4.4 Triangular Linear Equations

trtrs( A, B[, uplo='L'[, trans='N'[, diag='N']]])

Solves a triangular set of equations

$\begin{displaymath} AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad A^TX=B ... ...'T'}), \qquad A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}), \end{displaymath}$

where A is real or complex and triangular of order n, and B is a matrix with n rows. A and B are matrices with the same type ('d' or 'z'). trtrs() is similar to blas.trsm(), except that it raises an ArithmeticError if a diagonal element of A is zero (whereas blas.trsm() returns inf values).

trtri( A[, uplo='L'[, diag='N']]): Computes the inverse of a real or complex triangular matrix A. On exit, A contains the inverse.

tbtrs( A, B[, uplo='L'[, trans='T'[,diag='N']]])

Solves a triangular set of equations

$\begin{displaymath} AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad A^TX=B ... ...'T'}), \qquad A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}), \end{displaymath}$

where A is real or complex triangular band matrix of order n, and B is a matrix with n rows. The diagonals of A are stored in A using the BLAS conventions for triangular band matrices. A and B are matrices with the same type ('d' or 'z'). On exit, B is replaced by the solution X.