LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
zqrt04.f File Reference

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Functions/Subroutines

subroutine zqrt04 (M, N, NB, RESULT)
 ZQRT04 More...
 

Function/Subroutine Documentation

subroutine zqrt04 ( integer  M,
integer  N,
integer  NB,
double precision, dimension(6)  RESULT 
)

ZQRT04

Purpose:
 ZQRT04 tests ZGEQRT and ZGEMQRT.
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 zqrt04.f.

75  IMPLICIT NONE
76 *
77 * -- LAPACK test routine (version 3.4.1) --
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  COMPLEX*16, ALLOCATABLE :: af(:,:), q(:,:),
92  $ r(:,:), rwork(:), work( : ), t(:,:),
93  $ cf(:,:), df(:,:), a(:,:), c(:,:), d(:,:)
94 *
95 * .. Parameters ..
96  DOUBLE PRECISION zero
97  COMPLEX*16 one, czero
98  parameter( zero = 0.0, one = (1.0,0.0), czero=(0.0,0.0) )
99 * ..
100 * .. Local Scalars ..
101  INTEGER info, j, k, l, lwork
102  DOUBLE PRECISION anorm, eps, resid, cnorm, dnorm
103 * ..
104 * .. Local Arrays ..
105  INTEGER iseed( 4 )
106 * ..
107 * .. External Functions ..
108  DOUBLE PRECISION dlamch
109  DOUBLE PRECISION zlange, zlansy
110  LOGICAL lsame
111  EXTERNAL dlamch, zlange, zlansy, lsame
112 * ..
113 * .. Intrinsic Functions ..
114  INTRINSIC max, min
115 * ..
116 * .. Data statements ..
117  DATA iseed / 1988, 1989, 1990, 1991 /
118 *
119  eps = dlamch( 'Epsilon' )
120  k = min(m,n)
121  l = max(m,n)
122  lwork = max(2,l)*max(2,l)*nb
123 *
124 * Dynamically allocate local arrays
125 *
126  ALLOCATE ( a(m,n), af(m,n), q(m,m), r(m,l), rwork(l),
127  $ work(lwork), t(nb,n), c(m,n), cf(m,n),
128  $ d(n,m), df(n,m) )
129 *
130 * Put random numbers into A and copy to AF
131 *
132  ldt=nb
133  DO j=1,n
134  CALL zlarnv( 2, iseed, m, a( 1, j ) )
135  END DO
136  CALL zlacpy( 'Full', m, n, a, m, af, m )
137 *
138 * Factor the matrix A in the array AF.
139 *
140  CALL zgeqrt( m, n, nb, af, m, t, ldt, work, info )
141 *
142 * Generate the m-by-m matrix Q
143 *
144  CALL zlaset( 'Full', m, m, czero, one, q, m )
145  CALL zgemqrt( 'R', 'N', m, m, k, nb, af, m, t, ldt, q, m,
146  $ work, info )
147 *
148 * Copy R
149 *
150  CALL zlaset( 'Full', m, n, czero, czero, r, m )
151  CALL zlacpy( 'Upper', m, n, af, m, r, m )
152 *
153 * Compute |R - Q'*A| / |A| and store in RESULT(1)
154 *
155  CALL zgemm( 'C', 'N', m, n, m, -one, q, m, a, m, one, r, m )
156  anorm = zlange( '1', m, n, a, m, rwork )
157  resid = zlange( '1', m, n, r, m, rwork )
158  IF( anorm.GT.zero ) THEN
159  result( 1 ) = resid / (eps*max(1,m)*anorm)
160  ELSE
161  result( 1 ) = zero
162  END IF
163 *
164 * Compute |I - Q'*Q| and store in RESULT(2)
165 *
166  CALL zlaset( 'Full', m, m, czero, one, r, m )
167  CALL zherk( 'U', 'C', m, m, dreal(-one), q, m, dreal(one), r, m )
168  resid = zlansy( '1', 'Upper', m, r, m, rwork )
169  result( 2 ) = resid / (eps*max(1,m))
170 *
171 * Generate random m-by-n matrix C and a copy CF
172 *
173  DO j=1,n
174  CALL zlarnv( 2, iseed, m, c( 1, j ) )
175  END DO
176  cnorm = zlange( '1', m, n, c, m, rwork)
177  CALL zlacpy( 'Full', m, n, c, m, cf, m )
178 *
179 * Apply Q to C as Q*C
180 *
181  CALL zgemqrt( 'L', 'N', m, n, k, nb, af, m, t, nb, cf, m,
182  $ work, info)
183 *
184 * Compute |Q*C - Q*C| / |C|
185 *
186  CALL zgemm( 'N', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
187  resid = zlange( '1', m, n, cf, m, rwork )
188  IF( cnorm.GT.zero ) THEN
189  result( 3 ) = resid / (eps*max(1,m)*cnorm)
190  ELSE
191  result( 3 ) = zero
192  END IF
193 *
194 * Copy C into CF again
195 *
196  CALL zlacpy( 'Full', m, n, c, m, cf, m )
197 *
198 * Apply Q to C as QT*C
199 *
200  CALL zgemqrt( 'L', 'C', m, n, k, nb, af, m, t, nb, cf, m,
201  $ work, info)
202 *
203 * Compute |QT*C - QT*C| / |C|
204 *
205  CALL zgemm( 'C', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
206  resid = zlange( '1', m, n, cf, m, rwork )
207  IF( cnorm.GT.zero ) THEN
208  result( 4 ) = resid / (eps*max(1,m)*cnorm)
209  ELSE
210  result( 4 ) = zero
211  END IF
212 *
213 * Generate random n-by-m matrix D and a copy DF
214 *
215  DO j=1,m
216  CALL zlarnv( 2, iseed, n, d( 1, j ) )
217  END DO
218  dnorm = zlange( '1', n, m, d, n, rwork)
219  CALL zlacpy( 'Full', n, m, d, n, df, n )
220 *
221 * Apply Q to D as D*Q
222 *
223  CALL zgemqrt( 'R', 'N', n, m, k, nb, af, m, t, nb, df, n,
224  $ work, info)
225 *
226 * Compute |D*Q - D*Q| / |D|
227 *
228  CALL zgemm( 'N', 'N', n, m, m, -one, d, n, q, m, one, df, n )
229  resid = zlange( '1', n, m, df, n, rwork )
230  IF( cnorm.GT.zero ) THEN
231  result( 5 ) = resid / (eps*max(1,m)*dnorm)
232  ELSE
233  result( 5 ) = zero
234  END IF
235 *
236 * Copy D into DF again
237 *
238  CALL zlacpy( 'Full', n, m, d, n, df, n )
239 *
240 * Apply Q to D as D*QT
241 *
242  CALL zgemqrt( 'R', 'C', n, m, k, nb, af, m, t, nb, df, n,
243  $ work, info)
244 *
245 * Compute |D*QT - D*QT| / |D|
246 *
247  CALL zgemm( 'N', 'C', n, m, m, -one, d, n, q, m, one, df, n )
248  resid = zlange( '1', n, m, df, n, rwork )
249  IF( cnorm.GT.zero ) THEN
250  result( 6 ) = resid / (eps*max(1,m)*dnorm)
251  ELSE
252  result( 6 ) = zero
253  END IF
254 *
255 * Deallocate all arrays
256 *
257  DEALLOCATE ( a, af, q, r, rwork, work, t, c, d, cf, df)
258 *
259  RETURN
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:175
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, or the element of largest absolute value of a complex symmetric matrix.
Definition: zlansy.f:125
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
ZGEMQRT
Definition: zgemqrt.f:170
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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:108
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:101
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:117
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zgeqrt(M, N, NB, A, LDA, T, LDT, WORK, INFO)
ZGEQRT
Definition: zgeqrt.f:143

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