Calling BLAS bundled with Scipy. See also http://docs.scipy.org/doc/scipy-dev/reference/linalg.blas.html and http://docs.scipy.org/doc/scipy-dev/reference/linalg.lapack.html

example.pyx

import numpy as np
import scipy.linalg.blas

cdef extern from "f2pyptr.h":
    void *f2py_pointer(object) except NULL

ctypedef int dgemm_t(
	char *transa, char *transb,
	int *m, int *n, int *k,
	double *alpha,
	double *a, int *lda,
	double *b, int *ldb,
	double *beta,
	double *c, int *ldc)

# Since Scipy >= 0.12.0
cdef dgemm_t *dgemm = <dgemm_t*>f2py_pointer(scipy.linalg.blas.dgemm._cpointer)

def myfunc():
    cdef double[::1,:] a, b, c
    cdef int m, n, k, lda, ldb, ldc
    cdef double alpha, beta

    a = np.array([[1, 2], [3, 4]], float, order="F")
    b = np.array([[5, 6], [7, 8]], float, order="F")
    c = np.empty((2, 2), float, order="F")

    alpha = 1.0
    beta = 0.0
    lda = 2
    ldb = 2
    ldc = 2
    m = 2
    n = 2
    k = 2
    dgemm("N", "N", &m, &n, &k, &alpha, &a[0,0], &lda, &b[0,0], &ldb, &beta, &c[0,0], &ldc)
    print(np.asarray(c))
    print(np.dot(a, b))

f2pyptr.h

#ifndef F2PYPTR_H_
#define F2PYPTR_H_

#include <Python.h>

void *f2py_pointer(PyObject *obj) 
{
#if PY_VERSION_HEX < 0x03000000
    if (PyCObject_Check(obj)) {
        return PyCObject_AsVoidPtr(obj);
    }
#endif
#if PY_VERSION_HEX >= 0x02070000
    if (PyCapsule_CheckExact(obj)) {
        return PyCapsule_GetPointer(obj, NULL);
    }
#endif
    PyErr_SetString(PyExc_ValueError, "Not an object containing a void ptr");
    return NULL;
}

#endif

I'm new to this, but what is the difference between the above and the following,

from scipy.linalg.cython_blas import dgemm

which avoids having to work through fortran explicitly?

(I get about the same speed between your example and importing dgemm from cython_blas.)

I think this is the more appropriate way to call the built in cython_blas libs: https://stackoverflow.com/questions/44980665/using-the-scipy-cython-blas-interface-from-cython-not-working-on-vectors-mx1-1xn nevermind all the error handling around the type of input contiguous array (F or C) could just be removed. The above using f2pyptr.h is ignoring the SciPy direct link to Fortran which avoids that step. And this link is actually in the SciPy examples of how to call the interface. Just saying.