File VectorTransform.h

namespace faiss

Implementation of k-means clustering with many variants.

Copyright (c) Facebook, Inc. and its affiliates.

This source code is licensed under the MIT license found in the LICENSE file in the root directory of this source tree.

IDSelector is intended to define a subset of vectors to handle (for removal or as subset to search)

PQ4 SIMD packing and accumulation functions

The basic kernel accumulates nq query vectors with bbs = nb * 2 * 16 vectors and produces an output matrix for that. It is interesting for nq * nb <= 4, otherwise register spilling becomes too large.

The implementation of these functions is spread over 3 cpp files to reduce parallel compile times. Templates are instantiated explicitly.

This file contains callbacks for kernels that compute distances.

Throughout the library, vectors are provided as float * pointers. Most algorithms can be optimized when several vectors are processed (added/searched) together in a batch. In this case, they are passed in as a matrix. When n vectors of size d are provided as float * x, component j of vector i is

x[ i * d + j ]

where 0 <= i < n and 0 <= j < d. In other words, matrices are always compact. When specifying the size of the matrix, we call it an n*d matrix, which implies a row-major storage.

I/O functions can read/write to a filename, a file handle or to an object that abstracts the medium.

The read functions return objects that should be deallocated with delete. All references within these objectes are owned by the object.

Definition of inverted lists + a few common classes that implement the interface.

Since IVF (inverted file) indexes are of so much use for large-scale use cases, we group a few functions related to them in this small library. Most functions work both on IndexIVFs and IndexIVFs embedded within an IndexPreTransform.

In this file are the implementations of extra metrics beyond L2 and inner product

Implements a few neural net layers, mainly to support QINCo

Defines a few objects that apply transformations to a set of vectors Often these are pre-processing steps.

struct VectorTransform

#include <VectorTransform.h>

Any transformation applied on a set of vectors

Subclassed by faiss::CenteringTransform, faiss::ITQTransform, faiss::LinearTransform, faiss::NormalizationTransform, faiss::RemapDimensionsTransform

Public Functions

inline explicit VectorTransform(int d_in = 0, int d_out = 0)

! output dimension

virtual void train(idx_t n, const float *x)

Perform training on a representative set of vectors. Does nothing by default.

Parameters:

• n – nb of training vectors

• x – training vecors, size n * d

float *apply(idx_t n, const float *x) const

apply the transformation and return the result in an allocated pointer

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

Returns:

output vectors, size n * d_out

virtual void apply_noalloc(idx_t n, const float *x, float *xt) const = 0

apply the transformation and return the result in a provided matrix

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

• xt – output vectors, size n * d_out

virtual void reverse_transform(idx_t n, const float *xt, float *x) const

reverse transformation. May not be implemented or may return approximate result

virtual void check_identical(const VectorTransform &other) const = 0

inline virtual ~VectorTransform()

Public Members

int d_in

int d_out

! input dimension

bool is_trained

set if the VectorTransform does not require training, or if training is done already

struct LinearTransform : public faiss::VectorTransform

#include <VectorTransform.h>

Generic linear transformation, with bias term applied on output y = A * x + b

Subclassed by faiss::ITQMatrix, faiss::OPQMatrix, faiss::PCAMatrix, faiss::RandomRotationMatrix

Public Functions

explicit LinearTransform(int d_in = 0, int d_out = 0, bool have_bias = false)

both d_in > d_out and d_out < d_in are supported

virtual void apply_noalloc(idx_t n, const float *x, float *xt) const override

same as apply, but result is pre-allocated

void transform_transpose(idx_t n, const float *y, float *x) const

compute x = A^T * (x - b) is reverse transform if A has orthonormal lines

virtual void reverse_transform(idx_t n, const float *xt, float *x) const override

works only if is_orthonormal

void set_is_orthonormal()

compute A^T * A to set the is_orthonormal flag

void print_if_verbose(const char *name, const std::vector<double> &mat, int n, int d) const

virtual void check_identical(const VectorTransform &other) const override

inline ~LinearTransform() override

virtual void train(idx_t n, const float *x)

Perform training on a representative set of vectors. Does nothing by default.

Parameters:

• n – nb of training vectors

• x – training vecors, size n * d

float *apply(idx_t n, const float *x) const

apply the transformation and return the result in an allocated pointer

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

Returns:

output vectors, size n * d_out

Public Members

bool have_bias

bool is_orthonormal

! whether to use the bias term

check if matrix A is orthonormal (enables reverse_transform)

std::vector<float> A

Transformation matrix, size d_out * d_in.

std::vector<float> b

bias vector, size d_out

bool verbose

int d_in

int d_out

! input dimension

bool is_trained

set if the VectorTransform does not require training, or if training is done already

struct RandomRotationMatrix : public faiss::LinearTransform

#include <VectorTransform.h>

Randomly rotate a set of vectors.

Public Functions

inline RandomRotationMatrix(int d_in, int d_out)

both d_in > d_out and d_out < d_in are supported

void init(int seed)

must be called before the transform is used

virtual void train(idx_t n, const float *x) override

Perform training on a representative set of vectors. Does nothing by default.

Parameters:

• n – nb of training vectors

• x – training vecors, size n * d

inline RandomRotationMatrix()

virtual void apply_noalloc(idx_t n, const float *x, float *xt) const override

same as apply, but result is pre-allocated

void transform_transpose(idx_t n, const float *y, float *x) const

compute x = A^T * (x - b) is reverse transform if A has orthonormal lines

virtual void reverse_transform(idx_t n, const float *xt, float *x) const override

works only if is_orthonormal

void set_is_orthonormal()

compute A^T * A to set the is_orthonormal flag

void print_if_verbose(const char *name, const std::vector<double> &mat, int n, int d) const

virtual void check_identical(const VectorTransform &other) const override

float *apply(idx_t n, const float *x) const

apply the transformation and return the result in an allocated pointer

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

Returns:

output vectors, size n * d_out

Public Members

bool have_bias

bool is_orthonormal

! whether to use the bias term

check if matrix A is orthonormal (enables reverse_transform)

std::vector<float> A

Transformation matrix, size d_out * d_in.

std::vector<float> b

bias vector, size d_out

bool verbose

int d_in

int d_out

! input dimension

bool is_trained

set if the VectorTransform does not require training, or if training is done already

struct PCAMatrix : public faiss::LinearTransform

#include <VectorTransform.h>

Applies a principal component analysis on a set of vectors, with optionally whitening and random rotation.

Public Functions

explicit PCAMatrix(int d_in = 0, int d_out = 0, float eigen_power = 0, bool random_rotation = false)

virtual void train(idx_t n, const float *x) override

train on n vectors. If n < d_in then the eigenvector matrix will be completed with 0s

void copy_from(const PCAMatrix &other)

copy pre-trained PCA matrix

void prepare_Ab()

called after mean, PCAMat and eigenvalues are computed

virtual void apply_noalloc(idx_t n, const float *x, float *xt) const override

same as apply, but result is pre-allocated

void transform_transpose(idx_t n, const float *y, float *x) const

compute x = A^T * (x - b) is reverse transform if A has orthonormal lines

virtual void reverse_transform(idx_t n, const float *xt, float *x) const override

works only if is_orthonormal

void set_is_orthonormal()

compute A^T * A to set the is_orthonormal flag

void print_if_verbose(const char *name, const std::vector<double> &mat, int n, int d) const

virtual void check_identical(const VectorTransform &other) const override

float *apply(idx_t n, const float *x) const

apply the transformation and return the result in an allocated pointer

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

Returns:

output vectors, size n * d_out

Public Members

float eigen_power

after transformation the components are multiplied by eigenvalues^eigen_power

=0: no whitening =-0.5: full whitening

float epsilon

value added to eigenvalues to avoid division by 0 when whitening

bool random_rotation

random rotation after PCA

size_t max_points_per_d

ratio between # training vectors and dimension

int balanced_bins

try to distribute output eigenvectors in this many bins

std::vector<float> mean

Mean, size d_in.

std::vector<float> eigenvalues

eigenvalues of covariance matrix (= squared singular values)

std::vector<float> PCAMat

PCA matrix, size d_in * d_in.

bool have_bias

bool is_orthonormal

! whether to use the bias term

check if matrix A is orthonormal (enables reverse_transform)

std::vector<float> A

Transformation matrix, size d_out * d_in.

std::vector<float> b

bias vector, size d_out

bool verbose

int d_in

int d_out

! input dimension

bool is_trained

set if the VectorTransform does not require training, or if training is done already

struct ITQMatrix : public faiss::LinearTransform

#include <VectorTransform.h>

ITQ implementation from

Iterative quantization: A procrustean approach to learning binary codes for large-scale image retrieval,

Yunchao Gong, Svetlana Lazebnik, Albert Gordo, Florent Perronnin, PAMI’12.

Public Functions

explicit ITQMatrix(int d = 0)

virtual void train(idx_t n, const float *x) override

Perform training on a representative set of vectors. Does nothing by default.

Parameters:

• n – nb of training vectors

• x – training vecors, size n * d

virtual void apply_noalloc(idx_t n, const float *x, float *xt) const override

same as apply, but result is pre-allocated

void transform_transpose(idx_t n, const float *y, float *x) const

compute x = A^T * (x - b) is reverse transform if A has orthonormal lines

virtual void reverse_transform(idx_t n, const float *xt, float *x) const override

works only if is_orthonormal

void set_is_orthonormal()

compute A^T * A to set the is_orthonormal flag

void print_if_verbose(const char *name, const std::vector<double> &mat, int n, int d) const

virtual void check_identical(const VectorTransform &other) const override

float *apply(idx_t n, const float *x) const

apply the transformation and return the result in an allocated pointer

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

Returns:

output vectors, size n * d_out

Public Members

int max_iter

int seed

std::vector<double> init_rotation

bool have_bias

bool is_orthonormal

! whether to use the bias term

check if matrix A is orthonormal (enables reverse_transform)

std::vector<float> A

Transformation matrix, size d_out * d_in.

std::vector<float> b

bias vector, size d_out

bool verbose

int d_in

int d_out

! input dimension

bool is_trained

set if the VectorTransform does not require training, or if training is done already

struct ITQTransform : public faiss::VectorTransform

#include <VectorTransform.h>

The full ITQ transform, including normalizations and PCA transformation

Public Functions

explicit ITQTransform(int d_in = 0, int d_out = 0, bool do_pca = false)

virtual void train(idx_t n, const float *x) override

Perform training on a representative set of vectors. Does nothing by default.

Parameters:

• n – nb of training vectors

• x – training vecors, size n * d

virtual void apply_noalloc(idx_t n, const float *x, float *xt) const override

apply the transformation and return the result in a provided matrix

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

• xt – output vectors, size n * d_out

virtual void check_identical(const VectorTransform &other) const override

float *apply(idx_t n, const float *x) const

apply the transformation and return the result in an allocated pointer

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

Returns:

output vectors, size n * d_out

virtual void reverse_transform(idx_t n, const float *xt, float *x) const

reverse transformation. May not be implemented or may return approximate result

Public Members

std::vector<float> mean

bool do_pca

ITQMatrix itq

int max_train_per_dim

max training points per dimension

LinearTransform pca_then_itq

int d_in

int d_out

! input dimension

bool is_trained

set if the VectorTransform does not require training, or if training is done already

struct OPQMatrix : public faiss::LinearTransform

#include <VectorTransform.h>

Applies a rotation to align the dimensions with a PQ to minimize the reconstruction error. Can be used before an IndexPQ or an IndexIVFPQ. The method is the non-parametric version described in:

“Optimized Product Quantization for Approximate Nearest Neighbor Search” Tiezheng Ge, Kaiming He, Qifa Ke, Jian Sun, CVPR’13

Public Functions

explicit OPQMatrix(int d = 0, int M = 1, int d2 = -1)

if d2 != -1, output vectors of this dimension

virtual void train(idx_t n, const float *x) override

Perform training on a representative set of vectors. Does nothing by default.

Parameters:

• n – nb of training vectors

• x – training vecors, size n * d

virtual void apply_noalloc(idx_t n, const float *x, float *xt) const override

same as apply, but result is pre-allocated

void transform_transpose(idx_t n, const float *y, float *x) const

compute x = A^T * (x - b) is reverse transform if A has orthonormal lines

virtual void reverse_transform(idx_t n, const float *xt, float *x) const override

works only if is_orthonormal

void set_is_orthonormal()

compute A^T * A to set the is_orthonormal flag

void print_if_verbose(const char *name, const std::vector<double> &mat, int n, int d) const

virtual void check_identical(const VectorTransform &other) const override

float *apply(idx_t n, const float *x) const

apply the transformation and return the result in an allocated pointer

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

Returns:

output vectors, size n * d_out

Public Members

int M

nb of subquantizers

int niter = 50

Number of outer training iterations.

int niter_pq = 4

Number of training iterations for the PQ.

int niter_pq_0 = 40

same, for the first outer iteration

size_t max_train_points = 256 * 256

if there are too many training points, resample

bool verbose = false

ProductQuantizer *pq = nullptr

if non-NULL, use this product quantizer for training should be constructed with (d_out, M, _)

bool have_bias

bool is_orthonormal

! whether to use the bias term

check if matrix A is orthonormal (enables reverse_transform)

std::vector<float> A

Transformation matrix, size d_out * d_in.

std::vector<float> b

bias vector, size d_out

int d_in

int d_out

! input dimension

bool is_trained

set if the VectorTransform does not require training, or if training is done already

struct RemapDimensionsTransform : public faiss::VectorTransform

#include <VectorTransform.h>

remap dimensions for intput vectors, possibly inserting 0s strictly speaking this is also a linear transform but we don’t want to compute it with matrix multiplies

Public Functions

RemapDimensionsTransform(int d_in, int d_out, const int *map)

RemapDimensionsTransform(int d_in, int d_out, bool uniform = true)

remap input to output, skipping or inserting dimensions as needed if uniform: distribute dimensions uniformly otherwise just take the d_out first ones.

virtual void apply_noalloc(idx_t n, const float *x, float *xt) const override

apply the transformation and return the result in a provided matrix

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

• xt – output vectors, size n * d_out

virtual void reverse_transform(idx_t n, const float *xt, float *x) const override

reverse transform correct only when the mapping is a permutation

inline RemapDimensionsTransform()

virtual void check_identical(const VectorTransform &other) const override

virtual void train(idx_t n, const float *x)

Perform training on a representative set of vectors. Does nothing by default.

Parameters:

• n – nb of training vectors

• x – training vecors, size n * d

float *apply(idx_t n, const float *x) const

apply the transformation and return the result in an allocated pointer

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

Returns:

output vectors, size n * d_out

Public Members

std::vector<int> map

map from output dimension to input, size d_out -1 -> set output to 0

int d_in

int d_out

! input dimension

bool is_trained

set if the VectorTransform does not require training, or if training is done already

struct NormalizationTransform : public faiss::VectorTransform

#include <VectorTransform.h>

per-vector normalization

Public Functions

explicit NormalizationTransform(int d, float norm = 2.0)

NormalizationTransform()

virtual void apply_noalloc(idx_t n, const float *x, float *xt) const override

apply the transformation and return the result in a provided matrix

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

• xt – output vectors, size n * d_out

virtual void reverse_transform(idx_t n, const float *xt, float *x) const override

Identity transform since norm is not revertible.

virtual void check_identical(const VectorTransform &other) const override

virtual void train(idx_t n, const float *x)

Perform training on a representative set of vectors. Does nothing by default.

Parameters:

• n – nb of training vectors

• x – training vecors, size n * d

float *apply(idx_t n, const float *x) const

apply the transformation and return the result in an allocated pointer

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

Returns:

output vectors, size n * d_out

Public Members

float norm

int d_in

int d_out

! input dimension

bool is_trained

set if the VectorTransform does not require training, or if training is done already

struct CenteringTransform : public faiss::VectorTransform

#include <VectorTransform.h>

Subtract the mean of each component from the vectors.

Public Functions

explicit CenteringTransform(int d = 0)

virtual void train(idx_t n, const float *x) override

train on n vectors.

virtual void apply_noalloc(idx_t n, const float *x, float *xt) const override

subtract the mean

virtual void reverse_transform(idx_t n, const float *xt, float *x) const override

add the mean

virtual void check_identical(const VectorTransform &other) const override

float *apply(idx_t n, const float *x) const

apply the transformation and return the result in an allocated pointer

Parameters:

• n – number of vectors to transform

• x – input vectors, size n * d_in

Returns:

output vectors, size n * d_out

Public Members

std::vector<float> mean

Mean, size d_in = d_out.

int d_in

int d_out

! input dimension

bool is_trained

set if the VectorTransform does not require training, or if training is done already