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{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"Implement Moore-Penrose pseudoinverse for PMMatrix","articleBody":"https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse\r\n\r\nA simple (but slightly time-consuming) implementation can be based on SVD:\r\n```st\r\nPMMatrix \u003e\u003e pseudoinverse\r\n\t| svd u s v sPseudoinverse |\r\n\tsvd := PMSingularValueDecomposition decompose: matrix.\r\n\r\n\tu := svd leftSingularMatrix.\r\n\ts := svd diagonalSingularValueMatrix.\r\n\tv := svd rightSingularMatrix.\r\n\r\n\tsPseudoinverse := self pseudoinverseOfDiagonal: s.\r\n\t^ v * sPseudoinverse * u transpose\r\n```\r\n```st\r\nPMMatrix \u003e\u003e pseudoinverseOfDiagonal: aMatrix [\r\n\t\"To get pseudoinverse of a diagonal rectangular matrix, we take reciprocal of any no-zero element of the main diagonal, leaving all zeros in place. Then we transpose the matrix.\"\r\n\r\n\t| pseudoinverse diagonalSize |\r\n\r\n\t\"Rows become columns and columns become rows because we transpose\"\r\n\tpseudoinverse := PMMatrix\r\n\t\tzerosRows: aMatrix numberOfColumns\r\n\t\tcols: aMatrix numberOfRows.\r\n\r\n\t\"The size of the main diagonal of a rectangular matrix is its smallest dimension\"\r\n\tdiagonalSize := aMatrix numberOfRows min: aMatrix numberOfColumns.\r\n\r\n\t\"Inverting the elements on the main diaginal\"\r\n\t1 to: diagonalSize do: [ :i |\r\n\t\tpseudoinverse at: i at: i put: ((aMatrix at: i at: i) = 0\r\n\t\t\tifTrue: [ 0 ] ifFalse: [ 1 / (aMatrix at: i at: i) ]) ].\r\n\r\n\t^ pseudoinverse\r\n```","author":{"url":"https://github.com/olekscode","@type":"Person","name":"olekscode"},"datePublished":"2022-04-26T18:45:34.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":3},"url":"https://github.com/260/PolyMath/issues/260"}