Package 'rTensor2'

Description

Create a Tensor-class object from an array, matrix, or vector.

Usage

as.tensor(x, drop = FALSE)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

References

Imported from rTensor package version 1.4.8.

Examples

#From vector
vec <- runif(3); vecT <- as.tensor(vec); vecT
#From matrix
mat <- matrix(runif(2*3),nrow=2,ncol=3)
matT <- as.tensor(mat); matT
#From array
indices <- c(2,3,4)
arr <- array(runif(prod(indices)), dim = indices)
arrT <- as.tensor(arr); arrT

Description

Decompose a square matrix A into the product of a lower triangular matrix L and an upper triangular matrix U.

Usage

LU(A)

Arguments

Value

a lower triangular matrix L and an upper triangular matrix U so that A = LU.

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

z <- complex(real = rnorm(16), imag = rnorm(16))
A <- matrix(z,nrow=4)
LU(A)

Description

10000 MNIST training images (1000 of every digit), reformatted into a tensor: 28 x 10000 x 28. 1000 MNIST test images (100 of every digit), reformatted into a tensor: 28 x 1000 x 28

Usage

data("Mnist")

Format

The format is:

Mnist$train$images, Mnist$train$labels

Mnist$test$images, Mnist$test$labels

References

Deng L (2012). “The mnist database of handwritten digit images for machine learning research.” IEEE Signal Processing Magazine, 29(6), 141–142

Examples

data(tensor)

Description

Creates the polar/Jordan form of the P and D matrices after performing eigenvalue decomposition where the eigenvalue values are complex.

Usage

polar(P,D)

Arguments

Value

P the polar form (real-valued) matrix of eigenvectors.

D the polar form (real-valued) matrix of eigenvalues.

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

z <- complex(real = rnorm(16), imag = rnorm(16))
M <- matrix(z,nrow=4)
decomp <- eigen(M)
polar(decomp$vectors,decomp$values)

Description

Performs QR Decomposition of a Complex Matrix without pivoting.

Usage

QR(A)

Arguments

Value

an orthogonal matrix Q and an upper triangular matrix R so that A = QR.

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

z <- complex(real = rnorm(16), imag = rnorm(16))
A <- matrix(z,nrow=4)
QR(A)

Description

Generate a Tensor with specified modes with iid normal(0,1) entries.

Usage

rand_tensor(modes = c(3, 4, 5), drop = FALSE)

Arguments

Value

a Tensor object with modes given by modes

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

References

Imported from rTensor package version 1.4.8.

Examples

rand_tensor()
  rand_tensor(c(4,4,4))
  rand_tensor(c(10,2,1),TRUE)

Description

4 tensors (128 x 128 x 128) for 4 different gray scale images. boat, flashlight, keyboard, scooter.

Usage

data("raytrace")

Format

The format is:

raytrace$boat

raytrace$flashlight

raytrace$keyboard

raytrace$scooter

References

Hoover RC, Braman KS, Hao N (2011b). “Pose estimation from a single image using tensor decomposition and an algebra of circulants.” In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2928–2934. IEEE.

Examples

data(raytrace)

Description

Performs the transpose of a symmetric 3-mode tensor using any discrete transform.

Usage

t_tpose(tnsr,tform)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,3,4))
print(t_tpose(T,"dct"))

Description

Performs the Discrete Wavelet Transform of a 3-D Tensor.

Usage

tDWT(tnsr)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

References

G. Strang and T. Nguyen, Wavelets and filter banks. SIAM, 1996.

A. Haar, "Zur theorie der orthogonalen funktionensysteme", Mathematische annalen, vol. 69, no. 3, pp. 331-371, 1910.

Examples

T <- rand_tensor(modes=c(2,3,4))
print(tDWT(T))

Description

Performs a Eigenvalue decomposition of 3-mode tensor using any discrete transform.

Usage

tEIG(tnsr, tform)

Arguments

Value

a Tensor-class object

If Eigenvalue decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

P: A tensor of Eigenvectors ($n$ x $n$ x $k$)

D: An diagonal tensor of Eigenvalues ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

References

Kernfeld, E., Kilmer, M., & Aeron, S. (2015). Tensor-tensor products with invertible linear transforms. Linear Algebra and its Applications, 485, 545-570.

M. E. Kilmer, C. D. Martin, and L. Perrone, “A third-order generalization of the matrix svd as a product of third-order tensors,” Tufts University, Department of Computer Science, Tech. Rep. TR-2008-4, 2008

K. Braman, "Third-order tensors as linear operators on a space of matrices", Linear Algebra and its Applications, vol. 433, no. 7, pp. 1241-1253, 2010.

Examples

T <- rand_tensor(modes=c(2,2,4))
tEIG(T,"dst")

Description

Performs a Eigenvalue decomposition of 3-mode tensor using the discrete Cosine transform.

Usage

tEIGdct(tnsr)

Arguments

Value

a Tensor-class object

If Eigenvalue decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

P: A tensor of Eigenvectors ($n$ x $n$ x $k$)

D: An diagonal tensor of Eigenvalues ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tEIGdct(T))

Description

Performs a Eigenvalue decomposition of 3-mode tensor using the discrete Hadley transform.

Usage

tEIGdht(tnsr)

Arguments

Value

a Tensor-class object

If Eigenvalue decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

P: A tensor of Eigenvectors ($n$ x $n$ x $k$)

D: An diagonal tensor of Eigenvalues ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tEIGdht(T))

Description

Performs a Eigenvalue decomposition of 3-mode tensor using the discrete Sine transform.

Usage

tEIGdst(tnsr)

Arguments

Value

a Tensor-class object

If Eigenvalue decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

P: A tensor of Eigenvectors ($n$ x $n$ x $k$)

D: An diagonal tensor of Eigenvalues ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tEIGdst(T))

Description

Performs a Eigenvalue decomposition of 3-mode tensor using the discrete Walsh-Hadamard transform.

Usage

tEIGdwht(tnsr)

Arguments

Value

a Tensor-class object

If Eigenvalue decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

P: A tensor of Eigenvectors ($n$ x $n$ x $k$)

D: An diagonal tensor of Eigenvalues ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tEIGdwht(T))

Description

Performs a Eigenvalue decomposition of 3-mode tensor using the discrete Wavelet transform (Haar Wavelet).

Usage

tEIGdwt(tnsr)

Arguments

Value

a Tensor-class object

If Eigenvalue decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

P: A tensor of Eigenvectors ($n$ x $n$ x $k$)

D: An diagonal tensor of Eigenvalues ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

References

G. Strang and T. Nguyen, Wavelets and filter banks. SIAM, 1996.

A. Haar, “Zur theorie der orthogonalen funktionensysteme,” Mathema- tische annalen, vol. 69, no. 3, pp. 331–371, 1910.

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tEIGdwt(T))

Description

Performs a Eigenvalue decomposition of 3-mode tensor using the discrete Fourier transform.

Usage

tEIGfft(tnsr)

Arguments

Value

a Tensor-class object

If Eigenvalue decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

P: A tensor of Eigenvectors ($n$ x $n$ x $k$)

D: An diagonal tensor of Eigenvalues ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tEIGfft(T))

Description

Performs the Discrete Inverse Wavelet Transform of a 3-D Tensor.

Usage

tIDWT(tnsr)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

References

G. Strang and T. Nguyen, Wavelets and filter banks. SIAM, 1996.

A. Haar, "Zur theorie der orthogonalen funktionensysteme", Mathematische annalen, vol. 69, no. 3, pp. 331-371, 1910.

Examples

T <- rand_tensor(modes=c(2,3,4))
print(tIDWT(T))

Description

Performs the inverse of a tensor using the any discrete transform.

Usage

tINV(tnsr,tform)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tINV(T,"dst"))

Description

Performs the inverse of a tensor using the discrete cosine transform.

Usage

tINVdct(tnsr)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tINVdct(T))

Description

Performs the inverse of a tensor using the discrete Hartley transform.

Usage

tINVdht(tnsr)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tINVdht(T))

Description

Performs the inverse of a tensor using the discrete sine transform.

Usage

tINVdst(tnsr)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tINVdst(T))

Description

Performs the inverse of a tensor using the discrete Walsh-Hadamard transform.

Usage

tINVdwht(tnsr)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tINVdwht(T))

Description

Performs the inverse of a tensor using the discrete wavelet transform (Haar Wavelet).

Usage

tINVdwt(tnsr)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tINVdwt(T))

Description

Performs the inverse of a tensor using the discrete Fourier transform.

Usage

tINVfft(tnsr)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tINVfft(T))

Description

Performs linear discriminate analysis on a tensor using any discrete transform. Assumes tensor is sorted by classes.

Usage

tLDA(tnsr,nClass,nSamplesPerClass,tform)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

data("Mnist")
T <- Mnist$train$images
myorder <- order(Mnist$train$labels)
# tLDA need to be sorted by classes
T_sorted <- as.tensor(T[,myorder,])
# Using small tensor, 2 images for each class for demonstration
T <- T_sorted[,c(1:2,1001:1002,2001:2002,3001:3002,
      4001:4002,5001:5002,6001:6002,7001:7002,
      8001:8002,9001:9002),]
tLDA(T,10,2,"dct")

Description

Performs a tensor LU decomposition on any 3-mode tensor using any discrete transform.

Usage

tLU(tnsr,tform)

Arguments

Value

a Tensor-class object

If LU decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

L: The lower triangular tensor object ($n$ x $n$ x $k$)

U: The upper triangular tensor object ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

References

Kernfeld, E., Kilmer, M., & Aeron, S. (2015). Tensor-tensor products with invertible linear transforms. Linear Algebra and its Applications, 485, 545-570.

M. E. Kilmer, C. D. Martin, and L. Perrone, “A third-order generalization of the matrix svd as a product of third-order tensors,” Tufts University, Department of Computer Science, Tech. Rep. TR-2008-4, 2008

K. Braman, "Third-order tensors as linear operators on a space of matrices", Linear Algebra and its Applications, vol. 433, no. 7, pp. 1241-1253, 2010.

Examples

T <- rand_tensor(modes=c(2,2,4))
tLU(T,"dst")

Description

Performs a LU decomposition of 3-mode tensor using the discrete Cosine transform.

Usage

tLUdct(tnsr)

Arguments

Value

a Tensor-class object

If LU decomposition is performed on a $n x n x k$ tensor, the components in the returned value are:

L: The lower triangular tensor object ($n x n x k$)

U: The upper triangular tensor object ($n x n x k$)

Author(s)

Kyle Caudle [email protected]

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tLUdct(T))

Description

Performs a LU decomposition of 3-mode tensor using the discrete Hartley transform.

Usage

tLUdht(tnsr)

Arguments

Value

a Tensor-class object

If LU decomposition is performed on a $n x n x k$ tensor, the components in the returned value are:

L: The lower triangular tensor object ($n x n x k$)

U: The upper triangular tensor object ($n x n x k$)

Author(s)

Kyle Caudle [email protected]

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tLUdht(T))

Description

Performs a LU decomposition of 3-mode tensor using the discrete Sine transform.

Usage

tLUdst(tnsr)

Arguments

Value

a Tensor-class object

If LU decomposition is performed on a $n x n x k$ tensor, the components in the returned value are:

L: The lower triangular tensor object ($n x n x k$)

U: The upper triangular tensor object ($n x n x k$)

Author(s)

Kyle Caudle [email protected]

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tLUdst(T))

Description

Performs a LU decomposition of 3-mode tensor using the discrete Walsh-Hadamard transform.

Usage

tLUdwht(tnsr)

Arguments

Value

a Tensor-class object

If LU decomposition is performed on a $n x n x k$ tensor, the components in the returned value are:

L: The lower triangular tensor object ($n x n x k$)

U: The upper triangular tensor object ($n x n x k$)

Author(s)

Kyle Caudle [email protected]

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tLUdwht(T))

Description

Performs a LU decomposition of 3-mode tensor using the discrete Wavelet transform (Haar Wavelet).

Usage

tLUdwt(tnsr)

Arguments

Value

a Tensor-class object

If LU decomposition is performed on a $n x n x k$ tensor, the components in the returned value are:

L: The left singular value tensor object ($n x n x k$)

U: The right singular value tensor object ($n x n x k$)

Author(s)

Kyle Caudle [email protected]

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tLUdwt(T))

Description

Performs a LU decomposition of 3-mode tensor using the discrete Fourier transform.

Usage

tLUfft(tnsr)

Arguments

Value

a Tensor-class object

If LU decomposition is performed on a $n x n x k$ tensor, the components in the returned value are:

L: The lower triangular tensor object ($n x n x k$)

U: The upper triangular tensor object ($n x n x k$)

Author(s)

Kyle Caudle [email protected]

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tLUfft(T))

Description

Find the mean of a 3-mode tensor.

Usage

tmean(tnsr)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

tnsr <- rand_tensor(modes=c(3,4,5))
tmean(tnsr)

Description

Multiplies two 3-mode tensors using any discrete transform.

Usage

tmult(x,y,tform)

Arguments

Value

a Tensor-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T1 <- rand_tensor(modes=c(2,2,4))
T2 <- rand_tensor(modes=c(2,3,4))
print(tmult(T1,T2,"dst"))

Description

Performs a tensor QR decomposition on any 3-mode tensor using any discrete transform.

Usage

tQR(tnsr,tform)

Arguments

Value

a Tensor-class object

If the QR decomposition is performed on a $n \times n \times k$ tensor, the components in the returned value are:

Q: The left singular value tensor object ($n \times n \times k$)

R: The right singular value tensor object ($n \times n \times k$)

Author(s)

Kyle Caudle [email protected]

References

Kernfeld, E., Kilmer, M., & Aeron, S. (2015). Tensor-tensor products with invertible linear transforms. Linear Algebra and its Applications, 485, 545-570.

M. E. Kilmer, C. D. Martin, and L. Perrone, “A third-order generalization of the matrix svd as a product of third-order tensors,” Tufts University, Department of Computer Science, Tech. Rep. TR-2008-4, 2008

K. Braman, "Third-order tensors as linear operators on a space of matrices", Linear Algebra and its Applications, vol. 433, no. 7, pp. 1241-1253, 2010.

Examples

T <- rand_tensor(modes=c(2,2,4))
tQR(T,"dst")

Description

Performs a QR decomposition of 3-mode tensor using the discrete Cosine transform.

Usage

tQRdct(tnsr)

Arguments

Value

a Tensor-class object

If QR decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

Q: An orthogonal tensor ($n$ x $n$ x $k$).

R: An upper triangular tensor ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tQR(T,"dct"))

Description

Performs a QR decomposition of 3-mode tensor using the discrete Hartley transform.

Usage

tQRdht(tnsr)

Arguments

Value

a Tensor-class object

If QR decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

Q: An orthogonal tensor ($n$ x $n$ x $k$).

R: An upper triangular tensor ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tQRdht(T))

Description

Performs a QR decomposition of 3-mode tensor using the discrete Sine transform.

Usage

tQRdst(tnsr)

Arguments

Value

a Tensor-class object

If QR decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

Q: An orthogonal tensor ($n$ x $n$ x $k$).

R: An upper triangular tensor ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tQRdst(T))

Description

Performs a QR decomposition of 3-mode tensor using the discrete Walsh-Hadamard transform.

Usage

tQRdwht(tnsr)

Arguments

Value

a Tensor-class object

If QR decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

Q: An orthogonal tensor ($n$ x $n$ x $k$).

R: An upper triangular tensor ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tQRdwht(T))

Description

Performs a QR decomposition of 3-mode tensor using the discrete wavelet transform.

Usage

tQRdwt(tnsr)

Arguments

Value

a Tensor-class object

If QR decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

Q: An orthogonal tensor ($n$ x $n$ x $k$).

R: An upper triangular tensor ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tQRdwt(T))

Description

Performs a QR decomposition of 3-mode tensor using the discrete Fourier transform.

Usage

tQRfft(tnsr)

Arguments

Value

a Tensor-class object

If QR decomposition is performed on a $n$ x $n$ x $k$ tensor, the components in the returned value are:

Q: An orthogonal tensor ($n$ x $n$ x $k$).

R: An upper triangular tensor ($n$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,2,4))
print(tQRfft(T))

Description

Performs a tensor singular value decomposition on any 3-mode tensor using any discrete transform.

Usage

tSVD(tnsr,tform)

Arguments

Value

a Tensor-class object

If the SVD is performed on a $m$ x $n$ x $k$ tensor, the components in the returned value are:

U: The left singular value tensor object ($m$ x $m$ x $k$)

V: The right singular value tensor object ($n$ x $n$ x $k$)

S: A diagonal tensor ($m$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

References

Kernfeld, E., Kilmer, M., & Aeron, S. (2015). Tensor-tensor products with invertible linear transforms. Linear Algebra and its Applications, 485, 545-570.

M. E. Kilmer, C. D. Martin, and L. Perrone, “A third-order generalization of the matrix svd as a product of third-order tensors,” Tufts University, Department of Computer Science, Tech. Rep. TR-2008-4, 2008

K. Braman, "Third-order tensors as linear operators on a space of matrices", Linear Algebra and its Applications, vol. 433, no. 7, pp. 1241-1253, 2010.

Examples

T <- rand_tensor(modes=c(2,3,4))
print(tSVD(T,"dst"))

Description

Performs a tensor singular value decomposition on any 3-mode tensor using the discrete cosine transform.

Usage

tSVDdct(tnsr)

Arguments

Value

a Tensor-class object

If the SVD is performed on a $m$ x $n$ x $k$ tensor, the components in the returned value are:

U: The left singular value tensor object ($m$ x $m$ x $k$)

V: The right singular value tensor object ($n$ x $n$ x $k$)

S: A diagonal tensor ($m$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,3,4))
print(tSVDdct(T))

Description

Performs a tensor singular value decomposition on any 3-mode tensor using the discrete Harley transform.

Usage

tSVDdht(tnsr)

Arguments

Value

a Tensor-class object

If the SVD is performed on a $m$ x $n$ x $k$ tensor, the components in the returned value are:

U: The left singular value tensor object ($m$ x $m$ x $k$)

V: The right singular value tensor object ($n$ x $n$ x $k$)

S: A diagonal tensor ($m$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,3,4))
print(tSVDdht(T))

Description

Performs a tensor singular value decomposition on any 3-mode tensor using the discrete Sine transform.

Usage

tSVDdst(tnsr)

Arguments

Value

a Tensor-class object

If the SVD is performed on a $m$ x $n$ x $k$ tensor, the components in the returned value are:

U: The left singular value tensor object ($m$ x $m$ x $k$)

V: The right singular value tensor object ($n$ x $n$ x $k$)

S: A diagonal tensor ($m$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,3,4))
print(tSVDdst(T))

Description

Performs a tensor singular value decomposition on any 3-mode tensor using the discrete Walsh-Hadamard transform.

Usage

tSVDdwht(tnsr)

Arguments

Value

a Tensor-class object

If the SVD is performed on a $m$ x $n$ x $k$ tensor, the components in the returned value are:

U: The left singular value tensor object ($m$ x $m$ x $k$)

V: The right singular value tensor object ($n$ x $n$ x $k$)

S: A diagonal tensor ($m$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,3,4))
print(tSVDdwht(T))

Description

Performs a tensor singular value decomposition on any 3-mode tensor using the discrete wavelet transform (Haar Wavelet).

Usage

tSVDdwt(tnsr)

Arguments

Value

a Tensor-class object

If the SVD is performed on a $m$ x $n$ x $k$ tensor, the components in the returned value are:

U: The left singular value tensor object ($m$ x $m$ x $k$)

V: The right singular value tensor object ($n$ x $n$ x $k$)

S: A diagonal tensor ($m$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,3,4))
print(tSVDdwt(T))

Description

Performs a tensor singular value decomposition on any 3-mode tensor using the discrete Fourier transform.

Usage

tSVDfft(tnsr)

Arguments

Value

a Tensor-class object

If the SVD is performed on a $m$ x $n$ x $k$ tensor, the components in the returned value are:

U: The left singular value tensor object ($m$ x $m$ x $k$)

V: The right singular value tensor object ($n$ x $n$ x $k$)

S: A diagonal tensor ($m$ x $n$ x $k$)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Examples

T <- rand_tensor(modes=c(2,3,4))
print(tSVDfft(T))