Add New Vector Functions

[zhongzc]

What problem does the new feature solve?

We seek external contributors to help us implement various functions for vector operations in GreptimeDB. You can refer to this PR as a guide for implementing vec_scalar_add. Below is a list of functions we are considering. Each function comes with a brief description.

Please respond below with the function(s) you would like to contribute, ensuring to avoid overlap with other contributors. We look forward to your valuable contributions!

What does the feature do?

Vector Basic Functions:

• VEC_SCALAR_ADD(f32, vec): Adds a scalar to each element of a vector (use negative scalar for subtraction), returns a vector. feat(vector): add scalar add function  #5119
• VEC_SCALAR_MUL(f32, vec): Multiplies a scalar with each element of a vector (use 1/scalar for division), returns a vector. @linyihai feat: Add vector_scalar_mul function. #5166
• VEC_ADD(vec0, vec1): Adds corresponding elements of two vectors, returns a vector. @wty4427300
• VEC_SUB(vec0, vec1): Subtracts corresponding elements of two vectors, returns a vector. @KKould feat(vector): add sub function #5230
• VEC_MUL(vec0, vec1): Multiplies corresponding elements of two vectors, returns a vector. @linyihai feat: Add vec_mul function. #5205
• VEC_DIV(vec0, vec1): Divides corresponding elements of two vectors, returns a vector.
• VEC_SUM(col): Aggregates by summing elements across the same dimension, returns a vector.
• VEC_PRODUCT(col): Aggregates by multiplying elements across the same dimension, returns a vector.
• VEC_ELEM_SUM(vec): Sums all elements of the vector, returns a scalar.
• VEC_ELEM_PRODUCT(vec): Multiplies all elements of the vector, returns a scalar.
• VEC_NORM(vec): Normalizes the vector to length 1, effectively equivalent to VECTOR_SCALAR_MUL(1/SQRT(VECTOR_ELEM_SUM(VECTOR_MUL(v, v))), v), returns a vector.

Vector Properties/Access Functions:

• VEC_DIM(vec): Returns the dimension of the vector.
• VEC_KTH_ELEM(vec, k): Returns the k-th element of the vector.
• VEC_SUBVECTOR(vec, start, end): Returns a subvector from start to end index.

Conversion Functions (JSON <-> Vector):

• JSON_TO_VEC: Converts a JSON Array to a Vector.
• VEC_TO_JSON: Converts a Vector to a JSON Array.

Conversion Functions (String <-> Vector):

• PARSE_VEC: Converts a String to a Vector. feat(vector): add conversion between vector and string #5029
• VEC_TO_STRING: Converts a Vector to a String. feat(vector): add conversion between vector and string #5029

Vector Distance Functions:

• VEC_COS_DISTANCE(vec0, vec1): Returns the cosine distance between two vectors, returns a scalar. feat: add distance functions #4987
• VEC_L2SQ_DISTANCE(vec0, vec1): Returns the L2 squared distance between two vectors, returns a scalar. feat: add distance functions #4987
• VEC_DOT_PRODUCT(vec0, vec1): Returns the dot product of two vectors, returns a scalar. feat: add distance functions #4987

... Other possible functions

Implementation challenges

No response

[linyihai]

I'd look into VEC_SCALAR_MUL(f32, vec) :）

[wty4427300]

I want to try VEC_ADD(vec0, vec1):

[killme2008]

I'd look into VEC_SCALAR_MUL(f32, vec) :）

Cool, thank you!

[killme2008]

I want to try VEC_ADD(vec0, vec1):

Thanks!