solve_triangular#

ivy.solve_triangular(x1, x2, /, *, upper=True, adjoint=False, unit_diagonal=False, out=None)[source]#

Return the unique solution to the triangular system of linear equations AX = B.

Parameters:

x1 (Union[Array, NativeArray]) – Triangular coefficient array A of shape (…, N, N), with no zeros on diagonal.
x2 (Union[Array, NativeArray]) – Right-hand side array B of shape (…, N, K).
upper (bool, default: True) – Whether the input x1 is upper triangular.
adjoint (bool, default: False) – Whether to take the adjoint (conjugate transpose) of x1 as the matrix A.
unit_diagonal (bool, default: False) – Whether to ignore the diagonal entries of A and assume them all equal to 1.
out (Optional[Array], default: None) – Optional output array. If provided, the output array to store the result.

Return type:

Array

Returns:

ret – The solution X, which has the same shape as B.

Examples

With ivy.Array inputs:

>>> a = ivy.array([[3, 0, 0, 0],
...                [2, 1, 0, 0],
...                [1, 0, 1, 0],
...                [1, 1, 1, 1]], dtype=ivy.float32)
>>> b = ivy.array([[4],
...                [2],
...                [4],
...                [2]], dtype=ivy.float32)
>>> x = ivy.solve_triangular(a, b, upper=False)
>>> ivy.matmul(a, x)
ivy.array([[4.],
           [2.],
           [4.],
           [2.]])