# Authors: Gilles Louppe # Peter Prettenhofer # Brian Holt # Noel Dawe # Satrajit Gosh # Lars Buitinck # Arnaud Joly # Joel Nothman # Fares Hedayati # Jacob Schreiber # # License: BSD 3 clause from cython cimport final from libc.math cimport isnan from libc.stdlib cimport qsort from libc.string cimport memcpy from ._criterion cimport Criterion from ._utils cimport log from ._utils cimport rand_int from ._utils cimport rand_uniform from ._utils cimport RAND_R_MAX from ..utils._typedefs cimport int8_t import numpy as np from scipy.sparse import issparse cdef float64_t INFINITY = np.inf # Mitigate precision differences between 32 bit and 64 bit cdef float32_t FEATURE_THRESHOLD = 1e-7 # Constant to switch between algorithm non zero value extract algorithm # in SparsePartitioner cdef float32_t EXTRACT_NNZ_SWITCH = 0.1 cdef inline void _init_split(SplitRecord* self, intp_t start_pos) noexcept nogil: self.impurity_left = INFINITY self.impurity_right = INFINITY self.pos = start_pos self.feature = 0 self.threshold = 0. self.improvement = -INFINITY self.missing_go_to_left = False self.n_missing = 0 cdef class Splitter: """Abstract splitter class. Splitters are called by tree builders to find the best splits on both sparse and dense data, one split at a time. """ def __cinit__( self, Criterion criterion, intp_t max_features, intp_t min_samples_leaf, float64_t min_weight_leaf, object random_state, const int8_t[:] monotonic_cst, ): """ Parameters ---------- criterion : Criterion The criterion to measure the quality of a split. max_features : intp_t The maximal number of randomly selected features which can be considered for a split. min_samples_leaf : intp_t The minimal number of samples each leaf can have, where splits which would result in having less samples in a leaf are not considered. min_weight_leaf : float64_t The minimal weight each leaf can have, where the weight is the sum of the weights of each sample in it. random_state : object The user inputted random state to be used for pseudo-randomness monotonic_cst : const int8_t[:] Monotonicity constraints """ self.criterion = criterion self.n_samples = 0 self.n_features = 0 self.max_features = max_features self.min_samples_leaf = min_samples_leaf self.min_weight_leaf = min_weight_leaf self.random_state = random_state self.monotonic_cst = monotonic_cst self.with_monotonic_cst = monotonic_cst is not None def __getstate__(self): return {} def __setstate__(self, d): pass def __reduce__(self): return (type(self), (self.criterion, self.max_features, self.min_samples_leaf, self.min_weight_leaf, self.random_state, self.monotonic_cst), self.__getstate__()) cdef int init( self, object X, const float64_t[:, ::1] y, const float64_t[:] sample_weight, const unsigned char[::1] missing_values_in_feature_mask, ) except -1: """Initialize the splitter. Take in the input data X, the target Y, and optional sample weights. Returns -1 in case of failure to allocate memory (and raise MemoryError) or 0 otherwise. Parameters ---------- X : object This contains the inputs. Usually it is a 2d numpy array. y : ndarray, dtype=float64_t This is the vector of targets, or true labels, for the samples represented as a Cython memoryview. sample_weight : ndarray, dtype=float64_t The weights of the samples, where higher weighted samples are fit closer than lower weight samples. If not provided, all samples are assumed to have uniform weight. This is represented as a Cython memoryview. has_missing : bool At least one missing values is in X. """ self.rand_r_state = self.random_state.randint(0, RAND_R_MAX) cdef intp_t n_samples = X.shape[0] # Create a new array which will be used to store nonzero # samples from the feature of interest self.samples = np.empty(n_samples, dtype=np.intp) cdef intp_t[::1] samples = self.samples cdef intp_t i, j cdef float64_t weighted_n_samples = 0.0 j = 0 for i in range(n_samples): # Only work with positively weighted samples if sample_weight is None or sample_weight[i] != 0.0: samples[j] = i j += 1 if sample_weight is not None: weighted_n_samples += sample_weight[i] else: weighted_n_samples += 1.0 # Number of samples is number of positively weighted samples self.n_samples = j self.weighted_n_samples = weighted_n_samples cdef intp_t n_features = X.shape[1] self.features = np.arange(n_features, dtype=np.intp) self.n_features = n_features self.feature_values = np.empty(n_samples, dtype=np.float32) self.constant_features = np.empty(n_features, dtype=np.intp) self.y = y self.sample_weight = sample_weight if missing_values_in_feature_mask is not None: self.criterion.init_sum_missing() return 0 cdef int node_reset( self, intp_t start, intp_t end, float64_t* weighted_n_node_samples ) except -1 nogil: """Reset splitter on node samples[start:end]. Returns -1 in case of failure to allocate memory (and raise MemoryError) or 0 otherwise. Parameters ---------- start : intp_t The index of the first sample to consider end : intp_t The index of the last sample to consider weighted_n_node_samples : ndarray, dtype=float64_t pointer The total weight of those samples """ self.start = start self.end = end self.criterion.init( self.y, self.sample_weight, self.weighted_n_samples, self.samples, start, end ) weighted_n_node_samples[0] = self.criterion.weighted_n_node_samples return 0 cdef int node_split( self, ParentInfo* parent_record, SplitRecord* split, ) except -1 nogil: """Find the best split on node samples[start:end]. This is a placeholder method. The majority of computation will be done here. It should return -1 upon errors. """ pass cdef void node_value(self, float64_t* dest) noexcept nogil: """Copy the value of node samples[start:end] into dest.""" self.criterion.node_value(dest) cdef inline void clip_node_value(self, float64_t* dest, float64_t lower_bound, float64_t upper_bound) noexcept nogil: """Clip the value in dest between lower_bound and upper_bound for monotonic constraints.""" self.criterion.clip_node_value(dest, lower_bound, upper_bound) cdef float64_t node_impurity(self) noexcept nogil: """Return the impurity of the current node.""" return self.criterion.node_impurity() cdef inline void shift_missing_values_to_left_if_required( SplitRecord* best, intp_t[::1] samples, intp_t end, ) noexcept nogil: """Shift missing value sample indices to the left of the split if required. Note: this should always be called at the very end because it will move samples around, thereby affecting the criterion. This affects the computation of the children impurity, which affects the computation of the next node. """ cdef intp_t i, p, current_end # The partitioner partitions the data such that the missing values are in # samples[-n_missing:] for the criterion to consume. If the missing values # are going to the right node, then the missing values are already in the # correct position. If the missing values go left, then we move the missing # values to samples[best.pos:best.pos+n_missing] and update `best.pos`. if best.n_missing > 0 and best.missing_go_to_left: for p in range(best.n_missing): i = best.pos + p current_end = end - 1 - p samples[i], samples[current_end] = samples[current_end], samples[i] best.pos += best.n_missing # Introduce a fused-class to make it possible to share the split implementation # between the dense and sparse cases in the node_split_best and node_split_random # functions. The alternative would have been to use inheritance-based polymorphism # but it would have resulted in a ~10% overall tree fitting performance # degradation caused by the overhead frequent virtual method lookups. ctypedef fused Partitioner: DensePartitioner SparsePartitioner cdef inline int node_split_best( Splitter splitter, Partitioner partitioner, Criterion criterion, SplitRecord* split, ParentInfo* parent_record, bint with_monotonic_cst, const int8_t[:] monotonic_cst, ) except -1 nogil: """Find the best split on node samples[start:end] Returns -1 in case of failure to allocate memory (and raise MemoryError) or 0 otherwise. """ # Find the best split cdef intp_t start = splitter.start cdef intp_t end = splitter.end cdef intp_t end_non_missing cdef intp_t n_missing = 0 cdef bint has_missing = 0 cdef intp_t n_searches cdef intp_t n_left, n_right cdef bint missing_go_to_left cdef intp_t[::1] samples = splitter.samples cdef intp_t[::1] features = splitter.features cdef intp_t[::1] constant_features = splitter.constant_features cdef intp_t n_features = splitter.n_features cdef float32_t[::1] feature_values = splitter.feature_values cdef intp_t max_features = splitter.max_features cdef intp_t min_samples_leaf = splitter.min_samples_leaf cdef float64_t min_weight_leaf = splitter.min_weight_leaf cdef uint32_t* random_state = &splitter.rand_r_state cdef SplitRecord best_split, current_split cdef float64_t current_proxy_improvement = -INFINITY cdef float64_t best_proxy_improvement = -INFINITY cdef float64_t impurity = parent_record.impurity cdef float64_t lower_bound = parent_record.lower_bound cdef float64_t upper_bound = parent_record.upper_bound cdef intp_t f_i = n_features cdef intp_t f_j cdef intp_t p cdef intp_t p_prev cdef intp_t n_visited_features = 0 # Number of features discovered to be constant during the split search cdef intp_t n_found_constants = 0 # Number of features known to be constant and drawn without replacement cdef intp_t n_drawn_constants = 0 cdef intp_t n_known_constants = parent_record.n_constant_features # n_total_constants = n_known_constants + n_found_constants cdef intp_t n_total_constants = n_known_constants _init_split(&best_split, end) partitioner.init_node_split(start, end) # Sample up to max_features without replacement using a # Fisher-Yates-based algorithm (using the local variables `f_i` and # `f_j` to compute a permutation of the `features` array). # # Skip the CPU intensive evaluation of the impurity criterion for # features that were already detected as constant (hence not suitable # for good splitting) by ancestor nodes and save the information on # newly discovered constant features to spare computation on descendant # nodes. while (f_i > n_total_constants and # Stop early if remaining features # are constant (n_visited_features < max_features or # At least one drawn features must be non constant n_visited_features <= n_found_constants + n_drawn_constants)): n_visited_features += 1 # Loop invariant: elements of features in # - [:n_drawn_constant[ holds drawn and known constant features; # - [n_drawn_constant:n_known_constant[ holds known constant # features that haven't been drawn yet; # - [n_known_constant:n_total_constant[ holds newly found constant # features; # - [n_total_constant:f_i[ holds features that haven't been drawn # yet and aren't constant apriori. # - [f_i:n_features[ holds features that have been drawn # and aren't constant. # Draw a feature at random f_j = rand_int(n_drawn_constants, f_i - n_found_constants, random_state) if f_j < n_known_constants: # f_j in the interval [n_drawn_constants, n_known_constants[ features[n_drawn_constants], features[f_j] = features[f_j], features[n_drawn_constants] n_drawn_constants += 1 continue # f_j in the interval [n_known_constants, f_i - n_found_constants[ f_j += n_found_constants # f_j in the interval [n_total_constants, f_i[ current_split.feature = features[f_j] partitioner.sort_samples_and_feature_values(current_split.feature) n_missing = partitioner.n_missing end_non_missing = end - n_missing if ( # All values for this feature are missing, or end_non_missing == start or # This feature is considered constant (max - min <= FEATURE_THRESHOLD) feature_values[end_non_missing - 1] <= feature_values[start] + FEATURE_THRESHOLD ): # We consider this feature constant in this case. # Since finding a split among constant feature is not valuable, # we do not consider this feature for splitting. features[f_j], features[n_total_constants] = features[n_total_constants], features[f_j] n_found_constants += 1 n_total_constants += 1 continue f_i -= 1 features[f_i], features[f_j] = features[f_j], features[f_i] has_missing = n_missing != 0 criterion.init_missing(n_missing) # initialize even when n_missing == 0 # Evaluate all splits # If there are missing values, then we search twice for the most optimal split. # The first search will have all the missing values going to the right node. # The second search will have all the missing values going to the left node. # If there are no missing values, then we search only once for the most # optimal split. n_searches = 2 if has_missing else 1 for i in range(n_searches): missing_go_to_left = i == 1 criterion.missing_go_to_left = missing_go_to_left criterion.reset() p = start while p < end_non_missing: partitioner.next_p(&p_prev, &p) if p >= end_non_missing: continue if missing_go_to_left: n_left = p - start + n_missing n_right = end_non_missing - p else: n_left = p - start n_right = end_non_missing - p + n_missing # Reject if min_samples_leaf is not guaranteed if n_left < min_samples_leaf or n_right < min_samples_leaf: continue current_split.pos = p criterion.update(current_split.pos) # Reject if monotonicity constraints are not satisfied if ( with_monotonic_cst and monotonic_cst[current_split.feature] != 0 and not criterion.check_monotonicity( monotonic_cst[current_split.feature], lower_bound, upper_bound, ) ): continue # Reject if min_weight_leaf is not satisfied if ((criterion.weighted_n_left < min_weight_leaf) or (criterion.weighted_n_right < min_weight_leaf)): continue current_proxy_improvement = criterion.proxy_impurity_improvement() if current_proxy_improvement > best_proxy_improvement: best_proxy_improvement = current_proxy_improvement # sum of halves is used to avoid infinite value current_split.threshold = ( feature_values[p_prev] / 2.0 + feature_values[p] / 2.0 ) if ( current_split.threshold == feature_values[p] or current_split.threshold == INFINITY or current_split.threshold == -INFINITY ): current_split.threshold = feature_values[p_prev] current_split.n_missing = n_missing if n_missing == 0: current_split.missing_go_to_left = n_left > n_right else: current_split.missing_go_to_left = missing_go_to_left best_split = current_split # copy # Evaluate when there are missing values and all missing values goes # to the right node and non-missing values goes to the left node. if has_missing: n_left, n_right = end - start - n_missing, n_missing p = end - n_missing missing_go_to_left = 0 if not (n_left < min_samples_leaf or n_right < min_samples_leaf): criterion.missing_go_to_left = missing_go_to_left criterion.update(p) if not ((criterion.weighted_n_left < min_weight_leaf) or (criterion.weighted_n_right < min_weight_leaf)): current_proxy_improvement = criterion.proxy_impurity_improvement() if current_proxy_improvement > best_proxy_improvement: best_proxy_improvement = current_proxy_improvement current_split.threshold = INFINITY current_split.missing_go_to_left = missing_go_to_left current_split.n_missing = n_missing current_split.pos = p best_split = current_split # Reorganize into samples[start:best_split.pos] + samples[best_split.pos:end] if best_split.pos < end: partitioner.partition_samples_final( best_split.pos, best_split.threshold, best_split.feature, best_split.n_missing ) criterion.init_missing(best_split.n_missing) criterion.missing_go_to_left = best_split.missing_go_to_left criterion.reset() criterion.update(best_split.pos) criterion.children_impurity( &best_split.impurity_left, &best_split.impurity_right ) best_split.improvement = criterion.impurity_improvement( impurity, best_split.impurity_left, best_split.impurity_right ) shift_missing_values_to_left_if_required(&best_split, samples, end) # Respect invariant for constant features: the original order of # element in features[:n_known_constants] must be preserved for sibling # and child nodes memcpy(&features[0], &constant_features[0], sizeof(intp_t) * n_known_constants) # Copy newly found constant features memcpy(&constant_features[n_known_constants], &features[n_known_constants], sizeof(intp_t) * n_found_constants) # Return values parent_record.n_constant_features = n_total_constants split[0] = best_split return 0 # Sort n-element arrays pointed to by feature_values and samples, simultaneously, # by the values in feature_values. Algorithm: Introsort (Musser, SP&E, 1997). cdef inline void sort(float32_t* feature_values, intp_t* samples, intp_t n) noexcept nogil: if n == 0: return cdef intp_t maxd = 2 * log(n) introsort(feature_values, samples, n, maxd) cdef inline void swap(float32_t* feature_values, intp_t* samples, intp_t i, intp_t j) noexcept nogil: # Helper for sort feature_values[i], feature_values[j] = feature_values[j], feature_values[i] samples[i], samples[j] = samples[j], samples[i] cdef inline float32_t median3(float32_t* feature_values, intp_t n) noexcept nogil: # Median of three pivot selection, after Bentley and McIlroy (1993). # Engineering a sort function. SP&E. Requires 8/3 comparisons on average. cdef float32_t a = feature_values[0], b = feature_values[n / 2], c = feature_values[n - 1] if a < b: if b < c: return b elif a < c: return c else: return a elif b < c: if a < c: return a else: return c else: return b # Introsort with median of 3 pivot selection and 3-way partition function # (robust to repeated elements, e.g. lots of zero features). cdef void introsort(float32_t* feature_values, intp_t *samples, intp_t n, intp_t maxd) noexcept nogil: cdef float32_t pivot cdef intp_t i, l, r while n > 1: if maxd <= 0: # max depth limit exceeded ("gone quadratic") heapsort(feature_values, samples, n) return maxd -= 1 pivot = median3(feature_values, n) # Three-way partition. i = l = 0 r = n while i < r: if feature_values[i] < pivot: swap(feature_values, samples, i, l) i += 1 l += 1 elif feature_values[i] > pivot: r -= 1 swap(feature_values, samples, i, r) else: i += 1 introsort(feature_values, samples, l, maxd) feature_values += r samples += r n -= r cdef inline void sift_down(float32_t* feature_values, intp_t* samples, intp_t start, intp_t end) noexcept nogil: # Restore heap order in feature_values[start:end] by moving the max element to start. cdef intp_t child, maxind, root root = start while True: child = root * 2 + 1 # find max of root, left child, right child maxind = root if child < end and feature_values[maxind] < feature_values[child]: maxind = child if child + 1 < end and feature_values[maxind] < feature_values[child + 1]: maxind = child + 1 if maxind == root: break else: swap(feature_values, samples, root, maxind) root = maxind cdef void heapsort(float32_t* feature_values, intp_t* samples, intp_t n) noexcept nogil: cdef intp_t start, end # heapify start = (n - 2) / 2 end = n while True: sift_down(feature_values, samples, start, end) if start == 0: break start -= 1 # sort by shrinking the heap, putting the max element immediately after it end = n - 1 while end > 0: swap(feature_values, samples, 0, end) sift_down(feature_values, samples, 0, end) end = end - 1 cdef inline int node_split_random( Splitter splitter, Partitioner partitioner, Criterion criterion, SplitRecord* split, ParentInfo* parent_record, bint with_monotonic_cst, const int8_t[:] monotonic_cst, ) except -1 nogil: """Find the best random split on node samples[start:end] Returns -1 in case of failure to allocate memory (and raise MemoryError) or 0 otherwise. """ # Draw random splits and pick the best cdef intp_t start = splitter.start cdef intp_t end = splitter.end cdef intp_t[::1] features = splitter.features cdef intp_t[::1] constant_features = splitter.constant_features cdef intp_t n_features = splitter.n_features cdef intp_t max_features = splitter.max_features cdef intp_t min_samples_leaf = splitter.min_samples_leaf cdef float64_t min_weight_leaf = splitter.min_weight_leaf cdef uint32_t* random_state = &splitter.rand_r_state cdef SplitRecord best_split, current_split cdef float64_t current_proxy_improvement = - INFINITY cdef float64_t best_proxy_improvement = - INFINITY cdef float64_t impurity = parent_record.impurity cdef float64_t lower_bound = parent_record.lower_bound cdef float64_t upper_bound = parent_record.upper_bound cdef intp_t f_i = n_features cdef intp_t f_j # Number of features discovered to be constant during the split search cdef intp_t n_found_constants = 0 # Number of features known to be constant and drawn without replacement cdef intp_t n_drawn_constants = 0 cdef intp_t n_known_constants = parent_record.n_constant_features # n_total_constants = n_known_constants + n_found_constants cdef intp_t n_total_constants = n_known_constants cdef intp_t n_visited_features = 0 cdef float32_t min_feature_value cdef float32_t max_feature_value _init_split(&best_split, end) partitioner.init_node_split(start, end) # Sample up to max_features without replacement using a # Fisher-Yates-based algorithm (using the local variables `f_i` and # `f_j` to compute a permutation of the `features` array). # # Skip the CPU intensive evaluation of the impurity criterion for # features that were already detected as constant (hence not suitable # for good splitting) by ancestor nodes and save the information on # newly discovered constant features to spare computation on descendant # nodes. while (f_i > n_total_constants and # Stop early if remaining features # are constant (n_visited_features < max_features or # At least one drawn features must be non constant n_visited_features <= n_found_constants + n_drawn_constants)): n_visited_features += 1 # Loop invariant: elements of features in # - [:n_drawn_constant[ holds drawn and known constant features; # - [n_drawn_constant:n_known_constant[ holds known constant # features that haven't been drawn yet; # - [n_known_constant:n_total_constant[ holds newly found constant # features; # - [n_total_constant:f_i[ holds features that haven't been drawn # yet and aren't constant apriori. # - [f_i:n_features[ holds features that have been drawn # and aren't constant. # Draw a feature at random f_j = rand_int(n_drawn_constants, f_i - n_found_constants, random_state) if f_j < n_known_constants: # f_j in the interval [n_drawn_constants, n_known_constants[ features[n_drawn_constants], features[f_j] = features[f_j], features[n_drawn_constants] n_drawn_constants += 1 continue # f_j in the interval [n_known_constants, f_i - n_found_constants[ f_j += n_found_constants # f_j in the interval [n_total_constants, f_i[ current_split.feature = features[f_j] # Find min, max partitioner.find_min_max( current_split.feature, &min_feature_value, &max_feature_value ) if max_feature_value <= min_feature_value + FEATURE_THRESHOLD: features[f_j], features[n_total_constants] = features[n_total_constants], current_split.feature n_found_constants += 1 n_total_constants += 1 continue f_i -= 1 features[f_i], features[f_j] = features[f_j], features[f_i] # Draw a random threshold current_split.threshold = rand_uniform( min_feature_value, max_feature_value, random_state, ) if current_split.threshold == max_feature_value: current_split.threshold = min_feature_value # Partition current_split.pos = partitioner.partition_samples(current_split.threshold) # Reject if min_samples_leaf is not guaranteed if (((current_split.pos - start) < min_samples_leaf) or ((end - current_split.pos) < min_samples_leaf)): continue # Evaluate split # At this point, the criterion has a view into the samples that was partitioned # by the partitioner. The criterion will use the partition to evaluating the split. criterion.reset() criterion.update(current_split.pos) # Reject if min_weight_leaf is not satisfied if ((criterion.weighted_n_left < min_weight_leaf) or (criterion.weighted_n_right < min_weight_leaf)): continue # Reject if monotonicity constraints are not satisfied if ( with_monotonic_cst and monotonic_cst[current_split.feature] != 0 and not criterion.check_monotonicity( monotonic_cst[current_split.feature], lower_bound, upper_bound, ) ): continue current_proxy_improvement = criterion.proxy_impurity_improvement() if current_proxy_improvement > best_proxy_improvement: best_proxy_improvement = current_proxy_improvement best_split = current_split # copy # Reorganize into samples[start:best.pos] + samples[best.pos:end] if best_split.pos < end: if current_split.feature != best_split.feature: # TODO: Pass in best.n_missing when random splitter supports missing values. partitioner.partition_samples_final( best_split.pos, best_split.threshold, best_split.feature, 0 ) criterion.reset() criterion.update(best_split.pos) criterion.children_impurity( &best_split.impurity_left, &best_split.impurity_right ) best_split.improvement = criterion.impurity_improvement( impurity, best_split.impurity_left, best_split.impurity_right ) # Respect invariant for constant features: the original order of # element in features[:n_known_constants] must be preserved for sibling # and child nodes memcpy(&features[0], &constant_features[0], sizeof(intp_t) * n_known_constants) # Copy newly found constant features memcpy(&constant_features[n_known_constants], &features[n_known_constants], sizeof(intp_t) * n_found_constants) # Return values parent_record.n_constant_features = n_total_constants split[0] = best_split return 0 @final cdef class DensePartitioner: """Partitioner specialized for dense data. Note that this partitioner is agnostic to the splitting strategy (best vs. random). """ cdef: const float32_t[:, :] X cdef intp_t[::1] samples cdef float32_t[::1] feature_values cdef intp_t start cdef intp_t end cdef intp_t n_missing cdef const unsigned char[::1] missing_values_in_feature_mask def __init__( self, const float32_t[:, :] X, intp_t[::1] samples, float32_t[::1] feature_values, const unsigned char[::1] missing_values_in_feature_mask, ): self.X = X self.samples = samples self.feature_values = feature_values self.missing_values_in_feature_mask = missing_values_in_feature_mask cdef inline void init_node_split(self, intp_t start, intp_t end) noexcept nogil: """Initialize splitter at the beginning of node_split.""" self.start = start self.end = end self.n_missing = 0 cdef inline void sort_samples_and_feature_values( self, intp_t current_feature ) noexcept nogil: """Simultaneously sort based on the feature_values. Missing values are stored at the end of feature_values. The number of missing values observed in feature_values is stored in self.n_missing. """ cdef: intp_t i, current_end float32_t[::1] feature_values = self.feature_values const float32_t[:, :] X = self.X intp_t[::1] samples = self.samples intp_t n_missing = 0 const unsigned char[::1] missing_values_in_feature_mask = self.missing_values_in_feature_mask # Sort samples along that feature; by # copying the values into an array and # sorting the array in a manner which utilizes the cache more # effectively. if missing_values_in_feature_mask is not None and missing_values_in_feature_mask[current_feature]: i, current_end = self.start, self.end - 1 # Missing values are placed at the end and do not participate in the sorting. while i <= current_end: # Finds the right-most value that is not missing so that # it can be swapped with missing values at its left. if isnan(X[samples[current_end], current_feature]): n_missing += 1 current_end -= 1 continue # X[samples[current_end], current_feature] is a non-missing value if isnan(X[samples[i], current_feature]): samples[i], samples[current_end] = samples[current_end], samples[i] n_missing += 1 current_end -= 1 feature_values[i] = X[samples[i], current_feature] i += 1 else: # When there are no missing values, we only need to copy the data into # feature_values for i in range(self.start, self.end): feature_values[i] = X[samples[i], current_feature] sort(&feature_values[self.start], &samples[self.start], self.end - self.start - n_missing) self.n_missing = n_missing cdef inline void find_min_max( self, intp_t current_feature, float32_t* min_feature_value_out, float32_t* max_feature_value_out, ) noexcept nogil: """Find the minimum and maximum value for current_feature.""" cdef: intp_t p float32_t current_feature_value const float32_t[:, :] X = self.X intp_t[::1] samples = self.samples float32_t min_feature_value = X[samples[self.start], current_feature] float32_t max_feature_value = min_feature_value float32_t[::1] feature_values = self.feature_values feature_values[self.start] = min_feature_value for p in range(self.start + 1, self.end): current_feature_value = X[samples[p], current_feature] feature_values[p] = current_feature_value if current_feature_value < min_feature_value: min_feature_value = current_feature_value elif current_feature_value > max_feature_value: max_feature_value = current_feature_value min_feature_value_out[0] = min_feature_value max_feature_value_out[0] = max_feature_value cdef inline void next_p(self, intp_t* p_prev, intp_t* p) noexcept nogil: """Compute the next p_prev and p for iteratiing over feature values. The missing values are not included when iterating through the feature values. """ cdef: float32_t[::1] feature_values = self.feature_values intp_t end_non_missing = self.end - self.n_missing while ( p[0] + 1 < end_non_missing and feature_values[p[0] + 1] <= feature_values[p[0]] + FEATURE_THRESHOLD ): p[0] += 1 p_prev[0] = p[0] # By adding 1, we have # (feature_values[p] >= end) or (feature_values[p] > feature_values[p - 1]) p[0] += 1 cdef inline intp_t partition_samples(self, float64_t current_threshold) noexcept nogil: """Partition samples for feature_values at the current_threshold.""" cdef: intp_t p = self.start intp_t partition_end = self.end intp_t[::1] samples = self.samples float32_t[::1] feature_values = self.feature_values while p < partition_end: if feature_values[p] <= current_threshold: p += 1 else: partition_end -= 1 feature_values[p], feature_values[partition_end] = ( feature_values[partition_end], feature_values[p] ) samples[p], samples[partition_end] = samples[partition_end], samples[p] return partition_end cdef inline void partition_samples_final( self, intp_t best_pos, float64_t best_threshold, intp_t best_feature, intp_t best_n_missing, ) noexcept nogil: """Partition samples for X at the best_threshold and best_feature. If missing values are present, this method partitions `samples` so that the `best_n_missing` missing values' indices are in the right-most end of `samples`, that is `samples[end_non_missing:end]`. """ cdef: # Local invariance: start <= p <= partition_end <= end intp_t start = self.start intp_t p = start intp_t end = self.end - 1 intp_t partition_end = end - best_n_missing intp_t[::1] samples = self.samples const float32_t[:, :] X = self.X float32_t current_value if best_n_missing != 0: # Move samples with missing values to the end while partitioning the # non-missing samples while p < partition_end: # Keep samples with missing values at the end if isnan(X[samples[end], best_feature]): end -= 1 continue # Swap sample with missing values with the sample at the end current_value = X[samples[p], best_feature] if isnan(current_value): samples[p], samples[end] = samples[end], samples[p] end -= 1 # The swapped sample at the end is always a non-missing value, so # we can continue the algorithm without checking for missingness. current_value = X[samples[p], best_feature] # Partition the non-missing samples if current_value <= best_threshold: p += 1 else: samples[p], samples[partition_end] = samples[partition_end], samples[p] partition_end -= 1 else: # Partitioning routine when there are no missing values while p < partition_end: if X[samples[p], best_feature] <= best_threshold: p += 1 else: samples[p], samples[partition_end] = samples[partition_end], samples[p] partition_end -= 1 @final cdef class SparsePartitioner: """Partitioner specialized for sparse CSC data. Note that this partitioner is agnostic to the splitting strategy (best vs. random). """ cdef intp_t[::1] samples cdef float32_t[::1] feature_values cdef intp_t start cdef intp_t end cdef intp_t n_missing cdef const unsigned char[::1] missing_values_in_feature_mask cdef const float32_t[::1] X_data cdef const int32_t[::1] X_indices cdef const int32_t[::1] X_indptr cdef intp_t n_total_samples cdef intp_t[::1] index_to_samples cdef intp_t[::1] sorted_samples cdef intp_t start_positive cdef intp_t end_negative cdef bint is_samples_sorted def __init__( self, object X, intp_t[::1] samples, intp_t n_samples, float32_t[::1] feature_values, const unsigned char[::1] missing_values_in_feature_mask, ): if not (issparse(X) and X.format == "csc"): raise ValueError("X should be in csc format") self.samples = samples self.feature_values = feature_values # Initialize X cdef intp_t n_total_samples = X.shape[0] self.X_data = X.data self.X_indices = X.indices self.X_indptr = X.indptr self.n_total_samples = n_total_samples # Initialize auxiliary array used to perform split self.index_to_samples = np.full(n_total_samples, fill_value=-1, dtype=np.intp) self.sorted_samples = np.empty(n_samples, dtype=np.intp) cdef intp_t p for p in range(n_samples): self.index_to_samples[samples[p]] = p self.missing_values_in_feature_mask = missing_values_in_feature_mask cdef inline void init_node_split(self, intp_t start, intp_t end) noexcept nogil: """Initialize splitter at the beginning of node_split.""" self.start = start self.end = end self.is_samples_sorted = 0 self.n_missing = 0 cdef inline void sort_samples_and_feature_values( self, intp_t current_feature ) noexcept nogil: """Simultaneously sort based on the feature_values.""" cdef: float32_t[::1] feature_values = self.feature_values intp_t[::1] index_to_samples = self.index_to_samples intp_t[::1] samples = self.samples self.extract_nnz(current_feature) # Sort the positive and negative parts of `feature_values` sort(&feature_values[self.start], &samples[self.start], self.end_negative - self.start) if self.start_positive < self.end: sort( &feature_values[self.start_positive], &samples[self.start_positive], self.end - self.start_positive ) # Update index_to_samples to take into account the sort for p in range(self.start, self.end_negative): index_to_samples[samples[p]] = p for p in range(self.start_positive, self.end): index_to_samples[samples[p]] = p # Add one or two zeros in feature_values, if there is any if self.end_negative < self.start_positive: self.start_positive -= 1 feature_values[self.start_positive] = 0. if self.end_negative != self.start_positive: feature_values[self.end_negative] = 0. self.end_negative += 1 # XXX: When sparse supports missing values, this should be set to the # number of missing values for current_feature self.n_missing = 0 cdef inline void find_min_max( self, intp_t current_feature, float32_t* min_feature_value_out, float32_t* max_feature_value_out, ) noexcept nogil: """Find the minimum and maximum value for current_feature.""" cdef: intp_t p float32_t current_feature_value, min_feature_value, max_feature_value float32_t[::1] feature_values = self.feature_values self.extract_nnz(current_feature) if self.end_negative != self.start_positive: # There is a zero min_feature_value = 0 max_feature_value = 0 else: min_feature_value = feature_values[self.start] max_feature_value = min_feature_value # Find min, max in feature_values[start:end_negative] for p in range(self.start, self.end_negative): current_feature_value = feature_values[p] if current_feature_value < min_feature_value: min_feature_value = current_feature_value elif current_feature_value > max_feature_value: max_feature_value = current_feature_value # Update min, max given feature_values[start_positive:end] for p in range(self.start_positive, self.end): current_feature_value = feature_values[p] if current_feature_value < min_feature_value: min_feature_value = current_feature_value elif current_feature_value > max_feature_value: max_feature_value = current_feature_value min_feature_value_out[0] = min_feature_value max_feature_value_out[0] = max_feature_value cdef inline void next_p(self, intp_t* p_prev, intp_t* p) noexcept nogil: """Compute the next p_prev and p for iteratiing over feature values.""" cdef: intp_t p_next float32_t[::1] feature_values = self.feature_values if p[0] + 1 != self.end_negative: p_next = p[0] + 1 else: p_next = self.start_positive while (p_next < self.end and feature_values[p_next] <= feature_values[p[0]] + FEATURE_THRESHOLD): p[0] = p_next if p[0] + 1 != self.end_negative: p_next = p[0] + 1 else: p_next = self.start_positive p_prev[0] = p[0] p[0] = p_next cdef inline intp_t partition_samples(self, float64_t current_threshold) noexcept nogil: """Partition samples for feature_values at the current_threshold.""" return self._partition(current_threshold, self.start_positive) cdef inline void partition_samples_final( self, intp_t best_pos, float64_t best_threshold, intp_t best_feature, intp_t n_missing, ) noexcept nogil: """Partition samples for X at the best_threshold and best_feature.""" self.extract_nnz(best_feature) self._partition(best_threshold, best_pos) cdef inline intp_t _partition(self, float64_t threshold, intp_t zero_pos) noexcept nogil: """Partition samples[start:end] based on threshold.""" cdef: intp_t p, partition_end intp_t[::1] index_to_samples = self.index_to_samples float32_t[::1] feature_values = self.feature_values intp_t[::1] samples = self.samples if threshold < 0.: p = self.start partition_end = self.end_negative elif threshold > 0.: p = self.start_positive partition_end = self.end else: # Data are already split return zero_pos while p < partition_end: if feature_values[p] <= threshold: p += 1 else: partition_end -= 1 feature_values[p], feature_values[partition_end] = ( feature_values[partition_end], feature_values[p] ) sparse_swap(index_to_samples, samples, p, partition_end) return partition_end cdef inline void extract_nnz(self, intp_t feature) noexcept nogil: """Extract and partition values for a given feature. The extracted values are partitioned between negative values feature_values[start:end_negative[0]] and positive values feature_values[start_positive[0]:end]. The samples and index_to_samples are modified according to this partition. The extraction corresponds to the intersection between the arrays X_indices[indptr_start:indptr_end] and samples[start:end]. This is done efficiently using either an index_to_samples based approach or binary search based approach. Parameters ---------- feature : intp_t, Index of the feature we want to extract non zero value. """ cdef intp_t[::1] samples = self.samples cdef float32_t[::1] feature_values = self.feature_values cdef intp_t indptr_start = self.X_indptr[feature], cdef intp_t indptr_end = self.X_indptr[feature + 1] cdef intp_t n_indices = (indptr_end - indptr_start) cdef intp_t n_samples = self.end - self.start cdef intp_t[::1] index_to_samples = self.index_to_samples cdef intp_t[::1] sorted_samples = self.sorted_samples cdef const int32_t[::1] X_indices = self.X_indices cdef const float32_t[::1] X_data = self.X_data # Use binary search if n_samples * log(n_indices) < # n_indices and index_to_samples approach otherwise. # O(n_samples * log(n_indices)) is the running time of binary # search and O(n_indices) is the running time of index_to_samples # approach. if ((1 - self.is_samples_sorted) * n_samples * log(n_samples) + n_samples * log(n_indices) < EXTRACT_NNZ_SWITCH * n_indices): extract_nnz_binary_search(X_indices, X_data, indptr_start, indptr_end, samples, self.start, self.end, index_to_samples, feature_values, &self.end_negative, &self.start_positive, sorted_samples, &self.is_samples_sorted) # Using an index to samples technique to extract non zero values # index_to_samples is a mapping from X_indices to samples else: extract_nnz_index_to_samples(X_indices, X_data, indptr_start, indptr_end, samples, self.start, self.end, index_to_samples, feature_values, &self.end_negative, &self.start_positive) cdef int compare_SIZE_t(const void* a, const void* b) noexcept nogil: """Comparison function for sort. This must return an `int` as it is used by stdlib's qsort, which expects an `int` return value. """ return ((a)[0] - (b)[0]) cdef inline void binary_search(const int32_t[::1] sorted_array, int32_t start, int32_t end, intp_t value, intp_t* index, int32_t* new_start) noexcept nogil: """Return the index of value in the sorted array. If not found, return -1. new_start is the last pivot + 1 """ cdef int32_t pivot index[0] = -1 while start < end: pivot = start + (end - start) / 2 if sorted_array[pivot] == value: index[0] = pivot start = pivot + 1 break if sorted_array[pivot] < value: start = pivot + 1 else: end = pivot new_start[0] = start cdef inline void extract_nnz_index_to_samples(const int32_t[::1] X_indices, const float32_t[::1] X_data, int32_t indptr_start, int32_t indptr_end, intp_t[::1] samples, intp_t start, intp_t end, intp_t[::1] index_to_samples, float32_t[::1] feature_values, intp_t* end_negative, intp_t* start_positive) noexcept nogil: """Extract and partition values for a feature using index_to_samples. Complexity is O(indptr_end - indptr_start). """ cdef int32_t k cdef intp_t index cdef intp_t end_negative_ = start cdef intp_t start_positive_ = end for k in range(indptr_start, indptr_end): if start <= index_to_samples[X_indices[k]] < end: if X_data[k] > 0: start_positive_ -= 1 feature_values[start_positive_] = X_data[k] index = index_to_samples[X_indices[k]] sparse_swap(index_to_samples, samples, index, start_positive_) elif X_data[k] < 0: feature_values[end_negative_] = X_data[k] index = index_to_samples[X_indices[k]] sparse_swap(index_to_samples, samples, index, end_negative_) end_negative_ += 1 # Returned values end_negative[0] = end_negative_ start_positive[0] = start_positive_ cdef inline void extract_nnz_binary_search(const int32_t[::1] X_indices, const float32_t[::1] X_data, int32_t indptr_start, int32_t indptr_end, intp_t[::1] samples, intp_t start, intp_t end, intp_t[::1] index_to_samples, float32_t[::1] feature_values, intp_t* end_negative, intp_t* start_positive, intp_t[::1] sorted_samples, bint* is_samples_sorted) noexcept nogil: """Extract and partition values for a given feature using binary search. If n_samples = end - start and n_indices = indptr_end - indptr_start, the complexity is O((1 - is_samples_sorted[0]) * n_samples * log(n_samples) + n_samples * log(n_indices)). """ cdef intp_t n_samples if not is_samples_sorted[0]: n_samples = end - start memcpy(&sorted_samples[start], &samples[start], n_samples * sizeof(intp_t)) qsort(&sorted_samples[start], n_samples, sizeof(intp_t), compare_SIZE_t) is_samples_sorted[0] = 1 while (indptr_start < indptr_end and sorted_samples[start] > X_indices[indptr_start]): indptr_start += 1 while (indptr_start < indptr_end and sorted_samples[end - 1] < X_indices[indptr_end - 1]): indptr_end -= 1 cdef intp_t p = start cdef intp_t index cdef intp_t k cdef intp_t end_negative_ = start cdef intp_t start_positive_ = end while (p < end and indptr_start < indptr_end): # Find index of sorted_samples[p] in X_indices binary_search(X_indices, indptr_start, indptr_end, sorted_samples[p], &k, &indptr_start) if k != -1: # If k != -1, we have found a non zero value if X_data[k] > 0: start_positive_ -= 1 feature_values[start_positive_] = X_data[k] index = index_to_samples[X_indices[k]] sparse_swap(index_to_samples, samples, index, start_positive_) elif X_data[k] < 0: feature_values[end_negative_] = X_data[k] index = index_to_samples[X_indices[k]] sparse_swap(index_to_samples, samples, index, end_negative_) end_negative_ += 1 p += 1 # Returned values end_negative[0] = end_negative_ start_positive[0] = start_positive_ cdef inline void sparse_swap(intp_t[::1] index_to_samples, intp_t[::1] samples, intp_t pos_1, intp_t pos_2) noexcept nogil: """Swap sample pos_1 and pos_2 preserving sparse invariant.""" samples[pos_1], samples[pos_2] = samples[pos_2], samples[pos_1] index_to_samples[samples[pos_1]] = pos_1 index_to_samples[samples[pos_2]] = pos_2 cdef class BestSplitter(Splitter): """Splitter for finding the best split on dense data.""" cdef DensePartitioner partitioner cdef int init( self, object X, const float64_t[:, ::1] y, const float64_t[:] sample_weight, const unsigned char[::1] missing_values_in_feature_mask, ) except -1: Splitter.init(self, X, y, sample_weight, missing_values_in_feature_mask) self.partitioner = DensePartitioner( X, self.samples, self.feature_values, missing_values_in_feature_mask ) cdef int node_split( self, ParentInfo* parent_record, SplitRecord* split, ) except -1 nogil: return node_split_best( self, self.partitioner, self.criterion, split, parent_record, self.with_monotonic_cst, self.monotonic_cst, ) cdef class BestSparseSplitter(Splitter): """Splitter for finding the best split, using the sparse data.""" cdef SparsePartitioner partitioner cdef int init( self, object X, const float64_t[:, ::1] y, const float64_t[:] sample_weight, const unsigned char[::1] missing_values_in_feature_mask, ) except -1: Splitter.init(self, X, y, sample_weight, missing_values_in_feature_mask) self.partitioner = SparsePartitioner( X, self.samples, self.n_samples, self.feature_values, missing_values_in_feature_mask ) cdef int node_split( self, ParentInfo* parent_record, SplitRecord* split, ) except -1 nogil: return node_split_best( self, self.partitioner, self.criterion, split, parent_record, self.with_monotonic_cst, self.monotonic_cst, ) cdef class RandomSplitter(Splitter): """Splitter for finding the best random split on dense data.""" cdef DensePartitioner partitioner cdef int init( self, object X, const float64_t[:, ::1] y, const float64_t[:] sample_weight, const unsigned char[::1] missing_values_in_feature_mask, ) except -1: Splitter.init(self, X, y, sample_weight, missing_values_in_feature_mask) self.partitioner = DensePartitioner( X, self.samples, self.feature_values, missing_values_in_feature_mask ) cdef int node_split( self, ParentInfo* parent_record, SplitRecord* split, ) except -1 nogil: return node_split_random( self, self.partitioner, self.criterion, split, parent_record, self.with_monotonic_cst, self.monotonic_cst, ) cdef class RandomSparseSplitter(Splitter): """Splitter for finding the best random split, using the sparse data.""" cdef SparsePartitioner partitioner cdef int init( self, object X, const float64_t[:, ::1] y, const float64_t[:] sample_weight, const unsigned char[::1] missing_values_in_feature_mask, ) except -1: Splitter.init(self, X, y, sample_weight, missing_values_in_feature_mask) self.partitioner = SparsePartitioner( X, self.samples, self.n_samples, self.feature_values, missing_values_in_feature_mask ) cdef int node_split( self, ParentInfo* parent_record, SplitRecord* split, ) except -1 nogil: return node_split_random( self, self.partitioner, self.criterion, split, parent_record, self.with_monotonic_cst, self.monotonic_cst, )