blas_api.rst

BLAS/LAPACK API

Below a description of prometeo's BLAS/LAPACK API can be found:

LEVEL 1 BLAS

LEVEL 2 BLAS

• General matrix-vector multiplication (GEMV)

z ← β ⋅ y + α ⋅ op(A)x

pmt_gemv(A[.T], x, [y], z, [alpha=1.0], [beta=0.0])

• Solve linear system with (lower or upper) triangular matrix coefficient (TRSV)

op(A) x = b

pmt_trsv(A[.T], b, [lower=True])

• Matrix-vector multiplication with (lower or upper) triangular matrix coefficient (TRMV)

z ← op(A) x

pmt_trmv(A[.T], x, z, [lower=True])

LEVEL 3 BLAS

• General matrix-matrix multiplication (GEMM)

D ← β ⋅ C + α ⋅ op(A) op(B)

pmt_gemm(A[.T], B[.T], [C], D, [alpha=1.0], [beta=0.0])

• Symmetric rank k update (SYRK)

D ← β ⋅ C + α ⋅ op(A) op(B)

with C and D lower triangular.

pmt_syrk(A[.T], B[.T], [C], D, [alpha=1.0], [beta=0.0])

• Triangular matrix-matrix multiplication (TRMM)

D ← α ⋅ B A^⊤

with B upper triangular or

D ← α ⋅ A B

with A lower triangular.

pmt_trmm(A[.T], B, D, [alpha=1.0], [beta=0.0])

LAPACK

• Cholesky factorization (POTRF)

C = D D^⊤

with D lower triangular and C symmetric and positive definite

pmt_potrf(C, D)

• LU factorization (GETRF)

C = L P U

pmt_getr(C, D)

• QR factorization (GEQRF)

C = Q R

pmt_geqrf(C, D)