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shadow.go
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shadow.go
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// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package mat64
import "github.com/gonum/blas/blas64"
const (
// regionOverlap is the panic string used for the general case
// of a matrix region overlap between a source and destination.
regionOverlap = "mat64: bad region: overlap"
// regionIdentity is the panic string used for the specific
// case of complete agreement between a source and a destination.
regionIdentity = "mat64: bad region: identical"
// mismatchedStrides is the panic string used for overlapping
// data slices with differing strides.
mismatchedStrides = "mat64: bad region: different strides"
)
// checkOverlap returns false if the receiver does not overlap data elements
// referenced by the parameter and panics otherwise.
//
// checkOverlap methods return a boolean to allow the check call to be added to a
// boolean expression, making use of short-circuit operators.
func (m *Dense) checkOverlap(a blas64.General) bool {
mat := m.RawMatrix()
if cap(mat.Data) == 0 || cap(a.Data) == 0 {
return false
}
off := offset(mat.Data[:1], a.Data[:1])
if off == 0 {
// At least one element overlaps.
if mat.Cols == a.Cols && mat.Rows == a.Rows && mat.Stride == a.Stride {
panic(regionIdentity)
}
panic(regionOverlap)
}
if off > 0 && len(mat.Data) <= off {
// We know m is completely before a.
return false
}
if off < 0 && len(a.Data) <= -off {
// We know m is completely after a.
return false
}
if mat.Stride != a.Stride {
// Too hard, so assume the worst.
panic(mismatchedStrides)
}
if off < 0 {
off = -off
mat.Cols, a.Cols = a.Cols, mat.Cols
}
if rectanglesOverlap(off, mat.Cols, a.Cols, mat.Stride) {
panic(regionOverlap)
}
return false
}
// BUG(kortschak): Overlap detection for symmetric and triangular matrices is not
// precise; currently overlap is detected if the bounding rectangles overlap rather
// than exact overlap between visible elements.
func (s *SymDense) checkOverlap(a blas64.Symmetric) bool {
mat := s.RawSymmetric()
if cap(mat.Data) == 0 || cap(a.Data) == 0 {
return false
}
off := offset(mat.Data[:1], a.Data[:1])
if off == 0 {
// At least one element overlaps.
if mat.N == a.N && mat.Stride == a.Stride {
panic(regionIdentity)
}
panic(regionOverlap)
}
if off > 0 && len(mat.Data) <= off {
// We know s is completely before a.
return false
}
if off < 0 && len(a.Data) <= -off {
// We know s is completely after a.
return false
}
if mat.Stride != a.Stride {
// Too hard, so assume the worst.
panic(mismatchedStrides)
}
// TODO(kortschak) Make this analysis more precise.
if off > 0 {
off = -off
mat.N, a.N = a.N, mat.N
}
if rectanglesOverlap(off, mat.N, a.N, mat.Stride) {
panic(regionOverlap)
}
return false
}
func (t *TriDense) checkOverlap(a blas64.Triangular) bool {
mat := t.RawTriangular()
if cap(mat.Data) == 0 || cap(a.Data) == 0 {
return false
}
off := offset(mat.Data[:1], a.Data[:1])
if off == 0 {
// At least one element overlaps.
if mat.N == a.N && mat.Stride == a.Stride {
panic(regionIdentity)
}
panic(regionOverlap)
}
if off > 0 && len(mat.Data) <= off {
// We know t is completely before a.
return false
}
if off < 0 && len(a.Data) <= -off {
// We know t is completely after a.
return false
}
if mat.Stride != a.Stride {
// Too hard, so assume the worst.
panic(mismatchedStrides)
}
// TODO(kortschak) Make this analysis more precise.
if off > 0 {
off = -off
mat.N, a.N = a.N, mat.N
}
if rectanglesOverlap(off, mat.N, a.N, mat.Stride) {
panic(regionOverlap)
}
return false
}
func (v *Vector) checkOverlap(a blas64.Vector) bool {
mat := v.mat
if cap(mat.Data) == 0 || cap(a.Data) == 0 {
return false
}
off := offset(mat.Data[:1], a.Data[:1])
if off == 0 {
// At least one element overlaps.
if mat.Inc == a.Inc && len(mat.Data) == len(a.Data) {
panic(regionIdentity)
}
panic(regionOverlap)
}
if off > 0 && len(mat.Data) <= off {
// We know v is completely before a.
return false
}
if off < 0 && len(a.Data) <= -off {
// We know v is completely after a.
return false
}
if mat.Inc != a.Inc {
// Too hard, so assume the worst.
panic(mismatchedStrides)
}
if mat.Inc == 1 || off&mat.Inc == 0 {
panic(regionOverlap)
}
return false
}
// rectanglesOverlap returns whether the strided rectangles a and b overlap
// when b is offset by off elements after a but has at least one element before
// the end of a. a and b have aCols and bCols respectively.
//
// rectanglesOverlap works by shifting both matrices left such that the left
// column of a is at 0. The column indexes are flattened by obtaining the shifted
// relative left and right column positions modulo the common stride. This allows
// direct comparison of the column offsets when the matrix backing data slices
// are known to overlap.
func rectanglesOverlap(off, aCols, bCols, stride int) bool {
if stride == 1 {
// Unit stride means overlapping data
// slices must overlap as matrices.
return true
}
// Flatten the shifted matrix column positions
// so a starts at 0, modulo the common stride.
const aFrom = 0
aTo := aCols
// The mod stride operations here make the from
// and to indexes comparable between a and b when
// the data slices of a and b overlap.
bFrom := off % stride
bTo := (bFrom + bCols) % stride
// Compare the case where the b matrix is
// not wrapped.
if bFrom < bTo {
return aTo > bFrom
}
// Compare the case where the right column
// of b aligns with the stride of the backing
// data slice.
if bTo == 0 {
return bFrom < aTo
}
// Compare the case where the right column of
// b wraps around to the left again, modulo
// stride.
return bTo > aFrom
}