// Snrm2 computes the Euclidean norm of a vector,
// sqrt(\sum_i x[i] * x[i]).
// This function returns 0 if incX is negative.
//
// Float32 implementations are autogenerated and not directly tested.
func (Implementation) Snrm2(n int, x []float32, incX int) float32 {
if incX < 1 {
if incX == 0 {
panic(zeroIncX)
}
return 0
}
if n < 2 {
if n == 1 {
return math.Abs(x[0])
}
if n == 0 {
return 0
}
if n < 1 {
panic(negativeN)
}
}
var (
scale float32 = 0
sumSquares float32 = 1
)
if incX == 1 {
x = x[:n]
for _, v := range x {
absxi := math.Abs(v)
if scale < absxi {
sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
scale = absxi
} else {
sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
}
}
return scale * math.Sqrt(sumSquares)
}
for ix := 0; ix < n*incX; ix += incX {
val := x[ix]
if val == 0 {
continue
}
absxi := math.Abs(val)
if scale < absxi {
sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
scale = absxi
} else {
sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
}
}
return scale * math.Sqrt(sumSquares)
}
func (g general32) equalWithinAbs(a general32, tol float32) bool {
if g.rows != a.rows || g.cols != a.cols || g.stride != a.stride {
return false
}
for i, v := range g.data {
if math.Abs(a.data[i]-v) > tol {
return false
}
}
return true
}
// Isamax returns the index of the largest element of x. If there are multiple
// such indices the earliest is returned. Idamax returns -1 if incX is negative or if
// n == 0.
//
// Float32 implementations are autogenerated and not directly tested.
func (Implementation) Isamax(n int, x []float32, incX int) int {
if incX < 1 {
if incX == 0 {
panic(zeroIncX)
}
return -1
}
if n < 2 {
if n == 1 {
return 0
}
if n == 0 {
return -1 // Netlib returns invalid index when n == 0
}
if n < 1 {
panic(negativeN)
}
}
idx := 0
max := math.Abs(x[0])
if incX == 1 {
for i, v := range x {
absV := math.Abs(v)
if absV > max {
max = absV
idx = i
}
}
}
ix := incX
for i := 1; i < n; i++ {
v := x[ix]
absV := math.Abs(v)
if absV > max {
max = absV
idx = i
}
ix += incX
}
return idx
}
// Sasum computes the sum of the absolute values of the elements of x.
// \sum_i |x[i]|
// Sasum returns 0 if incX is negative.
//
// Float32 implementations are autogenerated and not directly tested.
func (Implementation) Sasum(n int, x []float32, incX int) float32 {
var sum float32
if n < 0 {
panic(negativeN)
}
if incX < 1 {
if incX == 0 {
panic(zeroIncX)
}
return 0
}
if incX == 1 {
x = x[:n]
for _, v := range x {
sum += math.Abs(v)
}
return sum
}
for i := 0; i < n; i++ {
sum += math.Abs(x[i*incX])
}
return sum
}
// Srotg computes the plane rotation
// _ _ _ _ _ _
// | c s | | a | | r |
// | -s c | * | b | = | 0 |
// ‾ ‾ ‾ ‾ ‾ ‾
// where
// r = ±(a^2 + b^2)
// c = a/r, the cosine of the plane rotation
// s = b/r, the sine of the plane rotation
//
// NOTE: There is a discrepancy between the refence implementation and the BLAS
// technical manual regarding the sign for r when a or b are zero.
// Srotg agrees with the definition in the manual and other
// common BLAS implementations.
//
// Float32 implementations are autogenerated and not directly tested.
func (Implementation) Srotg(a, b float32) (c, s, r, z float32) {
if b == 0 && a == 0 {
return 1, 0, a, 0
}
absA := math.Abs(a)
absB := math.Abs(b)
aGTb := absA > absB
r = math.Hypot(a, b)
if aGTb {
r = math.Copysign(r, a)
} else {
r = math.Copysign(r, b)
}
c = a / r
s = b / r
if aGTb {
z = s
} else if c != 0 { // r == 0 case handled above
z = 1 / c
} else {
z = 1
}
return
}
// Srotmg computes the modified Givens rotation. See
// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
// for more details.
//
// Float32 implementations are autogenerated and not directly tested.
func (Implementation) Srotmg(d1, d2, x1, y1 float32) (p blas.SrotmParams, rd1, rd2, rx1 float32) {
var p1, p2, q1, q2, u float32
const (
gam = 4096.0
gamsq = 16777216.0
rgamsq = 5.9604645e-8
)
if d1 < 0 {
p.Flag = blas.Rescaling
return
}
p2 = d2 * y1
if p2 == 0 {
p.Flag = blas.Identity
rd1 = d1
rd2 = d2
rx1 = x1
return
}
p1 = d1 * x1
q2 = p2 * y1
q1 = p1 * x1
absQ1 := math.Abs(q1)
absQ2 := math.Abs(q2)
if absQ1 < absQ2 && q2 < 0 {
p.Flag = blas.Rescaling
return
}
if d1 == 0 {
p.Flag = blas.Diagonal
p.H[0] = p1 / p2
p.H[3] = x1 / y1
u = 1 + p.H[0]*p.H[3]
rd1, rd2 = d2/u, d1/u
rx1 = y1 / u
return
}
// Now we know that d1 != 0, and d2 != 0. If d2 == 0, it would be caught
// when p2 == 0, and if d1 == 0, then it is caught above
if absQ1 > absQ2 {
p.H[1] = -y1 / x1
p.H[2] = p2 / p1
u = 1 - p.H[2]*p.H[1]
rd1 = d1
rd2 = d2
rx1 = x1
p.Flag = blas.OffDiagonal
// u must be greater than zero because |q1| > |q2|, so check from netlib
// is unnecessary
// This is left in for ease of comparison with complex routines
//if u > 0 {
rd1 /= u
rd2 /= u
rx1 *= u
//}
} else {
p.Flag = blas.Diagonal
p.H[0] = p1 / p2
p.H[3] = x1 / y1
u = 1 + p.H[0]*p.H[3]
rd1 = d2 / u
rd2 = d1 / u
rx1 = y1 * u
}
for rd1 <= rgamsq || rd1 >= gamsq {
if p.Flag == blas.OffDiagonal {
p.H[0] = 1
p.H[3] = 1
p.Flag = blas.Rescaling
} else if p.Flag == blas.Diagonal {
p.H[1] = -1
p.H[2] = 1
p.Flag = blas.Rescaling
}
if rd1 <= rgamsq {
rd1 *= gam * gam
rx1 /= gam
p.H[0] /= gam
p.H[2] /= gam
} else {
rd1 /= gam * gam
rx1 *= gam
p.H[0] *= gam
p.H[2] *= gam
}
}
for math.Abs(rd2) <= rgamsq || math.Abs(rd2) >= gamsq {
if p.Flag == blas.OffDiagonal {
p.H[0] = 1
p.H[3] = 1
p.Flag = blas.Rescaling
} else if p.Flag == blas.Diagonal {
p.H[1] = -1
p.H[2] = 1
p.Flag = blas.Rescaling
}
if math.Abs(rd2) <= rgamsq {
rd2 *= gam * gam
p.H[1] /= gam
p.H[3] /= gam
} else {
rd2 /= gam * gam
p.H[1] *= gam
p.H[3] *= gam
}
}
return
}
