qrfact(A)

..  qrfact(A) -> SPQR.Factorization

Compute the QR factorization of a sparse matrix ``A``. A fill-reducing permutation is used. The main application of this type is to solve least squares problems with ``\``. The function calls the C library SPQR and a few additional functions from the library are wrapped but not exported.

Examples

The qrfact(A, pivot=Val{false}) function computes the QR factorization of matrix A. The return type of F depends on the element type of A and whether pivoting is specified (with pivot==Val{true}). Here are some examples and explanations of its usage:

  1. Compute QR factorization of a matrix:

    julia> A = [1 2; 3 4; 5 6];
julia> F = qrfact(A)
QR{Float64,Array{Float64,2}} with factorizations Q and R:
Q factor:
3×3 LinearAlgebra.QRCompactWYQ{Float64,Array{Float64,2}}:
-0.16903   0.897085  -0.408248
-0.507092  -0.276026  -0.816497
-0.845154   0.345033   0.408248
R factor:
2×2 Array{Float64,2}:
-5.91608  -7.43735
 0.0       0.828078

    This example computes the QR factorization of matrix A and stores the result in F. The QR object F contains the Q factor and the R factor.

  2. Compute QR factorization with pivoting:

    julia> A = [1 2; 3 4; 5 6];
julia> F = qrfact(A, pivot=Val{true})
QRPivoted{Float64,Array{Float64,2}} with factorizations Q, R, and P:
Q factor:
3×3 LinearAlgebra.QRPackedQ{Float64,Array{Float64,2}}:
-0.16903   0.897085  -0.408248
-0.507092  -0.276026  -0.816497
-0.845154   0.345033   0.408248
R factor:
2×2 Array{Float64,2}:
-5.91608  -7.43735
 0.0       0.828078
P permutation:
3-element Array{Int64,1}:
3
2
1

    This example computes the QR factorization of matrix A with pivoting enabled. The QRPivoted object F contains the Q factor, the R factor, and the permutation matrix P.

  3. Access individual components of the factorization:

    julia> Q = F[:Q]
3×3 LinearAlgebra.QRCompactWYQ{Float64,Array{Float64,2}}:
-0.16903   0.897085  -0.408248
-0.507092  -0.276026  -0.816497
-0.845154   0.345033   0.408248

julia> R = F[:R]
2×2 Array{Float64,2}:
-5.91608  -7.43735
 0.0       0.828078

julia> P = F[:P]
3-element Array{Int64,1}:
3
2
1

    This example shows how to access the Q, R, and P components of the factorization F.

See Also

Ac_ldiv_B, Ac_ldiv_Bc, Ac_mul_B, Ac_mul_Bc, Ac_rdiv_B, Ac_rdiv_Bc, At_ldiv_B, At_ldiv_Bt, At_mul_B, At_mul_Bt, At_rdiv_B, At_rdiv_Bt, A_ldiv_Bc, A_ldiv_Bt, A_mul_B!, A_mul_Bc, A_mul_Bt, A_rdiv_Bc, A_rdiv_Bt, Bidiagonal, cond, conv2, det, diag, diagind, diagm, diff, eig, eigvals, eigvecs, expm, eye, full, inv, isdiag, ishermitian, isposdef, isposdef!, issym, istril, istriu, logabsdet, logdet, lyap, norm, qrfact, rank, repmat, rot180, rotl90, rotr90, sortrows, sqrtm, SymTridiagonal, trace, Tridiagonal, tril, tril!, triu, triu!, writedlm,

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