Command Line

ztm [Options] A B Vectors Result

Options: Standard options, see Standard Command Line Options.

-s Start: Start with the given seed vector number instead of 1.

A: Input file: Left factor (square matrix).

B: Input file: Right factor (square matrix).

Vectors: Input file: Vectors to be multiplied.

Result: Output file: Vectors.

Input Files

A: Left factor, m×m matrix.

B: Right factor, n×n matrix.

Vectors: Vectors to be multiplied, a r×(mn) matrix.

Output Files

Result: Vectors.

Description

This program reads two matrices from A and B, a list of vectors, and calculates the image of the vectors under A⊗B. A and B must be square matrices of dimension m and n, respetively This calculation could be done with the zte and zmu programs, but using ztm avoids the memory-consuming calculation of A⊗B.

Implementation Details

Let m, n be the dimensions of A and B, respectively. For each input vector v∊F^1×mn, the program computes the m×n matrix $\hat{v}$ with

$\hat{v}_{ik} = v_{(i-1)n + k}\qquad (1\leq i\leq m,\ 1\leq k\leq n)$

Then, v(A⊗B) can be computed by ordinary matrix operations:

$\widehat{v(A\otimes B)} = A^{tr}\cdot\hat{v}\cdot B$

Both matrices and one vector must fit into memory at the same time.