LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dqrt04()

subroutine dqrt04 ( integer  M,
integer  N,
integer  NB,
double precision, dimension(6)  RESULT 
)

DQRT04

Purpose:
 DQRT04 tests DGEQRT and DGEMQRT.
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 - 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 |
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012

Definition at line 75 of file dqrt04.f.

75  IMPLICIT NONE
76 *
77 * -- LAPACK test routine (version 3.7.0) --
78 * -- LAPACK is a software package provided by Univ. of Tennessee, --
79 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
80 * April 2012
81 *
82 * .. Scalar Arguments ..
83  INTEGER m, n, nb, ldt
84 * .. Return values ..
85  DOUBLE PRECISION result(6)
86 *
87 * =====================================================================
88 *
89 * ..
90 * .. Local allocatable arrays
91  DOUBLE PRECISION, ALLOCATABLE :: af(:,:), q(:,:),
92  $ r(:,:), rwork(:), work( : ), t(:,:),
93  $ cf(:,:), df(:,:), a(:,:), c(:,:), d(:,:)
94 *
95 * .. Parameters ..
96  DOUBLE PRECISION one, zero
97  parameter( zero = 0.0, one = 1.0 )
98 * ..
99 * .. Local Scalars ..
100  INTEGER info, j, k, l, lwork
101  DOUBLE PRECISION anorm, eps, resid, cnorm, dnorm
102 * ..
103 * .. Local Arrays ..
104  INTEGER iseed( 4 )
105 * ..
106 * .. External Functions ..
107  DOUBLE PRECISION dlamch, dlange, dlansy
108  LOGICAL lsame
109  EXTERNAL dlamch, dlange, dlansy, lsame
110 * ..
111 * .. Intrinsic Functions ..
112  INTRINSIC max, min
113 * ..
114 * .. Data statements ..
115  DATA iseed / 1988, 1989, 1990, 1991 /
116 *
117  eps = dlamch( 'Epsilon' )
118  k = min(m,n)
119  l = max(m,n)
120  lwork = max(2,l)*max(2,l)*nb
121 *
122 * Dynamically allocate local arrays
123 *
124  ALLOCATE ( a(m,n), af(m,n), q(m,m), r(m,l), rwork(l),
125  $ work(lwork), t(nb,n), c(m,n), cf(m,n),
126  $ d(n,m), df(n,m) )
127 *
128 * Put random numbers into A and copy to AF
129 *
130  ldt=nb
131  DO j=1,n
132  CALL dlarnv( 2, iseed, m, a( 1, j ) )
133  END DO
134  CALL dlacpy( 'Full', m, n, a, m, af, m )
135 *
136 * Factor the matrix A in the array AF.
137 *
138  CALL dgeqrt( m, n, nb, af, m, t, ldt, work, info )
139 *
140 * Generate the m-by-m matrix Q
141 *
142  CALL dlaset( 'Full', m, m, zero, one, q, m )
143  CALL dgemqrt( 'R', 'N', m, m, k, nb, af, m, t, ldt, q, m,
144  $ work, info )
145 *
146 * Copy R
147 *
148  CALL dlaset( 'Full', m, n, zero, zero, r, m )
149  CALL dlacpy( 'Upper', m, n, af, m, r, m )
150 *
151 * Compute |R - Q'*A| / |A| and store in RESULT(1)
152 *
153  CALL dgemm( 'T', 'N', m, n, m, -one, q, m, a, m, one, r, m )
154  anorm = dlange( '1', m, n, a, m, rwork )
155  resid = dlange( '1', m, n, r, m, rwork )
156  IF( anorm.GT.zero ) THEN
157  result( 1 ) = resid / (eps*max(1,m)*anorm)
158  ELSE
159  result( 1 ) = zero
160  END IF
161 *
162 * Compute |I - Q'*Q| and store in RESULT(2)
163 *
164  CALL dlaset( 'Full', m, m, zero, one, r, m )
165  CALL dsyrk( 'U', 'C', m, m, -one, q, m, one, r, m )
166  resid = dlansy( '1', 'Upper', m, r, m, rwork )
167  result( 2 ) = resid / (eps*max(1,m))
168 *
169 * Generate random m-by-n matrix C and a copy CF
170 *
171  DO j=1,n
172  CALL dlarnv( 2, iseed, m, c( 1, j ) )
173  END DO
174  cnorm = dlange( '1', m, n, c, m, rwork)
175  CALL dlacpy( 'Full', m, n, c, m, cf, m )
176 *
177 * Apply Q to C as Q*C
178 *
179  CALL dgemqrt( 'L', 'N', m, n, k, nb, af, m, t, nb, cf, m,
180  $ work, info)
181 *
182 * Compute |Q*C - Q*C| / |C|
183 *
184  CALL dgemm( 'N', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
185  resid = dlange( '1', m, n, cf, m, rwork )
186  IF( cnorm.GT.zero ) THEN
187  result( 3 ) = resid / (eps*max(1,m)*cnorm)
188  ELSE
189  result( 3 ) = zero
190  END IF
191 *
192 * Copy C into CF again
193 *
194  CALL dlacpy( 'Full', m, n, c, m, cf, m )
195 *
196 * Apply Q to C as QT*C
197 *
198  CALL dgemqrt( 'L', 'T', m, n, k, nb, af, m, t, nb, cf, m,
199  $ work, info)
200 *
201 * Compute |QT*C - QT*C| / |C|
202 *
203  CALL dgemm( 'T', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
204  resid = dlange( '1', m, n, cf, m, rwork )
205  IF( cnorm.GT.zero ) THEN
206  result( 4 ) = resid / (eps*max(1,m)*cnorm)
207  ELSE
208  result( 4 ) = zero
209  END IF
210 *
211 * Generate random n-by-m matrix D and a copy DF
212 *
213  DO j=1,m
214  CALL dlarnv( 2, iseed, n, d( 1, j ) )
215  END DO
216  dnorm = dlange( '1', n, m, d, n, rwork)
217  CALL dlacpy( 'Full', n, m, d, n, df, n )
218 *
219 * Apply Q to D as D*Q
220 *
221  CALL dgemqrt( 'R', 'N', n, m, k, nb, af, m, t, nb, df, n,
222  $ work, info)
223 *
224 * Compute |D*Q - D*Q| / |D|
225 *
226  CALL dgemm( 'N', 'N', n, m, m, -one, d, n, q, m, one, df, n )
227  resid = dlange( '1', n, m, df, n, rwork )
228  IF( cnorm.GT.zero ) THEN
229  result( 5 ) = resid / (eps*max(1,m)*dnorm)
230  ELSE
231  result( 5 ) = zero
232  END IF
233 *
234 * Copy D into DF again
235 *
236  CALL dlacpy( 'Full', n, m, d, n, df, n )
237 *
238 * Apply Q to D as D*QT
239 *
240  CALL dgemqrt( 'R', 'T', n, m, k, nb, af, m, t, nb, df, n,
241  $ work, info)
242 *
243 * Compute |D*QT - D*QT| / |D|
244 *
245  CALL dgemm( 'N', 'T', n, m, m, -one, d, n, q, m, one, df, n )
246  resid = dlange( '1', n, m, df, n, rwork )
247  IF( cnorm.GT.zero ) THEN
248  result( 6 ) = resid / (eps*max(1,m)*dnorm)
249  ELSE
250  result( 6 ) = zero
251  END IF
252 *
253 * Deallocate all arrays
254 *
255  DEALLOCATE ( a, af, q, r, rwork, work, t, c, d, cf, df)
256 *
257  RETURN
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:105
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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, or the element of largest absolute value of a real symmetric matrix.
Definition: dlansy.f:124
subroutine dgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
DGEMQRT
Definition: dgemqrt.f:170
subroutine dlarnv(IDIST, ISEED, N, X)
DLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: dlarnv.f:99
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:112
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:171
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:116
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dgeqrt(M, N, NB, A, LDA, T, LDT, WORK, INFO)
DGEQRT
Definition: dgeqrt.f:143
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