr * C - Q * C | / (eps * m * |C|),
93 *>
94 *> RESULT(4) = | (Q_gr**H) * C - (Q**H) * C | / (eps * m * |C|)
95 *>
96 *> RESULT(5) = | D * Q_qr - D * Q | / (eps * m * |D|)
97 *>
98 *> RESULT(6) = | D * (Q_qr**H) - D * (Q**H) | / (eps * m * |D|),
99 *>
100 *> where:
101 *> Q_qr * C, (Q_gr**H) * C, D * Q_qr, D * (Q_qr**H) are
102 *> computed using ZGEMQRT,
103 *>
104 *> Q * C, (Q**H) * C, D * Q, D * (Q**H) are
105 *> computed using ZGEMM.
106 *> \endverbatim
107 *
108 * Authors:
109 * ========
110 *
111 *> \author Univ. of Tennessee
112 *> \author Univ. of California Berkeley
113 *> \author Univ. of Colorado Denver
114 *> \author NAG Ltd.
115 *
116 *> \ingroup complex16_lin
117 *
118 * =====================================================================
119  SUBROUTINE zunhr_col02( M, N, MB1, NB1, NB2, RESULT )
120  IMPLICIT NONE
121 *
122 * -- LAPACK test routine --
123 * -- LAPACK is a software package provided by Univ. of Tennessee, --
124 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125 *
126 * .. Scalar Arguments ..
127  INTEGER M, N, MB1, NB1, NB2
128 * .. Return values ..
129  DOUBLE PRECISION RESULT(6)
130 *
131 * =====================================================================
132 *
133 * ..
134 * .. Local allocatable arrays
135  COMPLEX*16 , ALLOCATABLE :: A(:,:), AF(:,:), Q(:,:), R(:,:),
136  \$ WORK( : ), T1(:,:), T2(:,:), DIAG(:),
137  \$ C(:,:), CF(:,:), D(:,:), DF(:,:)
138  DOUBLE PRECISION, ALLOCATABLE :: RWORK(:)
139 *
140 * .. Parameters ..
141  DOUBLE PRECISION ZERO
142  parameter( zero = 0.0d+0 )
143  COMPLEX*16 CONE, CZERO
144  parameter( cone = ( 1.0d+0, 0.0d+0 ),
145  \$ czero = ( 0.0d+0, 0.0d+0 ) )
146 * ..
147 * .. Local Scalars ..
148  LOGICAL TESTZEROS
149  INTEGER INFO, J, K, L, LWORK, NB2_UB, NRB
150  DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
151 * ..
152 * .. Local Arrays ..
153  INTEGER ISEED( 4 )
154  COMPLEX*16 WORKQUERY( 1 )
155 * ..
156 * .. External Functions ..
157  DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
158  EXTERNAL dlamch, zlange, zlansy
159 * ..
160 * .. External Subroutines ..
161  EXTERNAL zlacpy, zlarnv, zlaset, zgetsqrhrt,
162  \$ zscal, zgemm, zgemqrt, zherk
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC ceiling, dble, max, min
166 * ..
167 * .. Scalars in Common ..
168  CHARACTER(LEN=32) SRNAMT
169 * ..
170 * .. Common blocks ..
171  COMMON / srmnamc / srnamt
172 * ..
173 * .. Data statements ..
174  DATA iseed / 1988, 1989, 1990, 1991 /
175 *
176 * TEST MATRICES WITH HALF OF MATRIX BEING ZEROS
177 *
178  testzeros = .false.
179 *
180  eps = dlamch( 'Epsilon' )
181  k = min( m, n )
182  l = max( m, n, 1)
183 *
184 * Dynamically allocate local arrays
185 *
186  ALLOCATE ( a(m,n), af(m,n), q(l,l), r(m,l), rwork(l),
187  \$ c(m,n), cf(m,n),
188  \$ d(n,m), df(n,m) )
189 *
190 * Put random numbers into A and copy to AF
191 *
192  DO j = 1, n
193  CALL zlarnv( 2, iseed, m, a( 1, j ) )
194  END DO
195  IF( testzeros ) THEN
196  IF( m.GE.4 ) THEN
197  DO j = 1, n
198  CALL zlarnv( 2, iseed, m/2, a( m/4, j ) )
199  END DO
200  END IF
201  END IF
202  CALL zlacpy( 'Full', m, n, a, m, af, m )
203 *
204 * Number of row blocks in ZLATSQR
205 *
206  nrb = max( 1, ceiling( dble( m - n ) / dble( mb1 - n ) ) )
207 *
208  ALLOCATE ( t1( nb1, n * nrb ) )
209  ALLOCATE ( t2( nb2, n ) )
210  ALLOCATE ( diag( n ) )
211 *
212 * Begin determine LWORK for the array WORK and allocate memory.
213 *
214 * ZGEMQRT requires NB2 to be bounded by N.
215 *
216  nb2_ub = min( nb2, n)
217 *
218 *
219  CALL zgetsqrhrt( m, n, mb1, nb1, nb2, af, m, t2, nb2,
220  \$ workquery, -1, info )
221 *
222  lwork = int( workquery( 1 ) )
223 *
224 * In ZGEMQRT, WORK is N*NB2_UB if SIDE = 'L',
225 * or M*NB2_UB if SIDE = 'R'.
226 *
227  lwork = max( lwork, nb2_ub * n, nb2_ub * m )
228 *
229  ALLOCATE ( work( lwork ) )
230 *
231 * End allocate memory for WORK.
232 *
233 *
234 * Begin Householder reconstruction routines
235 *
236 * Factor the matrix A in the array AF.
237 *
238  srnamt = 'ZGETSQRHRT'
239  CALL zgetsqrhrt( m, n, mb1, nb1, nb2, af, m, t2, nb2,
240  \$ work, lwork, info )
241 *
242 * End Householder reconstruction routines.
243 *
244 *
245 * Generate the m-by-m matrix Q
246 *
247  CALL zlaset( 'Full', m, m, czero, cone, q, m )
248 *
249  srnamt = 'ZGEMQRT'
250  CALL zgemqrt( 'L', 'N', m, m, k, nb2_ub, af, m, t2, nb2, q, m,
251  \$ work, info )
252 *
253 * Copy R
254 *
255  CALL zlaset( 'Full', m, n, czero, czero, r, m )
256 *
257  CALL zlacpy( 'Upper', m, n, af, m, r, m )
258 *
259 * TEST 1
260 * Compute |R - (Q**T)*A| / ( eps * m * |A| ) and store in RESULT(1)
261 *
262  CALL zgemm( 'C', 'N', m, n, m, -cone, q, m, a, m, cone, r, m )
263 *
264  anorm = zlange( '1', m, n, a, m, rwork )
265  resid = zlange( '1', m, n, r, m, rwork )
266  IF( anorm.GT.zero ) THEN
267  result( 1 ) = resid / ( eps * max( 1, m ) * anorm )
268  ELSE
269  result( 1 ) = zero
270  END IF
271 *
272 * TEST 2
273 * Compute |I - (Q**T)*Q| / ( eps * m ) and store in RESULT(2)
274 *
275  CALL zlaset( 'Full', m, m, czero, cone, r, m )
276  CALL zherk( 'U', 'C', m, m, -cone, q, m, cone, r, m )
277  resid = zlansy( '1', 'Upper', m, r, m, rwork )
278  result( 2 ) = resid / ( eps * max( 1, m ) )
279 *
280 * Generate random m-by-n matrix C
281 *
282  DO j = 1, n
283  CALL zlarnv( 2, iseed, m, c( 1, j ) )
284  END DO
285  cnorm = zlange( '1', m, n, c, m, rwork )
286  CALL zlacpy( 'Full', m, n, c, m, cf, m )
287 *
288 * Apply Q to C as Q*C = CF
289 *
290  srnamt = 'ZGEMQRT'
291  CALL zgemqrt( 'L', 'N', m, n, k, nb2_ub, af, m, t2, nb2, cf, m,
292  \$ work, info )
293 *
294 * TEST 3
295 * Compute |CF - Q*C| / ( eps * m * |C| )
296 *
297  CALL zgemm( 'N', 'N', m, n, m, -cone, q, m, c, m, cone, cf, m )
298  resid = zlange( '1', m, n, cf, m, rwork )
299  IF( cnorm.GT.zero ) THEN
300  result( 3 ) = resid / ( eps * max( 1, m ) * cnorm )
301  ELSE
302  result( 3 ) = zero
303  END IF
304 *
305 * Copy C into CF again
306 *
307  CALL zlacpy( 'Full', m, n, c, m, cf, m )
308 *
309 * Apply Q to C as (Q**T)*C = CF
310 *
311  srnamt = 'ZGEMQRT'
312  CALL zgemqrt( 'L', 'C', m, n, k, nb2_ub, af, m, t2, nb2, cf, m,
313  \$ work, info )
314 *
315 * TEST 4
316 * Compute |CF - (Q**T)*C| / ( eps * m * |C|)
317 *
318  CALL zgemm( 'C', 'N', m, n, m, -cone, q, m, c, m, cone, cf, m )
319  resid = zlange( '1', m, n, cf, m, rwork )
320  IF( cnorm.GT.zero ) THEN
321  result( 4 ) = resid / ( eps * max( 1, m ) * cnorm )
322  ELSE
323  result( 4 ) = zero
324  END IF
325 *
326 * Generate random n-by-m matrix D and a copy DF
327 *
328  DO j = 1, m
329  CALL zlarnv( 2, iseed, n, d( 1, j ) )
330  END DO
331  dnorm = zlange( '1', n, m, d, n, rwork )
332  CALL zlacpy( 'Full', n, m, d, n, df, n )
333 *
334 * Apply Q to D as D*Q = DF
335 *
336  srnamt = 'ZGEMQRT'
337  CALL zgemqrt( 'R', 'N', n, m, k, nb2_ub, af, m, t2, nb2, df, n,
338  \$ work, info )
339 *
340 * TEST 5
341 * Compute |DF - D*Q| / ( eps * m * |D| )
342 *
343  CALL zgemm( 'N', 'N', n, m, m, -cone, d, n, q, m, cone, df, n )
344  resid = zlange( '1', n, m, df, n, rwork )
345  IF( dnorm.GT.zero ) THEN
346  result( 5 ) = resid / ( eps * max( 1, m ) * dnorm )
347  ELSE
348  result( 5 ) = zero
349  END IF
350 *
351 * Copy D into DF again
352 *
353  CALL zlacpy( 'Full', n, m, d, n, df, n )
354 *
355 * Apply Q to D as D*QT = DF
356 *
357  srnamt = 'ZGEMQRT'
358  CALL zgemqrt( 'R', 'C', n, m, k, nb2_ub, af, m, t2, nb2, df, n,
359  \$ work, info )
360 *
361 * TEST 6
362 * Compute |DF - D*(Q**T)| / ( eps * m * |D| )
363 *
364  CALL zgemm( 'N', 'C', n, m, m, -cone, d, n, q, m, cone, df, n )
365  resid = zlange( '1', n, m, df, n, rwork )
366  IF( dnorm.GT.zero ) THEN
367  result( 6 ) = resid / ( eps * max( 1, m ) * dnorm )
368  ELSE
369  result( 6 ) = zero
370  END IF
371 *
372 * Deallocate all arrays
373 *
374  DEALLOCATE ( a, af, q, r, rwork, work, t1, t2, diag,
375  \$ c, d, cf, df )
376 *
377  RETURN
378 *
379 * End of ZUNHR_COL02
380 *
381  END
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:78
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:173
subroutine zunhr_col02(M, N, MB1, NB1, NB2, RESULT)
ZUNHR_COL02
Definition: zunhr_col02.f:120
subroutine zgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
ZGEMQRT
Definition: zgemqrt.f:168
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:99
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zgetsqrhrt(M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK, LWORK, INFO)
ZGETSQRHRT
Definition: zgetsqrhrt.f:179