Julie
e18d437924
GitHub is now enabling us to track accurately version and date. No need for this anymore.
287 lines
7.2 KiB
FortranFixed
287 lines
7.2 KiB
FortranFixed
*> \brief \b SQRT05
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE SQRT05(M,N,L,NB,RESULT)
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER LWORK, M, N, L, NB, LDT
|
|
* .. Return values ..
|
|
* REAL RESULT(6)
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> SQRT05 tests STPQRT and STPMQRT.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] M
|
|
*> \verbatim
|
|
*> M is INTEGER
|
|
*> Number of rows in lower part of the test matrix.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> Number of columns in test matrix.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] L
|
|
*> \verbatim
|
|
*> L is INTEGER
|
|
*> The number of rows of the upper trapezoidal part the
|
|
*> lower test matrix. 0 <= L <= M.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] NB
|
|
*> \verbatim
|
|
*> NB is INTEGER
|
|
*> Block size of test matrix. NB <= N.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] RESULT
|
|
*> \verbatim
|
|
*> RESULT is REAL 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 |
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \ingroup single_lin
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE SQRT05(M,N,L,NB,RESULT)
|
|
IMPLICIT NONE
|
|
*
|
|
* -- LAPACK test routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER LWORK, M, N, L, NB, LDT
|
|
* .. Return values ..
|
|
REAL RESULT(6)
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* ..
|
|
* .. Local allocatable arrays
|
|
REAL, ALLOCATABLE :: AF(:,:), Q(:,:),
|
|
$ R(:,:), RWORK(:), WORK( : ), T(:,:),
|
|
$ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
|
|
*
|
|
* .. Parameters ..
|
|
REAL ZERO, ONE
|
|
PARAMETER( ZERO = 0.0, ONE = 1.0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER INFO, J, K, M2, NP1
|
|
REAL ANORM, EPS, RESID, CNORM, DNORM
|
|
* ..
|
|
* .. Local Arrays ..
|
|
INTEGER ISEED( 4 )
|
|
* ..
|
|
* .. External Subroutine ..
|
|
EXTERNAL SGEMM, SLARNV, STPMQRT, STPQRT, SGEMQRT, SSYRK, SLACPY,
|
|
$ SLASET
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL SLAMCH
|
|
REAL SLANGE, SLANSY
|
|
LOGICAL LSAME
|
|
EXTERNAL SLAMCH, SLANGE, SLANSY, LSAME
|
|
* ..
|
|
* .. Data statements ..
|
|
DATA ISEED / 1988, 1989, 1990, 1991 /
|
|
*
|
|
EPS = SLAMCH( 'Epsilon' )
|
|
K = N
|
|
M2 = M+N
|
|
IF( M.GT.0 ) THEN
|
|
NP1 = N+1
|
|
ELSE
|
|
NP1 = 1
|
|
END IF
|
|
LWORK = M2*M2*NB
|
|
*
|
|
* Dynamically allocate all arrays
|
|
*
|
|
ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2),
|
|
$ WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N),
|
|
$ D(N,M2),DF(N,M2) )
|
|
*
|
|
* Put random stuff into A
|
|
*
|
|
LDT=NB
|
|
CALL SLASET( 'Full', M2, N, ZERO, ZERO, A, M2 )
|
|
CALL SLASET( 'Full', NB, N, ZERO, ZERO, T, NB )
|
|
DO J=1,N
|
|
CALL SLARNV( 2, ISEED, J, A( 1, J ) )
|
|
END DO
|
|
IF( M.GT.0 ) THEN
|
|
DO J=1,N
|
|
CALL SLARNV( 2, ISEED, M-L, A( N+1, J ) )
|
|
END DO
|
|
END IF
|
|
IF( L.GT.0 ) THEN
|
|
DO J=1,N
|
|
CALL SLARNV( 2, ISEED, MIN(J,L), A( N+M-L+1, J ) )
|
|
END DO
|
|
END IF
|
|
*
|
|
* Copy the matrix A to the array AF.
|
|
*
|
|
CALL SLACPY( 'Full', M2, N, A, M2, AF, M2 )
|
|
*
|
|
* Factor the matrix A in the array AF.
|
|
*
|
|
CALL STPQRT( M,N,L,NB,AF,M2,AF(NP1,1),M2,T,LDT,WORK,INFO)
|
|
*
|
|
* Generate the (M+N)-by-(M+N) matrix Q by applying H to I
|
|
*
|
|
CALL SLASET( 'Full', M2, M2, ZERO, ONE, Q, M2 )
|
|
CALL SGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2,
|
|
$ WORK, INFO )
|
|
*
|
|
* Copy R
|
|
*
|
|
CALL SLASET( 'Full', M2, N, ZERO, ZERO, R, M2 )
|
|
CALL SLACPY( 'Upper', M2, N, AF, M2, R, M2 )
|
|
*
|
|
* Compute |R - Q'*A| / |A| and store in RESULT(1)
|
|
*
|
|
CALL SGEMM( 'T', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 )
|
|
ANORM = SLANGE( '1', M2, N, A, M2, RWORK )
|
|
RESID = SLANGE( '1', M2, N, R, M2, RWORK )
|
|
IF( ANORM.GT.ZERO ) THEN
|
|
RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2))
|
|
ELSE
|
|
RESULT( 1 ) = ZERO
|
|
END IF
|
|
*
|
|
* Compute |I - Q'*Q| and store in RESULT(2)
|
|
*
|
|
CALL SLASET( 'Full', M2, M2, ZERO, ONE, R, M2 )
|
|
CALL SSYRK( 'U', 'C', M2, M2, -ONE, Q, M2, ONE,
|
|
$ R, M2 )
|
|
RESID = SLANSY( '1', 'Upper', M2, R, M2, RWORK )
|
|
RESULT( 2 ) = RESID / (EPS*MAX(1,M2))
|
|
*
|
|
* Generate random m-by-n matrix C and a copy CF
|
|
*
|
|
DO J=1,N
|
|
CALL SLARNV( 2, ISEED, M2, C( 1, J ) )
|
|
END DO
|
|
CNORM = SLANGE( '1', M2, N, C, M2, RWORK)
|
|
CALL SLACPY( 'Full', M2, N, C, M2, CF, M2 )
|
|
*
|
|
* Apply Q to C as Q*C
|
|
*
|
|
CALL STPMQRT( 'L','N', M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,
|
|
$ M2,CF(NP1,1),M2,WORK,INFO)
|
|
*
|
|
* Compute |Q*C - Q*C| / |C|
|
|
*
|
|
CALL SGEMM( 'N', 'N', M2, N, M2, -ONE, Q,M2,C,M2,ONE,CF,M2)
|
|
RESID = SLANGE( '1', M2, N, CF, M2, RWORK )
|
|
IF( CNORM.GT.ZERO ) THEN
|
|
RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM)
|
|
ELSE
|
|
RESULT( 3 ) = ZERO
|
|
END IF
|
|
*
|
|
* Copy C into CF again
|
|
*
|
|
CALL SLACPY( 'Full', M2, N, C, M2, CF, M2 )
|
|
*
|
|
* Apply Q to C as QT*C
|
|
*
|
|
CALL STPMQRT('L','T',M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2,
|
|
$ CF(NP1,1),M2,WORK,INFO)
|
|
*
|
|
* Compute |QT*C - QT*C| / |C|
|
|
*
|
|
CALL SGEMM('T','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2)
|
|
RESID = SLANGE( '1', M2, N, CF, M2, RWORK )
|
|
IF( CNORM.GT.ZERO ) THEN
|
|
RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM)
|
|
ELSE
|
|
RESULT( 4 ) = ZERO
|
|
END IF
|
|
*
|
|
* Generate random n-by-m matrix D and a copy DF
|
|
*
|
|
DO J=1,M2
|
|
CALL SLARNV( 2, ISEED, N, D( 1, J ) )
|
|
END DO
|
|
DNORM = SLANGE( '1', N, M2, D, N, RWORK)
|
|
CALL SLACPY( 'Full', N, M2, D, N, DF, N )
|
|
*
|
|
* Apply Q to D as D*Q
|
|
*
|
|
CALL STPMQRT('R','N',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N,
|
|
$ DF(1,NP1),N,WORK,INFO)
|
|
*
|
|
* Compute |D*Q - D*Q| / |D|
|
|
*
|
|
CALL SGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N)
|
|
RESID = SLANGE('1',N, M2,DF,N,RWORK )
|
|
IF( CNORM.GT.ZERO ) THEN
|
|
RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM)
|
|
ELSE
|
|
RESULT( 5 ) = ZERO
|
|
END IF
|
|
*
|
|
* Copy D into DF again
|
|
*
|
|
CALL SLACPY('Full',N,M2,D,N,DF,N )
|
|
*
|
|
* Apply Q to D as D*QT
|
|
*
|
|
CALL STPMQRT('R','T',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N,
|
|
$ DF(1,NP1),N,WORK,INFO)
|
|
|
|
*
|
|
* Compute |D*QT - D*QT| / |D|
|
|
*
|
|
CALL SGEMM( 'N', 'T', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N )
|
|
RESID = SLANGE( '1', N, M2, DF, N, RWORK )
|
|
IF( CNORM.GT.ZERO ) THEN
|
|
RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM)
|
|
ELSE
|
|
RESULT( 6 ) = ZERO
|
|
END IF
|
|
*
|
|
* Deallocate all arrays
|
|
*
|
|
DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
|
|
RETURN
|
|
END
|
|
|