Man Scilab

rankqr
Scilab Function

rankqr - rank revealing QR factorization

Calling Sequence

[Q,R,JPVT,RANK,SVAL]=rankqr(A, [RCOND,JPVT])

Parameters

Description

To compute (optionally) a rank-revealing QR factorization of a real general M-by-N real or complex matrix A , which may be rank-deficient, and estimate its effective rank using incremental condition estimation.

The routine uses a QR factorization with column pivoting:


        A * P = Q * R,  where  R = [ R11 R12 ],
                                   [  0  R22 ]

    

with R11 defined as the largest leading submatrix whose estimated condition number is less than 1/RCOND . The order of R11 , RANK , is the effective rank of A .

If the triangular factorization is a rank-revealing one (which will be the case if the leading columns were well- conditioned), then SVAL(1) will also be an estimate for the largest singular value of A , and SVAL(2) and SVAL(3) will be estimates for the RANK -th and (RANK+1) -st singular values of A , respectively.

By examining these values, one can confirm that the rank is well defined with respect to the chosen value of RCOND . The ratio SVAL(1)/SVAL(2) is an estimate of the condition number of R(1:RANK,1:RANK) .

Examples


A=rand(5,3)*rand(3,7);
[Q,R,JPVT,RANK,SVAL]=rankqr(A,%eps)
 
  

See Also

qr ,   rank ,  

Used Function

Slicot library routines MB03OD, ZB03OD.

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