use std::fmt::Formatter;
use num_traits::Zero;
use vortex_array::ArrayRef;
use vortex_array::ExecutionCtx;
use vortex_array::IntoArray;
use vortex_array::arrays::PrimitiveArray;
use vortex_array::arrays::ScalarFnArray;
use vortex_array::arrays::scalar_fn::ScalarFnArrayView;
use vortex_array::arrays::scalar_fn::plugin::ScalarFnArrayParts;
use vortex_array::arrays::scalar_fn::plugin::ScalarFnArrayVTable;
use vortex_array::dtype::DType;
use vortex_array::dtype::Nullability;
use vortex_array::expr::Expression;
use vortex_array::expr::and;
use vortex_array::match_each_float_ptype;
use vortex_array::scalar_fn::Arity;
use vortex_array::scalar_fn::ChildName;
use vortex_array::scalar_fn::EmptyOptions;
use vortex_array::scalar_fn::ExecutionArgs;
use vortex_array::scalar_fn::ScalarFnId;
use vortex_array::scalar_fn::ScalarFnVTable;
use vortex_array::scalar_fn::TypedScalarFnInstance;
use vortex_array::serde::ArrayChildren;
use vortex_buffer::Buffer;
use vortex_error::VortexResult;
use vortex_session::VortexSession;
use crate::scalar_fns::inner_product::InnerProduct;
use crate::scalar_fns::l2_denorm::DenormOrientation;
use crate::scalar_fns::l2_denorm::try_build_constant_l2_denorm;
use crate::scalar_fns::l2_norm::L2Norm;
use crate::utils::BinaryTensorOpMetadata;
use crate::utils::extract_l2_denorm_children;
use crate::utils::validate_binary_tensor_float_inputs;
#[derive(Clone)]
pub struct CosineSimilarity;
impl CosineSimilarity {
pub fn new() -> TypedScalarFnInstance<CosineSimilarity> {
TypedScalarFnInstance::new(CosineSimilarity, EmptyOptions)
}
pub fn try_new_array(lhs: ArrayRef, rhs: ArrayRef, len: usize) -> VortexResult<ScalarFnArray> {
ScalarFnArray::try_new(CosineSimilarity::new().erased(), vec![lhs, rhs], len)
}
}
impl ScalarFnVTable for CosineSimilarity {
type Options = EmptyOptions;
fn id(&self) -> ScalarFnId {
ScalarFnId::new("vortex.tensor.cosine_similarity")
}
fn arity(&self, _options: &Self::Options) -> Arity {
Arity::Exact(2)
}
fn child_name(&self, _options: &Self::Options, child_idx: usize) -> ChildName {
match child_idx {
0 => ChildName::from("lhs"),
1 => ChildName::from("rhs"),
_ => unreachable!("CosineSimilarity must have exactly two children"),
}
}
fn fmt_sql(
&self,
_options: &Self::Options,
expr: &Expression,
f: &mut Formatter<'_>,
) -> std::fmt::Result {
write!(f, "cosine_similarity(")?;
expr.child(0).fmt_sql(f)?;
write!(f, ", ")?;
expr.child(1).fmt_sql(f)?;
write!(f, ")")
}
fn return_dtype(&self, _options: &Self::Options, arg_dtypes: &[DType]) -> VortexResult<DType> {
let lhs = &arg_dtypes[0];
let rhs = &arg_dtypes[1];
let tensor_match = validate_binary_tensor_float_inputs(lhs, rhs)?;
let ptype = tensor_match.element_ptype();
let nullability = Nullability::from(lhs.is_nullable() || rhs.is_nullable());
Ok(DType::Primitive(ptype, nullability))
}
fn execute(
&self,
_options: &Self::Options,
args: &dyn ExecutionArgs,
ctx: &mut ExecutionCtx,
) -> VortexResult<ArrayRef> {
let mut lhs_ref = args.get(0)?;
let mut rhs_ref = args.get(1)?;
let len = args.row_count();
if let Some(sfn) = try_build_constant_l2_denorm(&lhs_ref, len, ctx)? {
lhs_ref = sfn.into_array();
}
if let Some(sfn) = try_build_constant_l2_denorm(&rhs_ref, len, ctx)? {
rhs_ref = sfn.into_array();
}
match DenormOrientation::classify(&lhs_ref, &rhs_ref) {
DenormOrientation::Both { lhs, rhs } => {
return self.execute_both_denorm(lhs, rhs, len, ctx);
}
DenormOrientation::One { denorm, plain } => {
return self.execute_one_denorm(denorm, plain, len, ctx);
}
DenormOrientation::Neither => {}
}
let validity = lhs_ref.validity()?.and(rhs_ref.validity()?)?;
let norm_lhs_arr = L2Norm::try_new_array(lhs_ref.clone(), len)?;
let norm_rhs_arr = L2Norm::try_new_array(rhs_ref.clone(), len)?;
let dot_arr = InnerProduct::try_new_array(lhs_ref, rhs_ref, len)?;
let dot: PrimitiveArray = dot_arr.into_array().execute(ctx)?;
let norm_l: PrimitiveArray = norm_lhs_arr.into_array().execute(ctx)?;
let norm_r: PrimitiveArray = norm_rhs_arr.into_array().execute(ctx)?;
match_each_float_ptype!(dot.ptype(), |T| {
let dots = dot.as_slice::<T>();
let norms_l = norm_l.as_slice::<T>();
let norms_r = norm_r.as_slice::<T>();
let buffer: Buffer<T> = (0..len)
.map(|i| {
let denom = norms_l[i] * norms_r[i];
if denom == T::zero() {
T::zero()
} else {
dots[i] / denom
}
})
.collect();
Ok(unsafe { PrimitiveArray::new_unchecked(buffer, validity) }.into_array())
})
}
fn validity(
&self,
_options: &Self::Options,
expression: &Expression,
) -> VortexResult<Option<Expression>> {
let lhs_validity = expression.child(0).validity()?;
let rhs_validity = expression.child(1).validity()?;
Ok(Some(and(lhs_validity, rhs_validity)))
}
fn is_null_sensitive(&self, _options: &Self::Options) -> bool {
false
}
fn is_fallible(&self, _options: &Self::Options) -> bool {
false
}
}
impl ScalarFnArrayVTable for CosineSimilarity {
fn serialize(
&self,
view: &ScalarFnArrayView<Self>,
_session: &VortexSession,
) -> VortexResult<Option<Vec<u8>>> {
Ok(Some(BinaryTensorOpMetadata::encode_from_view(view)?))
}
fn deserialize(
&self,
_dtype: &DType,
len: usize,
metadata: &[u8],
children: &dyn ArrayChildren,
session: &VortexSession,
) -> VortexResult<ScalarFnArrayParts<Self>> {
let reconstructed =
BinaryTensorOpMetadata::decode_children(metadata, len, children, session)?;
Ok(ScalarFnArrayParts {
options: EmptyOptions,
children: reconstructed,
})
}
}
impl CosineSimilarity {
fn execute_both_denorm(
&self,
lhs_ref: &ArrayRef,
rhs_ref: &ArrayRef,
len: usize,
ctx: &mut ExecutionCtx,
) -> VortexResult<ArrayRef> {
let validity = lhs_ref.validity()?.and(rhs_ref.validity()?)?;
let (normalized_l, norms_l) = extract_l2_denorm_children(lhs_ref);
let (normalized_r, norms_r) = extract_l2_denorm_children(rhs_ref);
let dot: PrimitiveArray = InnerProduct::try_new_array(normalized_l, normalized_r, len)?
.into_array()
.execute(ctx)?;
let norms_l: PrimitiveArray = norms_l.execute(ctx)?;
let norms_r: PrimitiveArray = norms_r.execute(ctx)?;
match_each_float_ptype!(dot.ptype(), |T| {
let dots = dot.as_slice::<T>();
let norms_l = norms_l.as_slice::<T>();
let norms_r = norms_r.as_slice::<T>();
let buffer: Buffer<T> = (0..len)
.map(|i| {
if norms_l[i] == T::zero() || norms_r[i] == T::zero() {
T::zero()
} else {
dots[i]
}
})
.collect();
Ok(unsafe { PrimitiveArray::new_unchecked(buffer, validity) }.into_array())
})
}
fn execute_one_denorm(
&self,
denorm_ref: &ArrayRef,
plain_ref: &ArrayRef,
len: usize,
ctx: &mut ExecutionCtx,
) -> VortexResult<ArrayRef> {
let validity = denorm_ref.validity()?.and(plain_ref.validity()?)?;
let (normalized, denorm_norms) = extract_l2_denorm_children(denorm_ref);
let dot_arr = InnerProduct::try_new_array(normalized, plain_ref.clone(), len)?;
let dot: PrimitiveArray = dot_arr.into_array().execute(ctx)?;
let denorm_norms: PrimitiveArray = denorm_norms.execute(ctx)?;
let norm_arr = L2Norm::try_new_array(plain_ref.clone(), len)?;
let plain_norm: PrimitiveArray = norm_arr.into_array().execute(ctx)?;
match_each_float_ptype!(dot.ptype(), |T| {
let dots = dot.as_slice::<T>();
let denorm_norms = denorm_norms.as_slice::<T>();
let plain_norms = plain_norm.as_slice::<T>();
let buffer: Buffer<T> = (0..len)
.map(|i| {
if denorm_norms[i] == T::zero() || plain_norms[i] == T::zero() {
T::zero()
} else {
dots[i] / plain_norms[i]
}
})
.collect();
Ok(unsafe { PrimitiveArray::new_unchecked(buffer, validity) }.into_array())
})
}
}
#[cfg(test)]
mod tests {
use rstest::rstest;
use vortex_array::ArrayPlugin;
use vortex_array::ArrayRef;
use vortex_array::IntoArray;
use vortex_array::VortexSessionExecute;
use vortex_array::arrays::MaskedArray;
use vortex_array::arrays::PrimitiveArray;
use vortex_array::arrays::ScalarFnArray;
use vortex_array::arrays::scalar_fn::plugin::ScalarFnArrayPlugin;
use vortex_array::validity::Validity;
use vortex_error::VortexResult;
use crate::scalar_fns::cosine_similarity::CosineSimilarity;
use crate::scalar_fns::l2_denorm::L2Denorm;
use crate::tests::SESSION;
use crate::types::vector::Vector;
use crate::utils::test_helpers::assert_close;
use crate::utils::test_helpers::constant_tensor_array;
use crate::utils::test_helpers::l2_denorm_array;
use crate::utils::test_helpers::tensor_array;
use crate::utils::test_helpers::vector_array;
fn eval_cosine_similarity(lhs: ArrayRef, rhs: ArrayRef, len: usize) -> VortexResult<Vec<f64>> {
let scalar_fn = CosineSimilarity::new().erased();
let result = ScalarFnArray::try_new(scalar_fn, vec![lhs, rhs], len)?;
let mut ctx = SESSION.create_execution_ctx();
let prim: PrimitiveArray = result.into_array().execute(&mut ctx)?;
Ok(prim.as_slice::<f64>().to_vec())
}
#[test]
fn unit_vectors_1d() -> VortexResult<()> {
let lhs = tensor_array(
&[3],
&[
1.0, 0.0, 0.0, 0.0, 1.0, 0.0, ],
)?;
let rhs = tensor_array(
&[3],
&[
1.0, 0.0, 0.0, 1.0, 0.0, 0.0, ],
)?;
assert_close(&eval_cosine_similarity(lhs, rhs, 2)?, &[1.0, 0.0]);
Ok(())
}
#[rstest]
#[case::opposite(&[3], &[1.0, 0.0, 0.0], &[-1.0, 0.0, 0.0], &[-1.0])]
#[case::non_unit(&[2], &[3.0, 4.0], &[4.0, 3.0], &[0.96])]
#[case::zero_norm(&[2], &[0.0, 0.0], &[1.0, 0.0], &[0.0])]
fn single_row(
#[case] shape: &[usize],
#[case] lhs_elems: &[f64],
#[case] rhs_elems: &[f64],
#[case] expected: &[f64],
) -> VortexResult<()> {
let lhs = tensor_array(shape, lhs_elems)?;
let rhs = tensor_array(shape, rhs_elems)?;
assert_close(&eval_cosine_similarity(lhs, rhs, 1)?, expected);
Ok(())
}
#[rstest]
#[case::matrix_2d(
&[2, 3],
&[
1.0, 0.0, 0.0, // row 0
0.0, 0.0, 0.0, // row 1
],
)]
#[case::tensor_3d(&[2, 2, 2], &[1.0; 8])]
fn self_similarity(#[case] shape: &[usize], #[case] elements: &[f64]) -> VortexResult<()> {
let lhs = tensor_array(shape, elements)?;
let rhs = tensor_array(shape, elements)?;
assert_close(&eval_cosine_similarity(lhs, rhs, 1)?, &[1.0]);
Ok(())
}
#[test]
fn scalar_0d() -> VortexResult<()> {
let lhs = tensor_array(&[], &[5.0, 3.0])?;
let rhs = tensor_array(&[], &[5.0, -3.0])?;
assert_close(&eval_cosine_similarity(lhs, rhs, 2)?, &[1.0, -1.0]);
Ok(())
}
#[test]
fn many_rows() -> VortexResult<()> {
let lhs = tensor_array(
&[4],
&[
1.0, 2.0, 3.0, 4.0, 0.0, 1.0, 0.0, 0.0, 5.0, 0.0, 5.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 7.0, ],
)?;
let rhs = lhs.clone();
assert_close(
&eval_cosine_similarity(lhs, rhs, 5)?,
&[1.0, 1.0, 1.0, 1.0, 1.0],
);
Ok(())
}
#[test]
fn constant_query_tensor() -> VortexResult<()> {
let data = tensor_array(
&[3],
&[
1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, ],
)?;
let query = constant_tensor_array(&[3], &[1.0, 0.0, 0.0], 4)?;
assert_close(
&eval_cosine_similarity(data, query, 4)?,
&[1.0, 0.0, 0.0, 1.0],
);
Ok(())
}
#[test]
fn vector_unit_vectors() -> VortexResult<()> {
let lhs = vector_array(
3,
&[
1.0, 0.0, 0.0, 0.0, 1.0, 0.0, ],
)?;
let rhs = vector_array(
3,
&[
1.0, 0.0, 0.0, 1.0, 0.0, 0.0, ],
)?;
assert_close(&eval_cosine_similarity(lhs, rhs, 2)?, &[1.0, 0.0]);
Ok(())
}
#[test]
fn vector_constant_query() -> VortexResult<()> {
let data = vector_array(
3,
&[
1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, ],
)?;
let query = Vector::constant_array(&[1.0, 0.0, 0.0], 4)?;
assert_close(
&eval_cosine_similarity(data, query, 4)?,
&[1.0, 0.0, 0.0, 1.0],
);
Ok(())
}
#[test]
fn null_input_row() -> VortexResult<()> {
let lhs = tensor_array(&[2], &[3.0, 4.0, 1.0, 0.0])?;
let rhs = tensor_array(&[2], &[3.0, 4.0, 0.0, 1.0])?;
let rhs = MaskedArray::try_new(rhs, Validity::from_iter([true, false]))?.into_array();
let scalar_fn = CosineSimilarity::new().erased();
let result = ScalarFnArray::try_new(scalar_fn, vec![lhs, rhs], 2)?;
let mut ctx = SESSION.create_execution_ctx();
let prim: PrimitiveArray = result.into_array().execute(&mut ctx)?;
assert!(prim.is_valid(0, &mut ctx)?);
assert!(!prim.is_valid(1, &mut ctx)?);
assert_close(&[prim.as_slice::<f64>()[0]], &[1.0]);
Ok(())
}
#[test]
fn both_denorm_self_similarity() -> VortexResult<()> {
let mut ctx = SESSION.create_execution_ctx();
let lhs = l2_denorm_array(&[2], &[0.6, 0.8, 1.0, 0.0], &[5.0, 1.0], &mut ctx)?;
let rhs = l2_denorm_array(&[2], &[0.6, 0.8, 1.0, 0.0], &[5.0, 1.0], &mut ctx)?;
assert_close(&eval_cosine_similarity(lhs, rhs, 2)?, &[1.0, 1.0]);
Ok(())
}
#[test]
fn both_denorm_orthogonal() -> VortexResult<()> {
let mut ctx = SESSION.create_execution_ctx();
let lhs = l2_denorm_array(&[2], &[1.0, 0.0], &[3.0], &mut ctx)?;
let rhs = l2_denorm_array(&[2], &[0.0, 1.0], &[4.0], &mut ctx)?;
assert_close(&eval_cosine_similarity(lhs, rhs, 1)?, &[0.0]);
Ok(())
}
#[test]
fn both_denorm_zero_norm() -> VortexResult<()> {
let mut ctx = SESSION.create_execution_ctx();
let lhs = l2_denorm_array(&[2], &[0.6, 0.8, 0.0, 0.0], &[5.0, 0.0], &mut ctx)?;
let rhs = l2_denorm_array(&[2], &[0.6, 0.8, 1.0, 0.0], &[5.0, 1.0], &mut ctx)?;
assert_close(&eval_cosine_similarity(lhs, rhs, 2)?, &[1.0, 0.0]);
Ok(())
}
#[test]
fn one_side_denorm_lhs() -> VortexResult<()> {
let mut ctx = SESSION.create_execution_ctx();
let lhs = l2_denorm_array(&[2], &[0.6, 0.8], &[5.0], &mut ctx)?;
let rhs = tensor_array(&[2], &[3.0, 4.0])?;
assert_close(&eval_cosine_similarity(lhs, rhs, 1)?, &[1.0]);
Ok(())
}
#[test]
fn one_side_denorm_rhs() -> VortexResult<()> {
let mut ctx = SESSION.create_execution_ctx();
let lhs = tensor_array(&[2], &[1.0, 0.0])?;
let rhs = l2_denorm_array(&[2], &[0.6, 0.8], &[5.0], &mut ctx)?;
assert_close(&eval_cosine_similarity(lhs, rhs, 1)?, &[0.6]);
Ok(())
}
#[test]
fn both_denorm_null_norms() -> VortexResult<()> {
let mut ctx = SESSION.create_execution_ctx();
let lhs = l2_denorm_array(&[2], &[0.6, 0.8, 1.0, 0.0], &[5.0, 1.0], &mut ctx)?;
let normalized_r = tensor_array(&[2], &[0.6, 0.8, 1.0, 0.0])?;
let norms_r = PrimitiveArray::from_option_iter([Some(5.0f64), None]).into_array();
let rhs = L2Denorm::try_new_array(normalized_r, norms_r, 2, &mut ctx)?.into_array();
let scalar_fn = CosineSimilarity::new().erased();
let result = ScalarFnArray::try_new(scalar_fn, vec![lhs, rhs], 2)?;
let prim: PrimitiveArray = result.into_array().execute(&mut ctx)?;
assert!(prim.is_valid(0, &mut ctx)?);
assert!(!prim.is_valid(1, &mut ctx)?);
assert_close(&[prim.as_slice::<f64>()[0]], &[1.0]);
Ok(())
}
#[test]
fn both_denorm_lossy_zero_stored_norm_returns_zero() -> VortexResult<()> {
let normalized_l = tensor_array(&[2], &[0.6, 0.8])?;
let norms_l = PrimitiveArray::from_iter([0.0f64]).into_array();
let lhs = unsafe { L2Denorm::new_array_unchecked(normalized_l, norms_l, 1)? }.into_array();
let normalized_r = tensor_array(&[2], &[0.6, 0.8])?;
let norms_r = PrimitiveArray::from_iter([0.0f64]).into_array();
let rhs = unsafe { L2Denorm::new_array_unchecked(normalized_r, norms_r, 1)? }.into_array();
assert_close(&eval_cosine_similarity(lhs, rhs, 1)?, &[0.0]);
Ok(())
}
#[test]
fn one_side_denorm_lossy_zero_stored_norm_returns_zero() -> VortexResult<()> {
let normalized = tensor_array(&[2], &[0.6, 0.8])?;
let norms = PrimitiveArray::from_iter([0.0f64]).into_array();
let denorm = unsafe { L2Denorm::new_array_unchecked(normalized, norms, 1)? }.into_array();
let plain = tensor_array(&[2], &[1.0, 0.0])?;
assert_close(
&eval_cosine_similarity(denorm.clone(), plain.clone(), 1)?,
&[0.0],
);
assert_close(&eval_cosine_similarity(plain, denorm, 1)?, &[0.0]);
Ok(())
}
#[test]
fn constant_lhs_matches_plain_tensor() -> VortexResult<()> {
let lhs = constant_tensor_array(&[3], &[1.0, 2.0, 2.0], 4)?;
let rhs = tensor_array(
&[3],
&[
1.0, 0.0, 0.0, 1.0, 2.0, 2.0, 0.0, 0.0, 1.0, 2.0, 1.0, 2.0, ],
)?;
assert_close(
&eval_cosine_similarity(lhs, rhs, 4)?,
&[1.0 / 3.0, 1.0, 2.0 / 3.0, 8.0 / 9.0],
);
Ok(())
}
#[test]
fn constant_rhs_matches_plain_tensor() -> VortexResult<()> {
let lhs = tensor_array(
&[3],
&[
1.0, 0.0, 0.0, 1.0, 2.0, 2.0, 0.0, 0.0, 1.0, 2.0, 1.0, 2.0, ],
)?;
let rhs = constant_tensor_array(&[3], &[1.0, 2.0, 2.0], 4)?;
assert_close(
&eval_cosine_similarity(lhs, rhs, 4)?,
&[1.0 / 3.0, 1.0, 2.0 / 3.0, 8.0 / 9.0],
);
Ok(())
}
#[test]
fn both_constant_tensors() -> VortexResult<()> {
let lhs = constant_tensor_array(&[3], &[1.0, 0.0, 0.0], 3)?;
let rhs = constant_tensor_array(&[3], &[1.0, 1.0, 0.0], 3)?;
let expected = 1.0 / 2.0_f64.sqrt();
assert_close(
&eval_cosine_similarity(lhs, rhs, 3)?,
&[expected, expected, expected],
);
Ok(())
}
#[test]
fn constant_zero_norm_query() -> VortexResult<()> {
let lhs = constant_tensor_array(&[3], &[0.0, 0.0, 0.0], 3)?;
let rhs = tensor_array(
&[3],
&[
1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, ],
)?;
assert_close(&eval_cosine_similarity(lhs, rhs, 3)?, &[0.0, 0.0, 0.0]);
Ok(())
}
#[test]
fn constant_self_similarity_nonunit() -> VortexResult<()> {
let lhs = constant_tensor_array(&[3], &[3.0, 4.0, 0.0], 5)?;
let rhs = constant_tensor_array(&[3], &[3.0, 4.0, 0.0], 5)?;
assert_close(&eval_cosine_similarity(lhs, rhs, 5)?, &[1.0; 5]);
Ok(())
}
#[test]
fn vector_constant_matches_plain() -> VortexResult<()> {
let lhs = Vector::constant_array(&[1.0, 2.0, 2.0], 4)?;
let rhs = vector_array(
3,
&[
1.0, 0.0, 0.0, 1.0, 2.0, 2.0, 0.0, 0.0, 1.0, 2.0, 1.0, 2.0, ],
)?;
assert_close(
&eval_cosine_similarity(lhs, rhs, 4)?,
&[1.0 / 3.0, 1.0, 2.0 / 3.0, 8.0 / 9.0],
);
Ok(())
}
#[rstest]
#[case::vector(cosine_vector_lhs(), cosine_vector_rhs(), 2)]
#[case::fixed_shape_tensor(cosine_tensor_lhs(), cosine_tensor_rhs(), 2)]
fn serde_round_trip(
#[case] lhs: ArrayRef,
#[case] rhs: ArrayRef,
#[case] len: usize,
) -> VortexResult<()> {
let original = CosineSimilarity::try_new_array(lhs.clone(), rhs.clone(), len)?.into_array();
let plugin = ScalarFnArrayPlugin::new(CosineSimilarity);
let metadata = plugin
.serialize(&original, &SESSION)?
.expect("CosineSimilarity serialize must produce metadata");
let children = vec![lhs, rhs];
let recovered = plugin.deserialize(
original.dtype(),
original.len(),
&metadata,
&[],
&children,
&SESSION,
)?;
assert_eq!(recovered.dtype(), original.dtype());
assert_eq!(recovered.len(), original.len());
assert_eq!(recovered.encoding_id(), original.encoding_id());
Ok(())
}
fn cosine_vector_lhs() -> ArrayRef {
vector_array(3, &[1.0, 0.0, 0.0, 3.0, 4.0, 0.0]).expect("valid vector array")
}
fn cosine_vector_rhs() -> ArrayRef {
vector_array(3, &[0.0, 1.0, 0.0, 3.0, 4.0, 0.0]).expect("valid vector array")
}
fn cosine_tensor_lhs() -> ArrayRef {
tensor_array(&[2], &[1.0, 0.0, 3.0, 4.0]).expect("valid tensor array")
}
fn cosine_tensor_rhs() -> ArrayRef {
tensor_array(&[2], &[0.0, 1.0, 3.0, 4.0]).expect("valid tensor array")
}
}