solve

solve(x1: array, x2: array, /) array

Returns the solution to the system of linear equations represented by the well-determined (i.e., full rank) linear matrix equation AX = B.

Note

Whether an array library explicitly checks whether an input array is full rank is implementation-defined.

Parameters
  • x1 (array) – coefficient array A having shape (..., M, M) and whose innermost two dimensions form square matrices. Must be of full rank (i.e., all rows or, equivalently, columns must be linearly independent). Should have a floating-point data type.

  • x2 (array) – ordinate (or “dependent variable”) array B. If x2 has shape (M,), x2 is equivalent to an array having shape (..., M, 1). If x2 has shape (..., M, K), each column k defines a set of ordinate values for which to compute a solution, and shape(x2)[:-1] must be compatible with shape(x1)[:-1] (see Broadcasting). Should have a floating-point data type.

Returns

out (array) – an array containing the solution to the system AX = B for each square matrix. The returned array must have the same shape as x2 (i.e., the array corresponding to B) and must have a floating-point data type determined by Type Promotion Rules.