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// Copyright ©2013 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 mat
import (
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
)
var (
dense *Dense
_ Matrix = dense
_ allMatrix = dense
_ denseMatrix = dense
_ Mutable = dense
_ ClonerFrom = dense
_ RowViewer = dense
_ ColViewer = dense
_ RawRowViewer = dense
_ Grower = dense
_ RawMatrixSetter = dense
_ RawMatrixer = dense
_ Reseter = dense
)
// Dense is a dense matrix representation.
type Dense struct {
mat blas64.General
capRows, capCols int
}
// NewDense creates a new Dense matrix with r rows and c columns. If data == nil,
// a new slice is allocated for the backing slice. If len(data) == r*c, data is
// used as the backing slice, and changes to the elements of the returned Dense
// will be reflected in data. If neither of these is true, NewDense will panic.
// NewDense will panic if either r or c is zero.
//
// The data must be arranged in row-major order, i.e. the (i*c + j)-th
// element in the data slice is the {i, j}-th element in the matrix.
func NewDense(r, c int, data []float64) *Dense {
if r <= 0 || c <= 0 {
if r == 0 || c == 0 {
panic(ErrZeroLength)
}
panic(ErrNegativeDimension)
}
if data != nil && r*c != len(data) {
panic(ErrShape)
}
if data == nil {
data = make([]float64, r*c)
}
return &Dense{
mat: blas64.General{
Rows: r,
Cols: c,
Stride: c,
Data: data,
},
capRows: r,
capCols: c,
}
}
// ReuseAs changes the receiver if it IsEmpty() to be of size r×c.
//
// ReuseAs re-uses the backing data slice if it has sufficient capacity,
// otherwise a new slice is allocated. The backing data is zero on return.
//
// ReuseAs panics if the receiver is not empty, and panics if
// the input sizes are less than one. To empty the receiver for re-use,
// Reset should be used.
func (m *Dense) ReuseAs(r, c int) {
if r <= 0 || c <= 0 {
if r == 0 || c == 0 {
panic(ErrZeroLength)
}
panic(ErrNegativeDimension)
}
if !m.IsEmpty() {
panic(ErrReuseNonEmpty)
}
m.reuseAsZeroed(r, c)
}
// reuseAsNonZeroed resizes an empty matrix to a r×c matrix,
// or checks that a non-empty matrix is r×c. It does not zero
// the data in the receiver.
func (m *Dense) reuseAsNonZeroed(r, c int) {
// reuseAs must be kept in sync with reuseAsZeroed.
if m.mat.Rows > m.capRows || m.mat.Cols > m.capCols {
// Panic as a string, not a mat.Error.
panic("mat: caps not correctly set")
}
if r == 0 || c == 0 {
panic(ErrZeroLength)
}
if m.IsEmpty() {
m.mat = blas64.General{
Rows: r,
Cols: c,
Stride: c,
Data: use(m.mat.Data, r*c),
}
m.capRows = r
m.capCols = c
return
}
if r != m.mat.Rows || c != m.mat.Cols {
panic(ErrShape)
}
}
// reuseAsZeroed resizes an empty matrix to a r×c matrix,
// or checks that a non-empty matrix is r×c. It zeroes
// all the elements of the matrix.
func (m *Dense) reuseAsZeroed(r, c int) {
// reuseAsZeroed must be kept in sync with reuseAsNonZeroed.
if m.mat.Rows > m.capRows || m.mat.Cols > m.capCols {
// Panic as a string, not a mat.Error.
panic("mat: caps not correctly set")
}
if r == 0 || c == 0 {
panic(ErrZeroLength)
}
if m.IsEmpty() {
m.mat = blas64.General{
Rows: r,
Cols: c,
Stride: c,
Data: useZeroed(m.mat.Data, r*c),
}
m.capRows = r
m.capCols = c
return
}
if r != m.mat.Rows || c != m.mat.Cols {
panic(ErrShape)
}
m.Zero()
}
// Zero sets all of the matrix elements to zero.
func (m *Dense) Zero() {
r := m.mat.Rows
c := m.mat.Cols
for i := 0; i < r; i++ {
zero(m.mat.Data[i*m.mat.Stride : i*m.mat.Stride+c])
}
}
// isolatedWorkspace returns a new dense matrix w with the size of a and
// returns a callback to defer which performs cleanup at the return of the call.
// This should be used when a method receiver is the same pointer as an input argument.
func (m *Dense) isolatedWorkspace(a Matrix) (w *Dense, restore func()) {
r, c := a.Dims()
if r == 0 || c == 0 {
panic(ErrZeroLength)
}
w = getWorkspace(r, c, false)
return w, func() {
m.Copy(w)
putWorkspace(w)
}
}
// Reset empties the matrix so that it can be reused as the
// receiver of a dimensionally restricted operation.
//
// Reset should not be used when the matrix shares backing data.
// See the Reseter interface for more information.
func (m *Dense) Reset() {
// Row, Cols and Stride must be zeroed in unison.
m.mat.Rows, m.mat.Cols, m.mat.Stride = 0, 0, 0
m.capRows, m.capCols = 0, 0
m.mat.Data = m.mat.Data[:0]
}
// IsEmpty returns whether the receiver is empty. Empty matrices can be the
// receiver for size-restricted operations. The receiver can be emptied using
// Reset.
func (m *Dense) IsEmpty() bool {
// It must be the case that m.Dims() returns
// zeros in this case. See comment in Reset().
return m.mat.Stride == 0
}
// asTriDense returns a TriDense with the given size and side. The backing data
// of the TriDense is the same as the receiver.
func (m *Dense) asTriDense(n int, diag blas.Diag, uplo blas.Uplo) *TriDense {
return &TriDense{
mat: blas64.Triangular{
N: n,
Stride: m.mat.Stride,
Data: m.mat.Data,
Uplo: uplo,
Diag: diag,
},
cap: n,
}
}
// DenseCopyOf returns a newly allocated copy of the elements of a.
func DenseCopyOf(a Matrix) *Dense {
d := &Dense{}
d.CloneFrom(a)
return d
}
// SetRawMatrix sets the underlying blas64.General used by the receiver.
// Changes to elements in the receiver following the call will be reflected
// in b.
func (m *Dense) SetRawMatrix(b blas64.General) {
m.capRows, m.capCols = b.Rows, b.Cols
m.mat = b
}
// RawMatrix returns the underlying blas64.General used by the receiver.
// Changes to elements in the receiver following the call will be reflected
// in returned blas64.General.
func (m *Dense) RawMatrix() blas64.General { return m.mat }
// Dims returns the number of rows and columns in the matrix.
func (m *Dense) Dims() (r, c int) { return m.mat.Rows, m.mat.Cols }
// Caps returns the number of rows and columns in the backing matrix.
func (m *Dense) Caps() (r, c int) { return m.capRows, m.capCols }
// T performs an implicit transpose by returning the receiver inside a Transpose.
func (m *Dense) T() Matrix {
return Transpose{m}
}
// ColView returns a Vector reflecting the column j, backed by the matrix data.
//
// See ColViewer for more information.
func (m *Dense) ColView(j int) Vector {
var v VecDense
v.ColViewOf(m, j)
return &v
}
// SetCol sets the values in the specified column of the matrix to the values
// in src. len(src) must equal the number of rows in the receiver.
func (m *Dense) SetCol(j int, src []float64) {
if j >= m.mat.Cols || j < 0 {
panic(ErrColAccess)
}
if len(src) != m.mat.Rows {
panic(ErrColLength)
}
blas64.Copy(
blas64.Vector{N: m.mat.Rows, Inc: 1, Data: src},
blas64.Vector{N: m.mat.Rows, Inc: m.mat.Stride, Data: m.mat.Data[j:]},
)
}
// SetRow sets the values in the specified rows of the matrix to the values
// in src. len(src) must equal the number of columns in the receiver.
func (m *Dense) SetRow(i int, src []float64) {
if i >= m.mat.Rows || i < 0 {
panic(ErrRowAccess)
}
if len(src) != m.mat.Cols {
panic(ErrRowLength)
}
copy(m.rawRowView(i), src)
}
// RowView returns row i of the matrix data represented as a column vector,
// backed by the matrix data.
//
// See RowViewer for more information.
func (m *Dense) RowView(i int) Vector {
var v VecDense
v.RowViewOf(m, i)
return &v
}
// RawRowView returns a slice backed by the same array as backing the
// receiver.
func (m *Dense) RawRowView(i int) []float64 {
if i >= m.mat.Rows || i < 0 {
panic(ErrRowAccess)
}
return m.rawRowView(i)
}
func (m *Dense) rawRowView(i int) []float64 {
return m.mat.Data[i*m.mat.Stride : i*m.mat.Stride+m.mat.Cols]
}
// DiagView returns the diagonal as a matrix backed by the original data.
func (m *Dense) DiagView() Diagonal {
n := min(m.mat.Rows, m.mat.Cols)
return &DiagDense{
mat: blas64.Vector{
N: n,
Inc: m.mat.Stride + 1,
Data: m.mat.Data[:(n-1)*m.mat.Stride+n],
},
}
}
// Slice returns a new Matrix that shares backing data with the receiver.
// The returned matrix starts at {i,j} of the receiver and extends k-i rows
// and l-j columns. The final row in the resulting matrix is k-1 and the
// final column is l-1.
// Slice panics with ErrIndexOutOfRange if the slice is outside the capacity
// of the receiver.
func (m *Dense) Slice(i, k, j, l int) Matrix {
mr, mc := m.Caps()
if i < 0 || mr <= i || j < 0 || mc <= j || k < i || mr < k || l < j || mc < l {
if i == k || j == l {
panic(ErrZeroLength)
}
panic(ErrIndexOutOfRange)
}
t := *m
t.mat.Data = t.mat.Data[i*t.mat.Stride+j : (k-1)*t.mat.Stride+l]
t.mat.Rows = k - i
t.mat.Cols = l - j
t.capRows -= i
t.capCols -= j
return &t
}
// Grow returns the receiver expanded by r rows and c columns. If the dimensions
// of the expanded matrix are outside the capacities of the receiver a new
// allocation is made, otherwise not. Note the receiver itself is not modified
// during the call to Grow.
func (m *Dense) Grow(r, c int) Matrix {
if r < 0 || c < 0 {
panic(ErrIndexOutOfRange)
}
if r == 0 && c == 0 {
return m
}
r += m.mat.Rows
c += m.mat.Cols
var t Dense
switch {
case m.mat.Rows == 0 || m.mat.Cols == 0:
t.mat = blas64.General{
Rows: r,
Cols: c,
Stride: c,
// We zero because we don't know how the matrix will be used.
// In other places, the mat is immediately filled with a result;
// this is not the case here.
Data: useZeroed(m.mat.Data, r*c),
}
case r > m.capRows || c > m.capCols:
cr := max(r, m.capRows)
cc := max(c, m.capCols)
t.mat = blas64.General{
Rows: r,
Cols: c,
Stride: cc,
Data: make([]float64, cr*cc),
}
t.capRows = cr
t.capCols = cc
// Copy the complete matrix over to the new matrix.
// Including elements not currently visible. Use a temporary structure
// to avoid modifying the receiver.
var tmp Dense
tmp.mat = blas64.General{
Rows: m.mat.Rows,
Cols: m.mat.Cols,
Stride: m.mat.Stride,
Data: m.mat.Data,
}
tmp.capRows = m.capRows
tmp.capCols = m.capCols
t.Copy(&tmp)
return &t
default:
t.mat = blas64.General{
Data: m.mat.Data[:(r-1)*m.mat.Stride+c],
Rows: r,
Cols: c,
Stride: m.mat.Stride,
}
}
t.capRows = r
t.capCols = c
return &t
}
// CloneFrom makes a copy of a into the receiver, overwriting the previous value of
// the receiver. The clone from operation does not make any restriction on shape and
// will not cause shadowing.
//
// See the ClonerFrom interface for more information.
func (m *Dense) CloneFrom(a Matrix) {
r, c := a.Dims()
mat := blas64.General{
Rows: r,
Cols: c,
Stride: c,
}
m.capRows, m.capCols = r, c
aU, trans := untransposeExtract(a)
switch aU := aU.(type) {
case *Dense:
amat := aU.mat
mat.Data = make([]float64, r*c)
if trans {
for i := 0; i < r; i++ {
blas64.Copy(blas64.Vector{N: c, Inc: amat.Stride, Data: amat.Data[i : i+(c-1)*amat.Stride+1]},
blas64.Vector{N: c, Inc: 1, Data: mat.Data[i*c : (i+1)*c]})
}
} else {
for i := 0; i < r; i++ {
copy(mat.Data[i*c:(i+1)*c], amat.Data[i*amat.Stride:i*amat.Stride+c])
}
}
case *VecDense:
amat := aU.mat
mat.Data = make([]float64, aU.mat.N)
blas64.Copy(blas64.Vector{N: aU.mat.N, Inc: amat.Inc, Data: amat.Data},
blas64.Vector{N: aU.mat.N, Inc: 1, Data: mat.Data})
default:
mat.Data = make([]float64, r*c)
w := *m
w.mat = mat
for i := 0; i < r; i++ {
for j := 0; j < c; j++ {
w.set(i, j, a.At(i, j))
}
}
*m = w
return
}
m.mat = mat
}
// Copy makes a copy of elements of a into the receiver. It is similar to the
// built-in copy; it copies as much as the overlap between the two matrices and
// returns the number of rows and columns it copied. If a aliases the receiver
// and is a transposed Dense or VecDense, with a non-unitary increment, Copy will
// panic.
//
// See the Copier interface for more information.
func (m *Dense) Copy(a Matrix) (r, c int) {
r, c = a.Dims()
if a == m {
return r, c
}
r = min(r, m.mat.Rows)
c = min(c, m.mat.Cols)
if r == 0 || c == 0 {
return 0, 0
}
aU, trans := untransposeExtract(a)
switch aU := aU.(type) {
case *Dense:
amat := aU.mat
if trans {
if amat.Stride != 1 {
m.checkOverlap(amat)
}
for i := 0; i < r; i++ {
blas64.Copy(blas64.Vector{N: c, Inc: amat.Stride, Data: amat.Data[i : i+(c-1)*amat.Stride+1]},
blas64.Vector{N: c, Inc: 1, Data: m.mat.Data[i*m.mat.Stride : i*m.mat.Stride+c]})
}
} else {
switch o := offset(m.mat.Data, amat.Data); {
case o < 0:
for i := r - 1; i >= 0; i-- {
copy(m.mat.Data[i*m.mat.Stride:i*m.mat.Stride+c], amat.Data[i*amat.Stride:i*amat.Stride+c])
}
case o > 0:
for i := 0; i < r; i++ {
copy(m.mat.Data[i*m.mat.Stride:i*m.mat.Stride+c], amat.Data[i*amat.Stride:i*amat.Stride+c])
}
default:
// Nothing to do.
}
}
case *VecDense:
var n, stride int
amat := aU.mat
if trans {
if amat.Inc != 1 {
m.checkOverlap(aU.asGeneral())
}
n = c
stride = 1
} else {
n = r
stride = m.mat.Stride
}
if amat.Inc == 1 && stride == 1 {
copy(m.mat.Data, amat.Data[:n])
break
}
switch o := offset(m.mat.Data, amat.Data); {
case o < 0:
blas64.Copy(blas64.Vector{N: n, Inc: -amat.Inc, Data: amat.Data},
blas64.Vector{N: n, Inc: -stride, Data: m.mat.Data})
case o > 0:
blas64.Copy(blas64.Vector{N: n, Inc: amat.Inc, Data: amat.Data},
blas64.Vector{N: n, Inc: stride, Data: m.mat.Data})
default:
// Nothing to do.
}
default:
m.checkOverlapMatrix(aU)
for i := 0; i < r; i++ {
for j := 0; j < c; j++ {
m.set(i, j, a.At(i, j))
}
}
}
return r, c
}
// Stack appends the rows of b onto the rows of a, placing the result into the
// receiver with b placed in the greater indexed rows. Stack will panic if the
// two input matrices do not have the same number of columns or the constructed
// stacked matrix is not the same shape as the receiver.
func (m *Dense) Stack(a, b Matrix) {
ar, ac := a.Dims()
br, bc := b.Dims()
if ac != bc || m == a || m == b {
panic(ErrShape)
}
m.reuseAsNonZeroed(ar+br, ac)
m.Copy(a)
w := m.Slice(ar, ar+br, 0, bc).(*Dense)
w.Copy(b)
}
// Augment creates the augmented matrix of a and b, where b is placed in the
// greater indexed columns. Augment will panic if the two input matrices do
// not have the same number of rows or the constructed augmented matrix is
// not the same shape as the receiver.
func (m *Dense) Augment(a, b Matrix) {
ar, ac := a.Dims()
br, bc := b.Dims()
if ar != br || m == a || m == b {
panic(ErrShape)
}
m.reuseAsNonZeroed(ar, ac+bc)
m.Copy(a)
w := m.Slice(0, br, ac, ac+bc).(*Dense)
w.Copy(b)
}
// Trace returns the trace of the matrix. The matrix must be square or Trace
// will panic.
func (m *Dense) Trace() float64 {
if m.mat.Rows != m.mat.Cols {
panic(ErrSquare)
}
// TODO(btracey): could use internal asm sum routine.
var v float64
for i := 0; i < m.mat.Rows; i++ {
v += m.mat.Data[i*m.mat.Stride+i]
}
return v
}
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