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ENH: implementing the Cholesky backpropagation through Scipy's BLAS
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David Menéndez Hurtado
parent
10c19d853f
commit
da7e4e3af6
5 changed files with 5156 additions and 3467 deletions
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@ -7,6 +7,7 @@
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import numpy as np
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from cython.parallel import prange, parallel
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cimport numpy as np
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cimport scipy.linalg.cython_blas as cblas
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def flat_to_triang(np.ndarray[double, ndim=2] flat, int M):
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"""take a matrix N x D and return a D X M x M array where
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@ -20,12 +21,13 @@ def flat_to_triang(np.ndarray[double, ndim=2] flat, int M):
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cdef int count = 0
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cdef np.ndarray[double, ndim=3] ret = np.zeros((D, M, M))
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cdef int d, m, mm
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for d in range(D):
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count = 0
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for m in range(M):
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for mm in range(m+1):
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ret[d, m, mm] = flat[count,d]
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count += 1
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with nogil:
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for d in range(D):
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count = 0
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for m in range(M):
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for mm in range(m+1):
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ret[d, m, mm] = flat[count,d]
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count += 1
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return ret
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def triang_to_flat(np.ndarray[double, ndim=3] L):
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@ -33,75 +35,82 @@ def triang_to_flat(np.ndarray[double, ndim=3] L):
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cdef int M = L.shape[1]
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cdef int N = M*(M+1)/2
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cdef int count = 0
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cdef np.ndarray[double, ndim=2] flat = np.empty((N, D))
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cdef np.ndarray[double, ndim=2, mode='c'] flat = np.empty((N, D))
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cdef int d, m, mm
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for d in range(D):
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count = 0
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for m in range(M):
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for mm in range(m+1):
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flat[count,d] = L[d, m, mm]
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count += 1
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with nogil:
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for d in range(D):
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count = 0
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for m in range(M):
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for mm in range(m+1):
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flat[count,d] = L[d, m, mm]
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count += 1
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return flat
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def backprop_gradient(np.ndarray[double, ndim=2] dL, np.ndarray[double, ndim=2] L):
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cdef np.ndarray[double, ndim=2] dL_dK = np.tril(dL).copy()
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cdef np.ndarray[double, ndim=2, mode='c'] dL_dK = np.tril(dL).copy()
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cdef int N = L.shape[0]
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cdef int k, j, i
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for k in range(N - 1, -1, -1):
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for j in range(k + 1, N):
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for i in range(j, N):
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dL_dK[i, k] -= dL_dK[i, j] * L[j, k]
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dL_dK[j, k] -= dL_dK[i, j] * L[i, k]
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for j in range(k + 1, N):
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dL_dK[j, k] /= L[k, k]
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dL_dK[k, k] -= L[j, k] * dL_dK[j, k]
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dL_dK[k, k] /= (2. * L[k, k])
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with nogil:
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for k in range(N - 1, -1, -1):
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for j in range(k + 1, N):
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for i in range(j, N):
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dL_dK[i, k] -= dL_dK[i, j] * L[j, k]
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dL_dK[j, k] -= dL_dK[i, j] * L[i, k]
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for j in range(k + 1, N):
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dL_dK[j, k] /= L[k, k]
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dL_dK[k, k] -= L[j, k] * dL_dK[j, k]
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dL_dK[k, k] /= (2. * L[k, k])
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return dL_dK
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def backprop_gradient_par(double[:,:] dL, double[:,:] L):
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cdef double[:,:] dL_dK = np.tril(dL).copy()
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cdef double[:,::1] dL_dK = np.tril(dL).copy()
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cdef int N = L.shape[0]
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cdef int k, j, i
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for k in range(N - 1, -1, -1):
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with nogil, parallel():
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for i in prange(k + 1, N):
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for j in range(k+1, i+1):
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dL_dK[i, k] -= dL_dK[i, j] * L[j, k]
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for j in range(i, N):
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dL_dK[i, k] -= dL_dK[j, i] * L[j, k]
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for j in range(k + 1, N):
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dL_dK[j, k] /= L[k, k]
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dL_dK[k, k] -= L[j, k] * dL_dK[j, k]
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dL_dK[k, k] /= (2. * L[k, k])
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with nogil:
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for k in range(N - 1, -1, -1):
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with parallel():
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for i in prange(k + 1, N):
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for j in range(k+1, i+1):
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dL_dK[i, k] -= dL_dK[i, j] * L[j, k]
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for j in range(i, N):
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dL_dK[i, k] -= dL_dK[j, i] * L[j, k]
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for j in range(k + 1, N):
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dL_dK[j, k] /= L[k, k]
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dL_dK[k, k] -= L[j, k] * dL_dK[j, k]
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dL_dK[k, k] /= (2. * L[k, k])
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return dL_dK
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#here's a pure C version...
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cdef extern from "cholesky_backprop.h" nogil:
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void chol_backprop(int N, double* dL, double* L)
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cdef void chol_backprop(int N, double[:] dL, double[:] L) nogil:
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cdef int i, k, n
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# DSYMV required constant arguments
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cdef double alpha=-1, beta=1
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cdef int incx=1
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# DSCAL required arguments
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cdef double scale
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dL[N*N - 1] /= (2. * L[N*N - 1])
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for k in range(N-2, -1, -1):
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n = N-k-1
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cblas.dsymv(uplo='l', n=&n, alpha=&alpha, a=&dL[(N*(k+1) + k+1)], lda=&N, x=&L[k*N+k+1], incx=&incx,
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beta=&beta, y=&dL[N*(k+1)+k], incy=&N)
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for i in xrange(0, N - k - 1):
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dL[N * (k + 1 + i) + k] -= dL[N * (k + 1) + k + i * (N + 1) + 1] * L[k * N + k + 1 + i]
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scale = 1.0/L[k*N+k]
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cblas.dscal(&n, &scale , &dL[(k+1)*N+k], &N)
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dL[k*N + k] -= cblas.ddot(&n, &dL[(k+1)*N+k], &N, &L[k*N+k+1], &incx)
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dL[k*N + k] /= (2.0 * L[k*N + k])
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def backprop_gradient_par_c(np.ndarray[double, ndim=2] dL, np.ndarray[double, ndim=2] L):
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cdef np.ndarray[double, ndim=2] dL_dK = np.tril(dL) # makes a copy, c-contig
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cdef np.ndarray[double, ndim=2, mode='c'] dL_dK = np.tril(dL) # makes a copy, c-contig
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cdef int N = L.shape[0]
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with nogil:
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chol_backprop(N, <double*> dL_dK.data, <double*> L.data)
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chol_backprop(N, dL_dK, L)
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return dL_dK
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cdef extern from "cholesky_backprop.h" nogil:
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void old_chol_backprop(int N, double* dL, double* L)
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def backprop_gradient_par_c_old(np.ndarray[double, ndim=2] dL, np.ndarray[double, ndim=2] L):
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cdef np.ndarray[double, ndim=2] dL_dK = np.tril(dL) # makes a copy, c-contig
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cdef int N = L.shape[0]
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with nogil:
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old_chol_backprop(N, <double*> dL_dK.data, <double*> L.data)
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return dL_dK
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