// Ddot computes the dot product of the two vectors
// \sum_i x[i]*y[i]
func (Implementation) Ddot(n int, x []float64, incX int, y []float64, incY int) float64 {
if n < 0 {
panic(negativeN)
}
if incX == 0 {
panic(zeroIncX)
}
if incY == 0 {
panic(zeroIncY)
}
if incX == 1 && incY == 1 {
if len(x) < n {
panic(badLenX)
}
if len(y) < n {
panic(badLenY)
}
return asm.DdotUnitary(x[:n], y)
}
var ix, iy int
if incX < 0 {
ix = (-n + 1) * incX
}
if incY < 0 {
iy = (-n + 1) * incY
}
if ix >= len(x) || ix+(n-1)*incX >= len(x) {
panic(badLenX)
}
if iy >= len(y) || iy+(n-1)*incY >= len(y) {
panic(badLenY)
}
return asm.DdotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
}
// Cholesky calculates the Cholesky decomposition of the matrix A and returns
// whether the matrix is positive definite. The returned matrix is either a
// lower triangular matrix such that A = L * L^T or an upper triangular matrix
// such that A = U^T * U depending on the upper parameter.
func (t *Triangular) Cholesky(a *SymDense, upper bool) (ok bool) {
n := a.Symmetric()
if t.isZero() {
t.mat = blas64.Triangular{
N: n,
Stride: n,
Diag: blas.NonUnit,
Data: use(t.mat.Data, n*n),
}
} else if n != t.mat.N {
panic(ErrShape)
}
mat := t.mat.Data
stride := t.mat.Stride
if upper {
t.mat.Uplo = blas.Upper
for j := 0; j < n; j++ {
var d float64
for k := 0; k < j; k++ {
s := asm.DdotInc(
mat, mat,
uintptr(k),
uintptr(stride), uintptr(stride),
uintptr(k), uintptr(j),
)
s = (a.at(j, k) - s) / t.at(k, k)
t.set(k, j, s)
d += s * s
}
d = a.at(j, j) - d
if d <= 0 {
t.Reset()
return false
}
t.set(j, j, math.Sqrt(math.Max(d, 0)))
}
} else {
t.mat.Uplo = blas.Lower
for j := 0; j < n; j++ {
var d float64
for k := 0; k < j; k++ {
s := asm.DdotUnitary(mat[k*stride:k*stride+(n-k)], mat[j*stride:j*stride+(n-k)])
s = (a.at(j, k) - s) / t.at(k, k)
t.set(j, k, s)
d += s * s
}
d = a.at(j, j) - d
if d <= 0 {
t.Reset()
return false
}
t.set(j, j, math.Sqrt(math.Max(d, 0)))
}
}
return true
}
// Dgemv computes
// y = alpha * a * x + beta * y if tA = blas.NoTrans
// y = alpha * A^T * x + beta * y if tA = blas.Trans or blas.ConjTrans
// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
func (Implementation) Dgemv(tA blas.Transpose, m, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) {
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
panic(badTranspose)
}
if m < 0 {
panic(mLT0)
}
if n < 0 {
panic(nLT0)
}
if lda < max(1, n) {
panic(badLdA)
}
if incX == 0 {
panic(zeroIncX)
}
if incY == 0 {
panic(zeroIncY)
}
// Quick return if possible
if m == 0 || n == 0 || (alpha == 0 && beta == 1) {
return
}
// Set up indexes
lenX := m
lenY := n
if tA == blas.NoTrans {
lenX = n
lenY = m
}
var kx, ky int
if incX > 0 {
kx = 0
} else {
kx = -(lenX - 1) * incX
}
if incY > 0 {
ky = 0
} else {
ky = -(lenY - 1) * incY
}
// First form y := beta * y
if incY > 0 {
Implementation{}.Dscal(lenY, beta, y, incY)
} else {
Implementation{}.Dscal(lenY, beta, y, -incY)
}
if alpha == 0 {
return
}
// Form y := alpha * A * x + y
if tA == blas.NoTrans {
if incX == 1 {
for i := 0; i < m; i++ {
y[i] += alpha * asm.DdotUnitary(a[lda*i:lda*i+n], x)
}
return
}
iy := ky
for i := 0; i < m; i++ {
y[iy] += alpha * asm.DdotInc(x, a[lda*i:lda*i+n], uintptr(n), uintptr(incX), 1, uintptr(kx), 0)
iy += incY
}
return
}
// Cases where a is not transposed.
if incX == 1 {
for i := 0; i < m; i++ {
tmp := alpha * x[i]
if tmp != 0 {
asm.DaxpyUnitary(tmp, a[lda*i:lda*i+n], y, y)
}
}
return
}
ix := kx
for i := 0; i < m; i++ {
tmp := alpha * x[ix]
if tmp != 0 {
asm.DaxpyInc(tmp, a[lda*i:lda*i+n], y, uintptr(n), 1, uintptr(incY), 0, uintptr(ky))
}
ix += incX
}
}
// Inner computes the generalized inner product
// x^T A y
// between vectors x and y with matrix A. This is only a true inner product if
// A is symmetric positive definite, though the operation works for any matrix A.
//
// Inner panics if x.Len != m or y.Len != n when A is an m x n matrix.
func Inner(x *Vector, A Matrix, y *Vector) float64 {
m, n := A.Dims()
if x.Len() != m {
panic(matrix.ErrShape)
}
if y.Len() != n {
panic(matrix.ErrShape)
}
if m == 0 || n == 0 {
return 0
}
var sum float64
switch b := A.(type) {
case RawSymmetricer:
bmat := b.RawSymmetric()
if bmat.Uplo != blas.Upper {
// Panic as a string not a mat64.Error.
panic(badSymTriangle)
}
for i := 0; i < x.Len(); i++ {
xi := x.at(i)
if xi != 0 {
if y.mat.Inc == 1 {
sum += xi * asm.DdotUnitary(
bmat.Data[i*bmat.Stride+i:i*bmat.Stride+n],
y.mat.Data[i:],
)
} else {
sum += xi * asm.DdotInc(
bmat.Data[i*bmat.Stride+i:i*bmat.Stride+n],
y.mat.Data[i*y.mat.Inc:], uintptr(n-i),
1, uintptr(y.mat.Inc),
0, 0,
)
}
}
yi := y.at(i)
if i != n-1 && yi != 0 {
if x.mat.Inc == 1 {
sum += yi * asm.DdotUnitary(
bmat.Data[i*bmat.Stride+i+1:i*bmat.Stride+n],
x.mat.Data[i+1:],
)
} else {
sum += yi * asm.DdotInc(
bmat.Data[i*bmat.Stride+i+1:i*bmat.Stride+n],
x.mat.Data[(i+1)*x.mat.Inc:], uintptr(n-i-1),
1, uintptr(x.mat.Inc),
0, 0,
)
}
}
}
case RawMatrixer:
bmat := b.RawMatrix()
for i := 0; i < x.Len(); i++ {
xi := x.at(i)
if xi != 0 {
if y.mat.Inc == 1 {
sum += xi * asm.DdotUnitary(
bmat.Data[i*bmat.Stride:i*bmat.Stride+n],
y.mat.Data,
)
} else {
sum += xi * asm.DdotInc(
bmat.Data[i*bmat.Stride:i*bmat.Stride+n],
y.mat.Data, uintptr(n),
1, uintptr(y.mat.Inc),
0, 0,
)
}
}
}
default:
for i := 0; i < x.Len(); i++ {
xi := x.at(i)
for j := 0; j < y.Len(); j++ {
sum += xi * A.At(i, j) * y.at(j)
}
}
}
return sum
}