<hankel-matrix> ( n -- matrix )
Extra matrix operations

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Vocabulary
math.matrices.extras

Inputs

n	an integer

Outputs

matrix

a matrix

Word description
A Hankel matrix is a symmetric, square-matrix in which each ascending skew-diagonal from left to right is constant. See hankel matrix.

The following is true of any Hankel matrixA: A[i][j] = A[j][i] = a[i+j-2].

The <toeplitz-matrix> is an upside-down Hankel matrix.

The <hilbert-matrix> is a special case of the Hankel matrix.

Examples

USING: math.matrices.extras prettyprint ; 4 <hankel-matrix> .
{ { 1 2 3 4 } { 2 3 4 0 } { 3 4 0 0 } { 4 0 0 0 } }

Definition

USING: kernel math sequences ;

IN: math.matrices.extras

: <hankel-matrix> ( n -- matrix )
    [ <iota> dup ] keep [ [ + abs 1 + dup ] ] dip
    [ > [ drop 0 ] when ] curry compose cartesian-map ;