4.4 Triangular Linear Equations

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

Solves a triangular set of equations

                ′ ′       T               ′ ′      H                ′ ′
AX = B   (trans = N ),    A  X = B  (trans = T),    A  X = B  (trans = C ),

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

AX = B   (trans = ′N′),   AT X = B  (trans = ′T′),   AHX  = B  (trans = ′C ′),

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.