LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dqrt05()

 subroutine dqrt05 ( integer M, integer N, integer L, integer NB, double precision, dimension(6) RESULT )

DQRT05

Purpose:
` DQRT05 tests DTPQRT and DTPMQRT.`
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 dqrt05.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 DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:),
96 \$ R(:,:), RWORK(:), WORK( : ), T(:,:),
97 \$ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
98*
99* .. Parameters ..
100 DOUBLE PRECISION ONE, ZERO
101 parameter( zero = 0.0, one = 1.0 )
102* ..
103* .. Local Scalars ..
104 INTEGER INFO, J, K, M2, NP1
105 DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
106* ..
107* .. Local Arrays ..
108 INTEGER ISEED( 4 )
109* ..
110* .. External Functions ..
111 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
112 LOGICAL LSAME
113 EXTERNAL dlamch, dlange, dlansy, lsame
114* ..
115* .. Data statements ..
116 DATA iseed / 1988, 1989, 1990, 1991 /
117*
118 eps = dlamch( 'Epsilon' )
119 k = n
120 m2 = m+n
121 IF( m.GT.0 ) THEN
122 np1 = n+1
123 ELSE
124 np1 = 1
125 END IF
126 lwork = m2*m2*nb
127*
128* Dynamically allocate all arrays
129*
130 ALLOCATE(a(m2,n),af(m2,n),q(m2,m2),r(m2,m2),rwork(m2),
131 \$ work(lwork),t(nb,n),c(m2,n),cf(m2,n),
132 \$ d(n,m2),df(n,m2) )
133*
134* Put random stuff into A
135*
136 ldt=nb
137 CALL dlaset( 'Full', m2, n, zero, zero, a, m2 )
138 CALL dlaset( 'Full', nb, n, zero, zero, t, nb )
139 DO j=1,n
140 CALL dlarnv( 2, iseed, j, a( 1, j ) )
141 END DO
142 IF( m.GT.0 ) THEN
143 DO j=1,n
144 CALL dlarnv( 2, iseed, m-l, a( min(n+m,n+1), j ) )
145 END DO
146 END IF
147 IF( l.GT.0 ) THEN
148 DO j=1,n
149 CALL dlarnv( 2, iseed, min(j,l), a( min(n+m,n+m-l+1), j ) )
150 END DO
151 END IF
152*
153* Copy the matrix A to the array AF.
154*
155 CALL dlacpy( 'Full', m2, n, a, m2, af, m2 )
156*
157* Factor the matrix A in the array AF.
158*
159 CALL dtpqrt( m,n,l,nb,af,m2,af(np1,1),m2,t,ldt,work,info)
160*
161* Generate the (M+N)-by-(M+N) matrix Q by applying H to I
162*
163 CALL dlaset( 'Full', m2, m2, zero, one, q, m2 )
164 CALL dgemqrt( 'R', 'N', m2, m2, k, nb, af, m2, t, ldt, q, m2,
165 \$ work, info )
166*
167* Copy R
168*
169 CALL dlaset( 'Full', m2, n, zero, zero, r, m2 )
170 CALL dlacpy( 'Upper', m2, n, af, m2, r, m2 )
171*
172* Compute |R - Q'*A| / |A| and store in RESULT(1)
173*
174 CALL dgemm( 'T', 'N', m2, n, m2, -one, q, m2, a, m2, one, r, m2 )
175 anorm = dlange( '1', m2, n, a, m2, rwork )
176 resid = dlange( '1', m2, n, r, m2, rwork )
177 IF( anorm.GT.zero ) THEN
178 result( 1 ) = resid / (eps*anorm*max(1,m2))
179 ELSE
180 result( 1 ) = zero
181 END IF
182*
183* Compute |I - Q'*Q| and store in RESULT(2)
184*
185 CALL dlaset( 'Full', m2, m2, zero, one, r, m2 )
186 CALL dsyrk( 'U', 'C', m2, m2, -one, q, m2, one, r, m2 )
187 resid = dlansy( '1', 'Upper', m2, r, m2, rwork )
188 result( 2 ) = resid / (eps*max(1,m2))
189*
190* Generate random m-by-n matrix C and a copy CF
191*
192 DO j=1,n
193 CALL dlarnv( 2, iseed, m2, c( 1, j ) )
194 END DO
195 cnorm = dlange( '1', m2, n, c, m2, rwork)
196 CALL dlacpy( 'Full', m2, n, c, m2, cf, m2 )
197*
198* Apply Q to C as Q*C
199*
200 CALL dtpmqrt( 'L','N', m,n,k,l,nb,af(np1,1),m2,t,ldt,cf,m2,
201 \$ cf(np1,1),m2,work,info)
202*
203* Compute |Q*C - Q*C| / |C|
204*
205 CALL dgemm( 'N', 'N', m2, n, m2, -one, q, m2, c, m2, one, cf, m2 )
206 resid = dlange( '1', m2, n, cf, m2, rwork )
207 IF( cnorm.GT.zero ) THEN
208 result( 3 ) = resid / (eps*max(1,m2)*cnorm)
209 ELSE
210 result( 3 ) = zero
211 END IF
212*
213* Copy C into CF again
214*
215 CALL dlacpy( 'Full', m2, n, c, m2, cf, m2 )
216*
217* Apply Q to C as QT*C
218*
219 CALL dtpmqrt( 'L','T',m,n,k,l,nb,af(np1,1),m2,t,ldt,cf,m2,
220 \$ cf(np1,1),m2,work,info)
221*
222* Compute |QT*C - QT*C| / |C|
223*
224 CALL dgemm('T','N',m2,n,m2,-one,q,m2,c,m2,one,cf,m2)
225 resid = dlange( '1', m2, n, cf, m2, rwork )
226 IF( cnorm.GT.zero ) THEN
227 result( 4 ) = resid / (eps*max(1,m2)*cnorm)
228 ELSE
229 result( 4 ) = zero
230 END IF
231*
232* Generate random n-by-m matrix D and a copy DF
233*
234 DO j=1,m2
235 CALL dlarnv( 2, iseed, n, d( 1, j ) )
236 END DO
237 dnorm = dlange( '1', n, m2, d, n, rwork)
238 CALL dlacpy( 'Full', n, m2, d, n, df, n )
239*
240* Apply Q to D as D*Q
241*
242 CALL dtpmqrt('R','N',n,m,n,l,nb,af(np1,1),m2,t,ldt,df,n,
243 \$ df(1,np1),n,work,info)
244*
245* Compute |D*Q - D*Q| / |D|
246*
247 CALL dgemm('N','N',n,m2,m2,-one,d,n,q,m2,one,df,n)
248 resid = dlange('1',n, m2,df,n,rwork )
249 IF( cnorm.GT.zero ) THEN
250 result( 5 ) = resid / (eps*max(1,m2)*dnorm)
251 ELSE
252 result( 5 ) = zero
253 END IF
254*
255* Copy D into DF again
256*
257 CALL dlacpy('Full',n,m2,d,n,df,n )
258*
259* Apply Q to D as D*QT
260*
261 CALL dtpmqrt('R','T',n,m,n,l,nb,af(np1,1),m2,t,ldt,df,n,
262 \$ df(1,np1),n,work,info)
263
264*
265* Compute |D*QT - D*QT| / |D|
266*
267 CALL dgemm( 'N', 'T', n, m2, m2, -one, d, n, q, m2, one, df, n )
268 resid = dlange( '1', n, m2, df, n, rwork )
269 IF( cnorm.GT.zero ) THEN
270 result( 6 ) = resid / (eps*max(1,m2)*dnorm)
271 ELSE
272 result( 6 ) = zero
273 END IF
274*
275* Deallocate all arrays
276*
277 DEALLOCATE ( a, af, q, r, rwork, work, t, c, d, cf, df)
278 RETURN
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dlarnv(IDIST, ISEED, N, X)
DLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: dlarnv.f:97
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:169
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:114
subroutine dgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
DGEMQRT
Definition: dgemqrt.f:168
subroutine dtpqrt(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
DTPQRT
Definition: dtpqrt.f:189
subroutine dtpmqrt(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
DTPMQRT
Definition: dtpmqrt.f:216
double precision function dlansy(NORM, UPLO, N, A, LDA, WORK)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansy.f:122
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