/* Jacobian
========
Calculates (with N=n-1):
df0dx0, df0dx1, df0dx2, ... df0dxN
df1dx0, df1dx1, df1dx2, ... df1dxN
. . . . . . . . . . . . .
dfNdx0, dfNdx1, dfNdx2, ... dfNdxN
INPUT:
ffcn : f(x) function
x : station where dfdx has to be calculated
fx : f @ x
w : workspace with size == n == len(x)
RETURNS:
J : dfdx @ x [must be pre-allocated] */
func Jacobian(J *la.Triplet, ffcn Cb_f, x, fx, w []float64, distr bool) (err error) {
ndim := len(x)
start, endp1 := 0, ndim
if distr {
id, sz := mpi.Rank(), mpi.Size()
start, endp1 = (id*ndim)/sz, ((id+1)*ndim)/sz
if J.Max() == 0 {
J.Init(ndim, ndim, (endp1-start)*ndim)
}
} else {
if J.Max() == 0 {
J.Init(ndim, ndim, ndim*ndim)
}
}
J.Start()
// NOTE: cannot split calculation by columns unless the f function is
// independently calculated by each MPI processor.
// Otherwise, the AllReduce in f calculation would
// join pieces of f from different processors calculated for
// different x values (δx[col] from different columns).
/*
for col := start; col < endp1; col++ {
xsafe := x[col]
delta := math.Sqrt(EPS * max(CTE1, math.Abs(xsafe)))
x[col] = xsafe + delta
ffcn(w, x) // fnew
io.Pforan("x = %v, f = %v\n", x, w)
for row := 0; row < ndim; row++ {
J.Put(row, col, (w[row]-fx[row])/delta)
}
x[col] = xsafe
}
*/
var df float64
for col := 0; col < ndim; col++ {
xsafe := x[col]
delta := math.Sqrt(EPS * max(CTE1, math.Abs(xsafe)))
x[col] = xsafe + delta
err = ffcn(w, x) // w := f(x+δx[col])
if err != nil {
return
}
for row := start; row < endp1; row++ {
df = w[row] - fx[row]
//if math.Abs(df) > EPS {
J.Put(row, col, df/delta)
//}
}
x[col] = xsafe
}
return
}
// Jacobian computes Jacobian (sparse) matrix
// Calculates (with N=n-1):
// df0dx0, df0dx1, df0dx2, ... df0dxN
// df1dx0, df1dx1, df1dx2, ... df1dxN
// . . . . . . . . . . . . .
// dfNdx0, dfNdx1, dfNdx2, ... dfNdxN
// INPUT:
// ffcn : f(x) function
// x : station where dfdx has to be calculated
// fx : f @ x
// w : workspace with size == n == len(x)
// RETURNS:
// J : dfdx @ x [must be pre-allocated]
func Jacobian(J *la.Triplet, ffcn Cb_f, x, fx, w []float64) (err error) {
ndim := len(x)
start, endp1 := 0, ndim
if J.Max() == 0 {
J.Init(ndim, ndim, ndim*ndim)
}
J.Start()
var df float64
for col := 0; col < ndim; col++ {
xsafe := x[col]
delta := math.Sqrt(EPS * max(CTE1, math.Abs(xsafe)))
x[col] = xsafe + delta
err = ffcn(w, x) // w := f(x+δx[col])
if err != nil {
return
}
for row := start; row < endp1; row++ {
df = w[row] - fx[row]
J.Put(row, col, df/delta)
}
x[col] = xsafe
}
return
}
