LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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sqrt04.f
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1*> \brief \b SQRT04
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 SQRT04(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*> SQRT04 tests SGEQRT and SGEMQRT.
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 - 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 single_lin
70*
71* =====================================================================
72 SUBROUTINE sqrt04(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 REAL RESULT(6)
83*
84* =====================================================================
85*
86* ..
87* .. Local allocatable arrays
88 REAL, ALLOCATABLE :: AF(:,:), Q(:,:),
89 $ R(:,:), RWORK(:), WORK( : ), T(:,:),
90 $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
91*
92* .. Parameters ..
93 REAL ONE, ZERO
94 parameter( zero = 0.0, one = 1.0 )
95* ..
96* .. Local Scalars ..
97 INTEGER INFO, J, K, L, LWORK
98 REAL ANORM, EPS, RESID, CNORM, DNORM
99* ..
100* .. Local Arrays ..
101 INTEGER ISEED( 4 )
102* ..
103* .. External Subroutine ..
105* ..
106* .. External Functions ..
107 REAL SLAMCH
108 REAL SLANGE, SLANSY
109 LOGICAL LSAME
110 EXTERNAL slamch, slange, slansy, lsame
111* ..
112* .. Intrinsic Functions ..
113 INTRINSIC max, min
114* ..
115* .. Data statements ..
116 DATA iseed / 1988, 1989, 1990, 1991 /
117*
118 eps = slamch( 'Epsilon' )
119 k = min(m,n)
120 l = max(m,n)
121 lwork = max(2,l)*max(2,l)*nb
122*
123* Dynamically allocate local arrays
124*
125 ALLOCATE ( a(m,n), af(m,n), q(m,m), r(m,l), rwork(l),
126 $ work(lwork), t(nb,n), c(m,n), cf(m,n),
127 $ d(n,m), df(n,m) )
128*
129* Put random numbers into A and copy to AF
130*
131 ldt=nb
132 DO j=1,n
133 CALL slarnv( 2, iseed, m, a( 1, j ) )
134 END DO
135 CALL slacpy( 'Full', m, n, a, m, af, m )
136*
137* Factor the matrix A in the array AF.
138*
139 CALL sgeqrt( m, n, nb, af, m, t, ldt, work, info )
140*
141* Generate the m-by-m matrix Q
142*
143 CALL slaset( 'Full', m, m, zero, one, q, m )
144 CALL sgemqrt( 'R', 'N', m, m, k, nb, af, m, t, ldt, q, m,
145 $ work, info )
146*
147* Copy R
148*
149 CALL slaset( 'Full', m, n, zero, zero, r, m )
150 CALL slacpy( 'Upper', m, n, af, m, r, m )
151*
152* Compute |R - Q'*A| / |A| and store in RESULT(1)
153*
154 CALL sgemm( 'T', 'N', m, n, m, -one, q, m, a, m, one, r, m )
155 anorm = slange( '1', m, n, a, m, rwork )
156 resid = slange( '1', m, n, r, m, rwork )
157 IF( anorm.GT.zero ) THEN
158 result( 1 ) = resid / (eps*max(1,m)*anorm)
159 ELSE
160 result( 1 ) = zero
161 END IF
162*
163* Compute |I - Q'*Q| and store in RESULT(2)
164*
165 CALL slaset( 'Full', m, m, zero, one, r, m )
166 CALL ssyrk( 'U', 'C', m, m, -one, q, m, one, r, m )
167 resid = slansy( '1', 'Upper', m, r, m, rwork )
168 result( 2 ) = resid / (eps*max(1,m))
169*
170* Generate random m-by-n matrix C and a copy CF
171*
172 DO j=1,n
173 CALL slarnv( 2, iseed, m, c( 1, j ) )
174 END DO
175 cnorm = slange( '1', m, n, c, m, rwork)
176 CALL slacpy( 'Full', m, n, c, m, cf, m )
177*
178* Apply Q to C as Q*C
179*
180 CALL sgemqrt( 'L', 'N', m, n, k, nb, af, m, t, nb, cf, m,
181 $ work, info)
182*
183* Compute |Q*C - Q*C| / |C|
184*
185 CALL sgemm( 'N', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
186 resid = slange( '1', m, n, cf, m, rwork )
187 IF( cnorm.GT.zero ) THEN
188 result( 3 ) = resid / (eps*max(1,m)*cnorm)
189 ELSE
190 result( 3 ) = zero
191 END IF
192*
193* Copy C into CF again
194*
195 CALL slacpy( 'Full', m, n, c, m, cf, m )
196*
197* Apply Q to C as QT*C
198*
199 CALL sgemqrt( 'L', 'T', m, n, k, nb, af, m, t, nb, cf, m,
200 $ work, info)
201*
202* Compute |QT*C - QT*C| / |C|
203*
204 CALL sgemm( 'T', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
205 resid = slange( '1', m, n, cf, m, rwork )
206 IF( cnorm.GT.zero ) THEN
207 result( 4 ) = resid / (eps*max(1,m)*cnorm)
208 ELSE
209 result( 4 ) = zero
210 END IF
211*
212* Generate random n-by-m matrix D and a copy DF
213*
214 DO j=1,m
215 CALL slarnv( 2, iseed, n, d( 1, j ) )
216 END DO
217 dnorm = slange( '1', n, m, d, n, rwork)
218 CALL slacpy( 'Full', n, m, d, n, df, n )
219*
220* Apply Q to D as D*Q
221*
222 CALL sgemqrt( 'R', 'N', n, m, k, nb, af, m, t, nb, df, n,
223 $ work, info)
224*
225* Compute |D*Q - D*Q| / |D|
226*
227 CALL sgemm( 'N', 'N', n, m, m, -one, d, n, q, m, one, df, n )
228 resid = slange( '1', n, m, df, n, rwork )
229 IF( cnorm.GT.zero ) THEN
230 result( 5 ) = resid / (eps*max(1,m)*dnorm)
231 ELSE
232 result( 5 ) = zero
233 END IF
234*
235* Copy D into DF again
236*
237 CALL slacpy( 'Full', n, m, d, n, df, n )
238*
239* Apply Q to D as D*QT
240*
241 CALL sgemqrt( 'R', 'T', n, m, k, nb, af, m, t, nb, df, n,
242 $ work, info)
243*
244* Compute |D*QT - D*QT| / |D|
245*
246 CALL sgemm( 'N', 'T', n, m, m, -one, d, n, q, m, one, df, n )
247 resid = slange( '1', n, m, df, n, rwork )
248 IF( cnorm.GT.zero ) THEN
249 result( 6 ) = resid / (eps*max(1,m)*dnorm)
250 ELSE
251 result( 6 ) = zero
252 END IF
253*
254* Deallocate all arrays
255*
256 DEALLOCATE ( a, af, q, r, rwork, work, t, c, d, cf, df)
257*
258 RETURN
259 END
260
subroutine sgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
SGEMM
Definition sgemm.f:188
subroutine sgemqrt(side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
SGEMQRT
Definition sgemqrt.f:168
subroutine sgeqrt(m, n, nb, a, lda, t, ldt, work, info)
SGEQRT
Definition sgeqrt.f:141
subroutine ssyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
SSYRK
Definition ssyrk.f:169
subroutine slacpy(uplo, m, n, a, lda, b, ldb)
SLACPY copies all or part of one two-dimensional array to another.
Definition slacpy.f:103
subroutine slarnv(idist, iseed, n, x)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition slarnv.f:97
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:110
subroutine sqrt04(m, n, nb, result)
SQRT04
Definition sqrt04.f:73