LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zqrt05()

 subroutine zqrt05 ( integer M, integer N, integer L, integer NB, double precision, dimension(6) RESULT )

ZQRT05

Purpose:
` ZQRT05 tests ZTPQRT and ZTPMQRT.`
Parameters
 [in] M ``` M is INTEGER Number of rows in lower part of the test matrix.``` [in] N ``` N is INTEGER Number of columns in test matrix.``` [in] L ``` L is INTEGER The number of rows of the upper trapezoidal part the lower test matrix. 0 <= L <= M.``` [in] NB ``` NB is INTEGER Block size of test matrix. NB <= N.``` [out] RESULT ``` RESULT is DOUBLE PRECISION array, dimension (6) Results of each of the six tests below. RESULT(1) = | A - Q R | RESULT(2) = | I - Q^H Q | 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 79 of file zqrt05.f.

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 DOUBLE PRECISION RESULT(6)
90*
91* =====================================================================
92*
93* ..
94* .. Local allocatable arrays
95 COMPLEX*16, ALLOCATABLE :: AF(:,:), Q(:,:),
96 \$ R(:,:), WORK( : ), T(:,:),
97 \$ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
98 DOUBLE PRECISION, ALLOCATABLE :: RWORK(:)
99*
100* .. Parameters ..
101 DOUBLE PRECISION ZERO
102 COMPLEX*16 ONE, CZERO
103 parameter( zero = 0.0, one = (1.0,0.0), czero=(0.0,0.0) )
104* ..
105* .. Local Scalars ..
106 INTEGER INFO, J, K, M2, NP1
107 DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
108* ..
109* .. Local Arrays ..
110 INTEGER ISEED( 4 )
111* ..
112* .. External Functions ..
113 DOUBLE PRECISION DLAMCH
114 DOUBLE PRECISION ZLANGE, ZLANSY
115 LOGICAL LSAME
116 EXTERNAL dlamch, zlange, zlansy, lsame
117* ..
118* .. Data statements ..
119 DATA iseed / 1988, 1989, 1990, 1991 /
120*
121 eps = dlamch( 'Epsilon' )
122 k = n
123 m2 = m+n
124 IF( m.GT.0 ) THEN
125 np1 = n+1
126 ELSE
127 np1 = 1
128 END IF
129 lwork = m2*m2*nb
130*
131* Dynamically allocate all arrays
132*
133 ALLOCATE(a(m2,n),af(m2,n),q(m2,m2),r(m2,m2),rwork(m2),
134 \$ work(lwork),t(nb,n),c(m2,n),cf(m2,n),
135 \$ d(n,m2),df(n,m2) )
136*
137* Put random stuff into A
138*
139 ldt=nb
140 CALL zlaset( 'Full', m2, n, czero, czero, a, m2 )
141 CALL zlaset( 'Full', nb, n, czero, czero, t, nb )
142 DO j=1,n
143 CALL zlarnv( 2, iseed, j, a( 1, j ) )
144 END DO
145 IF( m.GT.0 ) THEN
146 DO j=1,n
147 CALL zlarnv( 2, iseed, m-l, a( min(n+m,n+1), j ) )
148 END DO
149 END IF
150 IF( l.GT.0 ) THEN
151 DO j=1,n
152 CALL zlarnv( 2, iseed, min(j,l), a( min(n+m,n+m-l+1), j ) )
153 END DO
154 END IF
155*
156* Copy the matrix A to the array AF.
157*
158 CALL zlacpy( 'Full', m2, n, a, m2, af, m2 )
159*
160* Factor the matrix A in the array AF.
161*
162 CALL ztpqrt( m,n,l,nb,af,m2,af(np1,1),m2,t,ldt,work,info)
163*
164* Generate the (M+N)-by-(M+N) matrix Q by applying H to I
165*
166 CALL zlaset( 'Full', m2, m2, czero, one, q, m2 )
167 CALL zgemqrt( 'R', 'N', m2, m2, k, nb, af, m2, t, ldt, q, m2,
168 \$ work, info )
169*
170* Copy R
171*
172 CALL zlaset( 'Full', m2, n, czero, czero, r, m2 )
173 CALL zlacpy( 'Upper', m2, n, af, m2, r, m2 )
174*
175* Compute |R - Q'*A| / |A| and store in RESULT(1)
176*
177 CALL zgemm( 'C', 'N', m2, n, m2, -one, q, m2, a, m2, one, r, m2 )
178 anorm = zlange( '1', m2, n, a, m2, rwork )
179 resid = zlange( '1', m2, n, r, m2, rwork )
180 IF( anorm.GT.zero ) THEN
181 result( 1 ) = resid / (eps*anorm*max(1,m2))
182 ELSE
183 result( 1 ) = zero
184 END IF
185*
186* Compute |I - Q'*Q| and store in RESULT(2)
187*
188 CALL zlaset( 'Full', m2, m2, czero, one, r, m2 )
189 CALL zherk( 'U', 'C', m2, m2, dreal(-one), q, m2, dreal(one),
190 \$ r, m2 )
191 resid = zlansy( '1', 'Upper', m2, r, m2, rwork )
192 result( 2 ) = resid / (eps*max(1,m2))
193*
194* Generate random m-by-n matrix C and a copy CF
195*
196 DO j=1,n
197 CALL zlarnv( 2, iseed, m2, c( 1, j ) )
198 END DO
199 cnorm = zlange( '1', m2, n, c, m2, rwork)
200 CALL zlacpy( 'Full', m2, n, c, m2, cf, m2 )
201*
202* Apply Q to C as Q*C
203*
204 CALL ztpmqrt( 'L','N', m,n,k,l,nb,af(np1,1),m2,t,ldt,cf,m2,
205 \$ cf(np1,1),m2,work,info)
206*
207* Compute |Q*C - Q*C| / |C|
208*
209 CALL zgemm( 'N', 'N', m2, n, m2, -one, q, m2, c, m2, one, cf, m2 )
210 resid = zlange( '1', m2, n, cf, m2, rwork )
211 IF( cnorm.GT.zero ) THEN
212 result( 3 ) = resid / (eps*max(1,m2)*cnorm)
213 ELSE
214 result( 3 ) = zero
215 END IF
216*
217* Copy C into CF again
218*
219 CALL zlacpy( 'Full', m2, n, c, m2, cf, m2 )
220*
221* Apply Q to C as QT*C
222*
223 CALL ztpmqrt( 'L','C',m,n,k,l,nb,af(np1,1),m2,t,ldt,cf,m2,
224 \$ cf(np1,1),m2,work,info)
225*
226* Compute |QT*C - QT*C| / |C|
227*
228 CALL zgemm('C','N',m2,n,m2,-one,q,m2,c,m2,one,cf,m2)
229 resid = zlange( '1', m2, n, cf, m2, rwork )
230 IF( cnorm.GT.zero ) THEN
231 result( 4 ) = resid / (eps*max(1,m2)*cnorm)
232 ELSE
233 result( 4 ) = zero
234 END IF
235*
236* Generate random n-by-m matrix D and a copy DF
237*
238 DO j=1,m2
239 CALL zlarnv( 2, iseed, n, d( 1, j ) )
240 END DO
241 dnorm = zlange( '1', n, m2, d, n, rwork)
242 CALL zlacpy( 'Full', n, m2, d, n, df, n )
243*
244* Apply Q to D as D*Q
245*
246 CALL ztpmqrt('R','N',n,m,n,l,nb,af(np1,1),m2,t,ldt,df,n,
247 \$ df(1,np1),n,work,info)
248*
249* Compute |D*Q - D*Q| / |D|
250*
251 CALL zgemm('N','N',n,m2,m2,-one,d,n,q,m2,one,df,n)
252 resid = zlange('1',n, m2,df,n,rwork )
253 IF( cnorm.GT.zero ) THEN
254 result( 5 ) = resid / (eps*max(1,m2)*dnorm)
255 ELSE
256 result( 5 ) = zero
257 END IF
258*
259* Copy D into DF again
260*
261 CALL zlacpy('Full',n,m2,d,n,df,n )
262*
263* Apply Q to D as D*QT
264*
265 CALL ztpmqrt('R','C',n,m,n,l,nb,af(np1,1),m2,t,ldt,df,n,
266 \$ df(1,np1),n,work,info)
267
268*
269* Compute |D*QT - D*QT| / |D|
270*
271 CALL zgemm( 'N', 'C', n, m2, m2, -one, d, n, q, m2, one, df, n )
272 resid = zlange( '1', n, m2, df, n, rwork )
273 IF( cnorm.GT.zero ) THEN
274 result( 6 ) = resid / (eps*max(1,m2)*dnorm)
275 ELSE
276 result( 6 ) = zero
277 END IF
278*
279* Deallocate all arrays
280*
281 DEALLOCATE ( a, af, q, r, rwork, work, t, c, d, cf, df)
282 RETURN
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:173
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:115
subroutine zgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
ZGEMQRT
Definition: zgemqrt.f:168
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:99
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:106
subroutine ztpmqrt(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
ZTPMQRT
Definition: ztpmqrt.f:216
subroutine ztpqrt(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
ZTPQRT
Definition: ztpqrt.f:189
double precision function zlansy(NORM, UPLO, N, A, LDA, WORK)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansy.f:123
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