LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ clqt04()

 subroutine clqt04 ( integer m, integer n, integer nb, real, dimension(6) result )

DLQT04

Purpose:
CLQT04 tests CGELQT and CGEMLQT.
Parameters
 [in] M M is INTEGER Number of rows in test matrix. [in] N N is INTEGER Number of columns in test matrix. [in] NB NB is INTEGER Block size of test matrix. NB <= Min(M,N). [out] RESULT RESULT is DOUBLE PRECISION array, dimension (6) Results of each of the six tests below. RESULT(1) = | A - L Q | RESULT(2) = | I - Q Q^H | RESULT(3) = | Q C - Q C | RESULT(4) = | Q^H C - Q^H C | RESULT(5) = | C Q - C Q | RESULT(6) = | C Q^H - C Q^H |

Definition at line 72 of file clqt04.f.

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
81* .. Return values ..
82 REAL RESULT(6)
83*
84* =====================================================================
85*
86* ..
87* .. Local allocatable arrays
88 COMPLEX, ALLOCATABLE :: AF(:,:), Q(:,:),
89 \$ L(:,:), WORK( : ), T(:,:),
90 \$ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
91 REAL, ALLOCATABLE :: RWORK(:)
92*
93* .. Parameters ..
94 REAL ZERO
95 COMPLEX ONE, CZERO
96 parameter( zero = 0.0)
97 parameter( one = (1.0,0.0), czero=(0.0,0.0) )
98* ..
99* .. Local Scalars ..
100 INTEGER INFO, J, K, LL, LWORK, LDT
101 REAL ANORM, EPS, RESID, CNORM, DNORM
102* ..
103* .. Local Arrays ..
104 INTEGER ISEED( 4 )
105* ..
106* .. External Functions ..
107 REAL SLAMCH
108 REAL CLANGE, CLANSY
109 LOGICAL LSAME
110 EXTERNAL slamch, clange, clansy, 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 ll = max(m,n)
121 lwork = max(2,ll)*max(2,ll)*nb
122*
123* Dynamically allocate local arrays
124*
125 ALLOCATE ( a(m,n), af(m,n), q(n,n), l(ll,n), rwork(ll),
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 clarnv( 2, iseed, m, a( 1, j ) )
134 END DO
135 CALL clacpy( 'Full', m, n, a, m, af, m )
136*
137* Factor the matrix A in the array AF.
138*
139 CALL cgelqt( m, n, nb, af, m, t, ldt, work, info )
140*
141* Generate the n-by-n matrix Q
142*
143 CALL claset( 'Full', n, n, czero, one, q, n )
144 CALL cgemlqt( 'R', 'N', n, n, k, nb, af, m, t, ldt, q, n,
145 \$ work, info )
146*
147* Copy L
148*
149 CALL claset( 'Full', ll, n, czero, czero, l, ll )
150 CALL clacpy( 'Lower', m, n, af, m, l, ll )
151*
152* Compute |L - A*Q'| / |A| and store in RESULT(1)
153*
154 CALL cgemm( 'N', 'C', m, n, n, -one, a, m, q, n, one, l, ll )
155 anorm = clange( '1', m, n, a, m, rwork )
156 resid = clange( '1', m, n, l, ll, 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 claset( 'Full', n, n, czero, one, l, ll )
166 CALL cherk( 'U', 'C', n, n, real(-one), q, n, real(one), l, ll)
167 resid = clansy( '1', 'Upper', n, l, ll, rwork )
168 result( 2 ) = resid / (eps*max(1,n))
169*
170* Generate random m-by-n matrix C and a copy CF
171*
172 DO j=1,m
173 CALL clarnv( 2, iseed, n, d( 1, j ) )
174 END DO
175 dnorm = clange( '1', n, m, d, n, rwork)
176 CALL clacpy( 'Full', n, m, d, n, df, n )
177*
178* Apply Q to C as Q*C
179*
180 CALL cgemlqt( 'L', 'N', n, m, k, nb, af, m, t, nb, df, n,
181 \$ work, info)
182*
183* Compute |Q*D - Q*D| / |D|
184*
185 CALL cgemm( 'N', 'N', n, m, n, -one, q, n, d, n, one, df, n )
186 resid = clange( '1', n, m, df, n, rwork )
187 IF( dnorm.GT.zero ) THEN
188 result( 3 ) = resid / (eps*max(1,m)*dnorm)
189 ELSE
190 result( 3 ) = zero
191 END IF
192*
193* Copy D into DF again
194*
195 CALL clacpy( 'Full', n, m, d, n, df, n )
196*
197* Apply Q to D as QT*D
198*
199 CALL cgemlqt( 'L', 'C', n, m, k, nb, af, m, t, nb, df, n,
200 \$ work, info)
201*
202* Compute |QT*D - QT*D| / |D|
203*
204 CALL cgemm( 'C', 'N', n, m, n, -one, q, n, d, n, one, df, n )
205 resid = clange( '1', n, m, df, n, rwork )
206 IF( dnorm.GT.zero ) THEN
207 result( 4 ) = resid / (eps*max(1,m)*dnorm)
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,n
215 CALL clarnv( 2, iseed, m, c( 1, j ) )
216 END DO
217 cnorm = clange( '1', m, n, c, m, rwork)
218 CALL clacpy( 'Full', m, n, c, m, cf, m )
219*
220* Apply Q to C as C*Q
221*
222 CALL cgemlqt( 'R', 'N', m, n, k, nb, af, m, t, nb, cf, m,
223 \$ work, info)
224*
225* Compute |C*Q - C*Q| / |C|
226*
227 CALL cgemm( 'N', 'N', m, n, n, -one, c, m, q, n, one, cf, m )
228 resid = clange( '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 C into CF again
236*
237 CALL clacpy( 'Full', m, n, c, m, cf, m )
238*
239* Apply Q to D as D*QT
240*
241 CALL cgemlqt( 'R', 'C', m, n, k, nb, af, m, t, nb, cf, m,
242 \$ work, info)
243*
244* Compute |C*QT - C*QT| / |C|
245*
246 CALL cgemm( 'N', 'C', m, n, n, -one, c, m, q, n, one, cf, m )
247 resid = clange( '1', m, n, cf, m, 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, l, rwork, work, t, c, d, cf, df)
257*
258 RETURN
subroutine cgelqt(m, n, mb, a, lda, t, ldt, work, info)
CGELQT
Definition cgelqt.f:124
subroutine cgemlqt(side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
CGEMLQT
Definition cgemlqt.f:153
subroutine cgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CGEMM
Definition cgemm.f:188
subroutine cherk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
CHERK
Definition cherk.f:173
subroutine clacpy(uplo, m, n, a, lda, b, ldb)
CLACPY copies all or part of one two-dimensional array to another.
Definition clacpy.f:103
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function clange(norm, m, n, a, lda, work)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition clange.f:115
real function clansy(norm, uplo, n, a, lda, work)
CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clansy.f:123
subroutine clarnv(idist, iseed, n, x)
CLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition clarnv.f:99
subroutine claset(uplo, m, n, alpha, beta, a, lda)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition claset.f:106
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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