LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
dlqt05.f
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1 *> \brief \b DLQT05
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 DLQT05(M,N,L,NB,RESULT)
12 *
13 * .. Scalar Arguments ..
14 * INTEGER LWORK, M, N, L, NB, LDT
15 * .. Return values ..
16 * DOUBLE PRECISION RESULT(6)
17 *
18 *
19 *> \par Purpose:
20 * =============
21 *>
22 *> \verbatim
23 *>
24 *> DQRT05 tests DTPLQT and DTPMLQT.
25 *> \endverbatim
26 *
27 * Arguments:
28 * ==========
29 *
30 *> \param[in] M
31 *> \verbatim
32 *> M is INTEGER
33 *> Number of rows in lower part of the test matrix.
34 *> \endverbatim
35 *>
36 *> \param[in] N
37 *> \verbatim
38 *> N is INTEGER
39 *> Number of columns in test matrix.
40 *> \endverbatim
41 *>
42 *> \param[in] L
43 *> \verbatim
44 *> L is INTEGER
45 *> The number of rows of the upper trapezoidal part the
46 *> lower test matrix. 0 <= L <= M.
47 *> \endverbatim
48 *>
49 *> \param[in] NB
50 *> \verbatim
51 *> NB is INTEGER
52 *> Block size of test matrix. NB <= N.
53 *> \endverbatim
54 *>
55 *> \param[out] RESULT
56 *> \verbatim
57 *> RESULT is DOUBLE PRECISION array, dimension (6)
58 *> Results of each of the six tests below.
59 *>
60 *> RESULT(1) = | A - Q R |
61 *> RESULT(2) = | I - Q^H Q |
62 *> RESULT(3) = | Q C - Q C |
63 *> RESULT(4) = | Q^H C - Q^H C |
64 *> RESULT(5) = | C Q - C Q |
65 *> RESULT(6) = | C Q^H - C Q^H |
66 *> \endverbatim
67 *
68 * Authors:
69 * ========
70 *
71 *> \author Univ. of Tennessee
72 *> \author Univ. of California Berkeley
73 *> \author Univ. of Colorado Denver
74 *> \author NAG Ltd.
75 *
76 *> \ingroup double_lin
77 *
78 * =====================================================================
79  SUBROUTINE dlqt05(M,N,L,NB,RESULT)
80  IMPLICIT NONE
81 *
82 * -- LAPACK test routine --
83 * -- LAPACK is a software package provided by Univ. of Tennessee, --
84 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
85 *
86 * .. Scalar Arguments ..
87  INTEGER LWORK, M, N, L, NB, LDT
88 * .. Return values ..
89  DOUBLE PRECISION RESULT(6)
90 *
91 * =====================================================================
92 *
93 * ..
94 * .. Local allocatable arrays
95  DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:),
96  $ R(:,:), RWORK(:), WORK( : ), T(:,:),
97  $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
98 *
99 * .. Parameters ..
100  DOUBLE PRECISION ONE, ZERO
101  parameter( zero = 0.0, one = 1.0 )
102 * ..
103 * .. Local Scalars ..
104  INTEGER INFO, J, K, N2, NP1,i
105  DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
106 * ..
107 * .. Local Arrays ..
108  INTEGER ISEED( 4 )
109 * ..
110 * .. External Functions ..
111  DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
112  LOGICAL LSAME
113  EXTERNAL dlamch, dlange, dlansy, lsame
114 * ..
115 * .. Data statements ..
116  DATA iseed / 1988, 1989, 1990, 1991 /
117 *
118  eps = dlamch( 'Epsilon' )
119  k = m
120  n2 = m+n
121  IF( n.GT.0 ) THEN
122  np1 = m+1
123  ELSE
124  np1 = 1
125  END IF
126  lwork = n2*n2*nb
127 *
128 * Dynamically allocate all arrays
129 *
130  ALLOCATE(a(m,n2),af(m,n2),q(n2,n2),r(n2,n2),rwork(n2),
131  $ work(lwork),t(nb,m),c(n2,m),cf(n2,m),
132  $ d(m,n2),df(m,n2) )
133 *
134 * Put random stuff into A
135 *
136  ldt=nb
137  CALL dlaset( 'Full', m, n2, zero, zero, a, m )
138  CALL dlaset( 'Full', nb, m, zero, zero, t, nb )
139  DO j=1,m
140  CALL dlarnv( 2, iseed, m-j+1, a( j, j ) )
141  END DO
142  IF( n.GT.0 ) THEN
143  DO j=1,n-l
144  CALL dlarnv( 2, iseed, m, a( 1, min(n+m,m+1) + j - 1 ) )
145  END DO
146  END IF
147  IF( l.GT.0 ) THEN
148  DO j=1,l
149  CALL dlarnv( 2, iseed, m-j+1, a( j, min(n+m,n+m-l+1)
150  $ + j - 1 ) )
151  END DO
152  END IF
153 *
154 * Copy the matrix A to the array AF.
155 *
156  CALL dlacpy( 'Full', m, n2, a, m, af, m )
157 *
158 * Factor the matrix A in the array AF.
159 *
160  CALL dtplqt( m,n,l,nb,af,m,af(1,np1),m,t,ldt,work,info)
161 *
162 * Generate the (M+N)-by-(M+N) matrix Q by applying H to I
163 *
164  CALL dlaset( 'Full', n2, n2, zero, one, q, n2 )
165  CALL dgemlqt( 'L', 'N', n2, n2, k, nb, af, m, t, ldt, q, n2,
166  $ work, info )
167 *
168 * Copy L
169 *
170  CALL dlaset( 'Full', n2, n2, zero, zero, r, n2 )
171  CALL dlacpy( 'Lower', m, n2, af, m, r, n2 )
172 *
173 * Compute |L - A*Q*T| / |A| and store in RESULT(1)
174 *
175  CALL dgemm( 'N', 'T', m, n2, n2, -one, a, m, q, n2, one, r, n2)
176  anorm = dlange( '1', m, n2, a, m, rwork )
177  resid = dlange( '1', m, n2, r, n2, rwork )
178  IF( anorm.GT.zero ) THEN
179  result( 1 ) = resid / (eps*anorm*max(1,n2))
180  ELSE
181  result( 1 ) = zero
182  END IF
183 *
184 * Compute |I - Q*Q'| and store in RESULT(2)
185 *
186  CALL dlaset( 'Full', n2, n2, zero, one, r, n2 )
187  CALL dsyrk( 'U', 'N', n2, n2, -one, q, n2, one, r, n2 )
188  resid = dlansy( '1', 'Upper', n2, r, n2, rwork )
189  result( 2 ) = resid / (eps*max(1,n2))
190 *
191 * Generate random m-by-n matrix C and a copy CF
192 *
193  CALL dlaset( 'Full', n2, m, zero, one, c, n2 )
194  DO j=1,m
195  CALL dlarnv( 2, iseed, n2, c( 1, j ) )
196  END DO
197  cnorm = dlange( '1', n2, m, c, n2, rwork)
198  CALL dlacpy( 'Full', n2, m, c, n2, cf, n2 )
199 *
200 * Apply Q to C as Q*C
201 *
202  CALL dtpmlqt( 'L','N', n,m,k,l,nb,af(1, np1),m,t,ldt,cf,n2,
203  $ cf(np1,1),n2,work,info)
204 *
205 * Compute |Q*C - Q*C| / |C|
206 *
207  CALL dgemm( 'N', 'N', n2, m, n2, -one, q, n2, c, n2, one, cf, n2 )
208  resid = dlange( '1', n2, m, cf, n2, rwork )
209  IF( cnorm.GT.zero ) THEN
210  result( 3 ) = resid / (eps*max(1,n2)*cnorm)
211  ELSE
212  result( 3 ) = zero
213  END IF
214 
215 *
216 * Copy C into CF again
217 *
218  CALL dlacpy( 'Full', n2, m, c, n2, cf, n2 )
219 *
220 * Apply Q to C as QT*C
221 *
222  CALL dtpmlqt( 'L','T',n,m,k,l,nb,af(1,np1),m,t,ldt,cf,n2,
223  $ cf(np1,1),n2,work,info)
224 *
225 * Compute |QT*C - QT*C| / |C|
226 *
227  CALL dgemm('T','N',n2,m,n2,-one,q,n2,c,n2,one,cf,n2)
228  resid = dlange( '1', n2, m, cf, n2, rwork )
229 
230  IF( cnorm.GT.zero ) THEN
231  result( 4 ) = resid / (eps*max(1,n2)*cnorm)
232  ELSE
233  result( 4 ) = zero
234  END IF
235 *
236 * Generate random m-by-n matrix D and a copy DF
237 *
238  DO j=1,n2
239  CALL dlarnv( 2, iseed, m, d( 1, j ) )
240  END DO
241  dnorm = dlange( '1', m, n2, d, m, rwork)
242  CALL dlacpy( 'Full', m, n2, d, m, df, m )
243 *
244 * Apply Q to D as D*Q
245 *
246  CALL dtpmlqt('R','N',m,n,k,l,nb,af(1,np1),m,t,ldt,df,m,
247  $ df(1,np1),m,work,info)
248 *
249 * Compute |D*Q - D*Q| / |D|
250 *
251  CALL dgemm('N','N',m,n2,n2,-one,d,m,q,n2,one,df,m)
252  resid = dlange('1',m, n2,df,m,rwork )
253  IF( cnorm.GT.zero ) THEN
254  result( 5 ) = resid / (eps*max(1,n2)*dnorm)
255  ELSE
256  result( 5 ) = zero
257  END IF
258 *
259 * Copy D into DF again
260 *
261  CALL dlacpy('Full',m,n2,d,m,df,m )
262 *
263 * Apply Q to D as D*QT
264 *
265  CALL dtpmlqt('R','T',m,n,k,l,nb,af(1,np1),m,t,ldt,df,m,
266  $ df(1,np1),m,work,info)
267 
268 *
269 * Compute |D*QT - D*QT| / |D|
270 *
271  CALL dgemm( 'N', 'T', m, n2, n2, -one, d, m, q, n2, one, df, m )
272  resid = dlange( '1', m, n2, df, m, rwork )
273  IF( cnorm.GT.zero ) THEN
274  result( 6 ) = resid / (eps*max(1,n2)*dnorm)
275  ELSE
276  result( 6 ) = zero
277  END IF
278 *
279 * Deallocate all arrays
280 *
281  DEALLOCATE ( a, af, q, r, rwork, work, t, c, d, cf, df)
282  RETURN
283  END
subroutine dlarnv(IDIST, ISEED, N, X)
DLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: dlarnv.f:97
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:169
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
subroutine dlqt05(M, N, L, NB, RESULT)
DLQT05
Definition: dlqt05.f:80
subroutine dgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
DGEMLQT
Definition: dgemlqt.f:168
subroutine dtplqt(M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK, INFO)
DTPLQT
Definition: dtplqt.f:189
subroutine dtpmlqt(SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
DTPMLQT
Definition: dtpmlqt.f:214