math/mul

Element-wise multiplication

Usage

Y:=math/mul(X1, X2)

Computes the element-wise product of two numeric inputs. X1 and X2 may be scalars, vectors, or matrices. When one input is a scalar and the other is an array, the scalar is multiplied with every element of the array (scalar broadcasting). When multiplying vectors with matrices, broadcasting follows the rules in Details.

Note: math/mul performs Hadamard (element-wise) multiplication, not matrix-matrix linear algebra multiplication.

Input

Argument	Kind	Description
`X1`	`int`, `uint`, `float`, `rational`, `complex`, `[T]`, `[[T]]`	First factor. Supports scalars, vectors, and matrices.
`X2`	`int`, `uint`, `float`, `rational`, `complex`, `[T]`, `[[T]]`	Second factor. Must be shape-compatible with `X1` under broadcasting.

Supported scalar types: i8, i16, i32, i64, i128, u8, u16, u32, u64, u128, f32, f64, rational (R64), and complex (C64).

Output

Argument	Kind	Description
`Y`	matches input	Element-wise product of `X1 * X2`. The shape of `Y` follows broadcasting.

Examples

Multiply two scalars

y:=math/mul(6, 7)--

42

Multiply two vectors

x1:=[

1

2

3

]x2:=[

4

5

6

]

Multiply two matrices

a:=[

1 3

2 4

]b:=[

5 7

6 8

]

Multiply a matrix by a scalar (scalar broadcasting)

a:=[

1 3

2 4

]

Multiply a matrix by a column vector (broadcast by columns)

m:=[

1 3

2 4

]--

2x2

v:=[

10

20

]--

column vector length 2

Multiply a row vector by a matrix (broadcast by rows)

r:=[

100

200

]--

row vector length 2

m:=[

1 3

2 4

]--

2x2

Mixed types (float × int)

y:=math/mul(2.5, 4)--

10.0

Complex multiplication

y:=math/mul(1+2i, 3+-4i)--

(11 + 2i)

Details

Element-wise semantics. Multiplication is applied per element. Shapes must either match exactly or be compatible via broadcasting.

Broadcasting rules.

Scalar × Array or Array × Scalar: The scalar is multiplied with every element of the array.
Matrix × Column Vector (or Vector × Matrix): A length-m column vector can multiply an m×n matrix by multiplying the vector with each column of the matrix.
Matrix × Row Vector (or Row Vector × Matrix): A length-n row vector can multiply an m×n matrix by multiplying the vector with each row of the matrix.

Properties. math/mul is commutative and associative on compatible numeric types (ignoring floating-point rounding).

Type support. Implementations exist for signed/unsigned integers, floating-point, rationals, and complex numbers. When types differ, standard numeric promotions apply where defined by the runtime; otherwise a type error is raised.

Errors.

Shape mismatch that cannot be resolved by broadcasting.
Unsupported type combination.