ILMathlinsolve Method (InArrayfcomplex, InArrayfcomplex)

public static RetArray<fcomplex> linsolve(
	InArray<fcomplex> A,
	InArray<fcomplex> B
)

Public Shared Function linsolve ( 
	A As InArray(Of fcomplex),
	B As InArray(Of fcomplex)
) As RetArray(Of fcomplex)

Dim A As InArray(Of fcomplex)
Dim B As InArray(Of fcomplex)
Dim returnValue As RetArray(Of fcomplex)

returnValue = ILMath.linsolve(A, B)

Parameters

A

Type: ILNumericsInArrayfcomplex
Input matrix A. Size [n, q].

B

Type: ILNumericsInArrayfcomplex
Right hand side B. Size [n, m].

Return Value

Depending on the structure and properties of A the equation system is solved with different approaches:

• If A is square (q == n) and an upper or lower triangular matrix, the system is solved via backward- or forward substitution and the LAPACK function ?trtrs.
  Examples

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  Copy

  Array<fcomplex> A = randn<fcomplex>(4,4); // construct 4 x 4 matrix
              Array<fcomplex> B = vector<fcomplex>(1.0,2.0,3.0);
              Array<fcomplex> x = linsolve(A,B);

• if A is square, symmetric /hermitian and positive definite A is decomposed into a triangular equation system using cholesky factorization and solved via back-/ forward substitution.

• otherwise, if A is only square it will be decomposed into upper and lower triangular matrices using LU decomposition and the system than solved with the result.
• otherwise, if A is [n, q] with q != n, the system is solved using qr(InArrayfcomplex) decomposition. Note that A can be rank deficient.

The internal storage order of A and/or B may be silently changed when this function returns. The reason is that most functionality is performed in native LAPACK routines which require a certain storage layout (mostly ColumnMajor).

[ILNumerics Computing Engine]

Reference