SQPT01 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 REAL array, dimension (LDA, N)


          The original matrix A.

AF

          AF is REAL array, dimension (LDA,N)


          The (possibly partial) output of SGEQPF.  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 REAL array, dimension (K)


          Details of the Householder transformations as returned by


          SGEQPF.

JPVT

          JPVT is INTEGER array, dimension (N)


          Pivot information as returned by SGEQPF.

WORK

          WORK is REAL array, dimension (LWORK)

LWORK

          LWORK is INTEGER


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

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