LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zqrt04.f
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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 *> \date April 2012
70 *
71 *> \ingroup complex16_lin
72 *
73 * =====================================================================
74  SUBROUTINE zqrt04(M,N,NB,RESULT)
75  IMPLICIT NONE
76 *
77 * -- LAPACK test routine (version 3.7.0) --
78 * -- LAPACK is a software package provided by Univ. of Tennessee, --
79 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
80 * April 2012
81 *
82 * .. Scalar Arguments ..
83  INTEGER M, N, NB, LDT
84 * .. Return values ..
85  DOUBLE PRECISION RESULT(6)
86 *
87 * =====================================================================
88 *
89 * ..
90 * .. Local allocatable arrays
91  COMPLEX*16, ALLOCATABLE :: AF(:,:), Q(:,:),
92  $ r(:,:), work( : ), t(:,:),
93  $ cf(:,:), df(:,:), a(:,:), c(:,:), d(:,:)
94  DOUBLE PRECISION, ALLOCATABLE :: RWORK(:)
95 *
96 * .. Parameters ..
97  DOUBLE PRECISION ZERO
98  COMPLEX*16 ONE, CZERO
99  parameter( zero = 0.0, one = (1.0,0.0), czero=(0.0,0.0) )
100 * ..
101 * .. Local Scalars ..
102  INTEGER INFO, J, K, L, LWORK
103  DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
104 * ..
105 * .. Local Arrays ..
106  INTEGER ISEED( 4 )
107 * ..
108 * .. External Functions ..
109  DOUBLE PRECISION DLAMCH
110  DOUBLE PRECISION ZLANGE, ZLANSY
111  LOGICAL LSAME
112  EXTERNAL dlamch, zlange, zlansy, lsame
113 * ..
114 * .. Intrinsic Functions ..
115  INTRINSIC max, min
116 * ..
117 * .. Data statements ..
118  DATA iseed / 1988, 1989, 1990, 1991 /
119 *
120  eps = dlamch( 'Epsilon' )
121  k = min(m,n)
122  l = max(m,n)
123  lwork = max(2,l)*max(2,l)*nb
124 *
125 * Dynamically allocate local arrays
126 *
127  ALLOCATE ( a(m,n), af(m,n), q(m,m), r(m,l), rwork(l),
128  $ work(lwork), t(nb,n), c(m,n), cf(m,n),
129  $ d(n,m), df(n,m) )
130 *
131 * Put random numbers into A and copy to AF
132 *
133  ldt=nb
134  DO j=1,n
135  CALL zlarnv( 2, iseed, m, a( 1, j ) )
136  END DO
137  CALL zlacpy( 'Full', m, n, a, m, af, m )
138 *
139 * Factor the matrix A in the array AF.
140 *
141  CALL zgeqrt( m, n, nb, af, m, t, ldt, work, info )
142 *
143 * Generate the m-by-m matrix Q
144 *
145  CALL zlaset( 'Full', m, m, czero, one, q, m )
146  CALL zgemqrt( 'R', 'N', m, m, k, nb, af, m, t, ldt, q, m,
147  $ work, info )
148 *
149 * Copy R
150 *
151  CALL zlaset( 'Full', m, n, czero, czero, r, m )
152  CALL zlacpy( 'Upper', m, n, af, m, r, m )
153 *
154 * Compute |R - Q'*A| / |A| and store in RESULT(1)
155 *
156  CALL zgemm( 'C', 'N', m, n, m, -one, q, m, a, m, one, r, m )
157  anorm = zlange( '1', m, n, a, m, rwork )
158  resid = zlange( '1', m, n, r, m, rwork )
159  IF( anorm.GT.zero ) THEN
160  result( 1 ) = resid / (eps*max(1,m)*anorm)
161  ELSE
162  result( 1 ) = zero
163  END IF
164 *
165 * Compute |I - Q'*Q| and store in RESULT(2)
166 *
167  CALL zlaset( 'Full', m, m, czero, one, r, m )
168  CALL zherk( 'U', 'C', m, m, dreal(-one), q, m, dreal(one), r, m )
169  resid = zlansy( '1', 'Upper', m, r, m, rwork )
170  result( 2 ) = resid / (eps*max(1,m))
171 *
172 * Generate random m-by-n matrix C and a copy CF
173 *
174  DO j=1,n
175  CALL zlarnv( 2, iseed, m, c( 1, j ) )
176  END DO
177  cnorm = zlange( '1', m, n, c, m, rwork)
178  CALL zlacpy( 'Full', m, n, c, m, cf, m )
179 *
180 * Apply Q to C as Q*C
181 *
182  CALL zgemqrt( 'L', 'N', m, n, k, nb, af, m, t, nb, cf, m,
183  $ work, info)
184 *
185 * Compute |Q*C - Q*C| / |C|
186 *
187  CALL zgemm( 'N', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
188  resid = zlange( '1', m, n, cf, m, rwork )
189  IF( cnorm.GT.zero ) THEN
190  result( 3 ) = resid / (eps*max(1,m)*cnorm)
191  ELSE
192  result( 3 ) = zero
193  END IF
194 *
195 * Copy C into CF again
196 *
197  CALL zlacpy( 'Full', m, n, c, m, cf, m )
198 *
199 * Apply Q to C as QT*C
200 *
201  CALL zgemqrt( 'L', 'C', m, n, k, nb, af, m, t, nb, cf, m,
202  $ work, info)
203 *
204 * Compute |QT*C - QT*C| / |C|
205 *
206  CALL zgemm( 'C', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
207  resid = zlange( '1', m, n, cf, m, rwork )
208  IF( cnorm.GT.zero ) THEN
209  result( 4 ) = resid / (eps*max(1,m)*cnorm)
210  ELSE
211  result( 4 ) = zero
212  END IF
213 *
214 * Generate random n-by-m matrix D and a copy DF
215 *
216  DO j=1,m
217  CALL zlarnv( 2, iseed, n, d( 1, j ) )
218  END DO
219  dnorm = zlange( '1', n, m, d, n, rwork)
220  CALL zlacpy( 'Full', n, m, d, n, df, n )
221 *
222 * Apply Q to D as D*Q
223 *
224  CALL zgemqrt( 'R', 'N', n, m, k, nb, af, m, t, nb, df, n,
225  $ work, info)
226 *
227 * Compute |D*Q - D*Q| / |D|
228 *
229  CALL zgemm( 'N', 'N', n, m, m, -one, d, n, q, m, one, df, n )
230  resid = zlange( '1', n, m, df, n, rwork )
231  IF( cnorm.GT.zero ) THEN
232  result( 5 ) = resid / (eps*max(1,m)*dnorm)
233  ELSE
234  result( 5 ) = zero
235  END IF
236 *
237 * Copy D into DF again
238 *
239  CALL zlacpy( 'Full', n, m, d, n, df, n )
240 *
241 * Apply Q to D as D*QT
242 *
243  CALL zgemqrt( 'R', 'C', n, m, k, nb, af, m, t, nb, df, n,
244  $ work, info)
245 *
246 * Compute |D*QT - D*QT| / |D|
247 *
248  CALL zgemm( 'N', 'C', n, m, m, -one, d, n, q, m, one, df, n )
249  resid = zlange( '1', n, m, df, n, rwork )
250  IF( cnorm.GT.zero ) THEN
251  result( 6 ) = resid / (eps*max(1,m)*dnorm)
252  ELSE
253  result( 6 ) = zero
254  END IF
255 *
256 * Deallocate all arrays
257 *
258  DEALLOCATE ( a, af, q, r, rwork, work, t, c, d, cf, df)
259 *
260  RETURN
261  END
262 
subroutine zqrt04(M, N, NB, RESULT)
ZQRT04
Definition: zqrt04.f:75
subroutine zgeqrt(M, N, NB, A, LDA, T, LDT, WORK, INFO)
ZGEQRT
Definition: zgeqrt.f:143
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:108
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:175
subroutine zgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
ZGEMQRT
Definition: zgemqrt.f:170
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:101