LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cqrt05.f
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00001 *> \brief \b CQRT05
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE CQRT05(M,N,L,NB,RESULT)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       INTEGER LWORK, M, N, L, NB, LDT
00015 *       .. Return values ..
00016 *       REAL RESULT(6)
00017 *  
00018 *
00019 *> \par Purpose:
00020 *  =============
00021 *>
00022 *> \verbatim
00023 *>
00024 *> CQRT05 tests CTPQRT and CTPMQRT.
00025 *> \endverbatim
00026 *
00027 *  Arguments:
00028 *  ==========
00029 *
00030 *> \param[in] M
00031 *> \verbatim
00032 *>          M is INTEGER
00033 *>          Number of rows in lower part of the test matrix.
00034 *> \endverbatim
00035 *>
00036 *> \param[in] N
00037 *> \verbatim
00038 *>          N is INTEGER
00039 *>          Number of columns in test matrix.
00040 *> \endverbatim
00041 *>
00042 *> \param[in] L
00043 *> \verbatim
00044 *>          L is INTEGER
00045 *>          The number of rows of the upper trapezoidal part the
00046 *>          lower test matrix.  0 <= L <= M.
00047 *> \endverbatim
00048 *>          
00049 *> \param[in] NB
00050 *> \verbatim
00051 *>          NB is INTEGER
00052 *>          Block size of test matrix.  NB <= N.
00053 *> \endverbatim
00054 *>
00055 *> \param[out] RESULT
00056 *> \verbatim
00057 *>          RESULT is REAL array, dimension (6)
00058 *>          Results of each of the six tests below.
00059 *>
00060 *>          RESULT(1) = | A - Q R |
00061 *>          RESULT(2) = | I - Q^H Q |
00062 *>          RESULT(3) = | Q C - Q C |
00063 *>          RESULT(4) = | Q^H C - Q^H C |
00064 *>          RESULT(5) = | C Q - C Q | 
00065 *>          RESULT(6) = | C Q^H - C Q^H |
00066 *> \endverbatim
00067 *
00068 *  Authors:
00069 *  ========
00070 *
00071 *> \author Univ. of Tennessee 
00072 *> \author Univ. of California Berkeley 
00073 *> \author Univ. of Colorado Denver 
00074 *> \author NAG Ltd. 
00075 *
00076 *> \date April 2012
00077 *
00078 *> \ingroup complex_lin
00079 *
00080 *  =====================================================================
00081       SUBROUTINE CQRT05(M,N,L,NB,RESULT)
00082       IMPLICIT NONE
00083 *
00084 *  -- LAPACK test routine (version 3.4.1) --
00085 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00086 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00087 *     April 2012
00088 *
00089 *     .. Scalar Arguments ..
00090       INTEGER LWORK, M, N, L, NB, LDT
00091 *     .. Return values ..
00092       REAL RESULT(6)
00093 *
00094 *  =====================================================================
00095 *      
00096 *     ..
00097 *     .. Local allocatable arrays 
00098       COMPLEX, ALLOCATABLE :: AF(:,:), Q(:,:),
00099      $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
00100      $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
00101 *
00102 *     .. Parameters ..
00103       REAL ZERO
00104       COMPLEX ONE, CZERO
00105       PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) )
00106 *     ..
00107 *     .. Local Scalars ..
00108       INTEGER INFO, J, K, M2, NP1
00109       REAL   ANORM, EPS, RESID, CNORM, DNORM
00110 *     ..
00111 *     .. Local Arrays ..
00112       INTEGER            ISEED( 4 )
00113 *     ..
00114 *     .. External Functions ..
00115       REAL SLAMCH 
00116       REAL CLANGE, CLANSY
00117       LOGICAL  LSAME
00118       EXTERNAL SLAMCH, CLANGE, CLANSY, LSAME
00119 *     ..
00120 *     .. Data statements ..
00121       DATA ISEED / 1988, 1989, 1990, 1991 /
00122 *      
00123       EPS = SLAMCH( 'Epsilon' )
00124       K = N
00125       M2 = M+N
00126       IF( M.GT.0 ) THEN
00127          NP1 = N+1
00128       ELSE
00129          NP1 = 1
00130       END IF
00131       LWORK = M2*M2*NB
00132 *
00133 *     Dynamically allocate all arrays
00134 *
00135       ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2),
00136      $           WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N), 
00137      $           D(N,M2),DF(N,M2) )
00138 *
00139 *     Put random stuff into A
00140 *
00141       LDT=NB
00142       CALL CLASET( 'Full', M2, N, CZERO, CZERO, A, M2 )
00143       CALL CLASET( 'Full', NB, N, CZERO, CZERO, T, NB )
00144       DO J=1,N
00145          CALL CLARNV( 2, ISEED, J, A( 1, J ) )
00146       END DO
00147       IF( M.GT.0 ) THEN
00148          DO J=1,N
00149             CALL CLARNV( 2, ISEED, M-L, A( MIN(N+M,N+1), J ) )
00150          END DO
00151       END IF
00152       IF( L.GT.0 ) THEN
00153          DO J=1,N
00154             CALL CLARNV( 2, ISEED, MIN(J,L), A( MIN(N+M,N+M-L+1), J ) )
00155          END DO
00156       END IF
00157 *
00158 *     Copy the matrix A to the array AF.
00159 *
00160       CALL CLACPY( 'Full', M2, N, A, M2, AF, M2 )
00161 *
00162 *     Factor the matrix A in the array AF.
00163 *
00164       CALL CTPQRT( M,N,L,NB,AF,M2,AF(NP1,1),M2,T,LDT,WORK,INFO)
00165 *
00166 *     Generate the (M+N)-by-(M+N) matrix Q by applying H to I
00167 *
00168       CALL CLASET( 'Full', M2, M2, CZERO, ONE, Q, M2 )
00169       CALL CGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2,
00170      $              WORK, INFO )
00171 *
00172 *     Copy R
00173 *
00174       CALL CLASET( 'Full', M2, N, CZERO, CZERO, R, M2 )
00175       CALL CLACPY( 'Upper', M2, N, AF, M2, R, M2 )
00176 *
00177 *     Compute |R - Q'*A| / |A| and store in RESULT(1)
00178 *
00179       CALL CGEMM( 'C', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 )
00180       ANORM = CLANGE( '1', M2, N, A, M2, RWORK )
00181       RESID = CLANGE( '1', M2, N, R, M2, RWORK )
00182       IF( ANORM.GT.ZERO ) THEN
00183          RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2))
00184       ELSE
00185          RESULT( 1 ) = ZERO
00186       END IF
00187 *
00188 *     Compute |I - Q'*Q| and store in RESULT(2)
00189 *
00190       CALL CLASET( 'Full', M2, M2, CZERO, ONE, R, M2 )
00191       CALL CHERK( 'U', 'C', M2, M2, REAL(-ONE), Q, M2, REAL(ONE), 
00192      $            R, M2 )
00193       RESID = CLANSY( '1', 'Upper', M2, R, M2, RWORK )
00194       RESULT( 2 ) = RESID / (EPS*MAX(1,M2))
00195 *
00196 *     Generate random m-by-n matrix C and a copy CF
00197 *
00198       DO J=1,N
00199          CALL CLARNV( 2, ISEED, M2, C( 1, J ) )
00200       END DO
00201       CNORM = CLANGE( '1', M2, N, C, M2, RWORK)
00202       CALL CLACPY( 'Full', M2, N, C, M2, CF, M2 )
00203 *
00204 *     Apply Q to C as Q*C
00205 *
00206       CALL CTPMQRT( 'L','N', M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2,
00207      $               CF(NP1,1),M2,WORK,INFO)
00208 *
00209 *     Compute |Q*C - Q*C| / |C|
00210 *
00211       CALL CGEMM( 'N', 'N', M2, N, M2, -ONE, Q, M2, C, M2, ONE, CF, M2 )
00212       RESID = CLANGE( '1', M2, N, CF, M2, RWORK )
00213       IF( CNORM.GT.ZERO ) THEN
00214          RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM)
00215       ELSE
00216          RESULT( 3 ) = ZERO
00217       END IF
00218 *
00219 *     Copy C into CF again
00220 *
00221       CALL CLACPY( 'Full', M2, N, C, M2, CF, M2 )
00222 *
00223 *     Apply Q to C as QT*C
00224 *
00225       CALL CTPMQRT( 'L','C',M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2,
00226      $              CF(NP1,1),M2,WORK,INFO) 
00227 *
00228 *     Compute |QT*C - QT*C| / |C|
00229 *
00230       CALL CGEMM('C','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2)
00231       RESID = CLANGE( '1', M2, N, CF, M2, RWORK )
00232       IF( CNORM.GT.ZERO ) THEN
00233          RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM)
00234       ELSE
00235          RESULT( 4 ) = ZERO
00236       END IF     
00237 *
00238 *     Generate random n-by-m matrix D and a copy DF
00239 *
00240       DO J=1,M2
00241          CALL CLARNV( 2, ISEED, N, D( 1, J ) )
00242       END DO
00243       DNORM = CLANGE( '1', N, M2, D, N, RWORK)
00244       CALL CLACPY( 'Full', N, M2, D, N, DF, N )
00245 *
00246 *     Apply Q to D as D*Q
00247 *
00248       CALL CTPMQRT('R','N',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N,
00249      $             DF(1,NP1),N,WORK,INFO)
00250 *
00251 *     Compute |D*Q - D*Q| / |D|
00252 *
00253       CALL CGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N)
00254       RESID = CLANGE('1',N, M2,DF,N,RWORK )
00255       IF( CNORM.GT.ZERO ) THEN
00256          RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM)
00257       ELSE
00258          RESULT( 5 ) = ZERO
00259       END IF
00260 *
00261 *     Copy D into DF again
00262 *
00263       CALL CLACPY('Full',N,M2,D,N,DF,N )
00264 *
00265 *     Apply Q to D as D*QT
00266 *
00267       CALL CTPMQRT('R','C',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N,
00268      $             DF(1,NP1),N,WORK,INFO)     
00269        
00270 *
00271 *     Compute |D*QT - D*QT| / |D|
00272 *
00273       CALL CGEMM( 'N', 'C', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N )
00274       RESID = CLANGE( '1', N, M2, DF, N, RWORK )
00275       IF( CNORM.GT.ZERO ) THEN
00276          RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM)
00277       ELSE
00278          RESULT( 6 ) = ZERO
00279       END IF
00280 *
00281 *     Deallocate all arrays
00282 *
00283       DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
00284       RETURN
00285       END
00286 
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