Exemple #1
0
// 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)
}
Exemple #2
0
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
}
Exemple #3
0
// 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
}
Exemple #4
0
// 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
}
Exemple #5
0
// 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
}
Exemple #6
0
// 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
}