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/*******************************************************************************
* Copyright (c) 2015-2018 Skymind, Inc.
*
* This program and the accompanying materials are made available under the
* terms of the Apache License, Version 2.0 which is available at
* https://www.apache.org/licenses/LICENSE-2.0.
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations
* under the License.
*
* SPDX-License-Identifier: Apache-2.0
******************************************************************************/
package org.nd4j.linalg.indexing;
import org.nd4j.linalg.exception.ND4JArraySizeException;
import org.nd4j.shade.guava.primitives.Ints;
import org.nd4j.shade.guava.primitives.Longs;
import org.nd4j.linalg.api.ndarray.INDArray;
import org.nd4j.linalg.api.shape.Shape;
import org.nd4j.linalg.exception.ND4JIllegalStateException;
import org.nd4j.linalg.factory.NDArrayFactory;
import org.nd4j.linalg.factory.Nd4j;
import org.nd4j.common.util.ArrayUtil;
import org.nd4j.linalg.util.LongUtils;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
/**
* Indexing util.
*
* @author Adam Gibson
*/
public class Indices {
/**
* Compute the linear offset
* for an index in an ndarray.
*
* For c ordering this is just the index itself.
* For fortran ordering, the following algorithm is used.
*
* Assuming an ndarray is a list of vectors.
* The index of the vector relative to the given index is calculated.
*
* vectorAlongDimension is then used along the last dimension
* using the computed index.
*
* The offset + the computed column wrt the index: (index % the size of the last dimension)
* will render the given index in fortran ordering
* @param index the index
* @param arr the array
* @return the linear offset
*/
public static int rowNumber(int index, INDArray arr) {
double otherTest = ((double) index) / arr.size(-1);
int test = (int) Math.floor(otherTest);
if (arr.vectorsAlongDimension(-1) > Integer.MAX_VALUE)
throw new ND4JArraySizeException();
int vectors = (int) arr.vectorsAlongDimension(-1);
if (test >= vectors)
return vectors - 1;
return test;
}
/**
* Compute the linear offset
* for an index in an ndarray.
*
* For c ordering this is just the index itself.
* For fortran ordering, the following algorithm is used.
*
* Assuming an ndarray is a list of vectors.
* The index of the vector relative to the given index is calculated.
*
* vectorAlongDimension is then used along the last dimension
* using the computed index.
*
* The offset + the computed column wrt the index: (index % the size of the last dimension)
* will render the given index in fortran ordering
* @param index the index
* @param arr the array
* @return the linear offset
*/
public static long linearOffset(int index, INDArray arr) {
if (arr.ordering() == NDArrayFactory.C) {
double otherTest = ((double) index) % arr.size(-1);
int test = (int) Math.floor(otherTest);
INDArray vec = arr.vectorAlongDimension(test, -1);
long otherDim = arr.vectorAlongDimension(test, -1).offset() + index;
return otherDim;
} else {
int majorStride = arr.stride(-2);
long vectorsAlongDimension = arr.vectorsAlongDimension(-1);
double rowCalc = (double) (index * majorStride) / (double) arr.length();
int floor = (int) Math.floor(rowCalc);
INDArray arrVector = arr.vectorAlongDimension(floor, -1);
long columnIndex = index % arr.size(-1);
long retOffset = arrVector.linearIndex(columnIndex);
return retOffset;
}
}
/**
* The offsets (begin index) for each index
*
* @param indices the indices
* @return the offsets for the given set of indices
*/
public static long[] offsets(long[] shape, INDArrayIndex... indices) {
//offset of zero for every new axes
long[] ret = new long[shape.length];
if (indices.length == shape.length) {
for (int i = 0; i < indices.length; i++) {
ret[i] = indices[i].offset();
}
if (ret.length == 1) {
ret = new long[] {ret[0], 0};
}
}
else {
int numPoints = NDArrayIndex.numPoints(indices);
if (numPoints > 0) {
List nonZeros = new ArrayList<>();
for (int i = 0; i < indices.length; i++)
if (indices[i].offset() > 0)
nonZeros.add(indices[i].offset());
if (nonZeros.size() > shape.length)
throw new IllegalStateException("Non zeros greater than shape unable to continue");
else {
//push all zeros to the back
for (int i = 0; i < nonZeros.size(); i++)
ret[i] = nonZeros.get(i);
}
} else {
int shapeIndex = 0;
for (int i = 0; i < indices.length; i++) {
ret[i] = indices[shapeIndex++].offset();
}
}
if (ret.length == 1) {
ret = new long[] {ret[0], 0};
}
}
return ret;
}
/**
* Fill in the missing indices to be the
* same length as the original shape.
*
* Think of this as what fills in the indices for numpy or matlab:
* Given a which is (4,3,2) in numpy:
*
* a[1:3] is filled in by the rest
* to give back the full slice
*
* This algorithm fills in that delta
*
* @param shape the original shape
* @param indexes the indexes to start from
* @return the filled in indices
*/
public static INDArrayIndex[] fillIn(int[] shape, INDArrayIndex... indexes) {
if (shape.length == indexes.length)
return indexes;
INDArrayIndex[] newIndexes = new INDArrayIndex[shape.length];
System.arraycopy(indexes, 0, newIndexes, 0, indexes.length);
for (int i = indexes.length; i < shape.length; i++) {
newIndexes[i] = NDArrayIndex.interval(0, shape[i]);
}
return newIndexes;
}
/**
* Prunes indices of greater length than the shape
* and fills in missing indices if there are any
*
* @param originalShape the original shape to adjust to
* @param indexes the indexes to adjust
* @return the adjusted indices
*/
public static INDArrayIndex[] adjustIndices(int[] originalShape, INDArrayIndex... indexes) {
if (Shape.isVector(originalShape) && indexes.length == 1)
return indexes;
if (indexes.length < originalShape.length)
indexes = fillIn(originalShape, indexes);
if (indexes.length > originalShape.length) {
INDArrayIndex[] ret = new INDArrayIndex[originalShape.length];
System.arraycopy(indexes, 0, ret, 0, originalShape.length);
return ret;
}
if (indexes.length == originalShape.length)
return indexes;
for (int i = 0; i < indexes.length; i++) {
if (indexes[i].end() >= originalShape[i] || indexes[i] instanceof NDArrayIndexAll)
indexes[i] = NDArrayIndex.interval(0, originalShape[i] - 1);
}
return indexes;
}
/**
* Calculate the strides based on the given indices
*
* @param ordering the ordering to calculate strides for
* @param indexes the indices to calculate stride for
* @return the strides for the given indices
*/
public static int[] strides(char ordering, NDArrayIndex... indexes) {
return Nd4j.getStrides(shape(indexes), ordering);
}
/**
* Calculate the shape for the given set of indices.
*
* The shape is defined as (for each dimension)
* the difference between the end index + 1 and
* the begin index
*
* @param indices the indices to calculate the shape for
* @return the shape for the given indices
*/
public static int[] shape(INDArrayIndex... indices) {
int[] ret = new int[indices.length];
for (int i = 0; i < ret.length; i++) {
// FIXME: LONG
ret[i] = (int) indices[i].length();
}
List nonZeros = new ArrayList<>();
for (int i = 0; i < ret.length; i++) {
if (ret[i] > 0)
nonZeros.add(ret[i]);
}
return ArrayUtil.toArray(nonZeros);
}
/**
* Returns whether indices are contiguous
* by a certain amount or not
*
* @param indices the indices to test
* @param diff the difference considered to be contiguous
* @return whether the given indices are contiguous or not
*/
public static boolean isContiguous(int[] indices, int diff) {
if (indices.length < 1)
return true;
for (int i = 1; i < indices.length; i++) {
if (Math.abs(indices[i] - indices[i - 1]) > diff)
return false;
}
return true;
}
/**
* Create an n dimensional index
* based on the given interval indices.
* Start and end represent the begin and
* end of each interval
* @param start the start indexes
* @param end the end indexes
* @return the interval index relative to the given
* start and end indices
*/
public static INDArrayIndex[] createFromStartAndEnd(INDArray start, INDArray end) {
if (start.length() != end.length())
throw new IllegalArgumentException("Start length must be equal to end length");
else {
if (start.length() > Integer.MAX_VALUE)
throw new ND4JIllegalStateException("Can't proceed with INDArray with length > Integer.MAX_VALUE");
INDArrayIndex[] indexes = new INDArrayIndex[(int) start.length()];
for (int i = 0; i < indexes.length; i++) {
indexes[i] = NDArrayIndex.interval(start.getInt(i), end.getInt(i));
}
return indexes;
}
}
/**
* Create indices representing intervals
* along each dimension
* @param start the start index
* @param end the end index
* @param inclusive whether the last
* index should be included
* @return the ndarray indexes covering
* each dimension
*/
public static INDArrayIndex[] createFromStartAndEnd(INDArray start, INDArray end, boolean inclusive) {
if (start.length() != end.length())
throw new IllegalArgumentException("Start length must be equal to end length");
else {
if (start.length() > Integer.MAX_VALUE)
throw new ND4JIllegalStateException("Can't proceed with INDArray with length > Integer.MAX_VALUE");
INDArrayIndex[] indexes = new INDArrayIndex[(int) start.length()];
for (int i = 0; i < indexes.length; i++) {
indexes[i] = NDArrayIndex.interval(start.getInt(i), end.getInt(i), inclusive);
}
return indexes;
}
}
/**
* Calculate the shape for the given set of indices and offsets.
*
* The shape is defined as (for each dimension)
* the difference between the end index + 1 and
* the begin index
*
* If specified, this will check for whether any of the indices are >= to end - 1
* and if so, prune it down
*
* @param shape the original shape
* @param indices the indices to calculate the shape for
* @return the shape for the given indices
*/
public static int[] shape(int[] shape, INDArrayIndex... indices) {
return LongUtils.toInts(shape(LongUtils.toLongs(shape), indices));
}
public static long[] shape(long[] shape, INDArrayIndex... indices) {
int newAxesPrepend = 0;
boolean encounteredAll = false;
List accumShape = new ArrayList<>();
//bump number to read from the shape
int shapeIndex = 0;
//list of indexes to prepend to for new axes
//if all is encountered
List prependNewAxes = new ArrayList<>();
for (int i = 0; i < indices.length; i++) {
INDArrayIndex idx = indices[i];
if (idx instanceof NDArrayIndexAll)
encounteredAll = true;
//point: do nothing but move the shape counter
if (idx instanceof PointIndex) {
shapeIndex++;
continue;
}
//new axes encountered, need to track whether to prepend or
//to set the new axis in the middle
else if (idx instanceof NewAxis) {
//prepend the new axes at different indexes
if (encounteredAll) {
prependNewAxes.add(i);
}
//prepend to the beginning
//rather than a set index
else
newAxesPrepend++;
continue;
}
//points and intervals both have a direct desired length
else if (idx instanceof IntervalIndex && !(idx instanceof NDArrayIndexAll)
|| idx instanceof SpecifiedIndex) {
accumShape.add(idx.length());
shapeIndex++;
continue;
}
accumShape.add(shape[shapeIndex]);
shapeIndex++;
}
while (shapeIndex < shape.length) {
accumShape.add(shape[shapeIndex++]);
}
while (accumShape.size() < 2) {
accumShape.add(1L);
}
//only one index and matrix, remove the first index rather than the last
//equivalent to this is reversing the list with the prepended one
if (indices.length == 1 && indices[0] instanceof PointIndex && shape.length == 2) {
Collections.reverse(accumShape);
}
//prepend for new axes; do this first before
//doing the indexes to prepend to
if (newAxesPrepend > 0) {
for (int i = 0; i < newAxesPrepend; i++)
accumShape.add(0, 1L);
}
/**
* For each dimension
* where we want to prepend a dimension
* we need to add it at the index such that
* we account for the offset of the number of indexes
* added up to that point.
*
* We do this by doing an offset
* for each item added "so far"
*
* Note that we also have an offset of - 1
* because we want to prepend to the given index.
*
* When prepend new axes for in the middle is triggered
* i is already > 0
*/
for (int i = 0; i < prependNewAxes.size(); i++) {
accumShape.add(prependNewAxes.get(i) - i, 1L);
}
return Longs.toArray(accumShape);
}
/**
* Return the stride to be used for indexing
* @param arr the array to get the strides for
* @param indexes the indexes to use for computing stride
* @param shape the shape of the output
* @return the strides used for indexing
*/
public static int[] stride(INDArray arr, INDArrayIndex[] indexes, int... shape) {
List strides = new ArrayList<>();
int strideIndex = 0;
//list of indexes to prepend to for new axes
//if all is encountered
List prependNewAxes = new ArrayList<>();
for (int i = 0; i < indexes.length; i++) {
//just like the shape, drops the stride
if (indexes[i] instanceof PointIndex) {
strideIndex++;
continue;
} else if (indexes[i] instanceof NewAxis) {
}
}
/**
* For each dimension
* where we want to prepend a dimension
* we need to add it at the index such that
* we account for the offset of the number of indexes
* added up to that point.
*
* We do this by doing an offset
* for each item added "so far"
*
* Note that we also have an offset of - 1
* because we want to prepend to the given index.
*
* When prepend new axes for in the middle is triggered
* i is already > 0
*/
for (int i = 0; i < prependNewAxes.size(); i++) {
strides.add(prependNewAxes.get(i) - i, 1);
}
return Ints.toArray(strides);
}
/**
* Check if the given indexes
* over the specified array
* are searching for a scalar
* @param indexOver the array to index over
* @param indexes the index query
* @return true if the given indexes are searching
* for a scalar false otherwise
*/
public static boolean isScalar(INDArray indexOver, INDArrayIndex... indexes) {
boolean allOneLength = true;
for (int i = 0; i < indexes.length; i++) {
allOneLength = allOneLength && indexes[i].length() == 1;
}
int numNewAxes = NDArrayIndex.numNewAxis(indexes);
if (allOneLength && numNewAxes == 0 && indexes.length == indexOver.rank())
return true;
else if (allOneLength && indexes.length == indexOver.rank() - numNewAxes) {
return allOneLength;
}
return allOneLength;
}
}
