LinearAlgebra

namespace: Rindow\Math\Matrix
classname: LinearAlgebra

Linear algebra library for arrays. For this library, speed is more important than flexibility.

The input data area and output data area are shared by many functions. So note that the contents of the input array will be destroyed.

The BLAS library and the MATH library specified by “MatrixOperator” are used internally. When the OpenBLAS FFI is specified, high-speed operations are possible.

Methods

constructor
array
toNDArray
scalar
isInt
isFloat
expandDims
squeeze
alloc
zeros
ones
zerosLike
fill
astype
copy
scal
axpy
dot
asum
iamax
iamin
amax
amin
nrm2
rotg
rot
swap
gemv
gemm
matmul
symm
syrk
syr2k
trmm
trsm
svd
omatcopy
sum
imax
imin
max
min
increment
reciprocal
maximum
minimum
greater
greaterEqual
less
lessEqual
multiply
add
square
sqrt
rsqrt
pow
exp
log
tanh
sin
cos
tan
equal
notEqual
not
duplicate
transpose
gather
gatherb
scatter
scatterb
scatterAdd
scatterbAdd
slice
stick
stack
concat
split
repeat
onehot
softmax
reduceArgMax
reduceMax
reduceSum
reduceMean
im2col
col2im
randomUniform
randomNormal
randomSequence
bandpart
imagecopy
searchsorted
cumsum
nan2num
isnan
linspace
range
einsum
einsum4p1
masking

constructor

$la = $matrixoperator->la();

Example

$mo = new MatrixOperator();
$la = $mo->la();

array

public function array(mixed $array, ?int $dtype=null) : NDArray

NDArray with value specified by PHP array type.

Arguments

array: PHP array or scalar, NDArray
- If an NDArray is provided, it will return as is.
dtype: data type.
- If omitted, default float type is used.

Example

$x = $mo->la()->array([[1,2],[3,4]],dtype:NDArray::float32);

toNDArray

public function toNDArray(NDArray $ndarray) : NDArray

Ensure that the data resides within the host memory.

Arguments

ndarray: NDArray
- If there is no data in the host memory, then we raise an exception.

Example

$x = $mo->la()->toNDArray($x);

scalar

public function scalar(mixed $array) : mixed

Convert scalar values in the NDArray to PHP scalars.

Arguments

array: NDArray or PHP scalar vaulue.
- If an PHP scalar vaulue is provided, it will return as is.

Example

$x = $mo->la()->scalar($x);

isInt

public function isInt(NDArray $value) : bool

Check if an array element is of type int.

Arguments

array: NDArray.

Result

isint: true if the array element is of type int.

Example

$isInt = $mo->la()->isInt($x);

isFloat

public function isFloat(NDArray $value) : bool

Check if an array element is of type float.

Arguments

array: NDArray.

Result

isFloat: true if the array element is of type float.

Example

$isFloat = $mo->la()->isFloat($x);

expandDims

public function expandDims(NDArray $x, int $axis) : NDArray

Expand the NDArray dimension.

Arguments

x: NDArray.
axis: Array dimension.

Example

$x = $mo->zeros([2,3]);
$x = $mo->la()->expandDims($x,axis:1);
// x->shape() : [2,1,3]

squeeze

public function squeeze(NDArray $x, ?int $axis=null) : NDArray

Reduces the dimensions of an array.

Arguments

x: NDArray.
axis: The dimension to reduce. Must have a size of 1
- If omitted, all dimensions with a size of 1 will be reduced.

Example

$x = $mo->zeros([2,1,3]);
$x = $mo->la()->squeeze($x,axis:1);
// x->shape() : [2,3]

alloc

public function alloc(array $shape,$dtype=null)

Creates the specified NDArray and does not initialize its contents.

Arguments

shape: Shape of array
dtype: data type of array

Example

$x = $mo->la()->alloc([2,2]);

zeros

$\begin{align*} X := 0 \end{align*}$

public function zeros(NDArray $X) : NDArray

Initialize the array with zeros.

Arguments

X: The array to be initialized

Result

An initialized array. The same instance as the input array.

Example

$x = $mo->la()->zeros($mo->la()->alloc([2,2]));

ones

$\begin{align*} X := 1 \end{align*}$

public function ones(NDArray $X) : NDArray

Initialize the array with ones.

Arguments

X: The array to be initialized

Result

An initialized array. The same instance as the input array.

Example

$x = $mo->la()->ones($mo->la()->alloc([2,2]));

zerosLike

$\begin{align*} X := 0 \end{align*}$

public function zerosLike(NDArray $X) : NDArray

allocate and initialize the array with zeros.

Arguments

X: An array referencing the shape and data type of a new array.

Result

An initialized array. The same instance as the input array.

Example

$origX = $mo->la()->alloc([2,2],dtype:NDArray:float32);
$x = $mo->la()->zerosLike($origX);

fill

$\begin{align*} X := n \end{align*}$

public function fill(
    $value,
    NDArray $X
    )

Initialize the array with zeros.

Arguments

value: fill value
X: Destination array

Result

The same instance as X.

Example

$x = $mo->la()->alloc([2,2]);
$mo->la()->fill(1.0, $x);
## x =>
## [[1,1]
##  [1,1]]

astype

$\begin{align*} y_i := \left \{ \begin{array}{l} 1 \hspace{5mm} ( x_i = y_i ) \\ 0 \hspace{5mm} ( x_i \neq y_i ) \end{array} \right. \end{align*}$

public function astype(NDArray $X, $dtype) : NDArray

Cast an array to a specified data type.

Arguments

X: the vector X.
dtype: data type.
- NDArray data type constant

Result

new vector.

Examples

use Interop\Polite\Math\Matrix\NDArray;
$x = $mo->array([[1,2,3],[4,5,6]],NDArray::float32);
$y = $mo->la()->astype($x,NDArray::uint8);
## y => [[1,2,3],[4,5,6]] <uint8>

copy

$\begin{align*} Y := X \end{align*}$

public function copy(
    NDArray $X,
    NDArray $Y=null ) : NDArray

Copy array elements

Arguments

X: Original vector.
Y: Destination vector.
- If omitted, it will be allocated automatically.

Result

Same instance as vector Y.

Example

$x = $mo->array([1,-2,-3]);
$y = $mo->la()->copy($x);
## y => [1.0, -2.0, -3.0]

scal

$\begin{align*} X := \alpha X \end{align*}$

public function scal(
    float $alpha,
    NDArray $X) : NDArray

Scales a vector by a constant.

Arguments

alpha: a constant.
X: a vector.
- Input and output are shared.

Result

The same instance as the input array.

Example

$x = $mo->array([1,2,3]);
$mo->la()->scale(2,$x);

axpy

$\begin{align*} Y := \alpha X + Y \end{align*}$

public function axpy(
    NDArray $X,
    NDArray $Y,
    float $alpha=null) : NDArray

Scales a vector by a constant.

Arguments

X: the vector X.
Y: the vector Y.
- Input and output are shared.
alpha: a constant.
- Default is 1.0.

Result

The same instance as the Y.

Example

$x = $mo->array([1,2,3]);
$y = $mo->array([1,2,3]);
$mo->la()->axpy($x,$y,2.0);
## y => [ 3.0, 6.0, 9.0]

dot

$\begin{align*} f = \sum_{k=0}^n x_k y_k \end{align*}$

public function dot(
    NDArray $X,
    NDArray $Y)

Dot product of vectors. Vectors are treated as one-dimensional arrays, regardless of shape.

Arguments

X: the vector X.
Y: the vector Y.

Result

value of result.

Example

$x = $mo->array([1,2,3]);
$y = $mo->array([1,2,3]);
$z = $mo->la()->dot($x,$y);
## z => 14.0

asum

$\begin{align*} f = \sum_{k=0}^n \begin{vmatrix}x_k\end{vmatrix} \end{align*}$

public function asum(NDArray $X) : float

Sum of absolute values of array elements

Arguments

X: the vector X.

Result

value of result.

Example

$x = $mo->array([1,-2,-3]);
$z = $mo->la()->asum($x);
## z => 6.0

iamax

$\begin{align*} f = \arg \max \begin{vmatrix}x_k\end{vmatrix} \end{align*}$

public function iamax(NDArray $X) : int

Get the element number of the maximum absolute value in array element

Arguments

X: the vector X.

Result

value of result.

Example

$x = $mo->array([1,-2,-3]);
$z = $mo->la()->iamax($x);
## z => 2

iamin

$\begin{align*} f = \arg \min \begin{vmatrix}x_k\end{vmatrix} \end{align*}$

public function iamin(NDArray $X) : int

Get the element number of the minimum absolute value in array element

Arguments

X: the vector X.

Result

value of result.

Example

$x = $mo->array([1,-2,-3]);
$z = $mo->la()->iamin($x);
## z => 0

amax

$\begin{align*} f = \max \begin{vmatrix}x_k\end{vmatrix} \end{align*}$

public function amax(NDArray $X) : float

Get the maximum absolute value in array element

Arguments

X: the vector X.

Result

value of result.

Example

$x = $mo->array([1,-2,-3]);
$z = $mo->la()->amax($x);
## z => -3.0

amin

$\begin{align*} f = \min \begin{vmatrix}x_k\end{vmatrix} \end{align*}$

public function amin(NDArray $X) : float

Get the minimum absolute value in array element

Arguments

X: the vector X.

Result

value of result.

Example

$x = $mo->array([1,-2,-3]);
$z = $mo->la()->amin($x);
## z => 1.0

nrm2

$\begin{align*} f = \sqrt{\sum_{k=0}^n (x_k)^2} \end{align*}$

public function nrm2(NDArray $X) : float

Get the norm value in array element

Arguments

X: the vector X.

Result

value of result.

Example

$x = $mo->array([1,2,3]);
$z = $mo->la()->nrm2($x);
## z => 3.7416574954987

rotg

$\begin{align*} r,z,c,s = rotg (x, y) \end{align*}$

public function rotg(
    NDArray $X,
    NDArray $Y,
    NDArray $R=null,
    NDArray $Z=null,
    NDArray $C=null,
    NDArray $S=null) : array

Get the Givens rotation.

Currently, complex numbers are supported only when the backend is OpenBLAS or PhpBLAS. CLBlast also does not support real or complex numbers at all.

Arguments

X: the value of axis X.
Y: the value of axis Y.

Result

array of result.

Example

$x = $mo->array(3.0);
$y = $mo->array(4.0);
[$r,$z,$c,$s] = $mo->la()->rotg($x,$y);
echo $r->toArray()."\n";
echo $z->toArray()."\n";
echo $c->toArray()."\n";
echo $s->toArray()."\n";
## r => 5
## z => 1.6666666269302
## c => 0.60000002384186
## s => 0.80000001192093

$x = $mo->array([3.0]);
$y = $mo->array([4.0]);
[$r,$z,$c,$s] = $mo->la()->rotg($x,$y);
echo $r[0]."\n";
echo $z[0]."\n";
echo $c[0]."\n";
echo $s[0]."\n";
## r => 5
## z => 1.6666666269302
## c => 0.60000002384186
## s => 0.80000001192093

rot

$\begin{align*} X,Y := rot (X,Y,c,s) \end{align*}$

public function rot(
    NDArray $X,
    NDArray $Y,
    NDArray $C,
    NDArray $S) : void

Get Coordinate rotation.

Currently, complex numbers are supported only when the backend is PhpBLAS. OpenBLAS does not support complex numbers because it has cblas_csrot but not cblas_crot. CLBlast also does not support real or complex numbers at all.

Arguments

X: the value of axis X.
Y: the value of axis Y.
c: the value of cos.
s: the value of sin.

Result

array of result.

Example

$x = $mo->array([1,2,3]);
$y = $mo->array([1,2,3]);
$c = $mo->array([cos(pi()/4)]);
$s = $mo->array([sin(pi()/4)]);
$mo->la()->rot($x,$y,$c,$s);
echo $mo->toString($x)."\n";
echo $mo->toString($y)."\n";
## x => [1.4142135381699,2.8284270763397,4.2426404953003]
## y => [0,0,0]

swap

$\begin{align*} x,y := y,x \end{align*}$

public function swap(NDArray $X, NDArray $Y) : void

Swap the value in array element

Arguments

X: the vector X.
Y: the vector Y.

Result

value of result.

Example

$x = $mo->array([1, 2, 3]);
$y = $mo->array([4, 5, 6]);
$mo->la()->swap($x,$y);
## x => [4, 5, 6]
## y => [1, 2, 3]

gemv

$\begin{align*} y := \alpha A \times x + \beta y \end{align*}$

public function gemv(
    NDArray $A,
    NDArray $X,
    float $alpha=null,
    float $beta=null,
    NDArray $Y=null,
    bool $trans=null,
    bool $conj=null,
    ) : NDArray

Cross product of matrix and vector

Arguments

A: A matrix.
X: X vector.
alpha: constant value.
- If omitted, default is 1.0
beta: constant value.
- If omitted, default is 0.0
Y: Y vector.
- If omitted, it will be allocated automatically.
- Input and output are shared.
trans: transpose A matrix.
- If omitted, default is false.
conj: conjugate A matrix.
- If omitted, default is the same trans.

Result

Same instance as vector Y.

Example

$a = $mo->array([[1,2,3],[4,5,6]]);
$x = $mo->array([1,2,3]);
$y = $mo->array([1,1]);
$mo->la()->gemv($a,$x,2,3,$y);
## y => [31.0, 67.0]

gemm

$\begin{align*} C := \alpha A \times B + \beta C \end{align*}$

public function gemm(
    NDArray $A,
    NDArray $B,
    float $alpha=null,
    float $beta=null,
    NDArray $C=null,
    bool $transA=null,
    bool $transB=null,
    bool $conjA=null,
    bool $conjB=null,
    ) : NDArray

Cross product of matrix and matrix

Arguments

A: A matrix.
B: B matrix.
alpha: constant value.
- If omitted, default is 0.1
beta: constant value.
- If omitted, default is 0.0
C: C matrix.
- If omitted, it will be allocated automatically.
- Input and output are shared.
transA: transpose A matrix.
- If omitted, it is false.
transB: transpose B matrix.
- If omitted, it is false.
conjA: conjugate A matrix.
- If omitted, it is the same transA.
conjB: transpose B matrix.
- If omitted, it is the same transB.

Result

Same instance as vector C.

Example

$a = $mo->array([[1,2,3],[4,5,6]]);
$b = $mo->array([[1,2],[3,4],[5,6]]);
$c = $mo->array([[1,2],[3,4]]);
$mo->la()->gemm($a,$b,2,3,$c);
## c => [[47,62],[107,140]]

matmul

$\begin{align*} C := \alpha A \times B + \beta C \end{align*}$

public function matmul(
    NDArray $A,
    NDArray $B,
    ?bool $transA=null,
    ?bool $transB=null,
    ?NDArray $C=null,
    float|object|null $alpha=null,
    float|object|null $beta=null,
    ?bool $conjA=null,
    ?bool $conjB=null,
    ) : NDArray

Calculates the matrix multiplication of two multidimensional arrays. Batch processing is also possible depending on the number of dimensions.

Arguments

A: A matrix.
B: B matrix.
transA: transpose A matrix.
- If omitted, it is false.
transB: transpose B matrix.
- If omitted, it is false.
C: C matrix.
- If omitted, it will be allocated automatically.
- Input and output are shared.
alpha: constant value.
- If omitted, default is 0.1
beta: constant value.
- If omitted, default is 0.0
conjA: conjugate A matrix.
- If omitted, it is the same transA.
conjB: conjugate B matrix.
- If omitted, it is the same transB.

Result

Same instance as vector C.

Example

$a = $mo->array([[1,2,3],[4,5,6]]);
$b = $mo->array([[1,2],[3,4],[5,6]]);
$c = $mo->array([[1,2],[3,4]]);
$mo->la()->matmul($a,$b,alpha:2,beta:3,C:$c);
## c => [[47,62],[107,140]]

symm

$\begin{align*} C := \left \{ \begin{array}{l} A = Symmetric matrix \\ \alpha \times A B + \beta C \hspace{5mm} ( right = false ) \\ \alpha \times B A + \beta C \hspace{5mm} ( right = true ) \end{array} \right. \end{align*}$

public function symm(
    NDArray $A,
    NDArray $B,
    float $alpha=null,
    float $beta=null,
    NDArray $C=null,
    bool $right=null,
    bool $lower=null
    ) : NDArray

Cross product of matrix and matrix

Arguments

A: A matrix.
B: B matrix.
alpha: constant value.
- If omitted, default is 0.1
beta: constant value.
- If omitted, default is 0.0
C: C matrix.
- If omitted, it will be allocated automatically.
- Input and output are shared.
right: multiply from right side.
- If omitted, it is false.
lower: use lower side.
- If omitted, it is false.

Result

Same instance as vector C.

Example

$a = $mo->array([
    [1,2,3],
    [0,5,6],
    [0,0,9],
]);
$b = $mo->array([[1,2],[3,4],[5,6]]);
$c = $mo->la()->symm($a,$b);
## c =>
##  [[22.0,28.0],
##   [47.0,60.0],
##   [66.0,84.0]]

syrk

$\begin{align*} C := \left \{ \begin{array}{l} \alpha \times A A^T + \beta C \hspace{5mm} ( trans = false ) \\ \alpha \times A^T A + \beta C \hspace{5mm} ( trans = true ) \end{array} \right. \end{align*}$

public function syrk(
    NDArray $A,
    float $alpha=null,
    float $beta=null,
    NDArray $C=null,
    bool $lower=null,
    bool $trans=null,
    bool $conj=null,
    ) : NDArray

Cross product of a matrix and transposed

Arguments

A: A matrix.
alpha: constant value.
- If omitted, default is 0.1
beta: constant value.
- If omitted, default is 0.0
C: C matrix.
- If omitted, it will be allocated automatically.
- Input and output are shared.
lower: use lower side result.
- If omitted, it is false.
trans: transpose A matrix.
- If omitted, it is false.
conj: conjugate A matrix.
- If omitted, it is the same trans.

Result

Same instance as vector C.

Example

$a = $mo->array([
    [1,2],
    [3,4],
    [5,6],
]);
$c = $mo->la()->syrk($a);
## c =>
## [[5.0,11.0,17.0],
##  [0.0,25.0,39.0],
##  [0.0,0.0,61.0]]

syr2k

$\begin{align*} C := \left \{ \begin{array}{l} \alpha \times A B^T + \alpha \times B A^T + \beta C \hspace{5mm} ( trans = false ) \\ \alpha \times B A^T + \alpha \times A B^T + \beta C \hspace{5mm} ( trans = true ) \end{array} \right. \end{align*}$

public function syr2k(
    NDArray $A,
    NDArray $B,
    float $alpha=null,
    float $beta=null,
    NDArray $C=null,
    bool $lower=null,
    bool $trans=null,
    bool $conj=null,
    ) : NDArray

Cross product of a matrix and transposed

Arguments

A: A matrix.
B: B matrix.
alpha: constant value.
- If omitted, default is 0.1
beta: constant value.
- If omitted, default is 0.0
C: C matrix.
- If omitted, it will be allocated automatically.
- Input and output are shared.
lower: use lower side result.
- If omitted, it is false.
trans: transpose A matrix.
- If omitted, it is false.
conj: conjugate A matrix.
- If omitted, it is the same trans.

Result

Same instance as vector C.

Example

$a = $mo->array([
    [1,2,3],
    [4,5,6],
    [7,8,9],
    [10,11,12],
]);
$b = $mo->array([
    [1,3,5],
    [2,4,6],
    [7,9,11],
    [8,10,12],
]);
$c = $mo->la()->syr2k($a,$b);
## c =>
## [[10.0, 22.0,  34.0],
##  [ 0.0, 50.0,  78.0],
##  [ 0.0,  0.0, 122.0]]

trmm

$\begin{align*} B := \left \{ \begin{array}{l} \alpha \times A B \hspace{5mm} ( trans = false ) \\ \alpha \times B A \hspace{5mm} ( trans = true ) \end{array} \right. \end{align*}$

public function trmm(
    NDArray $A,
    NDArray $B,
    float $alpha=null,
    bool $right=null,
    bool $lower=null,
    bool $trans=null,
    bool $conj=null,
    bool $unit=null) : NDArray

Cross product of a triangular matrix

Arguments

A: A matrix.
B: B matrix.
alpha: constant value.
- If omitted, default is 0.1
lower: use lower side.
- If omitted, it is false.
right: multiply from right side.
- If omitted, it is false.
trans: transpose A matrix.
- If omitted, it is false.
conj: conjugate A matrix.
- If omitted, it is the same trans.
unit: unitriangular.
- If omitted, it is false.

Result

Same instance as vector C.

Example

$a = $mo->array([
    [1,2,3],
    [0,4,5],
    [0,0,6],
]);
$b = $mo->array([
    [1,2,3,4],
    [5,6,7,8],
    [9,10,11,12],
]);
$mo->la()->trmm($a,$b);
## b =>
##  [[38.0, 44.0, 50.0, 56.0],
##   [65.0, 74.0, 83.0, 92.0],
##   [54.0, 60.0, 66.0, 72.0]]

trsm

$\begin{align*} B := \left \{ \begin{array}{l} \alpha \times A^{-1} B \hspace{5mm} ( trans = false ) \\ \alpha \times B A^{-1} \hspace{5mm} ( trans = true ) \end{array} \right. \end{align*}$

public function trsm(
    NDArray $A,
    NDArray $B,
    float $alpha=null,
    bool $right=null,
    bool $lower=null,
    bool $trans=null,
    bool $conj=null,
    bool $unit=null) : NDArray

Cross product of a triangular matrix

Arguments

A: A matrix.
B: B matrix.
alpha: constant value.
- If omitted, default is 0.1
right: multiply from right side.
- If omitted, it is false.
lower: use lower side.
- If omitted, it is false.
trans: transpose A matrix.
- If omitted, it is false.
conj: conjugate A matrix.
- If omitted, it is the same trans.
unit: unitriangular.
- If omitted, it is false.

Result

Same instance as vector C.

Example

$a = $mo->array([
    [1,2,3],
    [0,4,5],
    [0,0,6],
]);
$b = $mo->array([
    [1,2,3,4],
    [5,6,7,8],
    [9,10,11,12],
]);
$mo->la()->trsm($a,$b);
## b =>
## [[-2.250,-1.833,-1.417,-1.000],
##  [-0.625,-0.583,-0.542,-0.500],
##  [ 1.500, 1.667, 1.833, 2.000]]

svd

$\begin{align*} U Σ V^T = M \end{align*}$

public function svd(NDArray $matrix,$fullMatrices=null)

Cross product of a triangular matrix Complex numbers are not currently supported.

Arguments

matrix: Input matrix.

Result

List of result value.
- U: left matrix.
- S: Sigma matrix.
- VT: right matrix.

Example

$x = $mo->la()->randomUniform([6,5],-10,10);
[$u,$s,$vt] = $mo->la()->svd($x);

omatcopy

    public function omatcopy(
        NDArray $A,
        ?bool $trans=null,
        ?bool $conj=null,
        float|object|null $alpha=null,
        ?NDArray $B=null,
        ) : NDArray

Copy array elements with transpose and conjugate

Arguments

matrix A: Input matrix.
trans: transpose A matrix.
- If omitted, it is false.
conj: conjugate A matrix.
- If omitted, it is the same trans.
alpha: multiply constant.
- If omitted, default is 1.0.
matrix B: Output matrix.

Result

matrix B: Output matrix.

Example

$a = $mo->array([
    [1,2,3],
    [4,5,6],
],dtype:NDArray::float32);
$b = $mo->la()->omatcopy($a,trans:true);
## b => [[1,4],[2,5],[3,6]]

sum

$\begin{align*} f = \sum_{k=0}^n x_k \end{align*}$

public function sum(NDArray $X) : float

Sum of array elements

Arguments

X: the vector X.

Result

value of result.

Example

$x = $mo->array([1,2,3]);
$z = $mo->la()->sum($x);
## z => 6.0

imax

$\begin{align*} f = \arg \max x_k \end{align*}$

public function imax(NDArray $X) : int

Get the element number of the maximum value in array element

Arguments

X: the vector X.

Result

value of result.

Example

$x = $mo->array([1,2,3]);
$z = $mo->la()->imax($x);
## z => 2

imin

$\begin{align*} f = \arg \min x_k \end{align*}$

public function imin(NDArray $X) : int

Get the element number of the minimum value in array element

Arguments

X: the vector X.

Result

value of result.

Example

$x = $mo->array([1,2,3]);
$z = $mo->la()->imin($x);
## z => 0

max

$\begin{align*} f = \max x_k \end{align*}$

public function max(NDArray $X) : float

Get the maximum value in array element

Arguments

X: the vector X.

Result

value of result.

Example

$x = $mo->array([1,2,3]);
$z = $mo->la()->max($x);
## z => 3

min

$\begin{align*} f = \min x_k \end{align*}$

public function min(NDArray $X) : float

Get the minimum value in array element

Arguments

X: the vector X.

Result

value of result.

Example

$x = $mo->array([1,2,3]);
$z = $mo->la()->min($x);
## z => 1

increment

$\begin{align*} X := \alpha X + \beta \end{align*}$

public function increment(
    NDArray $X,
    float $beta=null,
    float $alpha=null) : NDArray

Increment the entire array element by a constant

Arguments

X: the vector X.
- Input and output are shared.
beta: Increment constant.
alpha: multiply constant.

Result

Same instance as vector X.

Examples

$\begin{align*} X := X + 1 \end{align*}$

$x = $mo->array([1,2,3]);
$mo->la()->increment($x,1);
## x => [2.0, 3.0, 4.0]

$\begin{align*} X := 1 - X \end{align*}$

$x = $mo->array([1,2,3]);
$mo->la()->increment($x,1,-1);
## x => [0.0, -1.0, -2.0]

reciprocal

$\begin{align*} X := \frac{1}{\alpha X + \beta} \end{align*}$

public function reciprocal(
    NDArray $X,
    float $beta=null,
    float $alpha=null) : NDArray

Compute the reciprocal of a vector element

Arguments

X: the vector X.
- Input and output are shared.
beta: Increment constant.
alpha: multiply constant.

Result

Same instance as vector X.

Examples

$\begin{align*} X := \frac{1}{X + 1} \end{align*}$

$x = $mo->array([1,2,3]);
$mo->la()->reciprocal($x,1);
## x => [0.5, 0.33333334326744, 0.25]

$\begin{align*} X := \frac{1}{1 - X} \end{align*}$

$x = $mo->array([2,3,4]);
$mo->la()->reciprocal($x,1,-1);
## x => [-1,-0.5,-0.33333334326744]

maximum

$\begin{align*} a_mn := \left \{ \begin{array}{l} a_mn \hspace{5mm} (a_mn > x_n) \\ x_n \hspace{5mm} (a_mn \leqq x_n) \end{array} \right. \end{align*}$

    public function maximum(
        NDArray $A,
        int|float|NDArray $X,
        ) : NDArray

Set the larger of matrix elements and constant

Arguments

A: the matrix A.
- Input and output are shared.
X: Constant to compare. scalar value or vector.

Result

Same instance as matrix A.

Examples

$a = $mo->array([
    [2,3,4],
    [3,4,5],
]);
$x = $mo->array(
    [3,3,3]
)
$mo->la()->maximum($a,$x);
## a => [[3.0, 3.0, 4.0],[3.0,4.0,5.0]]

minimum

$\begin{align*} a_mn := \left \{ \begin{array}{l} a_mn \hspace{5mm} (a_mn < x_n) \\ x_n \hspace{5mm} (a_mn \geqq x_n) \end{array} \right. \end{align*}$

public function minimum(
    NDArray $A,
    int|float|NDArray $X,
    ) : NDArray

Set the smaller of the matrix elements and constant

Arguments

A: the matrix A.
- Input and output are shared.
X: Constant to compare. scalar value or vector.

Result

Same instance as matrix A.

Examples

$a = $mo->array([
    [2,3,4],
    [3,4,5],
]);
$x = $mo->array(
    [3,3,3]
)
$mo->la()->minimum($a,$x);
## a => [[2.0, 3.0, 3.0],[3.0,3.0,3.0]]

greater

$\begin{align*} a_mn := \left \{ \begin{array}{l} 1 \hspace{5mm} (a_mn > x_n) \\ 0 \hspace{5mm} (a_mn \leqq x_n) \end{array} \right. \end{align*}$

    public function greater(
        NDArray $A,
        int|float|NDArray $X,
        ) : NDArray

Check if matrix element is greater than constant

Arguments

A: the matrix A.
- Input and output are shared.
X: Constant to compare. scalar value or vector.

Result

Same instance as matrix A.

Examples

$a = $mo->array([
    [2,3,4],
    [3,4,5],
]);
$x = $mo->array(
    [3,3,3]
)
$mo->la()->greater($a,$x);
## a => [[0.0, 0.0, 1.0],[0.0,1.0,1.0]]

greaterEqual

$\begin{align*} a_mn := \left \{ \begin{array}{l} 1 \hspace{5mm} (a_mn \geqq x_n) \\ 0 \hspace{5mm} (a_mn < x_n) \end {array} \right. \end{align*}$

    public function greaterEqual(
        NDArray $A,
        int|float|NDArray $X,
        ) : NDArray

Check if matrix element is greater than or equal constant

Arguments

A: the matrix A.
- Input and output are shared.
X: Constant to compare. scalar value or vector.

Result

Same instance as matrix A.

Examples

$a = $mo->array([
    [2,3,4],
    [3,4,5],
]);
$x = $mo->array(
    [3,3,3]
)
$mo->la()->greaterEqual($a,$x);
## a => [[0.0, 1.0, 1.0],[1.0,1.0,1.0]]

less

$\begin{align*} a_mn := \left \{ \begin{array}{l} 1 \hspace{5mm} (a_mn < x_n) \\ 0 \hspace{5mm} (a_mn \geqq x_n) \end{array} \right. \end{align*}$

public function less(
    NDArray $A,
    int|float|NDArray $X,
    ) : NDArray

Check if matrix element is less than constant

Arguments

A: the matrix A.
- Input and output are shared.
X: Constant to compare. scalar value or vector.

Result

Same instance as matrix A.

Examples

$a = $mo->array([
    [2,3,4],
    [3,4,5],
]);
$x = $mo->array(
    [3,3,3]
)
$mo->la()->less($a,$x);
## a => [[1.0, 0.0, 0.0],[0.0,0.0,0.0]]

lessEqual

$\begin{align*} a_mn := \left \{ \begin{array}{l} 1 \hspace{5mm} (a_mn \leqq x_n) \\ 0 \hspace{5mm} (a_mn > x_n) \end{array} \right. \end{align*}$

    public function lessEqual(
        NDArray $A,
        int|float|NDArray $X,
        ) : NDArray

Check if matrix element is less than constant

Arguments

A: the matrix A.
- Input and output are shared.
X: Constant to compare. scalar value or vector.

Result

Same instance as matrix A.

Examples

$a = $mo->array([
    [2,3,4],
    [3,4,5],
]);
$x = $mo->array(
    [3,3,3]
)
$mo->la()->lessEqual($a,$x);
## a => [[1.0, 1.0, 0.0],[1.0,0.0,0.0]]

multiply

$\begin{align*} a_{ij} := x_j a_{ij} \end{align*}$

public function multiply(NDArray $X, NDArray $A, bool $trans=null) : NDArray

Broadcast vector X to array A and multiply.

Arguments

X: the vector X.
- It need not be a one-dimensional array.
A: the matrix A.
- Input and output are shared.
- The same shape as the shape of the vector X, or the shape of an array for multiple vectors X
trans: transpose the matrix A.
- default is false.

Result

Same instance as vector A.

Examples

$a = $mo->array([[1,2,3],[4,5,6]]);
$x = $mo->array([30,20,10]);
$mo->la()->multiply($x,$a);
## a => [[30.0, 40.0, 30.0],[120.0, 100.0, 60.0]]

$a = $mo->array([[1,2,3],[4,5,6]]);
$x = $mo->array([20,10]);
$mo->la()->multiply($x,$a,true);
## a => [[20.0, 40.0, 60.0],[40.0, 50.0, 60.0]]

add

$\begin{align*} a_{ij} := \alpha x_j + a_{ij} \end{align*}$

public function add(
   NDArray $X,
   NDArray $A,
   float $alpha=null,
   bool $trans=null
   ) : NDArray

Broadcast vector X to array A and add.

Arguments

X: the vector X.
- It need not be a one-dimensional array.
A: the matrix A.
- Input and output are shared.
- The same shape as the shape of the vector X, or the shape of an array for multiple vectors X
alpha: the constant
- default is 1.0
trans: transpose the matrix A.
- default is false.

Result

Same instance as vector A.

Examples

$\begin{align*} X := X + A \end{align*}$

$a = $mo->array([[1,2,3],[4,5,6]]);
$x = $mo->array([10,20,30]);
$mo->la()->add($x,$a);
## a => [[11.0, 22.0, 33.0],[14.0, 25.0, 36.0]]

$\begin{align*} X := A + X \end{align*}$

$a = $mo->array([[10,20,30],[40,50,60]]);
$x = $mo->array([1,2,3]);
$mo->la()->add($x,$a,-1);
## a => [[9,18,27],[39,48,57]]

square

$\begin{align*} x_k := (x_k)^2 \end{align*}$

public function square(NDArray $X) : NDArray

Square array elements

Arguments

X: the vector X.
- Input and output are shared.

Result

Same instance as vector X.

Examples

$x = $mo->array([[1,2,3],[4,5,6]]);
$mo->la()->square($x);
## x => [[1.0, 4.0, 9.0],[16.0, 25.0, 36.0]]

sqrt

$\begin{align*} x_k := \sqrt{x_k} \end{align*}$

public function sqrt(NDArray $X) : NDArray

Square root of array elements

Arguments

X: the vector X.
- Input and output are shared.

Result

Same instance as vector X.

Examples

$x = $mo->array([[0,1,4],[9,16,25]]);
$mo->la()->sqrt($x);
## x => [[0.0, 1.0, 2.0],[3.0, 4.0, 5.0]]

rsqrt

$\begin{align*} x_k := \frac{1}{\alpha \sqrt{x_k} + \beta} \end{align*}$

public function rsqrt(
    NDArray $X,
    float $beta=null,
    float $alpha=null) : NDArray

Square root of array elements and reciprocal it.

Arguments

X: the vector X.
- Input and output are shared.
alpha: constant value.
- If omitted, default is 1.0
beta: constant value.
- If omitted, default is 0.0

Result

Same instance as vector X.

Examples

$x = $mo->array([1,4,9,16,25]);
$mo->la()->rsqrt($x);
## x => [1,0.5,0.33333334326744,0.25,0.20000000298023]

pow

$\begin{align*} a_mn := (a_mn)^\alpha \end{align*}$

public function pow(
    NDArray $A,
    float|NDArray $alpha,
    ?bool $trans=null,
    ) : NDArray

To power array elements

Arguments

A: the matrix X.
- Input and output are shared.
alpha: the constant. scalar value or vector.
trans: transpose matrix A.

Result

Same instance as matrix X.

Examples

$a = $mo->array([[0,1,2],[3,4,5]]);
$alpha = $mo->array([3,3,3])
$mo->la()->pow($a,$alpha);
## a => [[0.0, 1.0, 8.0],[27.0, 64.0, 125.0]]

exp

$\begin{align*} x_k := e^{x_k} \end{align*}$

public function exp(NDArray $X) : NDArray

calculate “e” to a power

Arguments

X: the vector X.
- Input and output are shared.

Result

Same instance as vector X.

Examples

$x = $mo->array([[0,1,2],[3,4,5]]);
$mo->la()->exp($x);
## x => [[1.0, 2.7182817459106,7.3890562057495],[20.085536956787,54.598148345947,148.41316223145]]

log

$\begin{align*} x_k := \log x_k \end{align*}$

public function log(NDArray $X) : NDArray

Calculate the natural logarithm

Arguments

X: the vector X.
- Input and output are shared.

Result

Same instance as vector X.

Examples

$x = $mo->array([[1,2,3],[4,5,6]]);
$mo->la()->log($x);
## x => [[0.0, 0.6931471824646,1.0986123085022],[1.3862943649292,1.6094379425049,1.7917594909668]]

tanh

$\begin{align*} x_k := \tanh x_k \end{align*}$

public function tanh(NDArray $X) : NDArray

Calculate the hyperbolic tangent

Arguments

X: the vector X.
- Input and output are shared.

Result

Same instance as vector X.

Examples

$x = $mo->array([[1,2,3],[4,5,6]]);
$mo->la()->tanh($x);

sin

$\begin{align*} x_k := \sin x_k \end{align*}$

public function sin(
    NDArray $X
    ) : NDArray

Calculate the sin

Arguments

X: the vector X.
- Input and output are shared.

Result

Same instance as vector X.

Examples

$x = $mo->array([[1,2,3],[4,5,6]]);
$mo->la()->sin($x);

cos

$\begin{align*} x_k := \cos x_k \end{align*}$

public function cos(
    NDArray $X
    ) : NDArray

Calculate the cos

Arguments

X: the vector X.
- Input and output are shared.

Result

Same instance as vector X.

Examples

$x = $mo->array([[1,2,3],[4,5,6]]);
$mo->la()->cos($x);

tan

$\begin{align*} x_k := \tan x_k \end{align*}$

public function tan(
    NDArray $X
    ) : NDArray

Calculate the tan

Arguments

X: the vector X.
- Input and output are shared.

Result

Same instance as vector X.

Examples

$x = $mo->array([[1,2,3],[4,5,6]]);
$mo->la()->tan($x);

equal

$\begin{align*} y_i := \left \{ \begin{array}{l} 1 \hspace{5mm} ( x_i = y_i ) \\ 0 \hspace{5mm} ( x_i \neq y_i ) \end{array} \right. \end{align*}$

public function equal(
    NDArray $X,
    NDArray $Y) : NDArray

Compare the value of array elements

Arguments

X: the vector X.
Y: the vector Y.
- Input and output are shared.

Result

Same instance as vector Y.

Examples

$x = $mo->array([[1,2,3],[6,5,4]]);
$y = $mo->array([[1,0,3],[4,5,6]]);
$mo->la()->equal($x,$y);
## y => [[1,0,1],[0,1,0]]

notEqual

$\begin{align*} y_i := \left \{ \begin{array}{l} 1 \hspace{5mm} ( x_i \neq y_i ) \\ 0 \hspace{5mm} ( x_i = y_i ) \end{array} \right. \end{align*}$

public function notEqual(
    NDArray $X,
    NDArray $Y) : NDArray

Compare the value of array elements

Arguments

X: the vector X.
Y: the vector Y.
- Input and output are shared.

Result

Same instance as vector Y.

Examples

$x = $mo->array([[1,2,3],[6,5,4]]);
$y = $mo->array([[1,0,3],[4,5,6]]);
$mo->la()->notEqual($x,$y);
## y => [[0,1,0],[1,0,1]]

not

$\begin{align*} y_i := \left \{ \begin{array}{l} 1 \hspace{5mm} ( x_i = 0 ) \\ 0 \hspace{5mm} ( x_i \neq 0 ) \end{array} \right. \end{align*}$

public function not(NDArray $X) : NDArray

Invert the value as boolean of array elements.

Arguments

X: the vector X.
- Input and output are shared.

Result

Same instance as vector X.

Examples

$x = $mo->array([[1,0,3],[-1,5,0]]);
$mo->la()->not($x);
## x => [[0,1,0],[0,0,1]]

duplicate

$\begin{align*} a_{ij} := x_j \end{align*}$

public function duplicate(
    NDArray $input,
    ?int $repeats=null,
    ?bool $trans=null,
    ?NDArray $output=null) : NDArray

Copy vector X multiple times

Arguments

input: the vector X.
- It need not be a one-dimensional array.
repeats: Number of copies
- default is 1.
trans: transpose the matrix A.
- default is false.
output: Destination matrix.
- If omitted, it will be allocated automatically.

Result

Same instance as matrix output.

Examples

$x = $mo->array([1,2,3]);
$a = $mo->la()->duplicate($x,2);
## a => [[1.0,2.0,3.0],[1.0,2.0,3.0]]

$x = $mo->array([1,2]);
$a = $mo->la()->duplicate($x,3,true);
## a => [[1.0,1.0,1.0],[2.0,2.0,2.0]]

transpose

$\begin{align*} B = \alpha \times A^T \end{align*}$

public function transpose(
    NDArray $A,
    array|NDArray|null $perm=null,
    ?NDArray $B=null,
    ) : NDArray

Transpose a matrix

Arguments

A: input matrix.
perm: A list of destination dimensions to swap.
- If omitted, range($A->ndim()-1,0,-1).
B: output matrix

Result

Same instance as Matrix B.

Examples

$a = $mo->array([[1,2][3,4]]);
$b = $mo->la()->transpose($a);
## b => [[1,3],[2,4]]

gather

$\begin{align*} y := \left \{ \begin{array}{l} a_{x,k} \hspace{5mm} ( axis = null ) \\ a_{m,x,k} \hspace{5mm} ( axis \neq null ) \end{array} \right. \end{align*}$

public function gather(
    NDArray $A,
    NDArray $X,
    int $axis=null,
    NDArray $output=null,
    int $dtype=null) : NDArray

Select values from source array by indexes.

Arguments

A: source data.
X: selection index vector.
- N-dimensional integer array.
axis: selection dimension
- default is null.
- If null, Match from the beginning of the selector.
- If not null, Reduce on the specified axis.
output: Destination matrix.
- If omitted, it will be allocated automatically.

Result

Same instance as vector output.

Examples

$a = $mo->array([[1,2,3],[4,5,6],[7,8,9]]);
$x = $mo->array([0,2],NDArray::int32);
$b = $mo->la()->gather($a,$x);
## b => [[1,2,3],[7,8,9]]
$a = $mo->array([[1,2,3],[4,5,6],[7,8,9]]);
$x = $mo->array([2,1,0],NDArray::int32);
$b = $mo->la()->gather($a,$x,axis:0);
## b => [7,5,3]
$a = $mo->array([[1,2,3],[4,5,6],[7,8,9]]);
$x = $mo->array([2,1,0],NDArray::int32);
$b = $mo->la()->gather($a,$x,axis:1);
## b => [3,5,7]

gatherb

$\begin{align*} y := \left \{ \begin{array}{l} a_{x,k} \hspace{5mm} ( axis = null ) \\ a_{m,x,k} \hspace{5mm} ( axis \neq null ) \end{array} \right. \end{align*}$

    public function gatherb(
        NDArray $params,
        NDarray $indices,
        ?int $axis=null,
        ?int $batchDims=null,
        ?int $detailDepth=null,
        ?int $indexDepth=null,
        ?NDArray $outputs=null,
    ) : NDArray

Extended gather function.

params: (batches, m, numClass, k, len)
indices: (batches, n, k)
outputs: (batches, m, n, k, len)
outputs(batches, m, n, k, len) := A(batches, m, X(batches, n, k), k, len)

Arguments

params: source data.
indices: selection index vector.
- N-dimensional integer array.
axis: selection dimension
- default is the same of batchDims.
batchDims: define batch dimensions
- default is 0.
detailDepth: locate detail dimension
- default is axis+1.
indexDepth: define batch dimensions
- default is ndim of indexDepth.
output: Destination matrix.
- If omitted, it will be allocated automatically.

Result

Same instance as matrix output.

Examples

$shapeA = [4,3];
$a = $la->array([
    [0,1,2],
    [3,4,5],
    [6,7,8],
    [9,10,11],
]);
$x = $la->array([2,2,1,0],dtype:NDArray::int32);
$b = $la->gatherb($a,$x,axis:1,batchDims:1);
## b => [2,5,7,9]

scatter

$\begin{align*} y := \left \{ \begin{array}{l} a_{x,k} \hspace{5mm} ( axis = null ) \\ a_{m,x,k} \hspace{5mm} ( axis \neq null ) \end{array} \right. \end{align*}$

public function scatter(
    NDArray $X,
    NDArray $A,
    int $numClass,
    int $axis=null,
    NDArray $output=null,
    $dtype=null) : NDArray

Set values to array by indexes. Reverse operation of gather.

Arguments

X: selection index vector.
A: source data vector.
- N-dimensional integer array.
numClass: The size of the destination array.
- Must be integer
axis: selection dimension
- default is null.
- If null, Match from the beginning of the selector.
- If not null, Expand on the specified axis.
output: Destination array.

Result

Same instance as Matrix B.

Examples

$x = $mo->array([0,2],NDArray::int32);
$a = $mo->array([[1,2,3],[4,5,6]]);
$b = $mo->la()->scatter($x,$a,$n=3);
## b => [[1,2,3],[0,0,0],[4,5,6]]
$x = $mo->array([2,1,0],NDArray::int32);
$a = $mo->array([1,2,3]);
$b = $mo->la()->scatter($x,$a,$n=3,$axis=0);
## b => [[0,0,3],[0,2,0],[1,0,0]]
$x = $mo->array([2,1,0],NDArray::int32);
$a = $mo->array([1,2,3]);
$b = $mo->la()->scatter($x,$a,$n=3,$axis=1);
## b => [[0,0,1],[0,2,0],[3,0,0]]

scatterb

$\begin{align*} y := \left \{ \begin{array}{l} a_{x,k} \hspace{5mm} ( axis = null ) \\ a_{m,x,k} \hspace{5mm} ( axis \neq null ) \end{array} \right. \end{align*}$

public function scatterb(
    NDarray $indices,
    NDArray $updates,
    array $shape,
    ?int $axis=null,
    ?int $batchDims=null,
    ?int $detailDepth=null,
    ?int $indexDepth=null,
    ?NDArray $outputs=null,
): NDArray

Extended scatter function.

indices: (batches, n, k)
updates: (batches, m, n, k, len)
outputs: (batches, m, numClass, k, len)
outputs(batches, m, n, k, len) := A(batches, m, X(batches, n, k), k, len)

Arguments

indices: selection index vector.
- N-dimensional integer array.
updates: source data.
shape: shape of output data.
axis: selection dimension
- default is the same of batchDims.
batchDims: define batch dimensions
- default is 0.
detailDepth: locate detail dimension
- default is axis+1.
indexDepth: define batch dimensions
- default is ndim of indexDepth.
output: Destination matrix.
- If omitted, it will be allocated automatically.

Result

Same instance as Matrix output.

Examples

$shapeA = [4];
$a = $la->array([2,5,7,9]);
$x = $la->array([2,2,1,0],dtype:NDArray::int32);
$b = $la->scatterb($x,$a,$shapeB,axis:1,batchDims:1);
## b => [
##  [0,0,2],
##  [0,0,5],
##  [0,7,0],
##  [9,0,0]
## ]

scatterAdd

$\begin{align*} B_{x} := B_{x} + A_{x} \end{align*}$

public function scatterAdd(
    NDArray $X,
    NDArray $A,
    NDArray $B,
    int $axis=null,
    $dtype=null) : NDArray

Add values to array by indexes.

Arguments

X: selection index vector.
A: source data.
- N-dimensional integer array.
B: Destination data.
axis: selection dimension
- default is null.
- If null, Match from the beginning of the selector.
- If not null, Expand on the specified axis.

Result

Same instance as Matrix B.

Examples

$x = $mo->array([0,2],NDArray::int32);
$a = $mo->array([[1,2,3],[4,5,6]]);
$b = $mo->array([[1,1,1],[1,1,1],[1,1,1]]);
$mo->la()->scatterAdd($x,$a,$b);
## b => [[2,3,4],[1,1,1],[5,6,7]]
$x = $mo->array([2,1,0],NDArray::int32);
$a = $mo->array([1,2,3]);
$b = $mo->array([[1,1,1],[1,1,1],[1,1,1]]);
$mo->la()->scatterAdd($x,$a,$b,$axis=0);
## b => [[1,1,4],[1,3,1],[2,1,1]]
$x = $mo->array([2,1,0],NDArray::int32);
$a = $mo->array([1,2,3]);
$b = $mo->array([[1,1,1],[1,1,1],[1,1,1]]);
$mo->la()->scatterAdd($x,$a,$b,$axis=1);
## b => [[1,1,2],[1,3,1],[4,1,1]]

scatterbAdd

$\begin{align*} B_{x} := B_{x} + A_{x} \end{align*}$

public function scatterbAdd(
    NDarray $indices,
    NDArray $updates,
    array $shape,
    ?int $axis=null,
    ?int $batchDims=null,
    ?int $detailDepth=null,
    ?int $indexDepth=null,
    ?NDArray $outputs=null,
): NDArray

Extended scatterAdd function.

Arguments

indices: selection index vector.
- N-dimensional integer array.
updates: source data.
shape: shape of output data.
axis: selection dimension
- default is the same of batchDims.
batchDims: define batch dimensions
- default is 0.
detailDepth: locate detail dimension
- default is axis+1.
indexDepth: define batch dimensions
- default is ndim of indexDepth.
output: Destination matrix.
- If omitted, it will be allocated automatically.

Result

Same instance as Matrix output.

Examples

$shapeA = [4];
$a = $la->array([2,5,7,9]);
$x = $la->array([2,2,1,0],dtype:NDArray::int32);
$shapeB = [4,3];
$b = $la->scatterbAdd($x,$a,$shapeB,axis:1,batchDims:1);
## b => [
##  [0,0,2],
##  [0,0,5],
##  [0,7,0],
##  [9,0,0]
## ]

slice

public function slice(
    NDArray $input,
    array $begin,
    array $size,
    NDArray $output=null
    ) : NDArray

Slice a array with indicator.

Arguments

input: source data.
begin: begin of slice.
- Must be integer array.
size: size of slice.
- Must be integer array.
output: Destination array.

Result

Same instance as Matrix output.

Examples

$x = $mo->array($mo->arange(24,null,null,NDArray::float32)->reshape([2,4,3]));
$y = $la->slice(
    $x,
    $start=[0,1],
    $size=[-1,2]
    );
## y =>
##   [[[3,4,5],
##     [6,7,8],],
##    [[15,16,17],
##     [18,19,20],],
##   ]

stick

public function stick(
    NDArray $input,
    NDArray $output,
    array $begin,
    array $size
    ) : NDArray

Stick values to array with indicator.

Arguments

input: values.
output: Destination array.
begin: begin of value index.
- Must be integer array.
size: size of values.
- Must be integer array.
output: Destination array.

Result

Same instance as Matrix output.

Examples

$x = $mo->array($mo->arange(12,null,null,NDArray::float32)->reshape([2,2,3]));
$y = $mo->array($mo->zeros([2,4,3]));
$mo->la()->stick(
    $x,
    $y,
    $start=[0,1],
    $size=[-1,2]
    );
## y =>
##   [[[0,0,0],
##     [0,1,2],
##     [3,4,5],
##     [0,0,0]],
##    [[0,0,0],
##     [6,7,8],
##     [9,10,11],
##     [0,0,0]],]

stack

public function stack(
    array $values,
    int $axis=null
)

Concat arrays with a axis.

Arguments

values: list of input array.
- Must be list of NDArray that are same the shapes.
axis: Coordinate axes to combine.

Result

NDArray as Matrix output.

Examples

$a = $mo->array($mo->arange(6,0,null,NDArray::float32)->reshape([2,3]));
$b = $mo->array($mo->arange(6,6,null,NDArray::float32)->reshape([2,3]));
$y = $mo->la()->stack(
    [$a,$b],
    $axis=0
    );
## y =>
##  [[[0,1,2],
##    [3,4,5]],
##   [[6,7,8],
##    [9,10,11]],]

concat

public function concat(
    array $values,
    int $axis=null
) : NDArray

Concat arrays with a axis.

Arguments

values: list of input array.
- Must be list of NDArray that are same the shapes.
axis: Coordinate axes to combine.

Result

NDArray as Matrix output.

Examples

$a = $mo->array($mo->arange(6,$start=0,null,NDArray::float32)->reshape([3,2]));
$b = $mo->array($mo->arange(4,$start=6,null,NDArray::float32)->reshape([2,2]));
$y = $mo->la()->concat(
    [$a,$b],
    $axis=0
    );
## y =>
##  [[0,1],
##   [2,3],
##   [4,5],
##   [6,7],
##   [8,9],]

split

public function split(
    NDArray $input, array $sizeSplits, $axis=null
    ) : array

Split a array with a axis.

Arguments

input: input array.
sizeSplits: list of size.
- Must be integer list
axis: Coordinate axes to split.

Result

List of NDArray as Matrix output.

Examples

$x = $mo->array([
    [0,1],
    [2,3],
    [4,5],
    [6,7],
    [8,9],
]);
$y = $mo->la()->split(
    $x,
    [3,2],
    $axis=0
);
## $y[0] =>
##  [[0,1],
##   [2,3],
##   [4,5]]
## $y[1] =>
##  [[6,7],
##   [8,9]]

repeat

public function repeat(
    NDArray $A,
    int $repeats,
    ?int $axis=null,
    ?bool $keepdims=null
    ) : NDArray

Repeat array.

Arguments

A: values.
repeats: number of repeat.
axis: repeat axis.
- If null, flat array output
- If not null, repeat with specified axis.
keepdims: Keep dimensions.

Result

Repeaded Matrix output.

Examples

$A = $mo->array([[1,2,3],[4,5,6]]);
$B = $la->repeat($X,2);
## b => [1,2,3,4,5,6,1,2,3,4,5,6]
$B = $la->repeat($X,2,$axis=0);
## b => [[[1,2,3],[4,5,6]],[[1,2,3],[4,5,6]]]
$B = $la->repeat($X,2,$axis=1);
## b => [[[1,2,3],[1,2,3]],[[4,5,6],[4,5,6]]]

onehot

$\begin{align*} y_{ij} := \left \{ \begin{array}{l} a \hspace{5mm} ( x_i = j ) \\ 0 \hspace{5mm} ( x_i \neq j ) \end{array} \right. \end{align*}$

public function onehot(
    NDArray $X,
    int $numClass,
    float $a=null,
    NDArray $output=null) : NDArray

Convert classification number to the onehot format.

Arguments

X: classification numbers.
- Must be one-dimensional integer array.
numClass: Total number of classifications
a: Scalar value.
- Default is 1.0.
- The result is multiplied.
Y: Destination matrix.
- If omitted, it will be allocated automatically.
- If you specify an existing array, the result is added.

Result

Same instance as vector Y.

Examples

$\begin{align*} Y := {\rm onehot} X \end{align*}$

$x = $mo->array([0,1,2,0]);
$y = $mo->la()->onehot($x,3);
## y => [[1.0, 0.0, 0.0],[0.0, 1.0, 0.0],[0.0, 0.0, 1.0],[1.0, 0.0, 0.0]]

$\begin{align*} Y := Y - \frac{ 1 }{ 2 }{\rm onehot} X \end{align*}$

$y = $mo->array([[1,1,1],[1,1,1],[1,1,1],[1,1,1]]);
$x = $mo->array([0,1,2,0]);
$mo->la()->onehot($x,3,-0.5,$y);
## y => [[0.5, 1.0, 1.0],[1.0, 1.0, 5,0],[1.0, 1.0, 0.5],[0.5, 1.0, 1.0]]

softmax

$\begin{align*} y_i = \frac{ e^{x_i} }{ \sum_{j=0}^{n} e^{x_j}} \end{align*}$

public function softmax(
    NDArray $X
    ) : NDArray

Softmax function

Arguments

X: Must be a two-dimensional array.
- Input and output are shared.

Result

Same instance as vector X.

Examples

$x = $mo->array([[1,2,3],[4,5,6],[7,8,9]]);
$mo->la()->softmax($x);
## x => [[0.090030573308468,0.2447284758091,0.66524094343185],
## [0.090030573308468,0.2447284758091,0.66524094343185],
## [0.090030573308468,0.2447284758091,0.66524094343185]]

reduceArgMax

$\begin{align*} x_i = \arg {\rm maximum} (a_j) \end{align*}$

public function reduceArgMax( // reduceMaxArgEx
    NDArray $input,
    ?int $axis=null,
    ?bool $keepdims=null,
    ?NDArray $output=null,
    ?int $dtype=null) : NDArray

Aggregate the index of the array element with the maximum value for the specified dimension.

Arguments

A: source data array.
axis: Aggregate dimension
- Must be integer. If you give a negative number, it will be specified from the right.
keepdims: Keep dimensions.
output: Array to store the result.
- If omitted, it will be allocated automatically.
dtype: Data type when creating output array .
- If omitted, it will be int64 or int32.

Result

Same instance as matrix B.

Examples

$a = $mo->array([[1,2,3],[6,5,4]]);
$b = $mo->la()->reduceArgMax($a,1);
## b => [2,0]
$b = $mo->la()->reduceArgMax($a,0);
## b => [1,1,1]
$a = $mo->array([
    [[1,2],[5,6]],
    [[7,8],[3,4]]]);
$b = $mo->la()->reduceArgMax($a,1);
echo $mo->toString($b)."\n";
## b => [[1,1],[0,0]]

reduceMax

$\begin{align*} x_i = {\rm maximum} (a_j) \end{align*}$

public function reduceMax(
    NDArray $input,
    ?int $axis=null,
    ?bool $keepdims=null,
    ?NDArray $output=null,
    ?int $dtype=null) : NDArray

Aggregate the array element with the maximum value for the specified dimension.

Arguments

A: source data array.
axis: Aggregate dimension
- Must be integer. If you give a negative number, it will be specified from the right.
keepdims: Keep dimensions.
output: Array to store the result.
- If omitted, it will be allocated automatically.
dtype: Data type when creating output array .
- If omitted, same as original data

Result

Same instance as output matrix.

Examples

$a = $mo->array([[1,2,3],[6,5,4]]);
$b = $mo->la()->reduceMax($a,1);
## b => [3,6]
$b = $mo->la()->reduceMax($a,0);
## b => [6,5,4]
$a = $mo->array([
    [[1,2],[5,6]],
    [[7,8],[3,4]]]);
$b = $mo->la()->reduceMax($a,1);
echo $mo->toString($b)."\n";
## b => [[5,6],[7,8]]

reduceSum

$\begin{align*} x_i = \sum_{j=0}^n a_ij \end{align*}$

public function reduceSum( // reduceSumEx
    NDArray $input,
    ?int $axis=null,
    ?bool $keepdims=null,
    ?NDArray $output=null,
    ?int $dtype=null) : NDArray

Aggregate the sum of array elements in the specified dimension

Arguments

input: source data array.
axis: Aggregate dimension
- Must be integer. If you give a negative number, it will be specified from the right.
- Default is 0.
keepdims: Keep dimensions.
output: Array to store the result.
- If omitted, it will be allocated automatically.
dtype: Data type when creating output array.
- If omitted, same as original data

Result

Same instance as matrix output.

Examples

$a = $mo->array([[1,2,3],[6,5,4]]);
$b = $mo->la()->reduceSum($a,1);
## b => [6, 15]
$b = $mo->la()->reduceSum($a,0);
## b => [7, 7, 7]
$a = $mo->array([
    [[1,2],[5,6]],
    [[7,8],[3,4]]]);
$b = $mo->la()->reduceSum($a,1);
echo $mo->toString($b)."\n";
## b => [[6,8],[10,12]]

reduceMean

$\begin{align*} x_i = \frac{ \sum_{j=0}^n a_j }{ n } \end{align*}$

public function reduceMean(
    NDArray $input,
    ?int $axis=null,
    ?bool $keepdims=null,
    ?NDArray $output=null,
    ?int $dtype=null) : NDArray

Aggregate the average value of array elements in the specified dimension

Arguments

input: source data array.
axis: Aggregate dimension
- Must be 0 or 1.
keepdims: Keep dimensions.
output: Array to store the result.
- If omitted, it will be allocated automatically.
dtype: Data type when creating output array.
- If omitted, same as original data

Result

Same instance as output matrix.

Examples

$a = $mo->array([[1,2,3],[6,5,4]]);
$b = $mo->la()->reduceMean($a,1);
## b => [2,5]
$b = $mo->la()->reduceMean($a,0);
## b => [3.5, 3.5, 3.5]
$a = $mo->array([
    [[1,2],[5,6]],
    [[7,8],[3,4]]]);
$b = $mo->la()->reduceSum($a,1);
echo $mo->toString($b)."\n";
## b => [[3,4],[5,6]]

im2col

public function im2col(
    NDArray $images,
    array $filterSize=null,
    array $strides=null,
    bool $padding=null,
    bool $channels_first=null,
    array $dilation_rate=null,
    bool $cols_channels_first=null,
    NDArray $cols=null
    ) : NDArray

Convert image data to cols format.

Arguments

images: Batch set of 1D or 2D or 3D data with channels.
- The 1D data must be 3D NDArray. The 2D data must be 4D NDArray. The 3D data must be 5D NDArray.
filterSize: convolution filter size.
- Integer list that matches the input data.
strides: strides size.
- Integer list that matches the input data.
padding: Whether to padding.
- When padded, the output image will be the same size as the input image.
channels_first: Input image data format.
- The input image NDArray is whether the channel is the first axes.
- If false : images shape [batchs,image_width,channels]
- If true : images shape [batchs,channels,image_width]
dilation_rate: dilation rate size.
- Integer list that matches the input data.
cols_channels_first: Output image data format.
- The output cols NDArray is whether the channel is before the filters.
- If false : cols shape [batches,image_width,filter_size,channels]. Used in convolution.
- If true : cols shape [batches,image_width,channels,filter_size]. Used in pooling.
cols: Output cols data.
- Converted output.

Result

Same instance as Matrix Cols.

Examples

$batches = 8;
$channels = 3;
$images = $mo->ones([$batches,28,28,$channels]);
$cols = $la->im2col(
    $images,
    $filterSize=[4,4],
    $strides=[1,1],
    $padding=false,
    $channels_first=false,
    $dilation_rate=[1,1],
    $cols_channels_first=false
);
## cols->shape() => [8,25,25,4,4,3]

col2im

public function col2im(
    NDArray $cols,
    NDArray $images,
    array $filterSize=null,
    array $strides=null,
    bool $padding=null,
    bool $channels_first=null,
    array $dilation_rate=null,
    bool $cols_channels_first=null
    ) : NDArray

Convert cols format to image data.

Arguments

cols: Input cols data.
- Converted output.
images: Ouput batch set of 1D or 2D or 3D data with channels.
- The 1D data must be 3D NDArray. The 2D data must be 4D NDArray. The 3D data must be 5D NDArray.
filterSize: convolution filter size.
- Integer list that matches the input data.
strides: strides size.
- Integer list that matches the input data.
padding: Whether to padding.
- When padded, the output image will be the same size as the input image.
channels_first: Input image data format.
- The output image NDArray is whether the channel is the first axes.
dilation_rate: dilation rate size.
- Integer list that matches the input data.
cols_channels_first: Output image data format.
- The input cols NDArray is whether the channel is the first axes.

Result

Same instance as Matrix Cols.

Examples

$batches = 8;
$channels = 3;
$cols = $mo->ones([$batches,25,25,4,4,$channels]);
$images = $mo->ones([$batches,28,28,$channels]);
$la->col2im(
    $cols,
    $images,
    $filterSize=[4,4],
    $strides=[1,1],
    $padding=false,
    $channels_first=false,
    $dilation_rate=[1,1],
    $cols_channels_first=false
);

randomUniform

public function randomUniform(
    array $shape,
    int|float $low,
    int|float $high,
    ?int $dtype=null,
    ?int $seed=null,
    ?NDArray $X=null) : NDArray

Generate random numbers.

Arguments

shape: Output shape.
- Integer list.
low: lower value.
- float value.
high: higher value.
- float value.
dtype: NDArray data type.
- Constant of NDArray data type.
seed: seed for randomize.
output: output.
- The output image NDArray is whether the channel is the first axes.

Result

Same instance as Matrix Cols.

Examples

$x = $mo->la()->randomUniform(
    [2,2],
    0.0, 1.0
);

randomNormal

public function randomNormal(
    array $shape,
    float $mean,
    float $scale,
    ?int $dtype=null,
    ?int $seed=null,
    ?NDArray $X=null) : NDArray

Generate dormal distribution random numbers.

Arguments

shape: Output shape.
- Integer list.
mean: mean of values.
- float value.
scale: scale of values.
- float value.
dtype: NDArray data type.
- Constant of NDArray data type.
seed: seed for randomize.
output: output.
- The output image NDArray is whether the channel is the first axes.

Result

Same instance as Matrix output.

Examples

$x = $mo->la()->randomNormal(
    [2,2],
    0.0, 1.0
);

randomSequence

public function randomSequence(
    int $base,
    ?int $size=null,
    ?int $seed=null,
    ?int $dtype=null,
    ?NDArray $output=null,
    ) : NDArray

Randomly selected from the population. Returns a uniquely selected value from a population of sequential integers.

Arguments

base: Population size.
- Integer.
size: Data size to generate.
- If omitted, it is the same size as the population.
seed: seed for randomize.
dtype: NDArray data type.
output: output.

Result

output Matrix.

Examples

$x = $mo->la()->randomSequence(10);

bandpart

public function bandpart(
    NDArray $A,
    int $lower,
    int $upper,
) : NDArray

Sets everything outside the center band of the matrix to zero. The input matrix is not copied, it is rewritten.

Arguments

A: The matrix to be reset to a banded matrix.
- More than 2D
lower: band of lower. If negative, keep entire lower triangle.
upper: band of upper. If negative, keep entire upper triangle.

Result

same A object.

Examples

$a = $la->ones($la->alloc([5,5]));
$la->bandpart($a,-1,0);
## A = [[1,0,0,0,0],
##      [1,1,0,0,0],
##      [1,1,1,0,0],
##      [1,1,1,1,0],
##      [1,1,1,1,1]]

imagecopy

public function imagecopy(
    NDArray $A,
    NDArray $B=null,
    bool $channels_first=null,
    int $heightShift=null,
    int $widthShift=null,
    bool $verticalFlip=null,
    bool $horizontalFlip=null
    ) : NDArray

Copy 2D image data with various conversions

Arguments

A: Source 2D image data.
- 3D NDArray. [h,w,c] or [c,h,w]
B: Destination.
- Default is allocated output.
- Same shape as A.
channels_first: data format.
- Default false,
- If false, the format is channels_last [h,w,c].
- If true, the format is channels_first [c,h,w].
heightShift: Up and down shift range.
widthShift: Left and right shift range.
verticalFlip: Upside down.
horizontalFlip: Left-right reversal.

Result

same B object.

Examples

$A = $mo->array([
    [1,2,3],
    [4,5,6],
    [7,8,9]
])->reshape([3,3,1]);
$B = $mo->la()->imagecopy($A,null,null,null,
    $heightShift=null,$widthShift=null,$verticalFlip=true)->reshape([3,3]);
## B = [[3,2,1],
##      [6,5,4],
##      [9,8,7]]

searchsorted

public function searchsorted(
    NDArray $A,
    NDArray $X,
    ?bool $right=null,
    ?int $dtype=null,
    ?NDArray $Y=null
    ) : NDArray

Searches for where a value would go in a sorted sequence.

It compares the value of argument X in the sequence of argument A, and outputs the position where X does not exceed the value of A.

Arguments

A: A sorted one-dimensional array containing the sequences to be searched for, or a batch of such arrays.
- 1D or 2D
X: A sorted sequence of search values, or the search values for each batch if A is 2D.
right: Search from the right.
dtype: The data type of the output index array. Default is int32.
Y*: The index array where the value was found.

Result

same A object.

Examples

$A = $mo->array([0.1, 0.3, 0.5, 0.7, 0.9]);
$X = $mo->array([0.0, 0.5, 1.0]);
$Y = $la->searchsorted($A,$X);
# Y=[0,2,5],

$A = $mo->array([
    [1,   3,  5,   7,   9],
    [1,   2,  3,   4,   5],
    [0, 100, 20, 300, 400]
]);
$X = $mo->array([
    0,
    5,
    10
]);
$Y = $la->searchsorted($A,$X);
# Y=[
#   0,
#   4,
#   1
# ],

cumsum

public function cumsum(
    NDArray $inputs,
    ?int $axis=null,
    ?bool $exclusive=null,
    ?bool $reverse=null,
    ?NDArray $outputs=null
    ) : NDArray

Compute the cumulative sum of the tensor x along axis.

Arguments

inputs: source data.
axis: Must be in the range (-rank(x), rank(x)). Default is zero.
exclusive: If true, perform exclusive cumsum.
reverse: If true, reverse output
outputs*: output array

Result

same outputs object.

Examples

$X = $mo->array([1,2,1,2]);
$Y = $la->cumsum($X);
# outputs=[1,3,4,6],

$X = $mo->array([1,2,1,2]);
$Y = $la->cumsum($X,exclusive:true);
# outputs=[0,1,3,4],

$X = $mo->array([1,2,1,2]);
$Y = $la->cumsum($X,reverse:true);
# outputs=[6,5,3,2],

$X = $la->array([
    [1,2,3,4],
    [5,6,7,8],
]);
$Y = $la->cumsum($X,axis:1);
# Y= [
#  [1,3,6,10],
#  [5,11,18,26]
# ]

nan2num

public function nan2num(
    NDArray $X,
    ?float $alpha=null
    ) : NDArray

Replace NaN with numbers.

Arguments

X: Arrays containing NAN.
alpha: The replacement number. Default is zero.

Result

same X object.

Examples

$X = $mo->array([NAN,2,1,NAN]);
$la->cumsum($X);
# X=[0,2,1,0],

isnan

public function isnan(
    NDArray $X
    ) : NDArray

Returns which elements are NAN. Replaces NAN with 1, non-NAN with 0.

Arguments

X: Arrays containing NAN.

Result

same X object.

Examples

$X = $mo->array([NAN,2,1,NAN, INF]);
$la->cumsum($X);
# X=[1,0,0,1,0],

linspace

public function linspace(
    float $start,
    float $stop,
    int $num,
    ?int $dtype=null
    ) : NDArray

Generates uniformly spaced values at regular intervals.

Arguments

start: First entry in the range.
stop: Last entry in the range.
num: Number of values to generate.
dtype: Data type. Default float32

Result

output array.

Examples

$X = $la->linspace($start=10,$stop=100,$num=10);
# X = [10,20,30,40,50,60,70,80,90,100],

range

public function range(
    int|float $limit,
    int|float|null $start=null,
    int|float|null $delta=null,
    ?int $dtype=null
    ) : NDArray

Creates a sequence of numbers.

Arguments

limit: Last entry in the range.
start: First entry in the range. Defaults to 0
delta: Number that increments start. Defaults to 1.
dtype: Data type. Default float32

Result

output array.

Examples

$X = $la->range(5);
# X = [0,1,2,3,4],

$X = $la->range(start:1, limit:5);
# X = [1,2,3,4],

$X = $la->range(start:1, limit:10, delta:2);
# X = [1,3,5,7,9],

einsum

public function einsum(
    string $equation,
    NDArray $a,
    NDArray $b,
) : NDArray

Multiplication of multidimensional arrays using Einstein contraction notation.

Arguments

equation: a str describing the contraction,.
a: First array in equation.
b: Second array in equation.

Result

output array.

Examples

// cross product
$a = $mo->array([[1,2],[3,4]]);
$b = $mo->array([[5,6],[7,8]]);
$c = $la->einsum('ik,kj->ij',$a,$b);
# c = [
#     [19,22],
#     [43,50]
# ]

einsum4p1

public function einsum4p1(
    string $equation,
    NDArray $a,
    NDArray $b,
    ?NDArray $c=null,
) : NDArray

Speeding up einsum by limiting the dimensions of the array to 4+1 equations.

Arguments

equation: a str describing the contraction,.
a: First array in equation.
b: Second array in equation.
c: output

Result

same output array object.

Examples

// cross product
$a = $mo->array([[1,2],[3,4]]);
$b = $mo->array([[5,6],[7,8]]);
$c = $la->einsum4p1('ik,kj->ij',$a,$b);
# c = [
#     [19,22],
#     [43,50]
# ]

masking

public function masking(
    NDArray $mask,
    NDArray $data,
    ?int $batchDims=null,
    ?int $axis=null,
    ?float $fill=null,
    ?int $mode=null,
    ) : NDArray

Masks an array with the specified boolean array.

Arguments

mask: Boolean array. The value of true will remain unchanged, and 0 or the value specified by fill will be written to false locations.
data: Input data array.
batchDims: Interprets input array dimensions 0 through the specified dimension as the batching dimensions. default is zero.
axis: Masks the input array starting from the specified dimension. The skipped dimensions are broadcast with the mask array. default is the same to batchDims.
fill: The value to set for the masked element. default is zero.
mode: Whether to set or add the fill value. set=0, add=1. default is set.

Result

same data array object.

Examples

# X:(2,3)
# A:(2,3)
$X = $la->array([[true,false,true],[false,true,false]], dtype:NDArray::bool);
$A = $la->array([[1,10,100],[-1,-10,-100]]);
$la->masking($X,$A);
# A=[[1, 0,100],[0,-10, 0]]

// broadcast to details
// X:(2,3  )
// A:(2,3,4)
// outer:(2,3),bro:(4),inner:(),bro2:()
$X = $la->array([
    [true,false,true],
    [false,true,false]
], dtype:NDArray::bool);
$A = $la->array([
    [[1,11,111,1111],[2,12,122,1222],[-3,13,133,1333]],
    [[1,21,121,1211],[2,22,222,2222],[-3,23,233,2333]]
]);
$la->masking($X,$A,batchDims:$X->ndim(),axis:$A->ndim());
# A = [
#     [[1,11,111,1111],[0, 0,  0,   0],[-3,13,133,1333]],
#     [[0, 0,  0,   0],[2,22,222,2222],[0, 0,  0,   0]]
# ]

# broadcast to rows (implicit batchDims:0)
# X:(  2,3)
# A:(4,2,3)
# outer:(),bro:(4),inner:(2,3),bro2:()
$X = $la->array([[true,false,true],[false,true,false]],dtype:NDArray::bool);
$A = $la->array([
    [[1,11,111],[2,12,112]],
    [[1,21,211],[2,22,222]],
    [[1,31,311],[2,32,322]],
    [[1,41,411],[2,42,422]],
]);
$la->masking($X,$A,axis:1);
# A=[
#     [[1, 0,111],[0,12,  0]],
#     [[1, 0,211],[0,22,  0]],
#     [[1, 0,311],[0,32,  0]],
#     [[1, 0,411],[0,42,  0]],
# ]