ILMathqr Method (InArraycomplex, OutArraycomplex, OutArrayInt32, Boolean)

public static RetArray<complex> qr(
	InArray<complex> A,
	OutArray<complex> R = null,
	OutArray<int> E = null,
	bool economySize = false
)

Public Shared Function qr ( 
	A As InArray(Of complex),
	Optional R As OutArray(Of complex) = Nothing,
	Optional E As OutArray(Of Integer) = Nothing,
	Optional economySize As Boolean = false
) As RetArray(Of complex)

Dim A As InArray(Of complex)
Dim R As OutArray(Of complex)
Dim E As OutArray(Of Integer)
Dim economySize As Boolean
Dim returnValue As RetArray(Of complex)

returnValue = ILMath.qr(A, R, E, economySize)

Parameters

A

Type: ILNumericsInArraycomplex
Input matrix. Size [m x n].

R (Optional)

Type: ILNumericsOutArraycomplex
[Output, optional] Upper triangular matrix. Size [m x n] or [min(m,n) x n] depending on economySize (see remarks). Default: (null) do not compute R.

E (Optional)

Type: ILNumericsOutArrayInt32
[Output, optional] Permutation matrix from pivoting. Size [m x m]. Default: (null) do not return.E.

economySize (Optional)

Type: SystemBoolean
[Optional] True: return more efficient structures if possible. See remarks for details. Default: false.

Return Value

This function performs the QR decomposition on matrix A. It computes matrices Q, R and E, with Q ** R = A ** E, where '**' denotes matrix multiplication.

If R is null on entry, the function returns the compact QR decomposition result from qr(InArraycomplex).

If economySize is false, the function returns Q, R and E such that the equation

A * E = Q * R

If economySize is true ...

• and m >= n the size of Q and R will be [m x min(m,n)] and [min(m,n) x n] respectively. For m < n the sizes are not changed and as specified above.
• the output parameter E is returned as vector [n] with permutation indices rather than as a permutation matrix [n,n]. In this case the equation
  Copy

  A[":",E] == Q * R

  holds, except roundoff errors.

E reflects the pivoting of A done inside the LAPACK function performing the decomposition so that R shows increasing diagonal element values. If E is not requested (null) the equation Q ** R = A holds instead.

[ILNumerics Computing Engine]

Reference