Using the C++ Math Library

Numerical Linear Algebra

Matrix Analysis 

Function	Purpose
det	Determinant.
norm	Matrix or vector norm.
normest	Estimate the matrix 2-norm.
null	Orthonormal basis for the null space.
orth	Orthonormal basis for the range.
rank	Number of linearly independent rows or columns.
rcond	LINPACK reciprocal condition estimator.
rref	Reduced row echelon form.
subspace	Angle between two subspaces.
trace	Sum of diagonal elements.

Linear Equations 

Function	Purpose
chol	Cholesky factorization.
cond	Condition number with respect to inversion.
condest	1-norm condition number estimate.
inv	Matrix inverse.
lscov	Least squares in the presence of known covariance.
lu	Factors from Gaussian elimination.
nnls	Nonnegative least-squares.
pinv	Pseudoinverse.
qr	Orthogonal-triangular decomposition.

Eigenvalues and Singular Values 

Function	Purpose
condeig	Condition number with respect to eigenvalues.
eig	Eigenvalues and eigenvectors.
hess	Hessenberg form.
poly	Characteristic polynomial.
polyeig	Polynomial eigenvalue problem.
qz	Generalized eigenvalues.
schur	Schur decomposition.
svd	Singular value decomposition.

Matrix Functions 

Function	Purpose
expm	Matrix exponential.
funm	Evaluate general matrix function.
logm	Matrix logarithm.
sqrtm	Matrix square root.

Factorization Utilities 

Function	Purpose
balance	Diagonal scaling to improve eigenvalue accuracy.
cdf2rdf	Complex diagonal form to real block diagonal form.
planerot	Generate a Givens plane rotation.
qrdelete	Delete a column from a QR factorization.
qrinsert	Insert a column into a QR factorization.
rsf2csf	Real block diagonal form to complex diagonal form.

Specialized Math Functions

Data Analysis and Fourier Transform Functions