Linear Algebra (BLAS, LAPACK, etc.)#

This module contains functions for performing high-level linear algebra operations on tensors.

The functions in this module are designed to be used with the Tensor class and its subclasses.

BLAS Level 1 Functions#

BLAS Level 1 routines perform operations of both addition and reduction on vectors of data. Typical operations include scaling and dot products.

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BLAS Level 2 Functions#

BLAS Level 2 routines perform matrix-vector operations, such as matrix-vector multiplication, rank-1 and rank-2 matrix updates, and solution of triangular systems.

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BLAS Level 3 Functions#

BLAS Level 3 routines perform matrix-matrix operations, such as matrix-matrix multiplication, rank-k update, and solutions of triangular systems.

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LAPACK Functions#

LAPACK routines can be divided into the following groups according to the operations they perform:

  • Routines for solving systems of linear equations, factoring and inverting matrices, and estimating condition numbers.

  • Routines for solving least squares problems, eigenvalue and singular value problems, and Sylvester’s equations.

  • Auxiliary and utility routines used to perform certain subtasks, common low-level computation or related tasks.

LAPACK Linear Equation Computational Functions#

Note

These functions assume Fortran, column-major ordering.

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To be classified#

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