Convert a Hermite series to a polynomial. Convert an array representing the coefficients of a Hermite series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the "standard" basis) ordered from lowest to highest de
(c)
| 140 | |
| 141 | |
| 142 | def herm2poly(c): |
| 143 | """ |
| 144 | Convert a Hermite series to a polynomial. |
| 145 | |
| 146 | Convert an array representing the coefficients of a Hermite series, |
| 147 | ordered from lowest degree to highest, to an array of the coefficients |
| 148 | of the equivalent polynomial (relative to the "standard" basis) ordered |
| 149 | from lowest to highest degree. |
| 150 | |
| 151 | Parameters |
| 152 | ---------- |
| 153 | c : array_like |
| 154 | 1-D array containing the Hermite series coefficients, ordered |
| 155 | from lowest order term to highest. |
| 156 | |
| 157 | Returns |
| 158 | ------- |
| 159 | pol : ndarray |
| 160 | 1-D array containing the coefficients of the equivalent polynomial |
| 161 | (relative to the "standard" basis) ordered from lowest order term |
| 162 | to highest. |
| 163 | |
| 164 | See Also |
| 165 | -------- |
| 166 | poly2herm |
| 167 | |
| 168 | Notes |
| 169 | ----- |
| 170 | The easy way to do conversions between polynomial basis sets |
| 171 | is to use the convert method of a class instance. |
| 172 | |
| 173 | Examples |
| 174 | -------- |
| 175 | >>> from numpy.polynomial.hermite import herm2poly |
| 176 | >>> herm2poly([ 1. , 2.75 , 0.5 , 0.375]) |
| 177 | array([0., 1., 2., 3.]) |
| 178 | |
| 179 | """ |
| 180 | from .polynomial import polyadd, polysub, polymulx |
| 181 | |
| 182 | [c] = pu.as_series([c]) |
| 183 | n = len(c) |
| 184 | if n == 1: |
| 185 | return c |
| 186 | if n == 2: |
| 187 | c[1] *= 2 |
| 188 | return c |
| 189 | else: |
| 190 | c0 = c[-2] |
| 191 | c1 = c[-1] |
| 192 | # i is the current degree of c1 |
| 193 | for i in range(n - 1, 1, -1): |
| 194 | tmp = c0 |
| 195 | c0 = polysub(c[i - 2], c1*(2*(i - 1))) |
| 196 | c1 = polyadd(tmp, polymulx(c1)*2) |
| 197 | return polyadd(c0, polymulx(c1)*2) |
| 198 | |
| 199 | # |