LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cunhr_col02()

subroutine cunhr_col02 ( integer  M,
integer  N,
integer  MB1,
integer  NB1,
integer  NB2,
real, dimension(6)  RESULT 
)

CUNHR_COL02

Purpose:
 CUNHR_COL02 tests CUNGTSQR_ROW and CUNHR_COL inside CGETSQRHRT
 (which calls CLATSQR, CUNGTSQR_ROW and CUNHR_COL) using CGEMQRT.
 Therefore, CLATSQR (part of CGEQR), CGEMQRT (part of CGEMQR)
 have to be tested before this test.
Parameters
[in]M
          M is INTEGER
          Number of rows in test matrix.
[in]N
          N is INTEGER
          Number of columns in test matrix.
[in]MB1
          MB1 is INTEGER
          Number of row in row block in an input test matrix.
[in]NB1
          NB1 is INTEGER
          Number of columns in column block an input test matrix.
[in]NB2
          NB2 is INTEGER
          Number of columns in column block in an output test matrix.
[out]RESULT
          RESULT is REAL array, dimension (6)
          Results of each of the six tests below.

            A is a m-by-n test input matrix to be factored.
            so that A = Q_gr * ( R )
                               ( 0 ),

            Q_qr is an implicit m-by-m unitary Q matrix, the result
            of factorization in blocked WY-representation,
            stored in CGEQRT output format.

            R is a n-by-n upper-triangular matrix,

            0 is a (m-n)-by-n zero matrix,

            Q is an explicit m-by-m unitary matrix Q = Q_gr * I

            C is an m-by-n random matrix,

            D is an n-by-m random matrix.

          The six tests are:

          RESULT(1) = |R - (Q**H) * A| / ( eps * m * |A| )
            is equivalent to test for | A - Q * R | / (eps * m * |A|),

          RESULT(2) = |I - (Q**H) * Q| / ( eps * m ),

          RESULT(3) = | Q_qr * C - Q * C | / (eps * m * |C|),

          RESULT(4) = | (Q_gr**H) * C - (Q**H) * C | / (eps * m * |C|)

          RESULT(5) = | D * Q_qr - D * Q | / (eps * m * |D|)

          RESULT(6) = | D * (Q_qr**H) - D * (Q**H) | / (eps * m * |D|),

          where:
            Q_qr * C, (Q_gr**H) * C, D * Q_qr, D * (Q_qr**H) are
            computed using CGEMQRT,

            Q * C, (Q**H) * C, D * Q, D * (Q**H)  are
            computed using CGEMM.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 119 of file cunhr_col02.f.

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  REAL RESULT(6)
130 *
131 * =====================================================================
132 *
133 * ..
134 * .. Local allocatable arrays
135  COMPLEX , ALLOCATABLE :: A(:,:), AF(:,:), Q(:,:), R(:,:),
136  $ WORK( : ), T1(:,:), T2(:,:), DIAG(:),
137  $ C(:,:), CF(:,:), D(:,:), DF(:,:)
138  REAL , ALLOCATABLE :: RWORK(:)
139 *
140 * .. Parameters ..
141  REAL ZERO
142  parameter( zero = 0.0e+0 )
143  COMPLEX CONE, CZERO
144  parameter( cone = ( 1.0e+0, 0.0e+0 ),
145  $ czero = ( 0.0e+0, 0.0e+0 ) )
146 * ..
147 * .. Local Scalars ..
148  LOGICAL TESTZEROS
149  INTEGER INFO, J, K, L, LWORK, NB2_UB, NRB
150  REAL ANORM, EPS, RESID, CNORM, DNORM
151 * ..
152 * .. Local Arrays ..
153  INTEGER ISEED( 4 )
154  COMPLEX WORKQUERY( 1 )
155 * ..
156 * .. External Functions ..
157  REAL SLAMCH, CLANGE, CLANSY
158  EXTERNAL slamch, clange, clansy
159 * ..
160 * .. External Subroutines ..
161  EXTERNAL clacpy, clarnv, claset, cgetsqrhrt,
162  $ cscal, cgemm, cgemqrt, cherk
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC ceiling, real, 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 = slamch( '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 clarnv( 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 clarnv( 2, iseed, m/2, a( m/4, j ) )
199  END DO
200  END IF
201  END IF
202  CALL clacpy( 'Full', m, n, a, m, af, m )
203 *
204 * Number of row blocks in CLATSQR
205 *
206  nrb = max( 1, ceiling( real( m - n ) / real( 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 * CGEMQRT requires NB2 to be bounded by N.
215 *
216  nb2_ub = min( nb2, n)
217 *
218 *
219  CALL cgetsqrhrt( m, n, mb1, nb1, nb2, af, m, t2, nb2,
220  $ workquery, -1, info )
221 *
222  lwork = int( workquery( 1 ) )
223 *
224 * In CGEMQRT, 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 = 'CGETSQRHRT'
239  CALL cgetsqrhrt( 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 claset( 'Full', m, m, czero, cone, q, m )
248 *
249  srnamt = 'CGEMQRT'
250  CALL cgemqrt( 'L', 'N', m, m, k, nb2_ub, af, m, t2, nb2, q, m,
251  $ work, info )
252 *
253 * Copy R
254 *
255  CALL claset( 'Full', m, n, czero, czero, r, m )
256 *
257  CALL clacpy( '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 cgemm( 'C', 'N', m, n, m, -cone, q, m, a, m, cone, r, m )
263 *
264  anorm = clange( '1', m, n, a, m, rwork )
265  resid = clange( '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 claset( 'Full', m, m, czero, cone, r, m )
276  CALL cherk( 'U', 'C', m, m, -cone, q, m, cone, r, m )
277  resid = clansy( '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 clarnv( 2, iseed, m, c( 1, j ) )
284  END DO
285  cnorm = clange( '1', m, n, c, m, rwork )
286  CALL clacpy( 'Full', m, n, c, m, cf, m )
287 *
288 * Apply Q to C as Q*C = CF
289 *
290  srnamt = 'CGEMQRT'
291  CALL cgemqrt( '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 cgemm( 'N', 'N', m, n, m, -cone, q, m, c, m, cone, cf, m )
298  resid = clange( '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 clacpy( 'Full', m, n, c, m, cf, m )
308 *
309 * Apply Q to C as (Q**T)*C = CF
310 *
311  srnamt = 'CGEMQRT'
312  CALL cgemqrt( '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 cgemm( 'C', 'N', m, n, m, -cone, q, m, c, m, cone, cf, m )
319  resid = clange( '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 clarnv( 2, iseed, n, d( 1, j ) )
330  END DO
331  dnorm = clange( '1', n, m, d, n, rwork )
332  CALL clacpy( 'Full', n, m, d, n, df, n )
333 *
334 * Apply Q to D as D*Q = DF
335 *
336  srnamt = 'CGEMQRT'
337  CALL cgemqrt( '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 cgemm( 'N', 'N', n, m, m, -cone, d, n, q, m, cone, df, n )
344  resid = clange( '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 clacpy( 'Full', n, m, d, n, df, n )
354 *
355 * Apply Q to D as D*QT = DF
356 *
357  srnamt = 'CGEMQRT'
358  CALL cgemqrt( '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 cgemm( 'N', 'C', n, m, m, -cone, d, n, q, m, cone, df, n )
365  resid = clange( '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 CUNHR_COL02
380 *
subroutine cgetsqrhrt(M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK, LWORK, INFO)
CGETSQRHRT
Definition: cgetsqrhrt.f:179
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:173
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
subroutine cgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
CGEMQRT
Definition: cgemqrt.f:168
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
subroutine clarnv(IDIST, ISEED, N, X)
CLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: clarnv.f:99
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
real function clansy(NORM, UPLO, N, A, LDA, WORK)
CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansy.f:123
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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