Parameter- and constant-matrix atoms

Operations that combine an expression with fixed data — a registered parameter node or a constant matrix — so the data can flow through the differentiated graph (and, for parameters, be updated between evaluations).

Usage

sd_scalar_mult(param, child)
sd_vector_mult(param, child)
sd_convolve(param, child)
sd_quad_form(child, Qp, Qi, Qx)
sd_quad_form_dense(param, child, data)
sd_left_matmul(child, Ap, Ai, Ax, ncol)
sd_right_matmul(child, Ap, Ai, Ax, ncol)
sd_left_matmul_dense(param, child, m, n, data)
sd_right_matmul_dense(param, child, m, n, data)
sd_left_kron(param, child, p, q, r, s, active_blocks)
sd_right_kron(param, child, p, q, r, s, active_blocks)

Arguments

param

a parameter expression handle (see sd_parameter).

child

an expression handle (the variable argument).

Qp, Qi, Qx

the row-pointer, column-index and value arrays of a compressed-sparse-row (CSR) matrix \(Q\) for sd_quad_form's \(x^\top Q x\). \(Q\) must be symmetric, so its CSR arrays equal its compressed-sparse-column arrays and the @p, @i, @x slots of a Matrix::dgCMatrix holding \(Q\) can be passed directly.

Ap, Ai, Ax

the row-pointer, column-index and value arrays of a constant matrix \(A\) in compressed-sparse-row (CSR) form, for the sparse matrix products. These are the @p, @i, @x slots of a Matrix::dgCMatrix holding \(A^\top\), not \(A\).

ncol

number of columns of the sparse constant matrix \(A\).

m, n

row and column dimensions of the dense constant matrix.

p, q, r, s

for the Kronecker products \(Z = A \otimes B\): \(A\) is \(p \times q\) and \(B\) is \(r \times s\).

active_blocks

for the Kronecker products, an integer vector of 0-based column-major indices of the nonzero entries of the variable-free operand (param); only the output rows they cover are built. For a parametric operand pass every index, 0:(length - 1).

data

the dense constant-matrix entries in row-major order (length m * n for the matrix products, n * n for sd_quad_form_dense); for an R matrix M, pass as.vector(t(M)). Pass numeric(0) when the matrix comes from param.

Value

An expression handle.

Details

sd_scalar_mult, sd_vector_mult

multiply a child by a scalar / vector parameter.

sd_convolve

convolution of a parameter kernel with a child.

sd_quad_form

the quadratic form \(x^\top Q x\) with sparse constant \(Q\).

sd_quad_form_dense

the quadratic form \(x^\top Q x\) with a dense symmetric \(n \times n\) \(Q\), where \(n\) is the length of the vector child. Supply exactly one source: param = NULL and data for a constant \(Q\) (checked for symmetry), or a parameter handle of size \(n^2\) with data = numeric(0) for a parametric \(Q\) that follows sd_update_params. A parametric \(Q\) is not checked: keeping it symmetric is the caller's responsibility.

sd_left_matmul, sd_right_matmul

left / right product with a sparse constant matrix \(A\).

sd_left_matmul_dense, sd_right_matmul_dense

left / right product with a dense constant or parametric matrix.

sd_left_kron, sd_right_kron

the Kronecker product \(A \otimes B\) with the variable-free operand param on the left (\(A\)) or on the right (\(B\)) and the variable operand child on the other side. param may be a parameter or a constant made with sd_parameter(..., param_id = -1, ...).

A parameter cannot be the source of the sparse products sd_left_matmul / sd_right_matmul (the engine does not support it; 'sparsediffpy' accepts the argument but the engine then aborts); use the dense products for a parametric matrix.

See also

sd_parameter, sd_register_params