## Java中的稀疏矩阵/数组内容来源于 Stack Overflow，并遵循CC BY-SA 3.0许可协议进行翻译与使用

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### 2 个回答

Trie可以通过仅执行只读TWO数组索引来获取存储元素的有效位置，或者知道其是否存在于底层存储中，从而计算表中是否存在元素。

``````trie.values[trie.subrangePositions[(i & ~15) + (j >> 4)] +
((i & 15) << 4) + (j & 15)]
``````

``````/**
* Implement a sparse matrix. Currently limited to a static size
* (<code>SIZE_I</code>, <code>SIZE_I</code>).
*/
public class DoubleTrie {

/* Matrix logical options */
public static final int SIZE_I = 1024;
public static final int SIZE_J = 1024;
public static final double DEFAULT_VALUE = 0.0;

/* Internal splitting options */
private static final int SUBRANGEBITS_I = 4;
private static final int SUBRANGEBITS_J = 4;

/* Internal derived splitting constants */
private static final int SUBRANGE_I =
1 << SUBRANGEBITS_I;
private static final int SUBRANGE_J =
1 << SUBRANGEBITS_J;
private static final int SUBRANGEMASK_I =
SUBRANGE_I - 1;
private static final int SUBRANGEMASK_J =
SUBRANGE_J - 1;
private static final int SUBRANGE_POSITIONS =
SUBRANGE_I * SUBRANGE_J;

/* Internal derived default values for constructors */
private static final int SUBRANGES_I =
(SIZE_I + SUBRANGE_I - 1) / SUBRANGE_I;
private static final int SUBRANGES_J =
(SIZE_J + SUBRANGE_J - 1) / SUBRANGE_J;
private static final int SUBRANGES =
SUBRANGES_I * SUBRANGES_J;
private static final int DEFAULT_POSITIONS[] =
new int[SUBRANGES](0);
private static final double DEFAULT_VALUES[] =
new double[SUBRANGE_POSITIONS](DEFAULT_VALUE);

/* Internal fast computations of the splitting subrange and offset. */
private static final int subrangeOf(
final int i, final int j) {
return (i >> SUBRANGEBITS_I) * SUBRANGE_J +
(j >> SUBRANGEBITS_J);
}
private static final int positionOffsetOf(
final int i, final int j) {
return (i & SUBRANGEMASK_I) * MAX_J +
}

/**
* Utility missing in java.lang.System for arrays of comparable
* component types, including all native types like double here.
*/
public static final int arraycompare(
final double[] values1, final int position1,
final double[] values2, final int position2,
final int length) {
if (position1 >= 0 && position2 >= 0 && length >= 0) {
while (length-- > 0) {
double value1, value2;
if ((value1 = values1[position1 + length]) !=
(value2 = values2[position2 + length])) {
/* Note: NaN values are different from everything including
* all Nan values; they are are also neigher lower than nor
* greater than everything including NaN. Note that the two
* infinite values, as well as denormal values, are exactly
* ordered and comparable with <, <=, ==, >=, >=, !=. Note
* that in comments below, infinite is considered "defined".
*/
if (value1 < value2)
return -1;        /* defined < defined. */
if (value1 > value2)
return 1;         /* defined > defined. */
if (value1 == value2)
return 0;         /* defined == defined. */
/* One or both are NaN. */
if (value1 == value1) /* Is not a NaN? */
return -1;        /* defined < NaN. */
if (value2 == value2) /* Is not a NaN? */
return 1;         /* NaN > defined. */
/* Otherwise, both are NaN: check their precise bits in
* range 0x7FF0000000000001L..0x7FFFFFFFFFFFFFFFL
* including the canonical 0x7FF8000000000000L, or in
* range 0xFFF0000000000001L..0xFFFFFFFFFFFFFFFFL.
* Needed for sort stability only (NaNs are otherwise
* unordered).
*/
long raw1, raw2;
if ((raw1 = Double.doubleToRawLongBits(value1)) !=
(raw2 = Double.doubleToRawLongBits(value2)))
return raw1 < raw2 ? -1 : 1;
/* Otherwise the NaN are strictly equal, continue. */
}
}
return 0;
}
throw new ArrayIndexOutOfBoundsException(
"The positions and length can't be negative");
}

/**
* Utility shortcut for comparing ranges in the same array.
*/
public static final int arraycompare(
final double[] values,
final int position1, final int position2,
final int length) {
return arraycompare(values, position1, values, position2, length);
}

/**
* Utility missing in java.lang.System for arrays of equalizable
* component types, including all native types like double here.
*/
public static final boolean arrayequals(
final double[] values1, final int position1,
final double[] values2, final int position2,
final int length) {
return arraycompare(values1, position1, values2, position2, length) ==
0;
}

/**
* Utility shortcut for identifying ranges in the same array.
*/
public static final boolean arrayequals(
final double[] values,
final int position1, final int position2,
final int length) {
return arrayequals(values, position1, values, position2, length);
}

/**
* Utility shortcut for copying ranges in the same array.
*/
public static final void arraycopy(
final double[] values,
final int srcPosition, final int dstPosition,
final int length) {
arraycopy(values, srcPosition, values, dstPosition, length);
}

/**
* Utility shortcut for resizing an array, preserving values at start.
*/
public static final double[] arraysetlength(
double[] values,
final int newLength) {
final int oldLength =
values.length < newLength ? values.length : newLength;
System.arraycopy(values, 0, values = new double[newLength], 0,
oldLength);
return values;
}

/* Internal instance members. */
private double values[];
private int subrangePositions[];
private bool isSharedValues;
private bool isSharedSubrangePositions;

/* Internal method. */
private final reset(
final double[] values,
final int[] subrangePositions) {
this.isSharedValues =
(this.values = values) == DEFAULT_VALUES;
this.isSharedsubrangePositions =
(this.subrangePositions = subrangePositions) ==
DEFAULT_POSITIONS;
}

/**
* Reset the matrix to fill it with the same initial value.
*
* @param initialValue  The value to set in all cell positions.
*/
public reset(final double initialValue = DEFAULT_VALUE) {
reset(
(initialValue == DEFAULT_VALUE) ? DEFAULT_VALUES :
new double[SUBRANGE_POSITIONS](initialValue),
DEFAULT_POSITIONS);
}

/**
* Default constructor, using single default value.
*
* @param initialValue  Alternate default value to initialize all
*                      positions in the matrix.
*/
public DoubleTrie(final double initialValue = DEFAULT_VALUE) {
this.reset(initialValue);
}

/**
* This is a useful preinitialized instance containing the
* DEFAULT_VALUE in all cells.
*/
public static DoubleTrie DEFAULT_INSTANCE = new DoubleTrie();

/**
* Copy constructor. Note that the source trie may be immutable
* or not; but this constructor will create a new mutable trie
* even if the new trie initially shares some storage with its
* source when that source also uses shared storage.
*/
public DoubleTrie(final DoubleTrie source) {
this.values = (this.isSharedValues =
source.isSharedValues) ?
source.values :
source.values.clone();
this.subrangePositions = (this.isSharedSubrangePositions =
source.isSharedSubrangePositions) ?
source.subrangePositions :
source.subrangePositions.clone());
}

/**
* Fast indexed getter.
*
* @param i  Row of position to set in the matrix.
* @param j  Column of position to set in the matrix.
* @return   The value stored in matrix at that position.
*/
public double getAt(final int i, final int j) {
return values[subrangePositions[subrangeOf(i, j)] +
positionOffsetOf(i, j)];
}

/**
* Fast indexed setter.
*
* @param i      Row of position to set in the sparsed matrix.
* @param j      Column of position to set in the sparsed matrix.
* @param value  The value to set at this position.
* @return       The passed value.
* Note: this does not compact the sparsed matric after setting.
* @see compact(void)
*/
public double setAt(final int i, final int i, final double value) {
final int subrange       = subrangeOf(i, j);
final int positionOffset = positionOffsetOf(i, j);
// Fast check to see if the assignment will change something.
int subrangePosition, valuePosition;
if (Double.compare(
values[valuePosition =
(subrangePosition = subrangePositions[subrange]) +
positionOffset],
value) != 0) {
/* So we'll need to perform an effective assignment in values.
* Check if the current subrange to assign is shared of not.
* Note that we also include the DEFAULT_VALUES which may be
* shared by several other (not tested) trie instances,
* including those instanciated by the copy contructor. */
if (isSharedValues) {
values = values.clone();
isSharedValues = false;
}
/* Scan all other subranges to check if the position in values
* to assign is shared by another subrange. */
for (int otherSubrange = subrangePositions.length;
--otherSubrange >= 0; ) {
if (otherSubrange != subrange)
continue; /* Ignore the target subrange. */
/* Note: the following test of range is safe with future
* interleaving of common subranges (TODO in compact()),
* even though, for now, subranges are sharing positions
* only between their common start and end position, so we
* could as well only perform the simpler test <code>
* (otherSubrangePosition == subrangePosition)</code>,
* instead of testing the two bounds of the positions
* interval of the other subrange. */
int otherSubrangePosition;
if ((otherSubrangePosition =
subrangePositions[otherSubrange]) >=
valuePosition &&
otherSubrangePosition + SUBRANGE_POSITIONS <
valuePosition) {
/* The target position is shared by some other
* subrange, we need to make it unique by cloning the
* subrange to a larger values vector, copying all the
* current subrange values at end of the new vector,
* before assigning the new value. This will require
* changing the position of the current subrange, but
* before doing that, we first need to check if the
* subrangePositions array itself is also shared
* between instances (including the DEFAULT_POSITIONS
* that should be preserved, and possible arrays
* shared by an external factory contructor whose
* source trie was declared immutable in a derived
* class). */
if (isSharedSubrangePositions) {
subrangePositions = subrangePositions.clone();
isSharedSubrangePositions = false;
}
/* TODO: no attempt is made to allocate less than a
* fully independant subrange, using possible
* interleaving: this would require scanning all
* other existing values to find a match for the
* modified subrange of values; but this could
* potentially leave positions (in the current subrange
* of values) unreferenced by any subrange, after the
* change of position for the current subrange. This
* scanning could be prohibitively long for each
* assignement, and for now it's assumed that compact()
* will be used later, after those assignements. */
values = setlengh(
values,
(subrangePositions[subrange] =
subrangePositions = values.length) +
SUBRANGE_POSITIONS);
valuePosition = subrangePositions + positionOffset;
break;
}
}
/* Now perform the effective assignment of the value. */
values[valuePosition] = value;
}
}
return value;
}

/**
* Compact the storage of common subranges.
* TODO: This is a simple implementation without interleaving, which
* would offer a better data compression. However, interleaving with its
* O(N²) complexity where N is the total length of values, should
* be attempted only after this basic compression whose complexity is
* O(n²) with n being SUBRANGE_POSITIIONS times smaller than N.
*/
public void compact() {
final int oldValuesLength = values.length;
int newValuesLength = 0;
for (int oldPosition = 0;
oldPosition < oldValuesLength;
oldPosition += SUBRANGE_POSITIONS) {
int oldPosition = positions[subrange];
bool commonSubrange = false;
/* Scan values for possible common subranges. */
for (int newPosition = newValuesLength;
(newPosition -= SUBRANGE_POSITIONS) >= 0; )
if (arrayequals(values, newPosition, oldPosition,
SUBRANGE_POSITIONS)) {
commonSubrange = true;
/* Update the subrangePositions|] with all matching
* positions from oldPosition to newPosition. There may
* be several index to change, if the trie has already
* been compacted() before, and later reassigned. */
for (subrange = subrangePositions.length;
--subrange >= 0; )
if (subrangePositions[subrange] == oldPosition)
subrangePositions[subrange] = newPosition;
break;
}
if (!commonSubrange) {
/* Move down the non-common values, if some previous
* subranges have been compressed when they were common.
*/
if (!commonSubrange && oldPosition != newValuesLength) {
arraycopy(values, oldPosition, newValuesLength,
SUBRANGE_POSITIONS);
/* Advance compressed values to preserve these new ones. */
newValuesLength += SUBRANGE_POSITIONS;
}
}
}
/* Check the number of compressed values. */
if (newValuesLength < oldValuesLength) {
values = values.arraysetlength(newValuesLength);
isSharedValues = false;
}
}

}
``````

1. 它总是更快（并且内存更紧凑，意味着更好的局部性），以使用单个向量而不是双索引数组阵列（每个阵列单独分配）来表示矩阵。`double getAt(int, int)`方法中可以看到改进！
2. 您可以节省大量空间，但在分配值时可能需要一些时间来重新分配新的子范围。出于这个原因，子范围不应该太小，否则重新分配将过于频繁地设置您的矩阵。
3. 通过检测常见的子范围，可以将初始大矩阵自动转换为更紧凑的矩阵。一个典型的实现将包含一个`compact()`如上所述的方法。但是，如果get（）访问速度非常快并且set（）速度非常快，那么如果有许多常用的子范围要压缩，compact（）可能会非常缓慢（例如，在减去一个大型非稀疏随机填充矩阵时，或者将它乘以零：在这种情况下，通过实例化一个新的和删除旧的那个来重置该特里将更简单和更快）。
4. 常用子范围在数据中使用公共存储，因此该共享数据必须是只读的。如果您必须更改单个值而不更改矩阵的其余部分，则必须首先确保它在`subrangePositions`索引中仅被引用一次。否则，您需要在`values`矢量的任何位置（方便地结束）分配新的子区域，然后将此新子区域的位置存储到`subrangePositions`索引中。

Colt中使用的RC（行压缩）技术距离Tries较近，但这是另一个价格，这里使用的是压缩技术，对于最频繁的只读get（）操作访问时间非常缓慢，而且非常缓慢压缩setAt（）操作。此外，所使用的压缩并不是正交的，这与保存正交性的尝试的演示不同。尝试还可以保留相关查看操作的正交性，如跨步，转置（基于整数循环模块化操作的跨步操作），子排列（以及一般子查询，包括排序视图）。

Trove实现（基于int-> int映射）也基于类似于Colt的HashedSparseMatrix的散列技术，即它们具有相同的不便之处。尝试将会快得多，并且会消耗一定量的额外空间（但是这个空间可以在延迟的时间内进行优化并且比Trove和Colt更好，对最终的矩阵/ trie使用最终的compact（）离子操作）。

``````* Colt
* Commons Math
* Efficient Java Matrix Library (EJML)
* Jama
* jblas
* JScience (Older benchmarks only)
* Matrix Toolkit Java (MTJ)
* OjAlgo
* Parallel Colt
* Universal Java Matrix Package (UJMP)
``````