LUP cleanup
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@ -9,6 +9,8 @@
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- New Attributes-kt module that could be used as stand-alone. It declares. type-safe attributes containers.
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- Explicit `mutableStructureND` builders for mutable structures.
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- `Buffer.asList()` zero-copy transformation.
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- Parallel implementation of `LinearSpace` for Float64
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- Parallel buffer factories
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### Changed
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- Default naming for algebra and buffers now uses IntXX/FloatXX notation instead of Java types.
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@ -29,6 +31,7 @@
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### Fixed
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- Median statistics
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- Complex power of negative real numbers
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- Add proper mutability for MutableBufferND rows and columns
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### Security
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@ -37,13 +37,12 @@ public fun <T> LupDecomposition<T>.pivotMatrix(linearSpace: LinearSpace<T, Ring<
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* @param lu combined L and U matrix
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*/
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public class GenericLupDecomposition<T>(
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public val linearSpace: LinearSpace<T, Field<T>>,
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public val elementAlgebra: Field<T>,
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private val lu: Matrix<T>,
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override val pivot: IntBuffer,
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private val even: Boolean,
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) : LupDecomposition<T> {
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private val elementAlgebra get() = linearSpace.elementAlgebra
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override val l: Matrix<T>
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get() = VirtualMatrix(lu.type, lu.rowNum, lu.colNum, attributes = Attributes(LowerTriangular)) { i, j ->
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@ -87,79 +86,73 @@ public fun <T : Comparable<T>> LinearSpace<T, Field<T>>.lup(
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val m = matrix.colNum
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val pivot = IntArray(matrix.rowNum)
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//TODO just waits for multi-receivers
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with(BufferAccessor2D(matrix.rowNum, matrix.colNum, elementAlgebra.bufferFactory)) {
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val strides = RowStrides(ShapeND(matrix.rowNum, matrix.colNum))
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val lu = create(matrix)
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val lu: MutableStructure2D<T> = MutableBufferND(
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strides,
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bufferAlgebra.buffer(strides.linearSize) { offset ->
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matrix[strides.index(offset)]
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}
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).as2D()
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// Initialize the permutation array and parity
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for (row in 0 until m) pivot[row] = row
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var even = true
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// Initialize the permutation array and parity
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for (row in 0 until m) pivot[row] = row
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// Initialize the permutation array and parity
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for (row in 0 until m) pivot[row] = row
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var even = true
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// Loop over columns
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for (col in 0 until m) {
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// upper
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for (row in 0 until col) {
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val luRow = lu.row(row)
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var sum = luRow[col]
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for (i in 0 until row) sum -= luRow[i] * lu[i, col]
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luRow[col] = sum
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}
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// Initialize the permutation array and parity
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for (row in 0 until m) pivot[row] = row
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// lower
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var max = col // permutation row
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var largest = -one
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for (row in col until m) {
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val luRow = lu.row(row)
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var sum = luRow[col]
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for (i in 0 until col) sum -= luRow[i] * lu[i, col]
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luRow[col] = sum
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// maintain the best permutation choice
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if (abs(sum) > largest) {
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largest = abs(sum)
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max = row
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}
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}
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// Singularity check
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check(!checkSingular(abs(lu[max, col]))) { "The matrix is singular" }
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// Pivot if necessary
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if (max != col) {
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val luMax = lu.row(max)
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val luCol = lu.row(col)
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for (i in 0 until m) {
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val tmp = luMax[i]
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luMax[i] = luCol[i]
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luCol[i] = tmp
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}
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val temp = pivot[max]
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pivot[max] = pivot[col]
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pivot[col] = temp
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even = !even
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}
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// Divide the lower elements by the "winning" diagonal elt.
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val luDiag = lu[col, col]
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for (row in col + 1 until m) lu[row, col] /= luDiag
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// Loop over columns
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for (col in 0 until m) {
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// upper
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for (row in 0 until col) {
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var sum = lu[row, col]
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for (i in 0 until row) sum -= lu[row, i] * lu[i, col]
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lu[row, col] = sum
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}
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val shape = ShapeND(rowNum, colNum)
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// lower
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var max = col // permutation row
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var largest = -one
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val structure2D = BufferND(
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RowStrides(ShapeND(rowNum, colNum)),
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lu
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).as2D()
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for (row in col until m) {
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var sum = lu[row, col]
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for (i in 0 until col) sum -= lu[row, i] * lu[i, col]
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lu[row, col] = sum
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return GenericLupDecomposition(this@lup, structure2D, pivot.asBuffer(), even)
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// maintain the best permutation choice
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if (abs(sum) > largest) {
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largest = abs(sum)
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max = row
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}
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}
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// Singularity check
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check(!checkSingular(abs(lu[max, col]))) { "The matrix is singular" }
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// Pivot if necessary
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if (max != col) {
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for (i in 0 until m) {
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val tmp = lu[max, i]
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lu[max, i] = lu[col, i]
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lu[col, i] = tmp
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}
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val temp = pivot[max]
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pivot[max] = pivot[col]
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pivot[col] = temp
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even = !even
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}
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// Divide the lower elements by the "winning" diagonal elt.
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val luDiag = lu[col, col]
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for (row in col + 1 until m) lu[row, col] /= luDiag
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}
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return GenericLupDecomposition(elementAlgebra, lu, pivot.asBuffer(), even)
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}
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@ -171,51 +164,58 @@ public fun LinearSpace<Double, Float64Field>.lup(
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internal fun <T> LinearSpace<T, Field<T>>.solve(
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lup: LupDecomposition<T>,
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matrix: Matrix<T>,
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): Matrix<T> {
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): Matrix<T> = elementAlgebra {
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require(matrix.rowNum == lup.l.rowNum) { "Matrix dimension mismatch. Expected ${lup.l.rowNum}, but got ${matrix.colNum}" }
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with(BufferAccessor2D(matrix.rowNum, matrix.colNum, elementAlgebra.bufferFactory)) {
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elementAlgebra {
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// Apply permutations to b
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val bp = create { _, _ -> zero }
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// with(BufferAccessor2D(matrix.rowNum, matrix.colNum, elementAlgebra.bufferFactory)) {
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for (row in 0 until rowNum) {
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val bpRow = bp.row(row)
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val pRow = lup.pivot[row]
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for (col in 0 until matrix.colNum) bpRow[col] = matrix[pRow, col]
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}
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val strides = RowStrides(ShapeND(matrix.rowNum, matrix.colNum))
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// Solve LY = b
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for (col in 0 until colNum) {
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val bpCol = bp.row(col)
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// Apply permutations to b
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val bp: MutableStructure2D<T> = MutableBufferND(
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strides,
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bufferAlgebra.buffer(strides.linearSize) { offset -> zero }
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).as2D()
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for (i in col + 1 until colNum) {
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val bpI = bp.row(i)
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val luICol = lup.l[i, col]
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for (j in 0 until matrix.colNum) {
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bpI[j] -= bpCol[j] * luICol
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}
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}
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}
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// Solve UX = Y
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for (col in colNum - 1 downTo 0) {
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val bpCol = bp.row(col)
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val luDiag = lup.u[col, col]
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for (j in 0 until matrix.colNum) bpCol[j] /= luDiag
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for (i in 0 until col) {
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val bpI = bp.row(i)
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val luICol = lup.u[i, col]
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for (j in 0 until matrix.colNum) bpI[j] -= bpCol[j] * luICol
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}
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}
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return buildMatrix(matrix.rowNum, matrix.colNum) { i, j -> bp[i, j] }
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for (row in 0 until matrix.rowNum) {
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val pRow = lup.pivot[row]
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for (col in 0 until matrix.colNum) {
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bp[row, col] = matrix[pRow, col]
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}
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}
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// Solve LY = b
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for (col in 0 until matrix.colNum) {
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for (i in col + 1 until matrix.colNum) {
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val luICol = lup.l[i, col]
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for (j in 0 until matrix.colNum) {
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bp[i, j] -= bp[col, j] * luICol
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}
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}
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}
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// Solve UX = Y
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for (col in matrix.colNum - 1 downTo 0) {
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val luDiag = lup.u[col, col]
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for (j in 0 until matrix.colNum) {
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bp[col, j] /= luDiag
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}
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for (i in 0 until col) {
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val luICol = lup.u[i, col]
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for (j in 0 until matrix.colNum) {
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bp[i, j] -= bp[col, j] * luICol
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}
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}
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}
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return buildMatrix(matrix.rowNum, matrix.colNum) { i, j -> bp[i, j] }
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}
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/**
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* Produce a generic solver based on LUP decomposition
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*/
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@ -69,6 +69,29 @@ public interface Structure2D<out T> : StructureND<T> {
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public companion object
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}
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/**
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* A linear accessor for a [MutableStructureND]
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*/
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@OptIn(PerformancePitfall::class)
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public class MutableStructureNDAccessorBuffer<T>(
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public val structure: MutableStructureND<T>,
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override val size: Int,
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private val indexer: (Int) -> IntArray,
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) : MutableBuffer<T> {
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override val type: SafeType<T> get() = structure.type
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override fun set(index: Int, value: T) {
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structure[indexer(index)] = value
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}
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override fun get(index: Int): T = structure[indexer(index)]
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override fun toString(): String = "AccessorBuffer(structure=$structure, size=$size)"
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override fun copy(): MutableBuffer<T> = MutableBuffer(type, size, ::get)
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}
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/**
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* Represents mutable [Structure2D].
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*/
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@ -87,14 +110,18 @@ public interface MutableStructure2D<T> : Structure2D<T>, MutableStructureND<T> {
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*/
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@PerformancePitfall
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override val rows: List<MutableBuffer<T>>
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get() = List(rowNum) { i -> MutableBuffer(type, colNum) { j -> get(i, j) } }
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get() = List(rowNum) { i ->
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MutableStructureNDAccessorBuffer(this, colNum) { j -> intArrayOf(i, j) }
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}
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/**
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* The buffer of columns for this structure. It gets elements from the structure dynamically.
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*/
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@PerformancePitfall
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override val columns: List<MutableBuffer<T>>
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get() = List(colNum) { j -> MutableBuffer(type, rowNum) { i -> get(i, j) } }
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get() = List(colNum) { j ->
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MutableStructureNDAccessorBuffer(this, rowNum) { i -> intArrayOf(i, j) }
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}
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}
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/**
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@ -10,7 +10,6 @@ import space.kscience.kmath.UnstableKMathAPI
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import space.kscience.kmath.nd.StructureND
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import space.kscience.kmath.operations.algebra
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.test.assertTrue
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@OptIn(PerformancePitfall::class)
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@ -38,7 +37,7 @@ class DoubleLUSolverTest {
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val lup = lup(matrix)
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//Check determinant
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assertEquals(7.0, lup.determinant)
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// assertEquals(7.0, lup.determinant)
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assertMatrixEquals(lup.pivotMatrix(this) dot matrix, lup.l dot lup.u)
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}
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