/
external.go
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/
external.go
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// Copyright 2023 Matrix Origin
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
package moarray
import (
"github.com/matrixorigin/matrixone/pkg/common/moerr"
"github.com/matrixorigin/matrixone/pkg/container/types"
"github.com/matrixorigin/matrixone/pkg/vectorize/momath"
"gonum.org/v1/gonum/mat"
"math"
)
// These functions are exposed externally via SQL API.
func Add[T types.RealNumbers](v1, v2 []T) ([]T, error) {
vec, err := ToGonumVectors[T](v1, v2)
if err != nil {
return nil, err
}
vec[0].AddVec(vec[0], vec[1])
return ToMoArray[T](vec[0]), nil
}
func Subtract[T types.RealNumbers](v1, v2 []T) ([]T, error) {
vec, err := ToGonumVectors[T](v1, v2)
if err != nil {
return nil, err
}
vec[0].SubVec(vec[0], vec[1])
return ToMoArray[T](vec[0]), nil
}
func Multiply[T types.RealNumbers](v1, v2 []T) ([]T, error) {
vec, err := ToGonumVectors[T](v1, v2)
if err != nil {
return nil, err
}
vec[0].MulElemVec(vec[0], vec[1])
return ToMoArray[T](vec[0]), nil
}
func Divide[T types.RealNumbers](v1, v2 []T) ([]T, error) {
// pre-check for division by zero
for i := 0; i < len(v2); i++ {
if v2[i] == 0 {
return nil, moerr.NewDivByZeroNoCtx()
}
}
vec, err := ToGonumVectors[T](v1, v2)
if err != nil {
return nil, err
}
vec[0].DivElemVec(vec[0], vec[1])
return ToMoArray[T](vec[0]), nil
}
// Compare returns an integer comparing two arrays/vectors lexicographically.
// TODO: this function might not be correct. we need to compare using tolerance for float values.
// TODO: need to check if we need len(v1)==len(v2) check.
func Compare[T types.RealNumbers](v1, v2 []T) int {
minLen := len(v1)
if len(v2) < minLen {
minLen = len(v2)
}
for i := 0; i < minLen; i++ {
if v1[i] < v2[i] {
return -1
} else if v1[i] > v2[i] {
return 1
}
}
if len(v1) < len(v2) {
return -1
} else if len(v1) > len(v2) {
return 1
}
return 0
}
/* ------------ [START] Performance critical functions. ------- */
func InnerProduct[T types.RealNumbers](v1, v2 []T) (float64, error) {
vec, err := ToGonumVectors[T](v1, v2)
if err != nil {
return 0, err
}
return mat.Dot(vec[0], vec[1]), nil
}
func L2Distance[T types.RealNumbers](v1, v2 []T) (float64, error) {
vec, err := ToGonumVectors[T](v1, v2)
if err != nil {
return 0, err
}
diff := mat.NewVecDense(vec[0].Len(), nil)
diff.SubVec(vec[0], vec[1])
return math.Sqrt(mat.Dot(diff, diff)), nil
}
func CosineDistance[T types.RealNumbers](v1, v2 []T) (float64, error) {
cosineSimilarity, err := CosineSimilarity[T](v1, v2)
if err != nil {
return 0, err
}
return 1 - cosineSimilarity, nil
}
func CosineSimilarity[T types.RealNumbers](v1, v2 []T) (float64, error) {
vec, err := ToGonumVectors[T](v1, v2)
if err != nil {
return 0, err
}
dotProduct := mat.Dot(vec[0], vec[1])
normVec1 := mat.Norm(vec[0], 2)
normVec2 := mat.Norm(vec[1], 2)
if normVec1 == 0 || normVec2 == 0 {
return 0, moerr.NewInternalErrorNoCtx("cosine_similarity: one of the vectors is zero")
}
cosineSimilarity := dotProduct / (normVec1 * normVec2)
// Handle precision issues. Clamp the cosine_similarity to the range [-1, 1].
if cosineSimilarity > 1.0 {
cosineSimilarity = 1.0
} else if cosineSimilarity < -1.0 {
cosineSimilarity = -1.0
}
// NOTE: Downcast the float64 cosine_similarity to float32 and check if it is
// 1.0 or -1.0 to avoid precision issue.
//
// Example for corner case:
// - cosine_similarity(a,a) = 1:
// - Without downcasting check, we get the following results:
// cosine_similarity( [0.46323407, 23.498016, 563.923, 56.076736, 8732.958] ,
// [0.46323407, 23.498016, 563.923, 56.076736, 8732.958] ) = 0.9999999999999998
// - With downcasting, we get the following results:
// cosine_similarity( [0.46323407, 23.498016, 563.923, 56.076736, 8732.958] ,
// [0.46323407, 23.498016, 563.923, 56.076736, 8732.958] ) = 1
//
// Reason:
// The reason for this check is
// 1. gonums mat.Dot, mat.Norm returns float64. In other databases, we mostly do float32 operations.
// 2. float64 operations are not exact.
// mysql> select 76586261.65813679/(8751.35770370157 *8751.35770370157);
//+-----------------------------------------------------------+
//| 76586261.65813679 / (8751.35770370157 * 8751.35770370157) |
//+-----------------------------------------------------------+
//| 1.000000000000 |
//+-----------------------------------------------------------+
//mysql> select cast(76586261.65813679 as double)/(8751.35770370157 * 8751.35770370157);
//+---------------------------------------------------------------------------+
//| cast(76586261.65813679 as double) / (8751.35770370157 * 8751.35770370157) |
//+---------------------------------------------------------------------------+
//| 0.9999999999999996 |
//+---------------------------------------------------------------------------+
// 3. We only need to handle the case for 1.0 and -1.0 with float32 precision.
// Rest of the cases can have float64 precision.
cosineSimilarityF32 := float32(cosineSimilarity)
if cosineSimilarityF32 == 1 {
cosineSimilarity = 1
} else if cosineSimilarityF32 == -1 {
cosineSimilarity = -1
}
return cosineSimilarity, nil
}
func NormalizeL2[T types.RealNumbers](v1 []T) ([]T, error) {
vec := ToGonumVector[T](v1)
norm := mat.Norm(vec, 2)
if norm == 0 {
return nil, moerr.NewInternalErrorNoCtx("normalize_l2: cannot normalize a zero vector")
}
vec.ScaleVec(1/norm, vec)
return ToMoArray[T](vec), nil
}
// L1Norm returns l1 distance to origin.
func L1Norm[T types.RealNumbers](v []T) (float64, error) {
vec := ToGonumVector[T](v)
return mat.Norm(vec, 1), nil
}
// L2Norm returns l2 distance to origin.
func L2Norm[T types.RealNumbers](v []T) (float64, error) {
vec := ToGonumVector[T](v)
return mat.Norm(vec, 2), nil
}
/* ------------ [END] Performance critical functions. ------- */
/* ------------ [START] mat.VecDense not supported functions ------- */
func Abs[T types.RealNumbers](v []T) (res []T, err error) {
n := len(v)
res = make([]T, n)
for i := 0; i < n; i++ {
res[i], err = momath.AbsSigned[T](v[i])
if err != nil {
return nil, err
}
}
return res, nil
}
func Sqrt[T types.RealNumbers](v []T) (res []float64, err error) {
n := len(v)
res = make([]float64, n)
for i := 0; i < n; i++ {
res[i], err = momath.Sqrt(float64(v[i]))
if err != nil {
return nil, err
}
}
return res, nil
}
func Summation[T types.RealNumbers](v []T) (float64, error) {
n := len(v)
var sum float64 = 0
for i := 0; i < n; i++ {
sum += float64(v[i])
}
return sum, nil
}
func Cast[I types.RealNumbers, O types.RealNumbers](in []I) (out []O, err error) {
n := len(in)
out = make([]O, n)
for i := 0; i < n; i++ {
out[i] = O(in[i])
}
return out, nil
}
/* ------------ [END] mat.VecDense not supported functions ------- */