Matrix

Create

Action	Code	Details
Declare N by M matrix	matrix[N,M] m;
Declare constrained matrix	matrix<lower=0, upper=1>[N,M] m;
Declare matrix with values	matrix[3,2] m = [ [1, 2], [3, 4], [5, 6] ];
Declare matrix filled with zeros	matrix[N,M] m = rep_matrix(0, N, M);
Declare matrix from series of row vectors	matrix[3,M] m = [ rv1, rv2, rv3 ];
Declare matrix from series of column vectors	matrix[N,3] m = [ v1', v2', v3']';
Create N by M matrix from replicated column vector of length N	rep_matrix(v, M)
Create N by M matrix from replicated row vector of length N	rep_matrix(v, N)
Declare K by K covariance matrix	cov_matrix[K] Omega;
Declare K by K correlation matrix	corr_matrix[K] Sigma;
Declare K by K Cholesky factors of covariance matrix	cholesky_factor_cov[K] L;
Declare M by N Cholesky factors of covariance matrix	cholesky_factor_cov[M,N] L;
Declare Cholesky factors of correlation matrix	cholesky_factor_corr[K] L;

Properties

Action	Code	Details
Number of elements (NxM)	num_elements(m)
Dimension sizes	dims(m)
Number of columns (M)	cols(m)
Number of rows (N)	rows(m)

Extract

Action	Code	Details
Element at row i, column j	m[i,j]
Extract _j_th column	m[, j]
Extract _j_th column	col(m, j)
Extract _j_th column as a matrix	block(m, 1, j, N, 1)
Extract _i_th row	m[i, ]	Accessing column-wise is much faster than row-wise
Extract _i_th row	row(m, i)
Extract _i_th row as a matrix	block(m, i, 1, 1, M)
Diagonal	diagonal(m)

Derive

For many useful functions, see https://jrnold.github.io/ssmodels-in-stan/stan-functions.html

Map

Action	Code	Details
Inverse	inverse(m)
Sum elementwise	m + m2
Multiply elementwise	m .* m2
Column-wise vector multiplication	rep_matrix(v, N) .* m
Row-wise vector multiplication	rep_matrix(v', M) .* m

Grow

Action	Code	Details
Append vector as column	append_col(m, v)
Append vector as row	append_row(m, v)

Shrink

Action	Code	Details
Slice columns	m[, 2:3]
Slice rows	m[2:3, ]
Submatrix by slicing rows and columns	m[1:2, 3:4]
Submatrix by start row and columns with length	block(m, rowstart, colstart, rowN, colN)

Reshape

Change dimensions or form of the matrix

Action	Code	Details
Cross-product (post-multiply)	tcrossprod(m)	m * m'
Cross-product (pre-multiply)	crossprod(m)	m' * m
Quadratic form with matrix	quad_form(m, m2)	m2' * m * m2
Quadratic form with vector	quad_form(m, v)	v' * m * v

Computations

Action	Code	Details
Column-wise self dot product	columns_dot_self(m)
Row-wise self dot product	rows_dot_self(m)
Dot product between columns	columns_dot_product(m, m2)	vector result
Dot product between rows	rows_dot_product(m, m2)	vector result
QR decomposition	Q = qr_Q(m); R = qr_R(m);
Thin QR decomposition	Q = qr_thin_Q(m) * sqrt(N - 1); R = qr_thin_R(m) / sqrt(N - 1);

Convert

Action	Code	Details
To vector	to_vector(m)