LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sqrt05.f
Go to the documentation of this file.
00001 *> \brief \b SQRT05
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 SQRT05(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 *> SQRT05 tests STPQRT and STPMQRT.
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 single_lin
00079 *
00080 *  =====================================================================
00081       SUBROUTINE SQRT05(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       REAL, ALLOCATABLE :: AF(:,:), Q(:,:),
00099      $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
00100      $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
00101 *
00102 *     .. Parameters ..
00103       REAL ZERO, ONE
00104       PARAMETER( ZERO = 0.0, ONE = 1.0 )
00105 *     ..
00106 *     .. Local Scalars ..
00107       INTEGER INFO, J, K, M2, NP1
00108       REAL   ANORM, EPS, RESID, CNORM, DNORM
00109 *     ..
00110 *     .. Local Arrays ..
00111       INTEGER            ISEED( 4 )
00112 *     ..
00113 *     .. External Functions ..
00114       REAL SLAMCH 
00115       REAL SLANGE, SLANSY
00116       LOGICAL  LSAME
00117       EXTERNAL SLAMCH, SLANGE, SLANSY, LSAME
00118 *     ..
00119 *     .. Data statements ..
00120       DATA ISEED / 1988, 1989, 1990, 1991 /
00121 *      
00122       EPS = SLAMCH( 'Epsilon' )
00123       K = N
00124       M2 = M+N
00125       IF( M.GT.0 ) THEN
00126          NP1 = N+1
00127       ELSE
00128          NP1 = 1
00129       END IF
00130       LWORK = M2*M2*NB
00131 *
00132 *     Dynamically allocate all arrays
00133 *
00134       ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2),
00135      $           WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N), 
00136      $           D(N,M2),DF(N,M2) )
00137 *
00138 *     Put random stuff into A
00139 *
00140       LDT=NB
00141       CALL SLASET( 'Full', M2, N, ZERO, ZERO, A, M2 )
00142       CALL SLASET( 'Full', NB, N, ZERO, ZERO, T, NB )
00143       DO J=1,N
00144          CALL SLARNV( 2, ISEED, J, A( 1, J ) )
00145       END DO
00146       IF( M.GT.0 ) THEN
00147          DO J=1,N
00148             CALL SLARNV( 2, ISEED, M-L, A( N+1, J ) )
00149          END DO
00150       END IF
00151       IF( L.GT.0 ) THEN
00152          DO J=1,N
00153             CALL SLARNV( 2, ISEED, MIN(J,L), A( N+M-L+1, J ) )
00154          END DO
00155       END IF
00156 *
00157 *     Copy the matrix A to the array AF.
00158 *
00159       CALL SLACPY( 'Full', M2, N, A, M2, AF, M2 )
00160 *
00161 *     Factor the matrix A in the array AF.
00162 *
00163       CALL STPQRT( M,N,L,NB,AF,M2,AF(NP1,1),M2,T,LDT,WORK,INFO)
00164 *
00165 *     Generate the (M+N)-by-(M+N) matrix Q by applying H to I
00166 *
00167       CALL SLASET( 'Full', M2, M2, ZERO, ONE, Q, M2 )
00168       CALL SGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2,
00169      $              WORK, INFO )
00170 *
00171 *     Copy R
00172 *
00173       CALL SLASET( 'Full', M2, N, ZERO, ZERO, R, M2 )
00174       CALL SLACPY( 'Upper', M2, N, AF, M2, R, M2 )
00175 *
00176 *     Compute |R - Q'*A| / |A| and store in RESULT(1)
00177 *
00178       CALL SGEMM( 'T', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 )
00179       ANORM = SLANGE( '1', M2, N, A, M2, RWORK )
00180       RESID = SLANGE( '1', M2, N, R, M2, RWORK )
00181       IF( ANORM.GT.ZERO ) THEN
00182          RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2))
00183       ELSE
00184          RESULT( 1 ) = ZERO
00185       END IF
00186 *
00187 *     Compute |I - Q'*Q| and store in RESULT(2)
00188 *
00189       CALL SLASET( 'Full', M2, M2, ZERO, ONE, R, M2 )
00190       CALL SSYRK( 'U', 'C', M2, M2, -ONE, Q, M2, ONE, 
00191      $            R, M2 )
00192       RESID = SLANSY( '1', 'Upper', M2, R, M2, RWORK )
00193       RESULT( 2 ) = RESID / (EPS*MAX(1,M2))
00194 *
00195 *     Generate random m-by-n matrix C and a copy CF
00196 *
00197       DO J=1,N
00198          CALL SLARNV( 2, ISEED, M2, C( 1, J ) )
00199       END DO
00200       CNORM = SLANGE( '1', M2, N, C, M2, RWORK)
00201       CALL SLACPY( 'Full', M2, N, C, M2, CF, M2 )
00202 *
00203 *     Apply Q to C as Q*C
00204 *
00205       CALL STPMQRT( 'L','N', M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,
00206      $ M2,CF(NP1,1),M2,WORK,INFO)
00207 *
00208 *     Compute |Q*C - Q*C| / |C|
00209 *
00210       CALL SGEMM( 'N', 'N', M2, N, M2, -ONE, Q,M2,C,M2,ONE,CF,M2)
00211       RESID = SLANGE( '1', M2, N, CF, M2, RWORK )
00212       IF( CNORM.GT.ZERO ) THEN
00213          RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM)
00214       ELSE
00215          RESULT( 3 ) = ZERO
00216       END IF
00217 *
00218 *     Copy C into CF again
00219 *
00220       CALL SLACPY( 'Full', M2, N, C, M2, CF, M2 )
00221 *
00222 *     Apply Q to C as QT*C
00223 *
00224       CALL STPMQRT('L','T',M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2,
00225      $              CF(NP1,1),M2,WORK,INFO) 
00226 *
00227 *     Compute |QT*C - QT*C| / |C|
00228 *
00229       CALL SGEMM('T','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2)
00230       RESID = SLANGE( '1', M2, N, CF, M2, RWORK )
00231       IF( CNORM.GT.ZERO ) THEN
00232          RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM)
00233       ELSE
00234          RESULT( 4 ) = ZERO
00235       END IF     
00236 *
00237 *     Generate random n-by-m matrix D and a copy DF
00238 *
00239       DO J=1,M2
00240          CALL SLARNV( 2, ISEED, N, D( 1, J ) )
00241       END DO
00242       DNORM = SLANGE( '1', N, M2, D, N, RWORK)
00243       CALL SLACPY( 'Full', N, M2, D, N, DF, N )
00244 *
00245 *     Apply Q to D as D*Q
00246 *
00247       CALL STPMQRT('R','N',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N,
00248      $             DF(1,NP1),N,WORK,INFO)
00249 *
00250 *     Compute |D*Q - D*Q| / |D|
00251 *
00252       CALL SGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N)
00253       RESID = SLANGE('1',N, M2,DF,N,RWORK )
00254       IF( CNORM.GT.ZERO ) THEN
00255          RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM)
00256       ELSE
00257          RESULT( 5 ) = ZERO
00258       END IF
00259 *
00260 *     Copy D into DF again
00261 *
00262       CALL SLACPY('Full',N,M2,D,N,DF,N )
00263 *
00264 *     Apply Q to D as D*QT
00265 *
00266       CALL STPMQRT('R','T',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N,
00267      $             DF(1,NP1),N,WORK,INFO)     
00268        
00269 *
00270 *     Compute |D*QT - D*QT| / |D|
00271 *
00272       CALL SGEMM( 'N', 'T', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N )
00273       RESID = SLANGE( '1', N, M2, DF, N, RWORK )
00274       IF( CNORM.GT.ZERO ) THEN
00275          RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM)
00276       ELSE
00277          RESULT( 6 ) = ZERO
00278       END IF
00279 *
00280 *     Deallocate all arrays
00281 *
00282       DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
00283       RETURN
00284       END
00285 
 All Files Functions