!>
!> DQPT01 tests the QR-factorization with pivoting of a matrix A.  The
!> array AF contains the (possibly partial) QR-factorization of A, where
!> the upper triangle of AF(1:K,1:K) is a partial triangular factor,
!> the entries below the diagonal in the first K columns are the
!> Householder vectors, and the rest of AF contains a partially updated
!> matrix.
!>
!> This function returns ||A*P - Q*R|| / ( ||norm(A)||*eps*max(M,N) ),
!> where || . || is matrix one norm.
!> 

M

!>          M is INTEGER
!>          The number of rows of the matrices A and AF.
!> 

N

!>          N is INTEGER
!>          The number of columns of the matrices A and AF.
!> 

K

!>          K is INTEGER
!>          The number of columns of AF that have been reduced
!>          to upper triangular form.
!> 

A

!>          A is DOUBLE PRECISION array, dimension (LDA, N)
!>          The original matrix A.
!> 

AF

!>          AF is DOUBLE PRECISION array, dimension (LDA,N)
!>          The (possibly partial) output of DGEQPF.  The upper triangle
!>          of AF(1:k,1:k) is a partial triangular factor, the entries
!>          below the diagonal in the first k columns are the Householder
!>          vectors, and the rest of AF contains a partially updated
!>          matrix.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the arrays A and AF.
!> 

TAU

!>          TAU is DOUBLE PRECISION array, dimension (K)
!>          Details of the Householder transformations as returned by
!>          DGEQPF.
!> 

JPVT

!>          JPVT is INTEGER array, dimension (N)
!>          Pivot information as returned by DGEQPF.
!> 

WORK

!>          WORK is DOUBLE PRECISION array, dimension (LWORK)
!> 

LWORK

!>          LWORK is INTEGER
!>          The length of the array WORK.  LWORK >= M*N+N.
!> 

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