isDoublyStochastic -- whether a matrix is doubly stochastic

Synopsis

Usage:

isDoublyStochastic A
Inputs:
- A, a matrix,
Optional inputs:
- Tolerance => ..., default value .000001
Outputs:
- a Boolean value, whether $A$ is a doubly stochastic matrix

Description

This method determines whether a given matrix is doubly stochastic, i.e., is a real square matrix with all entries nonnegative and all row and column sums equal to $1$.

When working over an InexactFieldFamily like RR or CC, the option Tolerance can be used to specify the internal threshold for checking equality (any floating point number below the tolerance is treated as numerically zero).

i1 : O = randomOrthogonal 3

o1 = | .54916   .312336 .775158  |
     | .413897  .704145 -.576947 |
     | -.726025 .637672 .257413  |

                3         3
o1 : Matrix RR    <-- RR
              53        53

i2 : A = hadamard(O, O)

o2 = | .301576 .0975537 .60087   |
     | .171311 .495821  .332868  |
     | .527113 .406625  .0662616 |

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

i3 : isDoublyStochastic A

o3 = true

Ways to use isDoublyStochastic :

isDoublyStochastic(Matrix)

For the programmer

The object isDoublyStochastic is a method function with options.