testdata/lapack/TESTING/LIN/cqrt05.f
*> \brief \b CQRT05
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CQRT05(M,N,L,NB,RESULT)
*
* .. Scalar Arguments ..
* INTEGER LWORK, M, N, L, NB, LDT
* .. Return values ..
* REAL RESULT(6)
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CQRT05 tests CTPQRT and CTPMQRT.
*> \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.
*
*> \date April 2012
*
*> \ingroup complex_lin
*
* =====================================================================
SUBROUTINE CQRT05(M,N,L,NB,RESULT)
IMPLICIT NONE
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* April 2012
*
* .. Scalar Arguments ..
INTEGER LWORK, M, N, L, NB, LDT
* .. Return values ..
REAL RESULT(6)
*
* =====================================================================
*
* ..
* .. Local allocatable arrays
COMPLEX, ALLOCATABLE :: AF(:,:), Q(:,:),
$ R(:,:), WORK( : ), T(:,:),
$ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
REAL, ALLOCATABLE :: RWORK(:)
*
* .. Parameters ..
REAL ZERO
COMPLEX ONE, CZERO
PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) )
* ..
* .. Local Scalars ..
INTEGER INFO, J, K, M2, NP1
REAL ANORM, EPS, RESID, CNORM, DNORM
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 )
* ..
* .. External Functions ..
REAL SLAMCH
REAL CLANGE, CLANSY
LOGICAL LSAME
EXTERNAL SLAMCH, CLANGE, CLANSY, 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 CLASET( 'Full', M2, N, CZERO, CZERO, A, M2 )
CALL CLASET( 'Full', NB, N, CZERO, CZERO, T, NB )
DO J=1,N
CALL CLARNV( 2, ISEED, J, A( 1, J ) )
END DO
IF( M.GT.0 ) THEN
DO J=1,N
CALL CLARNV( 2, ISEED, M-L, A( MIN(N+M,N+1), J ) )
END DO
END IF
IF( L.GT.0 ) THEN
DO J=1,N
CALL CLARNV( 2, ISEED, MIN(J,L), A( MIN(N+M,N+M-L+1), J ) )
END DO
END IF
*
* Copy the matrix A to the array AF.
*
CALL CLACPY( 'Full', M2, N, A, M2, AF, M2 )
*
* Factor the matrix A in the array AF.
*
CALL CTPQRT( 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 CLASET( 'Full', M2, M2, CZERO, ONE, Q, M2 )
CALL CGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2,
$ WORK, INFO )
*
* Copy R
*
CALL CLASET( 'Full', M2, N, CZERO, CZERO, R, M2 )
CALL CLACPY( 'Upper', M2, N, AF, M2, R, M2 )
*
* Compute |R - Q'*A| / |A| and store in RESULT(1)
*
CALL CGEMM( 'C', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 )
ANORM = CLANGE( '1', M2, N, A, M2, RWORK )
RESID = CLANGE( '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 CLASET( 'Full', M2, M2, CZERO, ONE, R, M2 )
CALL CHERK( 'U', 'C', M2, M2, REAL(-ONE), Q, M2, REAL(ONE),
$ R, M2 )
RESID = CLANSY( '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 CLARNV( 2, ISEED, M2, C( 1, J ) )
END DO
CNORM = CLANGE( '1', M2, N, C, M2, RWORK)
CALL CLACPY( 'Full', M2, N, C, M2, CF, M2 )
*
* Apply Q to C as Q*C
*
CALL CTPMQRT( '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 CGEMM( 'N', 'N', M2, N, M2, -ONE, Q, M2, C, M2, ONE, CF, M2 )
RESID = CLANGE( '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 CLACPY( 'Full', M2, N, C, M2, CF, M2 )
*
* Apply Q to C as QT*C
*
CALL CTPMQRT( 'L','C',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 CGEMM('C','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2)
RESID = CLANGE( '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 CLARNV( 2, ISEED, N, D( 1, J ) )
END DO
DNORM = CLANGE( '1', N, M2, D, N, RWORK)
CALL CLACPY( 'Full', N, M2, D, N, DF, N )
*
* Apply Q to D as D*Q
*
CALL CTPMQRT('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 CGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N)
RESID = CLANGE('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 CLACPY('Full',N,M2,D,N,DF,N )
*
* Apply Q to D as D*QT
*
CALL CTPMQRT('R','C',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 CGEMM( 'N', 'C', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N )
RESID = CLANGE( '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