SBCL BLAS/LAPACK bindings

This is a set of (very few) SBCL bindings for BLAS/LAPACK. I just add whatever I need manually. This should be mostly for tests, so as not to make libraries reliant on SBCL-specific code.

Functions

List

• dgemm
• dgesv

Description

dgemm a b &key transa transb alpha beta c => x

Perform dgemm, double-float matrix multiplication: $X = \alpha \cdot A.B + \beta \cdot C$.

• a, b, c: Native 2D Common Lisp matrices of double-float elements. The rows and columns are multiplied as expected in matrix multiplication.
• transa, transb: Case-insensitive. Can be "n" for no transposition to apply. "t" or "c" to apply a transposition.
• alpha, beta: double-float scalars.
• x: Result matrix.

dgesv a b => x

Perform dgesv. Solve the linear system of equations for x: $Ax = B$ using LU decomposition. x is the matrix of solution corresponding to the right-hand sides in B. An error is emitted if the operation was impossible: eg. when A is degenerate.

• a, b: Native 2D matrices of double-float elements. a is necessarily square. b can have as many columns as right-hand sides.
• x: The sets of solutions, in columns, same indices as right-hand sides in b.

dgetrf a => lu ipiv

Perform dgetrf. LUP decomposition of matrix A. Returns L and U stored in a single matrix lu with the unit elements of L omitted. ipiv is the row swap vector to apply in sequence to lu in order to find A. We retrieve A with A = P.L.U. Error whenever A is (exactly) singular.

• a: Native 2D matrices of double-float elements. a is necessarily square and non-singular.
• lu: L and U matrices stored as a single square matrix.
• ipiv: Row permutations sequence.

Dependencies

LAPACK and BLAS should be installed on the system.

sbcl-lapack:

• array-operations

sbcl-lapack/test:

• rove

Run tests

(asdf:test-system "sbcl-lapack")

Choices

As far as possible, I try to:

• Use functional calls.
• Hide the return codes, turn them into errors and warnings.

Caveats

• The results are put in matrices with copying. Performance could be marginally improved.
• It is possible to make the system crash by providing wrong user inputs. I try to catch the most common mistakes though.

References

• https://www.netlib.org/lapack/explore-html/index.html Documentation for LAPACK/BLAS routines.