LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
sqrt05.f
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1 *> \brief \b SQRT05
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 SQRT05(M,N,L,NB,RESULT)
12 *
13 * .. Scalar Arguments ..
14 * INTEGER LWORK, M, N, L, NB, LDT
15 * .. Return values ..
16 * REAL RESULT(6)
17 *
18 *
19 *> \par Purpose:
20 * =============
21 *>
22 *> \verbatim
23 *>
24 *> SQRT05 tests STPQRT and STPMQRT.
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 REAL 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 single_lin
77 *
78 * =====================================================================
79  SUBROUTINE sqrt05(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  REAL RESULT(6)
90 *
91 * =====================================================================
92 *
93 * ..
94 * .. Local allocatable arrays
95  REAL, ALLOCATABLE :: AF(:,:), Q(:,:),
96  \$ R(:,:), RWORK(:), WORK( : ), T(:,:),
97  \$ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
98 *
99 * .. Parameters ..
100  REAL ZERO, ONE
101  parameter( zero = 0.0, one = 1.0 )
102 * ..
103 * .. Local Scalars ..
104  INTEGER INFO, J, K, M2, NP1
105  REAL ANORM, EPS, RESID, CNORM, DNORM
106 * ..
107 * .. Local Arrays ..
108  INTEGER ISEED( 4 )
109 * ..
110 * .. External Subroutine ..
111  EXTERNAL sgemm, slarnv, stpmqrt, stpqrt, sgemqrt, ssyrk, slacpy,
112  \$ slaset
113 * ..
114 * .. External Functions ..
115  REAL SLAMCH
116  REAL SLANGE, SLANSY
117  LOGICAL LSAME
118  EXTERNAL slamch, slange, slansy, lsame
119 * ..
120 * .. Data statements ..
121  DATA iseed / 1988, 1989, 1990, 1991 /
122 *
123  eps = slamch( 'Epsilon' )
124  k = n
125  m2 = m+n
126  IF( m.GT.0 ) THEN
127  np1 = n+1
128  ELSE
129  np1 = 1
130  END IF
131  lwork = m2*m2*nb
132 *
133 * Dynamically allocate all arrays
134 *
135  ALLOCATE(a(m2,n),af(m2,n),q(m2,m2),r(m2,m2),rwork(m2),
136  \$ work(lwork),t(nb,n),c(m2,n),cf(m2,n),
137  \$ d(n,m2),df(n,m2) )
138 *
139 * Put random stuff into A
140 *
141  ldt=nb
142  CALL slaset( 'Full', m2, n, zero, zero, a, m2 )
143  CALL slaset( 'Full', nb, n, zero, zero, t, nb )
144  DO j=1,n
145  CALL slarnv( 2, iseed, j, a( 1, j ) )
146  END DO
147  IF( m.GT.0 ) THEN
148  DO j=1,n
149  CALL slarnv( 2, iseed, m-l, a( n+1, j ) )
150  END DO
151  END IF
152  IF( l.GT.0 ) THEN
153  DO j=1,n
154  CALL slarnv( 2, iseed, min(j,l), a( n+m-l+1, j ) )
155  END DO
156  END IF
157 *
158 * Copy the matrix A to the array AF.
159 *
160  CALL slacpy( 'Full', m2, n, a, m2, af, m2 )
161 *
162 * Factor the matrix A in the array AF.
163 *
164  CALL stpqrt( m,n,l,nb,af,m2,af(np1,1),m2,t,ldt,work,info)
165 *
166 * Generate the (M+N)-by-(M+N) matrix Q by applying H to I
167 *
168  CALL slaset( 'Full', m2, m2, zero, one, q, m2 )
169  CALL sgemqrt( 'R', 'N', m2, m2, k, nb, af, m2, t, ldt, q, m2,
170  \$ work, info )
171 *
172 * Copy R
173 *
174  CALL slaset( 'Full', m2, n, zero, zero, r, m2 )
175  CALL slacpy( 'Upper', m2, n, af, m2, r, m2 )
176 *
177 * Compute |R - Q'*A| / |A| and store in RESULT(1)
178 *
179  CALL sgemm( 'T', 'N', m2, n, m2, -one, q, m2, a, m2, one, r, m2 )
180  anorm = slange( '1', m2, n, a, m2, rwork )
181  resid = slange( '1', m2, n, r, m2, rwork )
182  IF( anorm.GT.zero ) THEN
183  result( 1 ) = resid / (eps*anorm*max(1,m2))
184  ELSE
185  result( 1 ) = zero
186  END IF
187 *
188 * Compute |I - Q'*Q| and store in RESULT(2)
189 *
190  CALL slaset( 'Full', m2, m2, zero, one, r, m2 )
191  CALL ssyrk( 'U', 'C', m2, m2, -one, q, m2, one,
192  \$ r, m2 )
193  resid = slansy( '1', 'Upper', m2, r, m2, rwork )
194  result( 2 ) = resid / (eps*max(1,m2))
195 *
196 * Generate random m-by-n matrix C and a copy CF
197 *
198  DO j=1,n
199  CALL slarnv( 2, iseed, m2, c( 1, j ) )
200  END DO
201  cnorm = slange( '1', m2, n, c, m2, rwork)
202  CALL slacpy( 'Full', m2, n, c, m2, cf, m2 )
203 *
204 * Apply Q to C as Q*C
205 *
206  CALL stpmqrt( 'L','N', m,n,k,l,nb,af(np1,1),m2,t,ldt,cf,
207  \$ m2,cf(np1,1),m2,work,info)
208 *
209 * Compute |Q*C - Q*C| / |C|
210 *
211  CALL sgemm( 'N', 'N', m2, n, m2, -one, q,m2,c,m2,one,cf,m2)
212  resid = slange( '1', m2, n, cf, m2, rwork )
213  IF( cnorm.GT.zero ) THEN
214  result( 3 ) = resid / (eps*max(1,m2)*cnorm)
215  ELSE
216  result( 3 ) = zero
217  END IF
218 *
219 * Copy C into CF again
220 *
221  CALL slacpy( 'Full', m2, n, c, m2, cf, m2 )
222 *
223 * Apply Q to C as QT*C
224 *
225  CALL stpmqrt('L','T',m,n,k,l,nb,af(np1,1),m2,t,ldt,cf,m2,
226  \$ cf(np1,1),m2,work,info)
227 *
228 * Compute |QT*C - QT*C| / |C|
229 *
230  CALL sgemm('T','N',m2,n,m2,-one,q,m2,c,m2,one,cf,m2)
231  resid = slange( '1', m2, n, cf, m2, rwork )
232  IF( cnorm.GT.zero ) THEN
233  result( 4 ) = resid / (eps*max(1,m2)*cnorm)
234  ELSE
235  result( 4 ) = zero
236  END IF
237 *
238 * Generate random n-by-m matrix D and a copy DF
239 *
240  DO j=1,m2
241  CALL slarnv( 2, iseed, n, d( 1, j ) )
242  END DO
243  dnorm = slange( '1', n, m2, d, n, rwork)
244  CALL slacpy( 'Full', n, m2, d, n, df, n )
245 *
246 * Apply Q to D as D*Q
247 *
248  CALL stpmqrt('R','N',n,m,n,l,nb,af(np1,1),m2,t,ldt,df,n,
249  \$ df(1,np1),n,work,info)
250 *
251 * Compute |D*Q - D*Q| / |D|
252 *
253  CALL sgemm('N','N',n,m2,m2,-one,d,n,q,m2,one,df,n)
254  resid = slange('1',n, m2,df,n,rwork )
255  IF( cnorm.GT.zero ) THEN
256  result( 5 ) = resid / (eps*max(1,m2)*dnorm)
257  ELSE
258  result( 5 ) = zero
259  END IF
260 *
261 * Copy D into DF again
262 *
263  CALL slacpy('Full',n,m2,d,n,df,n )
264 *
265 * Apply Q to D as D*QT
266 *
267  CALL stpmqrt('R','T',n,m,n,l,nb,af(np1,1),m2,t,ldt,df,n,
268  \$ df(1,np1),n,work,info)
269
270 *
271 * Compute |D*QT - D*QT| / |D|
272 *
273  CALL sgemm( 'N', 'T', n, m2, m2, -one, d, n, q, m2, one, df, n )
274  resid = slange( '1', n, m2, df, n, rwork )
275  IF( cnorm.GT.zero ) THEN
276  result( 6 ) = resid / (eps*max(1,m2)*dnorm)
277  ELSE
278  result( 6 ) = zero
279  END IF
280 *
281 * Deallocate all arrays
282 *
283  DEALLOCATE ( a, af, q, r, rwork, work, t, c, d, cf, df)
284  RETURN
285  END
286
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 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 sgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
SGEMQRT
Definition: sgemqrt.f:168
subroutine stpmqrt(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
STPMQRT
Definition: stpmqrt.f:216
subroutine stpqrt(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
STPQRT
Definition: stpqrt.f:189
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:169
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
subroutine sqrt05(M, N, L, NB, RESULT)
SQRT05
Definition: sqrt05.f:80