In rikenbit/DelayedTensor: R package for sparse and out-of-core arithmetic and decomposition of Tensor

BiocStyle::markdown()

Authors: r packageDescription("DelayedTensor")[["Author"]]
Last modified: r file.info("DelayedTensor_2.Rmd")$mtime
Compiled: r date()

Setting

suppressPackageStartupMessages(library("DelayedTensor"))
suppressPackageStartupMessages(library("DelayedArray"))
suppressPackageStartupMessages(library("HDF5Array"))
suppressPackageStartupMessages(library("DelayedRandomArray"))

darr1 <- RandomUnifArray(c(2,3,4))
darr2 <- RandomUnifArray(c(2,3,4))

There are several settings in r Biocpkg("DelayedTensor").

First, the sparsity of the intermediate r Biocpkg("DelayedArray") objects calculated inside r Biocpkg("DelayedTensor") is set by setSparse.

Note that the sparse mode is experimental.

Whether it contributes to higher speed and lower memory is quite dependent on the sparsity of the r Biocpkg("DelayedArray"), and the current implementation does not recognize the block size, which may cause out-of-memory errors, when the data is extremely huge.

Here, we specify as.sparse as FALSE (this is also the default value for now).

DelayedTensor::setSparse(as.sparse=FALSE)

Next, the verbose message is suppressed by setVerbose. This is useful when we want to monitor the calculation process.

Here we specify as.verbose as FALSE (this is also the default value for now).

DelayedTensor::setVerbose(as.verbose=FALSE)

The block size of block processing is specified by setAutoBlockSize. When the sparse mode is off, all the functions of r Biocpkg("DelayedTensor") are performed as block processing, in which each block vector/matrix/tensor is expanded to memory space from on-disk file incrementally so as not to exceed the specified size.

Here, we specify the block size as 1E+8.

setAutoBlockSize(size=1E+8)

Finally, the temporal directory to store the intermediate HDF5 files during running r Biocpkg("DelayedTensor") is specified by setHDF5DumpDir.

Note that in many systems the /var directory has the storage limitation, so if there is no enough space, user should specify the other directory.

# tmpdir <- paste(sample(c(letters,1:9), 10), collapse="")
# dir.create(tmpdir, recursive=TRUE))
tmpdir <- tempdir()
setHDF5DumpDir(tmpdir)

These specified values are also extracted by each getter function.

DelayedTensor::getSparse()
DelayedTensor::getVerbose()
getAutoBlockSize()
getHDF5DumpDir()

Tensor Arithmetic Operations

Unfold/Fold Operations

Unfold (a.k.a. matricizing) operations are used to reshape a tensor into a matrix.

In unfold, row_idx and col_idx are specified to set which modes are used as the row/column.

dmat1 <- DelayedTensor::unfold(darr1, row_idx=c(1,2), col_idx=3)
dmat1

fold is the inverse operation of unfold, which is used to reshape a matrix into a tensor.

In fold, row_idx/col_idx are specified to set which modes correspond the row/column of the output tensor and modes is specified to set the mode of the output tensor.

dmat1_to_darr1 <- DelayedTensor::fold(dmat1,
    row_idx=c(1,2), col_idx=3, modes=dim(darr1))
dmat1_to_darr1
identical(as.array(darr1), as.array(dmat1_to_darr1))

There are some wrapper functions of unfold and fold.

For example, in k_unfold, mode m is used as the row, and the other modes are is used as the column.

k_fold is the inverse operation of k_unfold.

dmat2 <- DelayedTensor::k_unfold(darr1, m=1)
dmat2_to_darr1 <- k_fold(dmat2, m=1, modes=dim(darr1))
identical(as.array(darr1), as.array(dmat2_to_darr1))

dmat3 <- DelayedTensor::k_unfold(darr1, m=2)
dmat3_to_darr1 <- k_fold(dmat3, m=2, modes=dim(darr1))
identical(as.array(darr1), as.array(dmat3_to_darr1))

dmat4 <- DelayedTensor::k_unfold(darr1, m=3)
dmat4_to_darr1 <- k_fold(dmat4, m=3, modes=dim(darr1))
identical(as.array(darr1), as.array(dmat4_to_darr1))

In rs_unfold, mode m is used as the row, and the other modes are is used as the column.

rs_fold and rs_unfold also perform the same operations.

On the other hand, cs_unfold specifies the mode m as the column and the other modes are specified as the column.

cs_fold is the inverse operation of cs_unfold.

dmat8 <- DelayedTensor::cs_unfold(darr1, m=1)
dmat8_to_darr1 <- DelayedTensor::cs_fold(dmat8, m=1, modes=dim(darr1))
identical(as.array(darr1), as.array(dmat8_to_darr1))

dmat9 <- DelayedTensor::cs_unfold(darr1, m=2)
dmat9_to_darr1 <- DelayedTensor::cs_fold(dmat9, m=2, modes=dim(darr1))
identical(as.array(darr1), as.array(dmat9_to_darr1))

dmat10 <- DelayedTensor::cs_unfold(darr1, m=3)
dmat10_to_darr1 <- DelayedTensor::cs_fold(dmat10, m=3, modes=dim(darr1))
identical(as.array(darr1), as.array(dmat10_to_darr1))

In matvec, m=2 is specified as unfold.

unmatvec is the inverse operation of matvec.

dmat11 <- DelayedTensor::matvec(darr1)
dmat11_darr1 <- DelayedTensor::unmatvec(dmat11, modes=dim(darr1))
identical(as.array(darr1), as.array(dmat11_darr1))

ttm multiplies a tensor by a matrix.

m specifies in which mode the matrix will be multiplied.

dmatZ <- RandomUnifArray(c(10,4))
DelayedTensor::ttm(darr1, dmatZ, m=3)

ttl multiplies a tensor by multiple matrices.

ms specifies in which mode these matrices will be multiplied.

dmatX <- RandomUnifArray(c(10,2))
dmatY <- RandomUnifArray(c(10,3))
dlizt <- list(dmatX = dmatX, dmatY = dmatY)
DelayedTensor::ttl(darr1, dlizt, ms=c(1,2))

Vectorization

vec collapses a r Biocpkg("DelayedArray") into a 1D r Biocpkg("DelayedArray") (vector).

DelayedTensor::vec(darr1)

Norm Operations

fnorm calculates the Frobenius norm of a r Biocpkg("DelayedArray").

DelayedTensor::fnorm(darr1)

innerProd calculates the inner product value of two r Biocpkg("DelayedArray").

DelayedTensor::innerProd(darr1, darr2)

Outer Product

Inner product multiplies two tensors and collapses to 0D tensor (norm). On the other hand, the outer product is an operation that leaves all subscripts intact.

DelayedTensor::outerProd(darr1[,,1], darr2[,,1])

Diagonal Operations

Using DelayedDiagonalArray, we can originally create a diagonal r Biocpkg("DelayedArray") by specifying the dimensions (modes) and the values.

dgdarr <- DelayedTensor::DelayedDiagonalArray(c(5,6,7), 1:5)
dgdarr

Similar to the diag of the r CRANpkg("base") package, the diag of r Biocpkg("DelayedTensor") is used to extract and assign values to r Biocpkg("DelayedArray").

DelayedTensor::diag(dgdarr)

DelayedTensor::diag(dgdarr) <- c(1111, 2222, 3333, 4444, 5555)
DelayedTensor::diag(dgdarr)

Mode-wise Operations

modeSum calculates the summation for a given mode m of a r Biocpkg("DelayedArray"). The mode specified as m is collapsed into 1D as follows.

DelayedTensor::modeSum(darr1, m=1)
DelayedTensor::modeSum(darr1, m=2)
DelayedTensor::modeSum(darr1, m=3)

Similar to modeSum, modeMean calculates the average value for a given mode m of a r Biocpkg("DelayedArray").

DelayedTensor::modeMean(darr1, m=1)
DelayedTensor::modeMean(darr1, m=2)
DelayedTensor::modeMean(darr1, m=3)

Tensor Product Operations

There are some tensor specific product such as Hadamard product, Kronecker product, and Khatri-Rao product.

Hadamard Product

Suppose a tensor $A \in \Re ^{I \times J}$ and a tensor $B \in \Re ^{I \times J}$.

Hadamard product is defined as the element-wise product of $A$ and $B$.

Hadamard product can be extended to higher-order tensors.

$$ A \circ B = \begin{bmatrix} a_{11}b_{11} & a_{12}b_{12} & \cdots & a_{1J}b_{1J} \ a_{21}b_{21} & a_{22}b_{22} & \cdots & a_{2J}b_{2J} \ \vdots & \vdots & \ddots & \vdots \ a_{I1}b_{I1} & a_{I2}b_{I2} & \cdots & a_{IJ}b_{IJ} \ \end{bmatrix} $$

hadamard calculates Hadamard product of two r Biocpkg("DelayedArray") objects.

prod_h <- DelayedTensor::hadamard(darr1, darr2)
dim(prod_h)

hadamard_list calculates Hadamard product of multiple r Biocpkg("DelayedArray") objects.

prod_hl <- DelayedTensor::hadamard_list(list(darr1, darr2))
dim(prod_hl)

Kronecker Product

Suppose a tensor $A \in \Re ^{I \times J}$ and a tensor $B \in \Re ^{K \times L}$.

Kronecker product is defined as all the possible combination of element-wise product and the dimensions of output tensor are ${IK \times JL}$.

Kronecker product can be extended to higher-order tensors.

$$ A \otimes B = \begin{bmatrix} a_{11}B & a_{12}B & \cdots & a_{1J}B \ a_{21}B & a_{22}B & \cdots & a_{2J}B \ \vdots & \vdots & \ddots & \vdots \ a_{I1}B & a_{I2}B & \cdots & a_{IJ}B \ \end{bmatrix} $$

kronecker calculates Kronecker product of two r Biocpkg("DelayedArray") objects.

prod_kron <- DelayedTensor::kronecker(darr1, darr2)
dim(prod_kron)

kronecker_list calculates Kronecker product of multiple r Biocpkg("DelayedArray") objects.

prod_kronl <- DelayedTensor::kronecker_list(list(darr1, darr2))
dim(prod_kronl)

Khatri-Rao Product

Suppose a tensor $A \in \Re ^{I \times J}$ and a tensor $B \in \Re ^{K \times J}$.

Khatri-Rao product is defined as the column-wise Kronecker product and the dimensions of output tensor is ${IK \times J}$.

$$ A \odot B = \begin{bmatrix} a_{1} \otimes a_{1} & a_{2} \otimes a_{2} & \cdots & a_{J} \otimes a_{J} \ \end{bmatrix} $$

Khatri-Rao product can only be used for 2D tensors (matrices).

khatri_rao calculates Khatri-Rao product of two r Biocpkg("DelayedArray") objects.

prod_kr <- DelayedTensor::khatri_rao(darr1[,,1], darr2[,,1])
dim(prod_kr)

khatri_rao_list calculates Khatri-Rao product of multiple r Biocpkg("DelayedArray") objects.

prod_krl <- DelayedTensor::khatri_rao_list(list(darr1[,,1], darr2[,,1]))
dim(prod_krl)

Utilities Functions

list_rep replicates an arbitrary number of any R object.

str(DelayedTensor::list_rep(darr1, 3))

Bind Operations

modebind_list collapses multiple r Biocpkg("DelayedArray") objects into single r Biocpkg("DelayedArray") object.

m specifies the collapsed dimension.

dim(DelayedTensor::modebind_list(list(darr1, darr2), m=1))
dim(DelayedTensor::modebind_list(list(darr1, darr2), m=2))
dim(DelayedTensor::modebind_list(list(darr1, darr2), m=3))

rbind_list is the row-wise modebind_list and collapses multiple 2D r Biocpkg("DelayedArray") objects into single r Biocpkg("DelayedArray") object.

dim(DelayedTensor::rbind_list(list(darr1[,,1], darr2[,,1])))

cbind_list is the column-wise modebind_list and collapses multiple 2D r Biocpkg("DelayedArray") objects into single r Biocpkg("DelayedArray") object.

dim(DelayedTensor::cbind_list(list(darr1[,,1], darr2[,,1])))

Session information {.unnumbered}

sessionInfo()

rikenbit/DelayedTensor documentation built on Jan. 30, 2023, 6:15 p.m.