Tutorial_MatrixConverting

Introduction

In Smallapack, it is possible to create a new matrix from existing matrices. See Tutorial_MatrixCreation for learning how to create a matrix first.

Details

Extracting a sub-matrix

Extracting a single row/column (like matlab a(i,:) or a(:,j)):

(LapackSGEMatrix eye: 3 @ 2) atRow: 2.

(LapackSGEMatrix eye: 3 @ 2) atColumn: 1.

Extracting several rows/columns:

(LapackSGEMatrix eye: 5 @ 4) atRows: (1 to: 3).
(LapackSGEMatrix eye: 4 @ 5) atColumns: #(1 2 4).

Extrating an arbitrary sub-matrix:

(LapackSGEMatrix eye: 5 @ 4) atRows: (1 to: 3) atColumns: #(1 2 4).

Extracting main diagonal:

(LapackSGEMatrix eye: 5 @ 4) diagonal.

Extracting a super diagonal (above diagonal):

(LapackSGEMatrix fromSequence: #(11 21 31 12 22 32) nrow: 3 ncol: 2) diagonalAt: 1.

Extracting a sub diagonal (below diagonal):

(LapackSGEMatrix fromSequence: #(11 21 31 12 22 32) nrow: 3 ncol: 2) diagonalAt: -1.

Extracting a triangle:

(LapackSGEMatrix ones: 4@3) upperTriangle.
(LapackSGEMatrix ones: 4@3) lowerTriangle.

Extracting an upper triangle from first subdiagonal up to upper right:

(LapackSGEMatrix ones: 4@3) upperTriangle: -1.

Extracting an upper triangle from first super diagonal:

(LapackSGEMatrix ones: 4@3) upperTriangle: 1.

Extracting a lower triangle from first super diagonal, down to lower left:

(LapackSGEMatrix ones: 4@3) lowerTriangle: 1.

Extracting a upper triangle from second sub diagonal:

(LapackSGEMatrix ones: 4@3) lowerTriangle: -2.

Concatenating matrices

Concatenating the columns (like matlab [left , right]):

(LapackSGEMatrix eye: 3 @ 2) , (LapackSGEMatrix eye: 3 @ 3).

Concatenating the rows (like matlab [top ; bottom]):

(LapackSGEMatrix eye: 3 @ 2) ,, (LapackSGEMatrix eye: 2 @ 2).

Replicating a matrix (like matlab repmat(a,m,n)):

(LapackSGEMatrix eye: 3 @ 2) replicateNrow: 5 timesNcol: 4.
(LapackSGEMatrix eye: 3 @ 2) replicate: 5 @ 4.

Appending/prepending empty rows/columns:

(LapackSGEMatrix eye: 3 @ 2) prependRows: 2.
(LapackSGEMatrix eye: 3 @ 2) appendRows: 2.
(LapackSGEMatrix eye: 3 @ 2) prependColumns: 1.
(LapackSGEMatrix eye: 3 @ 2) appendColumns: 2.

Reshaping matrices

Making a row or column matrix (the order will be columnwise as the underlying sequence):

(LapackSGEMatrix fromSequence: #(11 21 31 12 22 32) nrow: 3 ncol: 2) asRowMatrix.
(LapackSGEMatrix fromSequence: #(11 21 31 12 22 32) nrow: 3 ncol: 2) asColumnMatrix.

General reshaping:

(LapackSGEMatrix eye: 3 @ 2) reshapeNrow: 2 ncol: 3.
(LapackSGEMatrix eye: 3 @ 2) reshape: 2 @ 3.