LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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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