Affine and shape atoms

Affine combinations and shape manipulations of expressions. These have constant (zero) second derivatives but participate in the Jacobian.

Arguments

left, right, child, c

expression handles.

d1, d2

target row and column dimensions (for sd_promote, sd_reshape, sd_broadcast, sd_index).

indices

0-based column-major flat indices selected by sd_index.

args

a list of expression handles to stack (sd_hstack, sd_vstack).

n_vars

total number of variables in the problem.

axis

reduction axis for sd_sum: -1 (all entries), 0 (down rows) or 1 (across columns).

Value

An expression handle.

Details

sd_add

elementwise sum of two expressions.

sd_sum

sum reduction along axis.

sd_trace

matrix trace.

sd_transpose

matrix transpose.

sd_diag_vec

diagonal matrix from a vector.

sd_diag_mat

diagonal vector from a matrix.

sd_upper_tri

the strict upper-triangular entries.

sd_promote

promote a scalar to shape d1 x d2.

sd_reshape

reshape to d1 x d2 (column-major).

sd_broadcast

broadcast to d1 x d2.

sd_index

select entries by 0-based flat indices.

sd_hstack, sd_vstack

horizontal / vertical stacking.

See also

sparsediff-elementwise, sparsediff-matrix