141 lines
4.0 KiB
FortranFixed
141 lines
4.0 KiB
FortranFixed
DOUBLE PRECISION FUNCTION ZQPT01( M, N, K, A, AF, LDA, TAU, JPVT,
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$ WORK, LWORK )
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*
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* -- LAPACK test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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INTEGER K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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INTEGER JPVT( * )
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COMPLEX*16 A( LDA, * ), AF( LDA, * ), TAU( * ),
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$ WORK( LWORK )
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* ..
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*
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* Purpose
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* =======
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*
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* ZQPT01 tests the QR-factorization with pivoting of a matrix A. The
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* array AF contains the (possibly partial) QR-factorization of A, where
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* the upper triangle of AF(1:k,1:k) is a partial triangular factor,
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* the entries below the diagonal in the first k columns are the
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* Householder vectors, and the rest of AF contains a partially updated
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* matrix.
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*
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* This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
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*
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* Arguments
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* =========
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*
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* M (input) INTEGER
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* The number of rows of the matrices A and AF.
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*
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* N (input) INTEGER
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* The number of columns of the matrices A and AF.
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*
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* K (input) INTEGER
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* The number of columns of AF that have been reduced
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* to upper triangular form.
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*
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* A (input) COMPLEX*16 array, dimension (LDA, N)
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* The original matrix A.
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*
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* AF (input) COMPLEX*16 array, dimension (LDA,N)
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* The (possibly partial) output of ZGEQPF. The upper triangle
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* of AF(1:k,1:k) is a partial triangular factor, the entries
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* below the diagonal in the first k columns are the Householder
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* vectors, and the rest of AF contains a partially updated
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* matrix.
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*
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* LDA (input) INTEGER
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* The leading dimension of the arrays A and AF.
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*
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* TAU (input) COMPLEX*16 array, dimension (K)
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* Details of the Householder transformations as returned by
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* ZGEQPF.
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*
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* JPVT (input) INTEGER array, dimension (N)
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* Pivot information as returned by ZGEQPF.
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*
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* WORK (workspace) COMPLEX*16 array, dimension (LWORK)
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*
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* LWORK (input) INTEGER
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* The length of the array WORK. LWORK >= M*N+N.
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, INFO, J
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DOUBLE PRECISION NORMA
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* ..
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* .. Local Arrays ..
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DOUBLE PRECISION RWORK( 1 )
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, ZLANGE
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EXTERNAL DLAMCH, ZLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZAXPY, ZCOPY, ZUNMQR
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE, DCMPLX, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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ZQPT01 = ZERO
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*
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* Test if there is enough workspace
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*
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IF( LWORK.LT.M*N+N ) THEN
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CALL XERBLA( 'ZQPT01', 10 )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.LE.0 .OR. N.LE.0 )
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$ RETURN
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*
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NORMA = ZLANGE( 'One-norm', M, N, A, LDA, RWORK )
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*
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DO 30 J = 1, K
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DO 10 I = 1, MIN( J, M )
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WORK( ( J-1 )*M+I ) = AF( I, J )
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10 CONTINUE
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DO 20 I = J + 1, M
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WORK( ( J-1 )*M+I ) = ZERO
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20 CONTINUE
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30 CONTINUE
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DO 40 J = K + 1, N
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CALL ZCOPY( M, AF( 1, J ), 1, WORK( ( J-1 )*M+1 ), 1 )
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40 CONTINUE
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*
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CALL ZUNMQR( 'Left', 'No transpose', M, N, K, AF, LDA, TAU, WORK,
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$ M, WORK( M*N+1 ), LWORK-M*N, INFO )
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*
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DO 50 J = 1, N
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*
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* Compare i-th column of QR and jpvt(i)-th column of A
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*
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CALL ZAXPY( M, DCMPLX( -ONE ), A( 1, JPVT( J ) ), 1,
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$ WORK( ( J-1 )*M+1 ), 1 )
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50 CONTINUE
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*
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ZQPT01 = ZLANGE( 'One-norm', M, N, WORK, M, RWORK ) /
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$ ( DBLE( MAX( M, N ) )*DLAMCH( 'Epsilon' ) )
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IF( NORMA.NE.ZERO )
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$ ZQPT01 = ZQPT01 / NORMA
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*
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RETURN
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*
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* End of ZQPT01
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*
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END
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