LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ dlqt04()

subroutine dlqt04 ( integer  M,
integer  N,
integer  NB,
double precision, dimension(6)  RESULT 
)

DLQT04

Purpose:
 DLQT04 tests DGELQT and DGEMLQT.
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 |
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 72 of file dlqt04.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, LDT
81 * .. Return values ..
82  DOUBLE PRECISION RESULT(6)
83 *
84 * =====================================================================
85 *
86 * ..
87 * .. Local allocatable arrays
88  DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:),
89  $ L(:,:), RWORK(:), WORK( : ), T(:,:),
90  $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
91 *
92 * .. Parameters ..
93  DOUBLE PRECISION ONE, ZERO
94  parameter( zero = 0.0, one = 1.0 )
95 * ..
96 * .. Local Scalars ..
97  INTEGER INFO, J, K, LL, LWORK
98  DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
99 * ..
100 * .. Local Arrays ..
101  INTEGER ISEED( 4 )
102 * ..
103 * .. External Functions ..
104  DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
105  LOGICAL LSAME
106  EXTERNAL dlamch, dlange, dlansy, lsame
107 * ..
108 * .. Intrinsic Functions ..
109  INTRINSIC max, min
110 * ..
111 * .. Data statements ..
112  DATA iseed / 1988, 1989, 1990, 1991 /
113 *
114  eps = dlamch( 'Epsilon' )
115  k = min(m,n)
116  ll = max(m,n)
117  lwork = max(2,ll)*max(2,ll)*nb
118 *
119 * Dynamically allocate local arrays
120 *
121  ALLOCATE ( a(m,n), af(m,n), q(n,n), l(ll,n), rwork(ll),
122  $ work(lwork), t(nb,n), c(m,n), cf(m,n),
123  $ d(n,m), df(n,m) )
124 *
125 * Put random numbers into A and copy to AF
126 *
127  ldt=nb
128  DO j=1,n
129  CALL dlarnv( 2, iseed, m, a( 1, j ) )
130  END DO
131  CALL dlacpy( 'Full', m, n, a, m, af, m )
132 *
133 * Factor the matrix A in the array AF.
134 *
135  CALL dgelqt( m, n, nb, af, m, t, ldt, work, info )
136 *
137 * Generate the n-by-n matrix Q
138 *
139  CALL dlaset( 'Full', n, n, zero, one, q, n )
140  CALL dgemlqt( 'R', 'N', n, n, k, nb, af, m, t, ldt, q, n,
141  $ work, info )
142 *
143 * Copy R
144 *
145  CALL dlaset( 'Full', m, n, zero, zero, l, ll )
146  CALL dlacpy( 'Lower', m, n, af, m, l, ll )
147 *
148 * Compute |L - A*Q'| / |A| and store in RESULT(1)
149 *
150  CALL dgemm( 'N', 'T', m, n, n, -one, a, m, q, n, one, l, ll )
151  anorm = dlange( '1', m, n, a, m, rwork )
152  resid = dlange( '1', m, n, l, ll, rwork )
153  IF( anorm.GT.zero ) THEN
154  result( 1 ) = resid / (eps*max(1,m)*anorm)
155  ELSE
156  result( 1 ) = zero
157  END IF
158 *
159 * Compute |I - Q'*Q| and store in RESULT(2)
160 *
161  CALL dlaset( 'Full', n, n, zero, one, l, ll )
162  CALL dsyrk( 'U', 'C', n, n, -one, q, n, one, l, ll )
163  resid = dlansy( '1', 'Upper', n, l, ll, rwork )
164  result( 2 ) = resid / (eps*max(1,n))
165 *
166 * Generate random m-by-n matrix C and a copy CF
167 *
168  DO j=1,m
169  CALL dlarnv( 2, iseed, n, d( 1, j ) )
170  END DO
171  dnorm = dlange( '1', n, m, d, n, rwork)
172  CALL dlacpy( 'Full', n, m, d, n, df, n )
173 *
174 * Apply Q to C as Q*C
175 *
176  CALL dgemlqt( 'L', 'N', n, m, k, nb, af, m, t, nb, df, n,
177  $ work, info)
178 *
179 * Compute |Q*D - Q*D| / |D|
180 *
181  CALL dgemm( 'N', 'N', n, m, n, -one, q, n, d, n, one, df, n )
182  resid = dlange( '1', n, m, df, n, rwork )
183  IF( dnorm.GT.zero ) THEN
184  result( 3 ) = resid / (eps*max(1,m)*dnorm)
185  ELSE
186  result( 3 ) = zero
187  END IF
188 *
189 * Copy D into DF again
190 *
191  CALL dlacpy( 'Full', n, m, d, n, df, n )
192 *
193 * Apply Q to D as QT*D
194 *
195  CALL dgemlqt( 'L', 'T', n, m, k, nb, af, m, t, nb, df, n,
196  $ work, info)
197 *
198 * Compute |QT*D - QT*D| / |D|
199 *
200  CALL dgemm( 'T', 'N', n, m, n, -one, q, n, d, n, one, df, n )
201  resid = dlange( '1', n, m, df, n, rwork )
202  IF( dnorm.GT.zero ) THEN
203  result( 4 ) = resid / (eps*max(1,m)*dnorm)
204  ELSE
205  result( 4 ) = zero
206  END IF
207 *
208 * Generate random n-by-m matrix D and a copy DF
209 *
210  DO j=1,n
211  CALL dlarnv( 2, iseed, m, c( 1, j ) )
212  END DO
213  cnorm = dlange( '1', m, n, c, m, rwork)
214  CALL dlacpy( 'Full', m, n, c, m, cf, m )
215 *
216 * Apply Q to C as C*Q
217 *
218  CALL dgemlqt( 'R', 'N', m, n, k, nb, af, m, t, nb, cf, m,
219  $ work, info)
220 *
221 * Compute |C*Q - C*Q| / |C|
222 *
223  CALL dgemm( 'N', 'N', m, n, n, -one, c, m, q, n, one, cf, m )
224  resid = dlange( '1', n, m, df, n, rwork )
225  IF( cnorm.GT.zero ) THEN
226  result( 5 ) = resid / (eps*max(1,m)*dnorm)
227  ELSE
228  result( 5 ) = zero
229  END IF
230 *
231 * Copy C into CF again
232 *
233  CALL dlacpy( 'Full', m, n, c, m, cf, m )
234 *
235 * Apply Q to D as D*QT
236 *
237  CALL dgemlqt( 'R', 'T', m, n, k, nb, af, m, t, nb, cf, m,
238  $ work, info)
239 *
240 * Compute |C*QT - C*QT| / |C|
241 *
242  CALL dgemm( 'N', 'T', m, n, n, -one, c, m, q, n, one, cf, m )
243  resid = dlange( '1', m, n, cf, m, rwork )
244  IF( cnorm.GT.zero ) THEN
245  result( 6 ) = resid / (eps*max(1,m)*dnorm)
246  ELSE
247  result( 6 ) = zero
248  END IF
249 *
250 * Deallocate all arrays
251 *
252  DEALLOCATE ( a, af, q, l, rwork, work, t, c, d, cf, df)
253 *
254  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 dgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
DGEMLQT
Definition: dgemlqt.f:168
subroutine dgelqt(M, N, MB, A, LDA, T, LDT, WORK, INFO)
DGELQT
Definition: dgelqt.f:139
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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