Version 1.0b1 API Documentation generated by Endo 2006-08-14

Classes

• LinAlgError

Function summary

• cholesky(a)
• det(a)
• eig(a)
• eigh(a, UPLO = 'L')
• eigvals(a)
• eigvalsh(a, UPLO = 'L')
• inv(a)
• lstsq(a, b, rcond = 1e-010)
• norm(x, ord = None)
• pinv(a, rcond = 1e-010)
• solve(a, b)
• svd(a, full_matrices = 1, compute_uv = 1)

Functions

• cholesky(a)
• det(a)

  The determinant of the 2-d array a

• eig(a)

  eig(a) returns u,v where u is the eigenvalues and v is a matrix of eigenvectors with vector v[:,i] corresponds to eigenvalue u[i]. Satisfies the equation dot(a, v[:,i]) = u[i]*v[:,i]

• eigh(a, UPLO = 'L')

  Compute eigenvalues for a Hermitian-symmetric matrix.

• eigvals(a)
• eigvalsh(a, UPLO = 'L')
• inv(a)
• lstsq(a, b, rcond = 1e-010)

  returns x,resids,rank,s
  where x minimizes 2-norm(|b - Ax|)
        resids is the sum square residuals
        rank is the rank of A
        s is the rank of the singular values of A in descending order
  
  If b is a matrix then x is also a matrix with corresponding columns.
  If the rank of A is less than the number of columns of A or greater than
  the number of rows, then residuals will be returned as an empty array
  otherwise resids = sum((b-dot(A,x)**2).
  Singular values less than s[0]*rcond are treated as zero.
  

• norm(x, ord = None)

  norm(x, ord=None) -> n

  Matrix or vector norm.

  Inputs:

  x -- a rank-1 (vector) or rank-2 (matrix) array ord -- the order of the norm.

  Comments:

  For arrays of any rank, if ord is None:

  calculate the square norm (Euclidean norm for vectors, Frobenius norm for matrices)

  For vectors ord can be any real number including Inf or -Inf.

  ord = Inf, computes the maximum of the magnitudes ord = -Inf, computes minimum of the magnitudes ord is finite, computes sum(abs(x)**ord)**(1.0/ord)

  For matrices ord can only be one of the following values:

  ord = 2 computes the largest singular value ord = -2 computes the smallest singular value ord = 1 computes the largest column sum of absolute values ord = -1 computes the smallest column sum of absolute values ord = Inf computes the largest row sum of absolute values ord = -Inf computes the smallest row sum of absolute values ord = 'fro' computes the frobenius norm sqrt(sum(diag(X.H * X)))

  For values ord < 0, the result is, strictly speaking, not a mathematical 'norm', but it may still be useful for numerical purposes.

• pinv(a, rcond = 1e-010)

  Return the (Moore-Penrose) pseudo-inverse of a 2-d array

  This method computes the generalized inverse using the singular-value decomposition and all singular values larger than rcond of the largest.

• solve(a, b)

  Return the solution of a*x = b

• svd(a, full_matrices = 1, compute_uv = 1)

  Singular Value Decomposition.
  
  u,s,vh = svd(a)
  
  If a is an M x N array, then the svd produces a factoring of the array
  into two unitary (orthogonal) 2-d arrays u (MxM) and vh (NxN) and a 
  min(M,N)-length array of singular values such that
     
                   a == dot(u,dot(S,vh)) 
  
  where S is an MxN array of zeros whose main diagonal is s. 
  
  if compute_uv == 0, then return only the singular values
  if full_matrices == 0, then only part of either u or vh is 
                         returned so that it is MxN
  

Imported names