Augment a delay distribution by left padding with new columns.

This function reshapes a discretized delay distribution matrix by left-padding it with n_col_augment columns. Because the output matrix must also be lower-triangular, additional rows are also padded to the top rows. This function allows one to extend further in the past the range of the initial delay distribution matrix. This is useful when convolving that delay distribution matrix with another delay distribution.

.left_augment_delay_distribution(delay_distribution_matrix, n_col_augment)

Arguments

delay_distribution_matrix	discretized delay distribution matrix
n_col_augment	an integer. Number of columns to left-pad delay_distribution_matrix with.

Value

If delay_distribution_matrix is of dimension N, then the result is of dimension N + n_col_augment.

Details

The columns that are added replicate the left-most column of delay_distribution_matrix.