next | previous | forward | backward | up | top | index | toc | Macaulay2 website
NumericalLinearAlgebra :: numericalImage

numericalImage -- Image of a matrix

Synopsis

Description

Computes the image of a matrix M numerically using singular value decomposition.

i1 : M = matrix {{1., 0, 1}, {0, 1, 1}, {1, 0, 1}}

o1 = | 1 0 1 |
     | 0 1 1 |
     | 1 0 1 |

                3          3
o1 : Matrix RR    <--- RR
              53         53
i2 : numericalImage(M, 0.01)

o2 = | -.627963 -.325058 |
     | -.459701 .888074  |
     | -.627963 -.325058 |

                3          2
o2 : Matrix RR    <--- RR
              53         53

Singular values less than the tolerance are treated as zero.

i3 : M = matrix {{0.999, 2}, {1, 2}}

o3 = | .999 2 |
     | 1    2 |

                2          2
o3 : Matrix RR    <--- RR
              53         53
i4 : numericalImage(M, 0.01)

o4 = | -.707036 |
     | -.707177 |

                2          1
o4 : Matrix RR    <--- RR
              53         53

Ways to use numericalImage :

For the programmer

The object numericalImage is a method function with options.