gallery

Arguments

name

matrix name available in the following list: "cauchy", "circul", "minij", moler and "ris

n1, ..., nn

double, scalars or vectors depend on the name of matrix

g

generated matrix

Description

g = gallery(name, n1, ..., nn) generates a name matrix. n1, ..., nn arguments depend on the generated matrix (see *name* matrix sections below for more details).

g = gallery(3) is a badly conditioned 3-by-3 matrix.

g = gallery(5) creates a 5-by-5 matrix with an interesting eigenvalue problem.

Cauchy matrix

g = gallery("cauchy", x [, y]) creates a n-by-n Cauchy matrix. x and y are vectors of length n. If x is scalar, then it will be interpreted as 1:x (same behavior for y).

The Cauchy matrix is defined by g(i,j) = 1/(x(i) + y(j)).

g = gallery("cauchy", x) computes g(i,j) = 1/(x(i) + x(j)).

Circulant matrix

g = gallery("circul", x) creates a n-by-n Circulant matrix whose first row is given by x. x is vector of length n. If x is scalar, then it will be interpreted as 1:x.

A circulant matrix is a square matrix whose each row is obtained from the previous one by circular permutation (right shift):

.

Minij matrix

g = gallery("minij", n) creates a n-by-n Minij matrix. This matrix is symmetric positive definite matrix with g(i,j) = min(i,j).

Moler matrix

g = gallery("moler", n) creates a n-by-n Moler matrix. This matrix is symmetric positive definite matrix with g(i,j) = min(i,j)- 2 and g(i,i) = i.

Ris matrix

g = gallery("ris", n) creates a n-by-n Ris matrix. This matrix is symmetric n-by-n Hankel matrix with g(i,j) = 0.5/(n - i - j + 1.5). Its eigenvalues have the property of clustering near +/- pi/2.

Examples

Cauchy matrix

g = gallery("cauchy", 3)
g = gallery("cauchy", 1:3, 2:4)

--> g = gallery("cauchy", 3)

 g = [3x3 double]

   0.5         0.3333333   0.25     
   0.3333333   0.25        0.2      
   0.25        0.2         0.1666667

--> g = gallery("cauchy", 1:3, 2:4)

 g = [3x3 double]

   0.3333333   0.25        0.2      
   0.25        0.2         0.1666667
   0.2         0.1666667   0.1428571
   

Circulant matrix

g = gallery("circul", 5)
g = gallery("circul", [4 8 -1])

--> g = gallery("circul", 5)

 g = [5x5 double]

   1.   2.   3.   4.   5.
   5.   1.   2.   3.   4.
   4.   5.   1.   2.   3.
   3.   4.   5.   1.   2.
   2.   3.   4.   5.   1.

--> g = gallery("circul", [4 8 -1])

 g = [3x3 double]

   4.   8.  -1.
  -1.   4.   8.
   8.  -1.   4.
              

Minij matrix

g = gallery("minij", 5)

--> g = gallery("minij", 5)

 g = [5x5 double]

   1.   1.   1.   1.   1.
   1.   2.   2.   2.   2.
   1.   2.   3.   3.   3.
   1.   2.   3.   4.   4.
   1.   2.   3.   4.   5.
              

Moler matrix

g = gallery("moler", 5)

--> gallery("moler", 5)

 ans = [5x5 double]

   1.  -1.  -1.  -1.  -1.
  -1.   2.   0.   0.   0.
  -1.   0.   3.   1.   1.
  -1.   0.   1.   4.   2.
  -1.   0.   1.   2.   5.
              

Ris matrix

g = gallery("ris", 3)

--> g = gallery("ris", 3)

 g = [3x3 double]

   0.2         0.3333333   1.       
   0.3333333   1.         -1.       
   1.         -1.         -0.3333333
              

See also

• toeplitz — Toeplitz matrix (chosen constant diagonal bands)
• hilbm — Hilbert matrix
• invhilb — Inverse of the Hilbert matrix
• magic — Magic square
• vander — Vandermonde matrix
• frank — Frank matrix
• pascal — Pascal matrix
• hankel — Hankel matrix

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