LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zqrt04.f
Go to the documentation of this file.
1 *> \brief \b ZQRT04
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 ZQRT04(M,N,NB,RESULT)
12 *
13 * .. Scalar Arguments ..
14 * INTEGER M, N, NB, LDT
15 * .. Return values ..
16 * DOUBLE PRECISION RESULT(6)
17 *
18 *
19 *> \par Purpose:
20 * =============
21 *>
22 *> \verbatim
23 *>
24 *> ZQRT04 tests ZGEQRT and ZGEMQRT.
25 *> \endverbatim
26 *
27 * Arguments:
28 * ==========
29 *
30 *> \param[in] M
31 *> \verbatim
32 *> M is INTEGER
33 *> Number of rows in 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] NB
43 *> \verbatim
44 *> NB is INTEGER
45 *> Block size of test matrix. NB <= Min(M,N).
46 *> \endverbatim
47 *>
48 *> \param[out] RESULT
49 *> \verbatim
50 *> RESULT is DOUBLE PRECISION array, dimension (6)
51 *> Results of each of the six tests below.
52 *>
53 *> RESULT(1) = | A - Q R |
54 *> RESULT(2) = | I - Q^H Q |
55 *> RESULT(3) = | Q C - Q C |
56 *> RESULT(4) = | Q^H C - Q^H C |
57 *> RESULT(5) = | C Q - C Q |
58 *> RESULT(6) = | C Q^H - C Q^H |
59 *> \endverbatim
60 *
61 * Authors:
62 * ========
63 *
64 *> \author Univ. of Tennessee
65 *> \author Univ. of California Berkeley
66 *> \author Univ. of Colorado Denver
67 *> \author NAG Ltd.
68 *
69 *> \ingroup complex16_lin
70 *
71 * =====================================================================
72  SUBROUTINE zqrt04(M,N,NB,RESULT)
73  IMPLICIT NONE
74 *
75 * -- LAPACK test routine --
76 * -- LAPACK is a software package provided by Univ. of Tennessee, --
77 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
78 *
79 * .. Scalar Arguments ..
80  INTEGER M, N, NB, LDT
81 * .. Return values ..
82  DOUBLE PRECISION RESULT(6)
83 *
84 * =====================================================================
85 *
86 * ..
87 * .. Local allocatable arrays
88  COMPLEX*16, ALLOCATABLE :: AF(:,:), Q(:,:),
89  $ R(:,:), WORK( : ), T(:,:),
90  $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
91  DOUBLE PRECISION, ALLOCATABLE :: RWORK(:)
92 *
93 * .. Parameters ..
94  DOUBLE PRECISION ZERO
95  COMPLEX*16 ONE, CZERO
96  parameter( zero = 0.0, one = (1.0,0.0), czero=(0.0,0.0) )
97 * ..
98 * .. Local Scalars ..
99  INTEGER INFO, J, K, L, LWORK
100  DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
101 * ..
102 * .. Local Arrays ..
103  INTEGER ISEED( 4 )
104 * ..
105 * .. External Functions ..
106  DOUBLE PRECISION DLAMCH
107  DOUBLE PRECISION ZLANGE, ZLANSY
108  LOGICAL LSAME
109  EXTERNAL dlamch, zlange, zlansy, lsame
110 * ..
111 * .. Intrinsic Functions ..
112  INTRINSIC max, min
113 * ..
114 * .. Data statements ..
115  DATA iseed / 1988, 1989, 1990, 1991 /
116 *
117  eps = dlamch( 'Epsilon' )
118  k = min(m,n)
119  l = max(m,n)
120  lwork = max(2,l)*max(2,l)*nb
121 *
122 * Dynamically allocate local arrays
123 *
124  ALLOCATE ( a(m,n), af(m,n), q(m,m), r(m,l), rwork(l),
125  $ work(lwork), t(nb,n), c(m,n), cf(m,n),
126  $ d(n,m), df(n,m) )
127 *
128 * Put random numbers into A and copy to AF
129 *
130  ldt=nb
131  DO j=1,n
132  CALL zlarnv( 2, iseed, m, a( 1, j ) )
133  END DO
134  CALL zlacpy( 'Full', m, n, a, m, af, m )
135 *
136 * Factor the matrix A in the array AF.
137 *
138  CALL zgeqrt( m, n, nb, af, m, t, ldt, work, info )
139 *
140 * Generate the m-by-m matrix Q
141 *
142  CALL zlaset( 'Full', m, m, czero, one, q, m )
143  CALL zgemqrt( 'R', 'N', m, m, k, nb, af, m, t, ldt, q, m,
144  $ work, info )
145 *
146 * Copy R
147 *
148  CALL zlaset( 'Full', m, n, czero, czero, r, m )
149  CALL zlacpy( 'Upper', m, n, af, m, r, m )
150 *
151 * Compute |R - Q'*A| / |A| and store in RESULT(1)
152 *
153  CALL zgemm( 'C', 'N', m, n, m, -one, q, m, a, m, one, r, m )
154  anorm = zlange( '1', m, n, a, m, rwork )
155  resid = zlange( '1', m, n, r, m, rwork )
156  IF( anorm.GT.zero ) THEN
157  result( 1 ) = resid / (eps*max(1,m)*anorm)
158  ELSE
159  result( 1 ) = zero
160  END IF
161 *
162 * Compute |I - Q'*Q| and store in RESULT(2)
163 *
164  CALL zlaset( 'Full', m, m, czero, one, r, m )
165  CALL zherk( 'U', 'C', m, m, dreal(-one), q, m, dreal(one), r, m )
166  resid = zlansy( '1', 'Upper', m, r, m, rwork )
167  result( 2 ) = resid / (eps*max(1,m))
168 *
169 * Generate random m-by-n matrix C and a copy CF
170 *
171  DO j=1,n
172  CALL zlarnv( 2, iseed, m, c( 1, j ) )
173  END DO
174  cnorm = zlange( '1', m, n, c, m, rwork)
175  CALL zlacpy( 'Full', m, n, c, m, cf, m )
176 *
177 * Apply Q to C as Q*C
178 *
179  CALL zgemqrt( 'L', 'N', m, n, k, nb, af, m, t, nb, cf, m,
180  $ work, info)
181 *
182 * Compute |Q*C - Q*C| / |C|
183 *
184  CALL zgemm( 'N', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
185  resid = zlange( '1', m, n, cf, m, rwork )
186  IF( cnorm.GT.zero ) THEN
187  result( 3 ) = resid / (eps*max(1,m)*cnorm)
188  ELSE
189  result( 3 ) = zero
190  END IF
191 *
192 * Copy C into CF again
193 *
194  CALL zlacpy( 'Full', m, n, c, m, cf, m )
195 *
196 * Apply Q to C as QT*C
197 *
198  CALL zgemqrt( 'L', 'C', m, n, k, nb, af, m, t, nb, cf, m,
199  $ work, info)
200 *
201 * Compute |QT*C - QT*C| / |C|
202 *
203  CALL zgemm( 'C', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
204  resid = zlange( '1', m, n, cf, m, rwork )
205  IF( cnorm.GT.zero ) THEN
206  result( 4 ) = resid / (eps*max(1,m)*cnorm)
207  ELSE
208  result( 4 ) = zero
209  END IF
210 *
211 * Generate random n-by-m matrix D and a copy DF
212 *
213  DO j=1,m
214  CALL zlarnv( 2, iseed, n, d( 1, j ) )
215  END DO
216  dnorm = zlange( '1', n, m, d, n, rwork)
217  CALL zlacpy( 'Full', n, m, d, n, df, n )
218 *
219 * Apply Q to D as D*Q
220 *
221  CALL zgemqrt( 'R', 'N', n, m, k, nb, af, m, t, nb, df, n,
222  $ work, info)
223 *
224 * Compute |D*Q - D*Q| / |D|
225 *
226  CALL zgemm( 'N', 'N', n, m, m, -one, d, n, q, m, one, df, n )
227  resid = zlange( '1', n, m, df, n, rwork )
228  IF( cnorm.GT.zero ) THEN
229  result( 5 ) = resid / (eps*max(1,m)*dnorm)
230  ELSE
231  result( 5 ) = zero
232  END IF
233 *
234 * Copy D into DF again
235 *
236  CALL zlacpy( 'Full', n, m, d, n, df, n )
237 *
238 * Apply Q to D as D*QT
239 *
240  CALL zgemqrt( 'R', 'C', n, m, k, nb, af, m, t, nb, df, n,
241  $ work, info)
242 *
243 * Compute |D*QT - D*QT| / |D|
244 *
245  CALL zgemm( 'N', 'C', n, m, m, -one, d, n, q, m, one, df, n )
246  resid = zlange( '1', n, m, df, n, rwork )
247  IF( cnorm.GT.zero ) THEN
248  result( 6 ) = resid / (eps*max(1,m)*dnorm)
249  ELSE
250  result( 6 ) = zero
251  END IF
252 *
253 * Deallocate all arrays
254 *
255  DEALLOCATE ( a, af, q, r, rwork, work, t, c, d, cf, df)
256 *
257  RETURN
258  END
259 
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 zqrt04(M, N, NB, RESULT)
ZQRT04
Definition: zqrt04.f:73
subroutine zgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
ZGEMQRT
Definition: zgemqrt.f:168
subroutine zgeqrt(M, N, NB, A, LDA, T, LDT, WORK, INFO)
ZGEQRT
Definition: zgeqrt.f:141
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