qr_decomposition: The QR Decomposition of a GPUmatrix object

In GPUmatrix: Basic Linear Algebra with GPU

The QR Decomposition of a GPUmatrix object

Description

These functions mimic the base qr family functions to operate on gpu.matrix-class objects.

Usage

## S4 method for signature 'gpu.matrix.tensorflow'
qr(x,...)
## S4 method for signature 'gpu.matrix.torch'
qr(x,...)

## S4 method for signature 'list'
qr.Q(qr,complete,Dvec)
## S4 method for signature 'list'
qr.R(qr,complete)
## S4 method for signature 'list'
qr.X(qr,complete)

## S4 method for signature 'list'
qr.coef(qr,y)
## S4 method for signature 'list'
qr.qy(qr,y)
## S4 method for signature 'list'
qr.qty(qr,y)
## S4 method for signature 'list'
qr.resid(qr,y)
## S4 method for signature 'ANY,gpu.matrix.tensorflow'
qr.solve(a,b)
## S4 method for signature 'ANY,gpu.matrix.torch'
qr.solve(a,b)
## S4 method for signature 'gpu.matrix.tensorflow,ANY'
qr.solve(a,b)
## S4 method for signature 'gpu.matrix.tensorflow,gpu.matrix.tensorflow'
qr.solve(a,b)
## S4 method for signature 'gpu.matrix.torch,ANY'
qr.solve(a,b)
## S4 method for signature 'gpu.matrix.torch,gpu.matrix.torch'
qr.solve(a,b)
## S4 method for signature 'list,ANY'
qr.solve(a,b)

Arguments

x	a gpu.matrix.
y, b	a gpu.matrix corresponding to the right-hand side of equations ax=b or ax=y.
...	further arguments passed to or from other methods.
qr	a list resulting from the application of the function qr.
complete	The same as in 'base' function qr.Q, and qr.X
Dvec	The same as in 'base' function qr.Q
a	a gpu.matrix corresponding to the left-hand side of equations ax=b or ax=y.

Details

The function qr internally calls the corresponding function of the library torch or tensorflow (depending on the type of input gpu.matrix-class).

The QR decomposition can be used to solve the equation Ax=b for a given matrix A, and a vector of observations b. In this context, the functions qr.coef, and qr.resid return the coefficients, and residuals values. Moreover, the functions qr.qy, and qr.qty returns Q %*% y and Q %*% t(y). Note that if parameter complete is TRUE then an arbitrary orthogonal completion of the X and Q matrix or wheter the R matrix is to be completed by binding zero-value rows beneath the square upper triangle.

The function solve.qr solves the system of equations Ax=b via the QR decomposition. This function internally calls the corresponding function of the library torch or tensorflow (depending on the type of input gpu.matrix-class).

If the input gpu.matrix-class object(s) are stored on the GPU, then the operations will be performed on the GPU. See gpu.matrix.

Value

The function qr returns a list with the following items:

q	The corresponding complete matrix Q resulting from the application of the QR decomposition to a. It is a gpu.matrix-class object.
r	The corresponding complete matrix R resulting from the application of the QR decomposition to a. It is a gpu.matrix-class object.
x	The matrix a. It is a gpu.matrix-class object.

Please note that the output returned by this function is different from the 'base' function qr, which returns an object of the 'qr' class.

After performing a QR decomposition on a matrix A, given the resulting object, the functions qr.X, qr.Q, and qr.R return the original matrix A, the matrix Q, and the matrix R respectively. The returned matrices are gpu.matrix-class objects.

The functions qr.coef and qr.resid return the coefficients and residuals when fitting the equation Ax=b. In this context, the functions qr.qy, and qr.qty returns Q %*% y and Q %*% t(y). The resulting vectors are objects of the class gpu.matrix.

The function qr.solve returns a gpu.matrix-class object containing the coefficients of the solution of the system of equations Ax=b by QR decomposition.

See Also

See qr, linalg_qr, torch_triangular_solve

Examples

## Not run: 
## overdetermined system
A <- gpu.matrix(runif(12),nrow =  4)
b <- gpu.matrix(rnorm(4),ncol=1)
qr.solve(a = A, b)
qr_gpu <- qr(A)
qr.solve(a=qr_gpu,b)
qr.coef(qr = qr_gpu,b)
qr.resid(qr = qr_gpu,b)
qr.qty(qr = qr_gpu,b)
qr.qy(qr = qr_gpu,b)
qr.X(qr = qr_gpu,complete = T)
qr.Q(qr = qr_gpu,complete = T)
qr.R(qr = qr_gpu,complete = T)


## underdetermined system
A <- gpu.matrix(runif(12),nrow =  3)
b <- gpu.matrix(rnorm(3),ncol=1)
qr.solve(a = A, b)
qr_gpu <- qr(A)
qr.solve(a=qr_gpu,b)
qr.coef(qr = qr_gpu,b)
qr.resid(qr = qr_gpu,b)
qr.qty(qr = qr_gpu,b)
qr.qy(qr = qr_gpu,b)
qr.X(qr = qr_gpu,complete = T)
qr.Q(qr = qr_gpu,complete = T)
qr.R(qr = qr_gpu,complete = T)

## End(Not run)

GPUmatrix documentation built on May 29, 2024, 11:02 a.m.