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xerus
xerus
Commits
8de067f0
Commit
8de067f0
authored
May 24, 2017
by
Ben Huber
Browse files
reduced xALS for the examples to less than 100 lines of code
parent
573be0c8
Pipeline
#734
passed with stages
in 8 minutes and 29 seconds
Changes
2
Pipelines
1
Hide whitespace changes
Inline
Side-by-side
doc/new/_posts/1000-11-10-minimal_als.md
0 → 100644
View file @
8de067f0
---
layout
:
post
title
:
"
The
ALS
Algorithm"
date
:
1000-12-10
topic
:
"
Examples"
section
:
"
Examples"
---
__
tabsInit
# The ALS Algorithm
Implementing the ALS algorithm for the first time was the most important step for us to understand the TT format and its
intricacies. We still think that it is a good point to start so we want to provide a simple implementation of the ALS
algorithm as an example. Using the
`xerus`
library this will be an efficient implementation using less than 100 lines of code.
src/xerus/algorithms/xals.cpp
View file @
8de067f0
...
...
@@ -19,7 +19,7 @@
/**
* @file
* @brief Implementation of
th
e A
DF
variant
s
.
* @brief Implementation of
a simpl
e A
LS
variant.
*/
#include <xerus/algorithms/xals.h>
...
...
@@ -29,9 +29,6 @@
#include <xerus/indexedTensorMoveable.h>
#include <xerus/misc/basicArraySupport.h>
#ifdef _OPENMP
#include <omp.h>
#endif
namespace
xerus
{
...
...
@@ -52,50 +49,42 @@ namespace xerus {
public:
InternalSolver
(
TTTensor
&
_x
,
const
TTOperator
&
_A
,
const
TTTensor
&
_b
)
:
d
(
_x
.
degree
()),
leftAStack
(
d
),
rightAStack
(
d
),
leftBStack
(
d
),
rightBStack
(
d
),
x
(
_x
),
A
(
_A
),
b
(
_b
)
{
}
InternalSolver
(
TTTensor
&
_x
,
const
TTOperator
&
_A
,
const
TTTensor
&
_b
)
:
d
(
_x
.
degree
()),
x
(
_x
),
A
(
_A
),
b
(
_b
)
{
leftAStack
.
emplace_back
(
Tensor
::
ones
(
std
::
vector
<
size_t
>
(
d
,
1ul
)));
rightAStack
.
emplace_back
(
Tensor
::
ones
(
std
::
vector
<
size_t
>
(
d
,
1ul
)));
leftBStack
.
emplace_back
(
Tensor
::
ones
(
std
::
vector
<
size_t
>
(
d
,
1ul
)));
rightBStack
.
emplace_back
(
Tensor
::
ones
(
std
::
vector
<
size_t
>
(
d
,
1ul
)));
}
void
calc
_left_stack
(
const
size_t
_position
)
{
Tensor
xi
=
x
.
get_component
(
_position
);
Tensor
Ai
=
A
.
get_component
(
_position
);
Tensor
bi
=
b
.
get_component
(
_position
);
void
push
_left_stack
(
const
size_t
_position
)
{
const
Tensor
&
xi
=
x
.
get_component
(
_position
);
const
Tensor
&
Ai
=
A
.
get_component
(
_position
);
const
Tensor
&
bi
=
b
.
get_component
(
_position
);
if
(
_position
==
0
)
{
xi
.
reinterpret_dimensions
({
xi
.
dimensions
[
1
],
xi
.
dimensions
[
2
]});
Ai
.
reinterpret_dimensions
({
Ai
.
dimensions
[
1
],
Ai
.
dimensions
[
2
],
Ai
.
dimensions
[
3
]});
bi
.
reinterpret_dimensions
({
bi
.
dimensions
[
1
],
bi
.
dimensions
[
2
]});
leftAStack
[
_position
](
i1
,
i2
,
i3
)
=
xi
(
k1
,
i1
)
*
Ai
(
k1
,
k2
,
i2
)
*
xi
(
k2
,
i3
);
leftBStack
[
_position
](
i1
,
i2
)
=
xi
(
k1
,
i1
)
*
bi
(
k1
,
i2
);
}
else
{
leftAStack
[
_position
](
i1
,
i2
,
i3
)
=
leftAStack
[
_position
-
1
](
j1
,
j2
,
j3
)
*
xi
(
j1
,
k1
,
i1
)
*
Ai
(
j2
,
k1
,
k2
,
i2
)
*
xi
(
j3
,
k2
,
i3
);
leftBStack
[
_position
](
i1
,
i2
)
=
leftBStack
[
_position
-
1
](
j1
,
j2
)
*
xi
(
j1
,
k1
,
i1
)
*
bi
(
j2
,
k1
,
i2
);
}
Tensor
tmpA
,
tmpB
;
tmpA
(
i1
,
i2
,
i3
)
=
leftAStack
.
back
()(
j1
,
j2
,
j3
)
*
xi
(
j1
,
k1
,
i1
)
*
Ai
(
j2
,
k1
,
k2
,
i2
)
*
xi
(
j3
,
k2
,
i3
);
leftAStack
.
emplace_back
(
std
::
move
(
tmpA
));
tmpB
(
i1
,
i2
)
=
leftBStack
.
back
()(
j1
,
j2
)
*
xi
(
j1
,
k1
,
i1
)
*
bi
(
j2
,
k1
,
i2
);
leftBStack
.
emplace_back
(
std
::
move
(
tmpB
));
}
void
calc
_right_stack
(
const
size_t
_position
)
{
Tensor
xi
=
x
.
get_component
(
_position
);
Tensor
Ai
=
A
.
get_component
(
_position
);
Tensor
bi
=
b
.
get_component
(
_position
);
void
push
_right_stack
(
const
size_t
_position
)
{
const
Tensor
&
xi
=
x
.
get_component
(
_position
);
const
Tensor
&
Ai
=
A
.
get_component
(
_position
);
const
Tensor
&
bi
=
b
.
get_component
(
_position
);
if
(
_position
==
d
-
1
)
{
xi
.
reinterpret_dimensions
({
xi
.
dimensions
[
0
],
xi
.
dimensions
[
1
]});
Ai
.
reinterpret_dimensions
({
Ai
.
dimensions
[
0
],
Ai
.
dimensions
[
1
],
Ai
.
dimensions
[
2
]});
bi
.
reinterpret_dimensions
({
bi
.
dimensions
[
0
],
bi
.
dimensions
[
1
]});
rightAStack
[
_position
](
i1
,
i2
,
i3
)
=
xi
(
i1
,
k1
)
*
Ai
(
i2
,
k1
,
k2
)
*
xi
(
i3
,
k2
);
rightBStack
[
_position
](
i1
,
i2
)
=
xi
(
i1
,
k1
)
*
bi
(
i2
,
k1
);
}
else
{
rightAStack
[
_position
](
i1
,
i2
,
i3
)
=
xi
(
i1
,
k1
,
j1
)
*
Ai
(
i2
,
k1
,
k2
,
j2
)
*
xi
(
i3
,
k2
,
j3
)
*
rightAStack
[
_position
+
1
](
j1
,
j2
,
j3
);
rightBStack
[
_position
](
i1
,
i2
)
=
xi
(
i1
,
k1
,
j1
)
*
bi
(
i2
,
k1
,
j2
)
*
rightBStack
[
_position
+
1
](
j1
,
j2
);
}
Tensor
tmpA
,
tmpB
;
tmpA
(
i1
,
i2
,
i3
)
=
xi
(
i1
,
k1
,
j1
)
*
Ai
(
i2
,
k1
,
k2
,
j2
)
*
xi
(
i3
,
k2
,
j3
)
*
rightAStack
.
back
()(
j1
,
j2
,
j3
);
rightAStack
.
emplace_back
(
std
::
move
(
tmpA
));
tmpB
(
i1
,
i2
)
=
xi
(
i1
,
k1
,
j1
)
*
bi
(
i2
,
k1
,
j2
)
*
rightBStack
.
back
()(
j1
,
j2
);
rightBStack
.
emplace_back
(
std
::
move
(
tmpB
));
}
double
calc_residual_norm
()
{
const
Index
i
,
j
;
TTTensor
tmp
;
tmp
(
i
&
0
)
=
A
(
i
/
2
,
j
/
2
)
*
x
(
j
&
0
)
-
b
(
i
&
0
);
tmp
(
i
1
&
0
)
=
A
(
i
1
/
2
,
j
1
/
2
)
*
x
(
j
1
&
0
)
-
b
(
i
1
&
0
);
return
frob_norm
(
tmp
);
}
...
...
@@ -103,13 +92,12 @@ namespace xerus {
void
solve
()
{
const
double
solutionsNorm
=
frob_norm
(
b
);
std
::
vector
<
double
>
residuals
(
10
,
1000.0
);
const
size_t
maxIterations
=
1
;
const
size_t
maxIterations
=
1000
;
// Rebuild right stack
x
.
move_core
(
0
,
true
);
for
(
size_t
corePosition
=
d
-
1
;
corePosition
>
0
;
--
corePosition
)
{
calc
_right_stack
(
corePosition
);
for
(
size_t
pos
=
d
-
1
;
pos
>
0
;
--
pos
)
{
push
_right_stack
(
pos
);
}
for
(
size_t
iteration
=
0
;
maxIterations
==
0
||
iteration
<
maxIterations
;
++
iteration
)
{
...
...
@@ -127,79 +115,30 @@ namespace xerus {
for
(
size_t
corePosition
=
0
;
corePosition
<
d
;
++
corePosition
)
{
Tensor
op
,
rhs
;
Tensor
Ai
=
A
.
get_component
(
corePosition
);
Tensor
bi
=
b
.
get_component
(
corePosition
);
const
Tensor
&
Ai
=
A
.
get_component
(
corePosition
);
const
Tensor
&
bi
=
b
.
get_component
(
corePosition
);
if
(
corePosition
==
0
)
{
Ai
.
reinterpret_dimensions
({
Ai
.
dimensions
[
1
],
Ai
.
dimensions
[
2
],
Ai
.
dimensions
[
3
]});
bi
.
reinterpret_dimensions
({
bi
.
dimensions
[
1
],
bi
.
dimensions
[
2
]});
op
(
i2
,
i3
,
j2
,
j3
)
=
Ai
(
i2
,
j2
,
k2
)
*
rightAStack
[
corePosition
+
1
](
i3
,
k2
,
j3
);
rhs
(
i2
,
i3
)
=
bi
(
i2
,
k2
)
*
rightBStack
[
corePosition
+
1
](
i3
,
k2
);
}
else
if
(
corePosition
==
d
-
1
)
{
Ai
.
reinterpret_dimensions
({
Ai
.
dimensions
[
0
],
Ai
.
dimensions
[
1
],
Ai
.
dimensions
[
2
]});
bi
.
reinterpret_dimensions
({
bi
.
dimensions
[
0
],
bi
.
dimensions
[
1
]});
op
(
i1
,
i2
,
j1
,
j2
)
=
leftAStack
[
corePosition
-
1
](
i1
,
k1
,
j1
)
*
Ai
(
k1
,
i2
,
j2
);
rhs
(
i1
,
i2
)
=
leftBStack
[
corePosition
-
1
](
i1
,
k1
)
*
bi
(
k1
,
i2
);
}
else
{
op
(
i1
,
i2
,
i3
,
j1
,
j2
,
j3
)
=
leftAStack
[
corePosition
-
1
](
i1
,
k1
,
j1
)
*
Ai
(
k1
,
i2
,
j2
,
k2
)
*
rightAStack
[
corePosition
+
1
](
i3
,
k2
,
j3
);
rhs
(
i1
,
i2
,
i3
)
=
leftBStack
[
corePosition
-
1
](
i1
,
k1
)
*
bi
(
k1
,
i2
,
k2
)
*
rightBStack
[
corePosition
+
1
](
i3
,
k2
);
}
solve_least_squares
(
x
.
component
(
corePosition
),
op
,
rhs
,
0
);
op
(
i1
,
i2
,
i3
,
j1
,
j2
,
j3
)
=
leftAStack
.
back
()(
i1
,
k1
,
j1
)
*
Ai
(
k1
,
i2
,
j2
,
k2
)
*
rightAStack
.
back
()(
i3
,
k2
,
j3
);
rhs
(
i1
,
i2
,
i3
)
=
leftBStack
.
back
()(
i1
,
k1
)
*
bi
(
k1
,
i2
,
k2
)
*
rightBStack
.
back
()(
i3
,
k2
);
if
(
corePosition
==
0
)
{
x
.
component
(
corePosition
).
reinterpret_dimensions
({
1
,
x
.
component
(
corePosition
).
dimensions
[
0
],
x
.
component
(
corePosition
).
dimensions
[
1
]});
}
else
if
(
corePosition
==
d
-
1
)
{
x
.
component
(
corePosition
).
reinterpret_dimensions
({
x
.
component
(
corePosition
).
dimensions
[
0
],
x
.
component
(
corePosition
).
dimensions
[
1
],
1
});
}
xerus
::
solve
(
x
.
component
(
corePosition
),
op
,
rhs
,
0
);
// If we have not yet reached the end of the sweep we need to take care of the core and update our stacks
if
(
corePosition
+
1
<
d
)
{
x
.
move_core
(
corePosition
+
1
,
true
);
calc_left_stack
(
corePosition
);
push_left_stack
(
corePosition
);
rightAStack
.
pop_back
();
rightBStack
.
pop_back
();
}
}
// Sweep Right -> Left
// Sweep Right -> Left : only move core and update stacks
x
.
move_core
(
0
,
true
);
for
(
size_t
corePosition
=
d
-
1
;
corePosition
>
0
;
--
corePosition
)
{
// Tensor op, rhs;
//
// Tensor Ai = A.get_component(corePosition);
// Tensor bi = b.get_component(corePosition);
//
// if(corePosition == 0) {
// Ai.reinterpret_dimensions({Ai.dimensions[1], Ai.dimensions[2], Ai.dimensions[3]});
// bi.reinterpret_dimensions({bi.dimensions[1], bi.dimensions[2]});
//
// op(i2, i3, j2, j3) = Ai(i2, j2, k2)*rightAStack[corePosition+1](i3, k2, j3);
// rhs(i2, i3) = bi(i2, k2)*rightBStack[corePosition+1](i3, k2);
// } else if(corePosition == d-1) {
// Ai.reinterpret_dimensions({Ai.dimensions[0], Ai.dimensions[1], Ai.dimensions[2]});
// bi.reinterpret_dimensions({bi.dimensions[0], bi.dimensions[1]});
//
// op(i1, i2, j1, j2) = leftAStack[corePosition-1](i1, k1, j1)*Ai(k1, i2, j2);
// rhs(i1, i2) = leftBStack[corePosition-1](i1, k1)*bi(k1, i2);
// } else {
// op(i1, i2, i3, j1, j2, j3) = leftAStack[corePosition-1](i1, k1, j1)*Ai(k1, i2, j2, k2)*rightAStack[corePosition+1](i3, k2, j3);
// rhs(i1, i2, i3) = leftBStack[corePosition-1](i1, k1)*bi(k1, i2, k2)*rightBStack[corePosition+1](i3, k2);
// }
//
// solve_least_squares(x.component(corePosition), op, rhs, 0);
//
// if(corePosition == 0) {
// x.component(corePosition).reinterpret_dimensions({1, x.component(corePosition).dimensions[0], x.component(corePosition).dimensions[1]});
// } else if(corePosition == d-1) {
// x.component(corePosition).reinterpret_dimensions({x.component(corePosition).dimensions[0], x.component(corePosition).dimensions[1], 1});
// }
// If we have not yet reached the end of the sweep we need to take care of the core and update our stacks
if
(
corePosition
>
0
)
{
x
.
move_core
(
corePosition
-
1
,
true
);
calc_right_stack
(
corePosition
);
}
push_right_stack
(
corePosition
);
leftAStack
.
pop_back
();
leftBStack
.
pop_back
();
}
}
...
...
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