LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
slqt04.f
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1 *> \brief \b SLQT04
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 SLQT04(M,N,NB,RESULT)
12 *
13 * .. Scalar Arguments ..
14 * INTEGER M, N, NB, LDT
15 * .. Return values ..
16 * REAL RESULT(6)
17 *
18 *
19 *> \par Purpose:
20 * =============
21 *>
22 *> \verbatim
23 *>
24 *> SLQT04 tests SGELQT and SGEMLQT.
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 REAL array, dimension (6)
51 *> Results of each of the six tests below.
52 *>
53 *> RESULT(1) = | A - L Q |
54 *> RESULT(2) = | I - Q Q^H |
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 double_lin
72 *
73 * =====================================================================
74  SUBROUTINE slqt04(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  REAL RESULT(6)
86 *
87 * =====================================================================
88 *
89 * ..
90 * .. Local allocatable arrays
91  REAL, ALLOCATABLE :: AF(:,:), Q(:,:),
92  $ l(:,:), rwork(:), work( : ), t(:,:),
93  $ cf(:,:), df(:,:), a(:,:), c(:,:), d(:,:)
94 *
95 * .. Parameters ..
96  REAL ONE, ZERO
97  parameter( zero = 0.0, one = 1.0 )
98 * ..
99 * .. Local Scalars ..
100  INTEGER INFO, J, K, LL, LWORK
101  REAL ANORM, EPS, RESID, CNORM, DNORM
102 * ..
103 * .. Local Arrays ..
104  INTEGER ISEED( 4 )
105 * ..
106 * .. External Functions ..
107  REAL SLAMCH, SLANGE, SLANSY
108  LOGICAL LSAME
109  EXTERNAL slamch, slange, slansy, lsame
110 * ..
111 * .. Intrinsic Functions ..
112  INTRINSIC max, min
113 * ..
114 * .. Data statements ..
115  DATA iseed / 1988, 1989, 1990, 1991 /
116 *
117  eps = slamch( 'Epsilon' )
118  k = min(m,n)
119  ll = max(m,n)
120  lwork = max(2,ll)*max(2,ll)*nb
121 *
122 * Dynamically allocate local arrays
123 *
124  ALLOCATE ( a(m,n), af(m,n), q(n,n), l(ll,n), rwork(ll),
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 slarnv( 2, iseed, m, a( 1, j ) )
133  END DO
134  CALL slacpy( 'Full', m, n, a, m, af, m )
135 *
136 * Factor the matrix A in the array AF.
137 *
138  CALL sgelqt( m, n, nb, af, m, t, ldt, work, info )
139 *
140 * Generate the n-by-n matrix Q
141 *
142  CALL slaset( 'Full', n, n, zero, one, q, n )
143  CALL sgemlqt( 'R', 'N', n, n, k, nb, af, m, t, ldt, q, n,
144  $ work, info )
145 *
146 * Copy R
147 *
148  CALL slaset( 'Full', m, n, zero, zero, l, ll )
149  CALL slacpy( 'Lower', m, n, af, m, l, ll )
150 *
151 * Compute |L - A*Q'| / |A| and store in RESULT(1)
152 *
153  CALL sgemm( 'N', 'T', m, n, n, -one, a, m, q, n, one, l, ll )
154  anorm = slange( '1', m, n, a, m, rwork )
155  resid = slange( '1', m, n, l, ll, 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 slaset( 'Full', n, n, zero, one, l, ll )
165  CALL ssyrk( 'U', 'C', n, n, -one, q, n, one, l, ll )
166  resid = slansy( '1', 'Upper', n, l, ll, rwork )
167  result( 2 ) = resid / (eps*max(1,n))
168 *
169 * Generate random m-by-n matrix C and a copy CF
170 *
171  DO j=1,m
172  CALL slarnv( 2, iseed, n, d( 1, j ) )
173  END DO
174  dnorm = slange( '1', n, m, d, n, rwork)
175  CALL slacpy( 'Full', n, m, d, n, df, n )
176 *
177 * Apply Q to C as Q*C
178 *
179  CALL sgemlqt( 'L', 'N', n, m, k, nb, af, m, t, nb, df, n,
180  $ work, info)
181 *
182 * Compute |Q*D - Q*D| / |D|
183 *
184  CALL sgemm( 'N', 'N', n, m, n, -one, q, n, d, n, one, df, n )
185  resid = slange( '1', n, m, df, n, rwork )
186  IF( dnorm.GT.zero ) THEN
187  result( 3 ) = resid / (eps*max(1,m)*dnorm)
188  ELSE
189  result( 3 ) = zero
190  END IF
191 *
192 * Copy D into DF again
193 *
194  CALL slacpy( 'Full', n, m, d, n, df, n )
195 *
196 * Apply Q to D as QT*D
197 *
198  CALL sgemlqt( 'L', 'T', n, m, k, nb, af, m, t, nb, df, n,
199  $ work, info)
200 *
201 * Compute |QT*D - QT*D| / |D|
202 *
203  CALL sgemm( 'T', 'N', n, m, n, -one, q, n, d, n, one, df, n )
204  resid = slange( '1', n, m, df, n, rwork )
205  IF( dnorm.GT.zero ) THEN
206  result( 4 ) = resid / (eps*max(1,m)*dnorm)
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,n
214  CALL slarnv( 2, iseed, m, c( 1, j ) )
215  END DO
216  cnorm = slange( '1', m, n, c, m, rwork)
217  CALL slacpy( 'Full', m, n, c, m, cf, m )
218 *
219 * Apply Q to C as C*Q
220 *
221  CALL sgemlqt( 'R', 'N', m, n, k, nb, af, m, t, nb, cf, m,
222  $ work, info)
223 *
224 * Compute |C*Q - C*Q| / |C|
225 *
226  CALL sgemm( 'N', 'N', m, n, n, -one, c, m, q, n, one, cf, m )
227  resid = slange( '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 C into CF again
235 *
236  CALL slacpy( 'Full', m, n, c, m, cf, m )
237 *
238 * Apply Q to D as D*QT
239 *
240  CALL sgemlqt( 'R', 'T', m, n, k, nb, af, m, t, nb, cf, m,
241  $ work, info)
242 *
243 * Compute |C*QT - C*QT| / |C|
244 *
245  CALL sgemm( 'N', 'T', m, n, n, -one, c, m, q, n, one, cf, m )
246  resid = slange( '1', m, n, cf, m, 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, l, rwork, work, t, c, d, cf, df)
256 *
257  RETURN
258  END
259 
subroutine sgelqt(M, N, MB, A, LDA, T, LDT, WORK, INFO)
Definition: sgelqt.f:124
subroutine sgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
Definition: sgemlqt.f:153
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:171
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: slaset.f:112
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: slarnv.f:99
subroutine slqt04(M, N, NB, RESULT)
SLQT04
Definition: slqt04.f:75
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:105