LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sqrt04.f
Go to the documentation of this file.
00001 *> \brief \b SQRT04
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 SQRT04(M,N,NB,RESULT)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       INTEGER M, N, NB, LDT
00015 *       .. Return values ..
00016 *       REAL RESULT(6)
00017 *  
00018 *
00019 *> \par Purpose:
00020 *  =============
00021 *>
00022 *> \verbatim
00023 *>
00024 *> SQRT04 tests SGEQRT and SGEMQRT.
00025 *> \endverbatim
00026 *
00027 *  Arguments:
00028 *  ==========
00029 *
00030 *> \param[in] M
00031 *> \verbatim
00032 *>          M is INTEGER
00033 *>          Number of rows in 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] NB
00043 *> \verbatim
00044 *>          NB is INTEGER
00045 *>          Block size of test matrix.  NB <= Min(M,N).
00046 *> \endverbatim
00047 *>
00048 *> \param[out] RESULT
00049 *> \verbatim
00050 *>          RESULT is REAL array, dimension (6)
00051 *>          Results of each of the six tests below.
00052 *>
00053 *>          RESULT(1) = | A - Q R |
00054 *>          RESULT(2) = | I - Q^H Q |
00055 *>          RESULT(3) = | Q C - Q C |
00056 *>          RESULT(4) = | Q^H C - Q^H C |
00057 *>          RESULT(5) = | C Q - C Q | 
00058 *>          RESULT(6) = | C Q^H - C Q^H |
00059 *> \endverbatim
00060 *
00061 *  Authors:
00062 *  ========
00063 *
00064 *> \author Univ. of Tennessee 
00065 *> \author Univ. of California Berkeley 
00066 *> \author Univ. of Colorado Denver 
00067 *> \author NAG Ltd. 
00068 *
00069 *> \date April 2012
00070 *
00071 *> \ingroup single_lin
00072 *
00073 *  =====================================================================
00074       SUBROUTINE SQRT04(M,N,NB,RESULT)
00075       IMPLICIT NONE
00076 *
00077 *  -- LAPACK test routine (version 3.4.1) --
00078 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00079 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00080 *     April 2012
00081 *
00082 *     .. Scalar Arguments ..
00083       INTEGER M, N, NB, LDT
00084 *     .. Return values ..
00085       REAL RESULT(6)
00086 *
00087 *  =====================================================================
00088 *
00089 *     ..
00090 *     .. Local allocatable arrays 
00091       REAL, ALLOCATABLE :: AF(:,:), Q(:,:),
00092      $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
00093      $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
00094 *
00095 *     .. Parameters ..
00096       REAL ONE, ZERO
00097       PARAMETER( ZERO = 0.0, ONE = 1.0 )
00098 *     ..
00099 *     .. Local Scalars ..
00100       INTEGER INFO, J, K, L, LWORK
00101       REAL   ANORM, EPS, RESID, CNORM, DNORM
00102 *     ..
00103 *     .. Local Arrays ..
00104       INTEGER            ISEED( 4 )
00105 *     ..
00106 *     .. External Functions ..
00107       REAL SLAMCH 
00108       REAL SLANGE, SLANSY
00109       LOGICAL  LSAME
00110       EXTERNAL SLAMCH, SLANGE, SLANSY, LSAME
00111 *     ..
00112 *     .. Intrinsic Functions ..
00113       INTRINSIC  MAX, MIN      
00114 *     ..
00115 *     .. Data statements ..
00116       DATA ISEED / 1988, 1989, 1990, 1991 /      
00117 *      
00118       EPS = SLAMCH( 'Epsilon' )
00119       K = MIN(M,N)
00120       L = MAX(M,N)
00121       LWORK = MAX(2,L)*MAX(2,L)*NB
00122 *
00123 *     Dynamically allocate local arrays
00124 *
00125       ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), 
00126      $           WORK(LWORK), T(NB,N), C(M,N), CF(M,N), 
00127      $           D(N,M), DF(N,M) )
00128 *
00129 *     Put random numbers into A and copy to AF
00130 *
00131       LDT=NB
00132       DO J=1,N
00133          CALL SLARNV( 2, ISEED, M, A( 1, J ) )
00134       END DO
00135       CALL SLACPY( 'Full', M, N, A, M, AF, M )
00136 *
00137 *     Factor the matrix A in the array AF.
00138 *
00139       CALL SGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO )
00140 *
00141 *     Generate the m-by-m matrix Q
00142 *
00143       CALL SLASET( 'Full', M, M, ZERO, ONE, Q, M )
00144       CALL SGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, 
00145      $              WORK, INFO )
00146 *
00147 *     Copy R
00148 *
00149       CALL SLASET( 'Full', M, N, ZERO, ZERO, R, M )
00150       CALL SLACPY( 'Upper', M, N, AF, M, R, M )
00151 *
00152 *     Compute |R - Q'*A| / |A| and store in RESULT(1)
00153 *
00154       CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M )
00155       ANORM = SLANGE( '1', M, N, A, M, RWORK )
00156       RESID = SLANGE( '1', M, N, R, M, RWORK )
00157       IF( ANORM.GT.ZERO ) THEN
00158          RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM)
00159       ELSE
00160          RESULT( 1 ) = ZERO
00161       END IF
00162 *
00163 *     Compute |I - Q'*Q| and store in RESULT(2)
00164 *
00165       CALL SLASET( 'Full', M, M, ZERO, ONE, R, M )
00166       CALL SSYRK( 'U', 'C', M, M, -ONE, Q, M, ONE, R, M )
00167       RESID = SLANSY( '1', 'Upper', M, R, M, RWORK )
00168       RESULT( 2 ) = RESID / (EPS*MAX(1,M))
00169 *
00170 *     Generate random m-by-n matrix C and a copy CF
00171 *
00172       DO J=1,N
00173          CALL SLARNV( 2, ISEED, M, C( 1, J ) )
00174       END DO
00175       CNORM = SLANGE( '1', M, N, C, M, RWORK)
00176       CALL SLACPY( 'Full', M, N, C, M, CF, M )
00177 *
00178 *     Apply Q to C as Q*C
00179 *
00180       CALL SGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, 
00181      $             WORK, INFO)
00182 *
00183 *     Compute |Q*C - Q*C| / |C|
00184 *
00185       CALL SGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
00186       RESID = SLANGE( '1', M, N, CF, M, RWORK )
00187       IF( CNORM.GT.ZERO ) THEN
00188          RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM)
00189       ELSE
00190          RESULT( 3 ) = ZERO
00191       END IF
00192 *
00193 *     Copy C into CF again
00194 *
00195       CALL SLACPY( 'Full', M, N, C, M, CF, M )
00196 *
00197 *     Apply Q to C as QT*C
00198 *
00199       CALL SGEMQRT( 'L', 'T', M, N, K, NB, AF, M, T, NB, CF, M, 
00200      $             WORK, INFO)
00201 *
00202 *     Compute |QT*C - QT*C| / |C|
00203 *
00204       CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
00205       RESID = SLANGE( '1', M, N, CF, M, RWORK )
00206       IF( CNORM.GT.ZERO ) THEN
00207          RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM)
00208       ELSE
00209          RESULT( 4 ) = ZERO
00210       END IF     
00211 *
00212 *     Generate random n-by-m matrix D and a copy DF
00213 *
00214       DO J=1,M
00215          CALL SLARNV( 2, ISEED, N, D( 1, J ) )
00216       END DO
00217       DNORM = SLANGE( '1', N, M, D, N, RWORK)
00218       CALL SLACPY( 'Full', N, M, D, N, DF, N )
00219 *
00220 *     Apply Q to D as D*Q
00221 *
00222       CALL SGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, 
00223      $             WORK, INFO)      
00224 *
00225 *     Compute |D*Q - D*Q| / |D|
00226 *
00227       CALL SGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
00228       RESID = SLANGE( '1', N, M, DF, N, RWORK )
00229       IF( CNORM.GT.ZERO ) THEN
00230          RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM)
00231       ELSE
00232          RESULT( 5 ) = ZERO
00233       END IF
00234 *
00235 *     Copy D into DF again
00236 *
00237       CALL SLACPY( 'Full', N, M, D, N, DF, N )
00238 *
00239 *     Apply Q to D as D*QT
00240 *
00241       CALL SGEMQRT( 'R', 'T', N, M, K, NB, AF, M, T, NB, DF, N, 
00242      $             WORK, INFO)      
00243 *
00244 *     Compute |D*QT - D*QT| / |D|
00245 *
00246       CALL SGEMM( 'N', 'T', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
00247       RESID = SLANGE( '1', N, M, DF, N, RWORK )
00248       IF( CNORM.GT.ZERO ) THEN
00249          RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM)
00250       ELSE
00251          RESULT( 6 ) = ZERO
00252       END IF
00253 *
00254 *     Deallocate all arrays
00255 *
00256       DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
00257 *
00258       RETURN
00259       END
00260 
 All Files Functions