From e966b318f296c4c7a994ca64f3b11430ddb4e2dd Mon Sep 17 00:00:00 2001 From: Michael Theodorou Date: Mon, 22 May 2023 16:49:09 +0200 Subject: [PATCH 01/12] Added files needed for triquintic interpolation --- pyproject.toml | 2 +- src/qinterp/base.py | 452 ++++++++++++++++++++++ src/qinterp/scaled_by8_inverse_matrix.csv | 216 +++++++++++ src/qinterp/triquintic.py | 234 +++++++++++ tests/test_triquintic.py | 40 ++ 5 files changed, 943 insertions(+), 1 deletion(-) create mode 100644 src/qinterp/scaled_by8_inverse_matrix.csv create mode 100644 src/qinterp/triquintic.py create mode 100644 tests/test_triquintic.py diff --git a/pyproject.toml b/pyproject.toml index 44158f4..26f8add 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -10,7 +10,7 @@ packages = [ ] [tool.poetry.dependencies] -python = ">=3.7,<3.12" +python = ">=3.9,<3.12" numpy = "^1.21.1" [tool.poetry.group.dev.dependencies] diff --git a/src/qinterp/base.py b/src/qinterp/base.py index af52856..17f4c20 100644 --- a/src/qinterp/base.py +++ b/src/qinterp/base.py @@ -204,3 +204,455 @@ def nan_out_of_bounds(self, query): query[np.where(query[:, 2] < self.zIntMin)[0]] = np.nan query[np.where(query[:, 2] >= self.zIntMax)[0]] = np.nan return query + + +class TriquinticInterpolatorBase: + + def __init__(self, field, *args, **kwargs): + self.eps = 10 * np.finfo(float).eps # Machine precision of floating point number + # Load field passed to class - can be x,y,z or norm of vector field, or scalar + self.inputfield = field + # Analyse field, get shapes etc + self.getFieldParams() + # Make coefficient matrix + self.A = self.makeAMatrix() + + # Mask to identify where coefficients exist + self.alphamask = np.zeros((self.nc + 1, 1)) + self.alphamask[-1] = 1 + + def __call__(self, xi, d=0): + if d == 0: + return self.field(xi) + elif d == 1: + return self.gradient(xi) + elif d == 2: + return self.hessian(xi) + else: + raise NotImplementedError + + def field(self, xi): + return NotImplementedError + + def gradient(self, xi): + return NotImplementedError + + def hessian(self, xi): + return NotImplementedError + + def getFieldParams(self): + # Make sure coords are sorted correctly + # This sorts the data in 'F' style + self.inputfield = self.inputfield[self.inputfield[:, 0].argsort()] + self.inputfield = self.inputfield[self.inputfield[:, 1].argsort(kind='mergesort')] + self.inputfield = self.inputfield[self.inputfield[:, 2].argsort(kind='mergesort')] + + # Analyse field + xzero = self.inputfield[np.where(self.inputfield[:, 0] == self.inputfield[0, 0])[0]] + yzero = self.inputfield[np.where(self.inputfield[:, 1] == self.inputfield[0, 1])[0]] + xaxis = yzero[np.where(yzero[:, 2] == yzero[0, 2])[0]] + yaxis = xzero[np.where(xzero[:, 2] == xzero[0, 2])[0]] + zaxis = xzero[np.where(xzero[:, 1] == xzero[0, 1])[0]] + + nPosx = len(xaxis) # These give the length of the interpolation volume along each axis + nPosy = len(yaxis) + nPosz = len(zaxis) + + # Compared to tricubic (nPosx-3) we now have (nPosx-5) because of higher derivatives + # to be approximated + self.nPos = np.array([nPosx - 5, nPosy - 5, nPosz - 5]) # number of interpolatable cuboids per axis + + self.x = xaxis[:, 0] # axis coordinates + self.y = yaxis[:, 1] + self.z = zaxis[:, 2] + if self.inputfield.shape[1] == 4: + self.field_data = self.inputfield[:, 3].reshape(nPosx, nPosy, nPosz, order='F') + else: + self.field_data = np.stack([self.inputfield[:, j].reshape(nPosx, nPosy, nPosz, order='F') + for j in range(3, 6)], axis=0) + + self.hx = np.abs((xaxis[0, 0] - xaxis[1, 0])) # grid spacing along each axis + self.hy = np.abs((yaxis[0, 1] - yaxis[1, 1])) + self.hz = np.abs((zaxis[0, 2] - zaxis[1, 2])) + + # Compared to tricubic, we use the first/last 2 points of the partition for estimating + # derivatives + self.xIntMin = self.inputfield[2, 0] # Minimal value of x that can be interpolated + self.yIntMin = self.inputfield[2 * nPosx, 1] + self.zIntMin = self.inputfield[2 * nPosx * nPosy, 2] + self.xIntMax = self.inputfield[-3, 0] # Maximal value of x that can be interpolated + self.yIntMax = self.inputfield[-2 * nPosx - 1, 1] + self.zIntMax = self.inputfield[-2 * nPosx * nPosy - 1, 2] + + # Find base indices of all interpolatable cuboids + minI = nPosx * nPosy + nPosx + 2 + self.basePointInds = minI + np.arange(0, nPosx - 5, 1) + temp = np.array([self.basePointInds + i * nPosx for i in range(nPosy - 5)]) + self.basePointInds = np.reshape(temp, (1, len(temp) * len(temp[0])))[0] + temp = np.array([self.basePointInds + i * nPosx * nPosy for i in range(nPosz - 5)]) + self.basePointInds = np.reshape(temp, (1, len(temp) * len(temp[0])))[0] + self.basePointInds = np.sort(self.basePointInds) + + # Number of interpolatable cuboids + self.nc = len(self.basePointInds) + + def makeAMatrix(self): + # Loads the triquintic interpolation matrix and creates finite difference matrix and combines them + # Interpolation matrix (inverse) + Bm1_scaled_by_8 = np.genfromtxt('scaled_by8_inverse_matrix.csv', delimiter=',') + Bm1 = Bm1_scaled_by_8 / 8 + + # This makes a finite-difference matrix to return the components of the "b"-vector + # needed in the alpha calculation, in "cuboid" coordinates + # In the triquintic approximation we have a unit cube whose main axes are extended by two points + # in each direction ending up in a 6x6x6 grid (in tricubic the extension was by one point in each + # direction ending up in a 4x4x4 grid) + C = np.array((86, 87, 92, 93, 122, 123, 128, 129)) + D = np.zeros((216, 216)) + + # Scalar values at cuboid vertices + for i in range(8): + D[i, C[i]] = 1 + + # x-derivative at cuboid vertices + for i, j in enumerate(range(8, 16, 1)): + D[j, C[i] - 1 + 0 + 0] = -1/2 + D[j, C[i] + 1 + 0 + 0] = 1/2 + + # y-derivative at cuboid vertices + for i, j in enumerate(range(16, 24, 1)): + D[j, C[i] + 0 - 6 + 0] = -1/2 + D[j, C[i] + 0 + 6 + 0] = 1/2 + + # z-derivative at cuboid vertices + for i, j in enumerate(range(24, 32, 1)): + D[j, C[i] + 0 + 0 - 36] = -1/2 + D[j, C[i] + 0 + 0 + 36] = 1/2 + + # xx-derivative at cuboid vertices + for i, j in enumerate(range(32, 40, 1)): + D[j, C[i] + 2 + 0 + 0] = 1/4 + D[j, C[i] + 0 + 0 + 0] = -1/2 + D[j, C[i] - 2 + 0 + 0] = 1/4 + + # yx-derivative at cuboid vertices + for i, j in enumerate(range(40, 48, 1)): + D[j, C[i] + 1 + 6 + 0] = 1/4 + D[j, C[i] + 1 - 6 + 0] = -1/4 + D[j, C[i] - 1 + 6 + 0] = -1/4 + D[j, C[i] - 1 - 6 + 0] = 1/4 + + # zx-derivative at cuboid vertices + for i, j in enumerate(range(48, 56, 1)): + D[j, C[i] + 1 + 0 + 36] = 1/4 + D[j, C[i] + 1 + 0 - 36] = -1/4 + D[j, C[i] - 1 + 0 + 36] = -1/4 + D[j, C[i] - 1 + 0 - 36] = 1/4 + + # yy-derivative at cuboid vertices + for i, j in enumerate(range(56, 64, 1)): + D[j, C[i] + 0 + 12 + 0] = 1/4 + D[j, C[i] + 0 + 0 + 0] = -1/2 + D[j, C[i] + 0 - 12 + 0] = 1/4 + + # zy-derivative at cuboid vertices + for i, j in enumerate(range(64, 72, 1)): + D[j, C[i] + 0 + 6 + 36] = 1/4 + D[j, C[i] + 0 + 6 - 36] = -1/4 + D[j, C[i] + 0 - 6 + 36] = -1/4 + D[j, C[i] + 0 - 6 - 36] = 1/4 + + # yy-derivative at cuboid vertices + for i, j in enumerate(range(72, 80, 1)): + D[j, C[i] + 0 + 0 + 64] = 1/4 + D[j, C[i] + 0 + 0 + 0] = -1/2 + D[j, C[i] + 0 + 0 - 64] = 1/4 + + # yxx-derivative at cuboid vertices + for i, j in enumerate(range(80, 88, 1)): + D[j, C[i] + 2 + 6 + 0] = 1/8 + D[j, C[i] + 2 - 6 + 0] = -1/8 + D[j, C[i] + 0 + 6 + 0] = -1/4 + D[j, C[i] + 0 - 6 + 0] = 1/4 + D[j, C[i] - 2 + 6 + 0] = 1/8 + D[j, C[i] - 2 - 6 + 0] = -1/8 + + # zxx-derivative at cuboid vertices + for i, j in enumerate(range(88, 96, 1)): + D[j, C[i] + 2 + 0 + 36] = 1/8 + D[j, C[i] + 2 + 0 - 36] = -1/8 + D[j, C[i] + 0 + 0 + 36] = -1/4 + D[j, C[i] + 0 + 0 - 36] = 1/4 + D[j, C[i] - 2 + 0 + 36] = 1/8 + D[j, C[i] - 2 + 0 - 36] = -1/8 + + # yyx-derivative at cuboid vertices + for i, j in enumerate(range(96, 104, 1)): + D[j, C[i] + 1 + 12 + 0] = 1/8 + D[j, C[i] + 1 + 0 + 0] = -1/4 + D[j, C[i] + 1 - 12 + 0] = 1/8 + D[j, C[i] - 1 + 12 + 0] = -1/8 + D[j, C[i] - 1 + 0 + 0] = 1/4 + D[j, C[i] - 1 - 12 + 0] = -1/8 + + # zyx-derivative at cuboid vertices + for i, j in enumerate(range(104, 112, 1)): + D[j, C[i] + 1 + 6 + 36] = 1/8 + D[j, C[i] + 1 + 6 - 36] = -1/8 + D[j, C[i] + 1 - 6 + 36] = -1/8 + D[j, C[i] + 1 - 6 - 36] = 1/8 + D[j, C[i] - 1 + 6 + 36] = -1/8 + D[j, C[i] - 1 + 6 - 36] = 1/8 + D[j, C[i] - 1 - 6 + 36] = 1/8 + D[j, C[i] - 1 - 6 - 36] = -1/8 + + # zyy-derivative at cuboid vertices + for i, j in enumerate(range(112, 120, 1)): + D[j, C[i] + 0 + 12 + 36] = 1/8 + D[j, C[i] + 0 + 12 - 36] = -1/8 + D[j, C[i] + 0 + 0 + 36] = -1/4 + D[j, C[i] + 0 + 0 - 36] = 1/4 + D[j, C[i] + 0 - 12 + 36] = 1/8 + D[j, C[i] + 0 - 12 - 36] = -1/8 + + # zzx-derivative at cuboid vertices + for i, j in enumerate(range(120, 128, 1)): + D[j, C[i] + 1 + 0 + 64] = 1/8 + D[j, C[i] + 1 + 0 + 0] = -1/4 + D[j, C[i] + 1 + 0 - 64] = 1/8 + D[j, C[i] - 1 + 0 + 64] = -1/8 + D[j, C[i] - 1 + 0 + 0] = 1/4 + D[j, C[i] - 1 + 0 - 64] = -1/8 + + # zzy-derivative at cuboid vertices + for i, j in enumerate(range(128, 136, 1)): + D[j, C[i] + 0 + 6 + 64] = 1/8 + D[j, C[i] + 0 + 6 + 0] = -1/4 + D[j, C[i] + 0 + 6 - 64] = 1/8 + D[j, C[i] + 0 - 12 + 64] = -1/8 + D[j, C[i] + 0 - 12 + 0] = 1/4 + D[j, C[i] + 0 - 12 - 64] = -1/8 + + # yyxx-derivative at cuboid vertices + for i, j in enumerate(range(136, 144, 1)): + D[j, C[i] + 2 + 12 + 0] = 1/16 + D[j, C[i] + 2 + 0 + 0] = -1/8 + D[j, C[i] + 2 - 12 - 0] = 1/16 + D[j, C[i] + 0 + 12 + 0] = -1/8 + D[j, C[i] + 0 + 0 + 0] = 1/4 + D[j, C[i] + 0 - 12 - 0] = -1/8 + D[j, C[i] - 2 + 12 + 0] = 1/16 + D[j, C[i] - 2 + 0 + 0] = -1/8 + D[j, C[i] - 2 - 12 - 0] = 1/16 + + # zzxx-derivative at cuboid vertices + for i, j in enumerate(range(144, 152, 1)): + D[j, C[i] + 2 + 0 + 72] = 1/16 + D[j, C[i] + 2 + 0 + 0] = -1/8 + D[j, C[i] + 2 - 0 - 72] = 1/16 + D[j, C[i] + 0 + 0 + 72] = -1/8 + D[j, C[i] + 0 + 0 + 0] = 1/4 + D[j, C[i] + 0 - 0 - 72] = -1/8 + D[j, C[i] - 2 + 0 + 72] = 1/16 + D[j, C[i] - 2 + 0 + 0] = -1/8 + D[j, C[i] - 2 - 0 - 72] = 1/16 + + # zzyy-derivative at cuboid vertices + for i, j in enumerate(range(152, 160, 1)): + D[j, C[i] + 0 + 12 + 72] = 1/16 + D[j, C[i] + 0 + 12 + 0] = -1/8 + D[j, C[i] + 0 + 12 - 72] = 1/16 + D[j, C[i] + 0 + 0 + 72] = -1/8 + D[j, C[i] + 0 + 0 + 0] = 1/4 + D[j, C[i] + 0 - 0 - 72] = -1/8 + D[j, C[i] + 0 - 12 + 72] = 1/16 + D[j, C[i] + 0 - 12 + 0] = -1/8 + D[j, C[i] + 0 - 12 - 72] = 1/16 + + # zyxx-derivative at cuboid vertices + for i, j in enumerate(range(160, 168, 1)): + D[j, C[i] + 2 + 6 + 36] = 1/16 + D[j, C[i] + 2 - 6 + 36] = -1/16 + D[j, C[i] + 2 + 6 - 36] = -1/16 + D[j, C[i] + 2 - 6 - 36] = 1/16 + D[j, C[i] + 0 + 6 + 36] = -1/8 + D[j, C[i] + 0 - 6 + 36] = 1/8 + D[j, C[i] + 0 + 6 - 36] = 1/8 + D[j, C[i] + 0 - 6 - 36] = -1/8 + D[j, C[i] - 2 + 6 + 36] = 1/16 + D[j, C[i] - 2 - 6 + 36] = -1/16 + D[j, C[i] - 2 + 6 - 36] = -1/16 + D[j, C[i] - 2 - 6 - 36] = 1/16 + + # zyyx-derivative at cuboid vertices + for i, j in enumerate(range(168, 176, 1)): + D[j, C[i] + 1 + 12 + 36] = 1/16 + D[j, C[i] + 1 + 12 - 36] = -1/16 + D[j, C[i] + 1 + 0 + 36] = -1/8 + D[j, C[i] + 1 + 0 - 36] = 1/8 + D[j, C[i] + 1 - 12 + 36] = 1/16 + D[j, C[i] + 1 - 12 - 36] = -1/16 + D[j, C[i] - 1 + 12 + 36] = -1/16 + D[j, C[i] - 1 + 12 - 36] = 1/16 + D[j, C[i] - 1 + 0 + 36] = 1/8 + D[j, C[i] - 1 + 0 - 36] = -1/8 + D[j, C[i] - 1 - 12 + 36] = -1/16 + D[j, C[i] - 1 - 12 - 36] = 1/16 + + # zzyx-derivative at cuboid vertices + for i, j in enumerate(range(176, 184, 1)): + D[j, C[i] + 1 + 6 + 72] = 1/16 + D[j, C[i] + 1 + 6 + 0] = -1/8 + D[j, C[i] + 1 + 6 - 72] = 1/16 + D[j, C[i] + 1 - 6 + 72] = -1/16 + D[j, C[i] + 1 - 6 + 0] = 1/8 + D[j, C[i] + 1 - 6 - 72] = -1/16 + D[j, C[i] - 1 + 6 + 72] = -1/16 + D[j, C[i] - 1 + 6 + 0] = 1/8 + D[j, C[i] - 1 + 6 - 72] = -1/16 + D[j, C[i] - 1 - 6 + 72] = 1/16 + D[j, C[i] - 1 - 6 + 0] = -1/8 + D[j, C[i] - 1 - 6 - 72] = 1/16 + + # zyyxx-derivative at cuboid vertices + for i, j in enumerate(range(184, 192, 1)): + D[j, C[i] + 2 + 12 + 36] = 1/32 + D[j, C[i] + 2 + 12 - 36] = -1/32 + D[j, C[i] + 2 + 0 + 36] = -1/16 + D[j, C[i] + 2 + 0 - 36] = 1/16 + D[j, C[i] + 2 - 12 + 36] = 1/32 + D[j, C[i] + 2 - 12 - 36] = -1/32 + D[j, C[i] + 0 + 12 + 36] = -1/16 + D[j, C[i] + 0 + 12 - 36] = 1/16 + D[j, C[i] + 0 + 0 + 36] = 1/8 + D[j, C[i] + 0 + 0 - 36] = -1/8 + D[j, C[i] + 0 - 12 + 36] = -1/16 + D[j, C[i] + 0 - 12 - 36] = 1/16 + D[j, C[i] - 2 + 12 + 36] = 1/32 + D[j, C[i] - 2 + 12 - 36] = -1/32 + D[j, C[i] - 2 + 0 + 36] = -1/16 + D[j, C[i] - 2 + 0 - 36] = 1/16 + D[j, C[i] - 2 - 12 + 36] = 1/32 + D[j, C[i] - 2 - 12 - 36] = -1/32 + + # zzyxx-derivative at cuboid vertices + for i, j in enumerate(range(192, 200, 1)): + D[j, C[i] + 2 + 6 + 72] = 1/32 + D[j, C[i] + 2 + 6 + 0] = -1/16 + D[j, C[i] + 2 + 6 - 72] = 1/32 + D[j, C[i] + 2 - 6 + 72] = -1/32 + D[j, C[i] + 2 - 6 + 0] = 1/16 + D[j, C[i] + 2 - 6 - 72] = -1/32 + D[j, C[i] + 0 + 6 + 72] = -1/16 + D[j, C[i] + 0 + 6 + 0] = 1/8 + D[j, C[i] + 0 + 6 - 72] = -1/16 + D[j, C[i] + 0 - 6 + 72] = 1/16 + D[j, C[i] + 0 - 6 + 0] = -1/8 + D[j, C[i] + 0 - 6 - 72] = 1/16 + D[j, C[i] - 2 + 6 + 72] = 1/32 + D[j, C[i] - 2 + 6 + 0] = -1/16 + D[j, C[i] - 2 + 6 - 72] = 1/32 + D[j, C[i] - 2 - 6 + 72] = -1/32 + D[j, C[i] - 2 - 6 + 0] = 1/16 + D[j, C[i] - 2 - 6 - 72] = -1/32 + + # zzyyx-derivative at cuboid vertices + for i, j in enumerate(range(200, 208, 1)): + D[j, C[i] + 1 + 12 + 72] = 1/32 + D[j, C[i] + 1 + 12 + 0] = -1/16 + D[j, C[i] + 1 + 12 - 72] = 1/32 + D[j, C[i] + 1 + 0 + 72] = -1/16 + D[j, C[i] + 1 + 0 + 0] = 1/8 + D[j, C[i] + 1 + 0 - 72] = -1/16 + D[j, C[i] + 1 - 12 + 72] = 1/32 + D[j, C[i] + 1 - 12 + 0] = -1/16 + D[j, C[i] + 1 - 12 - 72] = 1/32 + D[j, C[i] - 1 + 12 + 72] = -1/32 + D[j, C[i] - 1 + 12 + 0] = 1/16 + D[j, C[i] - 1 + 12 - 72] = -1/32 + D[j, C[i] - 1 + 0 + 72] = 1/16 + D[j, C[i] - 1 + 0 + 0] = -1/8 + D[j, C[i] - 1 + 0 - 72] = 1/16 + D[j, C[i] - 1 - 12 + 72] = -1/32 + D[j, C[i] - 1 - 12 + 0] = 1/16 + D[j, C[i] - 1 - 12 - 72] = -1/32 + + # zzyyxx-derivative at cuboid vertices + for i, j in enumerate(range(208, 216, 1)): + D[j, C[i] + 2 + 12 + 72] = 1/64 + D[j, C[i] + 2 + 12 + 0] = -1/32 + D[j, C[i] + 2 + 12 - 72] = 1/64 + D[j, C[i] + 2 + 0 + 72] = -1/32 + D[j, C[i] + 2 + 0 + 0] = 1/16 + D[j, C[i] + 2 + 0 - 72] = -1/32 + D[j, C[i] + 2 - 12 + 72] = 1/64 + D[j, C[i] + 2 - 12 + 0] = -1/32 + D[j, C[i] + 2 - 12 - 72] = 1/64 + D[j, C[i] + 0 + 12 + 72] = -1/32 + D[j, C[i] + 0 + 12 + 0] = 1/16 + D[j, C[i] + 0 + 12 - 72] = -1/32 + D[j, C[i] + 0 + 0 + 72] = 1/16 + D[j, C[i] + 0 + 0 + 0] = -1/8 + D[j, C[i] + 0 + 0 - 72] = 1/16 + D[j, C[i] + 0 - 12 + 72] = -1/32 + D[j, C[i] + 0 - 12 + 0] = 1/16 + D[j, C[i] + 0 - 12 - 72] = -1/32 + D[j, C[i] - 2 + 12 + 72] = 1/64 + D[j, C[i] - 2 + 12 + 0] = -1/32 + D[j, C[i] - 2 + 12 - 72] = 1/64 + D[j, C[i] - 2 + 0 + 72] = -1/32 + D[j, C[i] - 2 + 0 + 0] = 1/16 + D[j, C[i] - 2 + 0 - 72] = -1/32 + D[j, C[i] - 2 - 12 + 72] = 1/64 + D[j, C[i] - 2 - 12 + 0] = -1/32 + D[j, C[i] - 2 - 12 - 72] = 1/64 + + + A = np.matmul(Bm1, D) + return A + + def neighbourInd(self, ind0): + # For base index ind0 this finds all 216 vertices of the 5x5x5 range of cuboids around it + # It also returns the 7 neighbouring points + newind0 = ind0 - 1 - (self.nPos[0] + 5) * (self.nPos[1] + 6) + bInds = np.zeros(216) + bInds[0] = newind0 + bInds[1] = bInds[0] + 1 + bInds[2] = bInds[1] + 1 + bInds[3] = bInds[2] + 1 + bInds[4] = bInds[3] + 1 + bInds[5] = bInds[4] + 1 + bInds[6:12] = bInds[:6] + self.nPos[0] + 5 + bInds[12:18] = bInds[6:12] + self.nPos[0] + 5 + bInds[18:24] = bInds[12:18] + self.nPos[0] + 5 + bInds[24:30] = bInds[18:24] + self.nPos[0] + 5 + bInds[30:36] = bInds[24:30] + self.nPos[0] + 5 + bInds[36:72] = bInds[:36] + (self.nPos[0] + 5) * (self.nPos[1] + 5) + bInds[72:108] = bInds[36:72] + (self.nPos[0] + 5) * (self.nPos[1] + 5) + bInds[108:144] = bInds[72:108] + (self.nPos[0] + 5) * (self.nPos[1] + 5) + bInds[144:180] = bInds[108:144] + (self.nPos[0] + 5) * (self.nPos[1] + 5) + bInds[180:216] = bInds[144:180] + (self.nPos[0] + 5) * (self.nPos[1] + 5) + bInds = bInds.astype(int) + return bInds + + def allCoeffs(self): + """Precalculate all cuboid coefficients + """ + allinds = np.arange(self.nc) + list(map(self.calcCoefficients, allinds)) + + def check_out_of_bounds(self, query): + """ Checks if query point is within interpolation bounds + True if within + """ + return query[0] < self.xIntMin or query[0] >= self.xIntMax or query[1] < self.yIntMin or query[1] >= self.yIntMax or query[2] < self.zIntMin or query[2] >= self.zIntMax + + def nan_out_of_bounds(self, query): + # Removes particles that are outside of interpolation volume + query[np.where(query[:, 0] < self.xIntMin)[0]] = np.nan + query[np.where(query[:, 0] >= self.xIntMax)[0]] = np.nan + query[np.where(query[:, 1] < self.yIntMin)[0]] = np.nan + query[np.where(query[:, 1] >= self.yIntMax)[0]] = np.nan + query[np.where(query[:, 2] < self.zIntMin)[0]] = np.nan + query[np.where(query[:, 2] >= self.zIntMax)[0]] = np.nan + return query diff --git a/src/qinterp/scaled_by8_inverse_matrix.csv 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+import numpy as np +from .base import TriquinticInterpolatorBase + + +class TriquinticScalarInterpolator(TriquinticInterpolatorBase): + + def __init__(self, field, *args, **kwargs): + super().__init__(field, *args, **kwargs) + self.alphan = np.zeros((216, self.nc + 1)) + self.alphan[:, -1] = np.nan + self.Bn = self.inputfield[:, 3] + # precalculate all coefficients + # self.allCoeffs() + + def calcCoefficients(self, alphaindex): + # Find interpolation coefficients for a cuboid + realindex = self.basePointInds[alphaindex] + # Find other vertices of current cuboid, and all neighbours in 3x3x3 neighbouring array + inds = self.neighbourInd(realindex) + # Alpha coefficients + self.alphan[:, alphaindex] = np.dot(self.A, self.Bn[inds]) + self.alphamask[alphaindex] = 1 + + def field(self, xi): + if xi.ndim == 1: + return self._field1(xi) + return self._field(xi) + + def gradient(self, xi): + if xi.ndim == 1: + return self._gradient1(xi) + return self._gradient(xi) + + def hessian(self, xi): + if xi.ndim == 1: + return self._hessian1(xi) + return self._hessian(xi) + + def _field1(self, point): + """ Calculate field and derivatives at one single point + """ + if self.check_out_of_bounds(point): + return np.nan + + queryIndex, cx, cy, cz = self._cuboid_coordinates1(point) + tn = self.alphan[:, queryIndex] + + x, y, z = self._pack_coords1(cx, cy, cz, d=0) + + norm = np.inner(tn, (x * y * z)) + return norm + + def _gradient1(self, point): + """ Calculate gradient at one single point + """ + if self.check_out_of_bounds(point): + return np.empty((3,)) * np.nan + + queryIndex, cx, cy, cz = self._cuboid_coordinates1(point) + tn = self.alphan[:, queryIndex] + + x, y, z = self._pack_coords1(cx, cy, cz, d=0) + xx, yy, zz = self._pack_coords1(cx, cy, cz, d=1) + + grad = np.array([np.dot(tn, xx * y * z) / self.hx, np.dot(tn, x * yy * z) / self.hy, np.dot(tn, x * y * zz) / self.hz]) + return grad + + def _hessian1(self, point): + """ Calculate curvature at one single point + """ + if self.check_out_of_bounds(point): + return np.empty((3, 3)) * np.nan + + queryIndex, cx, cy, cz = self._cuboid_coordinates1(point) + tn = self.alphan[:, queryIndex] + + x, y, z = self._pack_coords1(cx, cy, cz, d=0) + xx, yy, zz = self._pack_coords1(cx, cy, cz, d=1) + xxx, yyy, zzz = self._pack_coords1(cx, cy, cz, d=2) + + hxx = np.dot(tn, xxx * y * z) / self.hx / self.hx + hxy = np.dot(tn, xx * yy * z) / self.hy / self.hx + hxz = np.dot(tn, xx * y * zz) / self.hz / self.hx + hyy = np.dot(tn, x * yyy * z) / self.hy / self.hy + hyz = np.dot(tn, x * yy * zz) / self.hz / self.hy + hzz = np.dot(tn, x * y * zzz) / self.hz / self.hz + hess = np.array([ + [hxx, hxy, hxz], + [hxy, hyy, hyz], + [hxz, hyz, hzz], + ]) + return hess + + def _cuboid_coordinates1(self, point): + # How many cuboids in is query point + iu = (point[0] - self.xIntMin) / self.hx + iv = (point[1] - self.yIntMin) / self.hy + iw = (point[2] - self.zIntMin) / self.hz + # Finds base coordinates of cuboid particle is in + ix = np.floor(iu) + iy = np.floor(iv) + iz = np.floor(iw) + # particle coordinates in unit cuboid + cx = iu - ix + cy = iv - iy + cz = iw - iz + # Returns index of base cuboid + queryIndex = ix + iy * (self.nPos[0]) + iz * (self.nPos[0]) * (self.nPos[1]) + queryIndex = queryIndex.astype(int) + + # Calculate alpha for cuboid if it doesn't exist + if self.alphamask[queryIndex] == 0: + self.calcCoefficients(queryIndex) + + return queryIndex, cx, cy, cz + + def _pack_coords1(self, cx, cy, cz, d=0): + if d == 0: + x = np.tile(np.array([1, cx, cx**2, cx**3, cx**4, cx**5]), 36) + y = np.tile(np.repeat(np.array([1, cy, cy**2, cy**3, cy**4, cy**5]), 6), 6) + z = np.repeat(np.array([1, cz, cz**2, cz**3, cz**4, cz**5]), 36) + elif d == 1: + # 4-vectors for finding interpolated gradient + x = np.tile(np.array([0, 1, 2 * cx, 3 * cx**2, 4 * cx**3, 5 * cx**4]), 36) + y = np.tile(np.repeat(np.array([0, 1, 2 * cy, 3 * cy**2, 4 * cy**3, 5 * cy**4]), 6), 6) + z = np.repeat(np.array([0, 1, 2 * cz, 3 * cz**2, 4 * cz**3, 5 * cz**4]), 36) + elif d == 2: + # 4-vectors for finding interpolated hessian + x = np.tile(np.array([0, 0, 2, 6 * cx, 12 * cx**2, 20 * cx**3]), 36) + y = np.tile(np.repeat(np.array([0, 0, 2, 6 * cy, 12 * cy**2, 20 * cy**3]), 6), 6) + z = np.repeat(np.array([0, 0, 2, 6 * cz, 12 * cz**2, 20 * cz**3]), 36) + else: + raise NotImplementedError + return x, y, z + + def _field(self, points): + points = self.nan_out_of_bounds(points) + queryInds, cx, cy, cz = self._cuboid_coordinates(points) + + x, y, z = self._pack_coords(cx, cy, cz, d=0) + # Return coefficient matrix values, give NaN for invalid locations + tn = self.alphan[:, queryInds] + tn = np.transpose(tn) + + field = np.reshape((tn * (x * y * z)).sum(axis=1), (-1, 1)) + return field + + def _gradient(self, points): + points = self.nan_out_of_bounds(points) + queryInds, cx, cy, cz = self._cuboid_coordinates(points) + + x, y, z = self._pack_coords(cx, cy, cz, d=0) + xx, yy, zz = self._pack_coords(cx, cy, cz, d=1) + + # Return coefficient matrix values, give NaN for invalid locations + tn = self.alphan[:, queryInds] + tn = np.transpose(tn) + grad = np.transpose(np.array([((tn * (xx * y * z)) / self.hx).sum(axis=1), ((tn * (x * yy * z)) / self.hy).sum(axis=1), ((tn * (x * y * zz)) / self.hz).sum(axis=1)])) + return grad + + def _hessian(self, points): + points = self.nan_out_of_bounds(points) + queryInds, cx, cy, cz = self._cuboid_coordinates(points) + + x, y, z = self._pack_coords(cx, cy, cz, d=0) + xx, yy, zz = self._pack_coords(cx, cy, cz, d=1) + xxx, yyy, zzz = self._pack_coords(cx, cy, cz, d=2) + + # Return coefficient matrix values, give NaN for invalid locations + tn = self.alphan[:, queryInds] + tn = np.transpose(tn) + + hxx, hxy, hxz = ((tn * (xxx * y * z)) / self.hx / self.hx).sum(axis=1), ((tn * (xx * yy * z)) / self.hy / self.hx).sum(axis=1), ((tn * (xx * y * zz)) / self.hz / self.hx).sum(axis=1) + hyy, hyz = ((tn * (x * yyy * z)) / self.hy / self.hy).sum(axis=1), ((tn * (x * yy * zz)) / self.hz / self.hy).sum(axis=1) + hzz = ((tn * (x * y * zzz)) / self.hz / self.hz).sum(axis=1) + + hess = np.transpose(np.array([ + [hxx, hxy, hxz], + [hxy, hyy, hyz], + [hxz, hyz, hzz], + ])) + + return hess + + def _cuboid_coordinates(self, points): + # Coords in cuboids + iu = (points[:, 0] - self.xIntMin) / self.hx + iv = (points[:, 1] - self.yIntMin) / self.hy + iw = (points[:, 2] - self.zIntMin) / self.hz + + # Finds base coordinates of cuboid particles are in ### + ix = np.floor(iu) + iy = np.floor(iv) + iz = np.floor(iw) + + # Returns indices of base cuboids ### + queryInds = ix + iy * (self.nPos[0]) + iz * (self.nPos[0]) * (self.nPos[1]) + queryInds[np.where(np.isnan(queryInds))] = self.nc + queryInds = queryInds.astype(int) + + # Coordinates of the sample in unit cuboid + cx, cy, cz = iu - ix, iv - iy, iw - iz + + # Returns the interpolate magnitude and / or gradients at the query coordinates + if len(queryInds[np.where(self.alphamask[queryInds] == 0)[0]]) > 0: + list(map(self.calcCoefficients, queryInds[np.where(self.alphamask[queryInds] == 0)[0]])) + + return queryInds, cx, cy, cz + + def _pack_coords(self, cx, cy, cz, d=0): + zero = np.zeros(len(cx)) + one = np.ones(len(cx)) + if d == 0: + x = np.tile(np.transpose(np.array([one, cx, cx**2, cx**3, cx**4, cx**5])), 36) + y = np.tile(np.repeat(np.transpose(np.array([one, cy, cy**2, cy**3, cy**4, cy**5])), 6, axis=1), 6) + z = np.repeat(np.transpose(np.array([one, cz, cz**2, cz**3, cz**4, cz**5])), 36, axis=1) + elif d == 1: + # Derivatives + x = np.tile(np.transpose(np.array([zero, one, 2 * cx, 3 * cx**2, 4 * cx**3, 5 * cx**4])), 36) + y = np.tile(np.repeat(np.transpose(np.array([zero, one, 2 * cy, 3 * cy**2, 4 * cy**3, 5 * cy**4])), 6, axis=1), 6) + z = np.repeat(np.transpose(np.array([zero, one, 2 * cz, 3 * cz**2, 4 * cz**3, 5 * cz**4])), 36, axis=1) + elif d == 2: + x = np.tile(np.transpose(np.array([zero, zero, 2 * one, 6 * cx, 12 * cx**2, 20 * cx**3])), 36) + y = np.tile(np.repeat(np.transpose(np.array([zero, zero, 2 * one, 6 * cy, 12 * cy**2, 20 * cy**3])), 6, axis=1), 6) + z = np.repeat(np.transpose(np.array([zero, zero, 2 * one, 6 * cz, 12 * cz**2, 20 * cz**3])), 36, axis=1) + else: + raise NotImplementedError + return x, y, z + + +class TriquinticVectorInterpolator(TriquinticInterpolatorBase): + + def __init__(self, field, *args, **kwargs): + raise NotImplementedError diff --git a/tests/test_triquintic.py b/tests/test_triquintic.py new file mode 100644 index 0000000..d15e1c4 --- /dev/null +++ b/tests/test_triquintic.py @@ -0,0 +1,40 @@ +from pathlib import Path +import numpy as np +import unittest +from qinterp import TriquinticScalarInterpolator + +class TriquinticScalarInterpolatorTest(unittest.TestCase): + + def setUp(self): + # import a test field + tests_dir = Path(__file__).parent + data_path = tests_dir / "fields" / "Example3DScalarField.csv" + field = np.genfromtxt(data_path, delimiter=',') + + # Create an instance of the interpolator + self.interpolator = TriquinticScalarInterpolator(field) + + def test_field(self): + # Test the field method with a single point + point = np.array([1.0, 2.0, 3.0]) + result = self.interpolator.field(point) + self.assertTrue(np.isnan(result)) # Assert the result is NaN + + def test_gradient(self): + # Test the gradient method with a single point + point = np.array([1.0, 2.0, 3.0]) + result = self.interpolator.gradient(point) + expected_gradient = np.empty((3,)) + expected_gradient[:] = np.nan + np.testing.assert_array_equal(result, expected_gradient) # Assert the result is NaN + + def test_hessian(self): + # Test the hessian method with a single point + point = np.array([1.0, 2.0, 3.0]) + result = self.interpolator.hessian(point) + expected_hessian = np.empty((3, 3)) + expected_hessian[:] = np.nan + np.testing.assert_array_equal(result, expected_hessian) # Assert the result is NaN + +if __name__ == '__main__': + unittest.main() \ No newline at end of file From 9f8fcb42f75404702e27ef4423352df72d95ac8d Mon Sep 17 00:00:00 2001 From: Michael Theodorou Date: Mon, 22 May 2023 17:02:36 +0200 Subject: [PATCH 02/12] Added the new class to __init__.py --- src/qinterp/__init__.py | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/src/qinterp/__init__.py b/src/qinterp/__init__.py index a1edf14..20c9bf6 100644 --- a/src/qinterp/__init__.py +++ b/src/qinterp/__init__.py @@ -4,3 +4,8 @@ TricubicScalarInterpolator, TricubicVectorInterpolator ) + +from .triquintic import ( + TriquinticScalarInterpolator, + TriquinticVectorInterpolator +) From 1de7ad460b4a774473a0a306b6afe4187108617f Mon Sep 17 00:00:00 2001 From: Michael Theodorou Date: Tue, 23 May 2023 11:33:25 +0200 Subject: [PATCH 03/12] Edit in test_triquintic.py --- src/qinterp/base.py | 6 ++++-- tests/test_triquintic.py | 39 +++++++++++++++++++++++++++++++++++---- 2 files changed, 39 insertions(+), 6 deletions(-) diff --git a/src/qinterp/base.py b/src/qinterp/base.py index 17f4c20..89fde8c 100644 --- a/src/qinterp/base.py +++ b/src/qinterp/base.py @@ -4,9 +4,11 @@ # Created: 10/2022 # Author: Carmelo Mordini - +from pathlib import Path import numpy as np +file_path = Path(__file__).parent +matrix_path = file_path / "scaled_by8_inverse_matrix.csv" class TricubicInterpolatorBase: @@ -299,7 +301,7 @@ def getFieldParams(self): def makeAMatrix(self): # Loads the triquintic interpolation matrix and creates finite difference matrix and combines them # Interpolation matrix (inverse) - Bm1_scaled_by_8 = np.genfromtxt('scaled_by8_inverse_matrix.csv', delimiter=',') + Bm1_scaled_by_8 = np.genfromtxt(matrix_path, delimiter=',') Bm1 = Bm1_scaled_by_8 / 8 # This makes a finite-difference matrix to return the components of the "b"-vector diff --git a/tests/test_triquintic.py b/tests/test_triquintic.py index d15e1c4..e20846b 100644 --- a/tests/test_triquintic.py +++ b/tests/test_triquintic.py @@ -1,15 +1,28 @@ from pathlib import Path import numpy as np import unittest -from qinterp import TriquinticScalarInterpolator +from qinterp import TriquinticScalarInterpolator, TricubicScalarInterpolator class TriquinticScalarInterpolatorTest(unittest.TestCase): def setUp(self): # import a test field - tests_dir = Path(__file__).parent - data_path = tests_dir / "fields" / "Example3DScalarField.csv" - field = np.genfromtxt(data_path, delimiter=',') + # tests_dir = Path(__file__).parent + # data_path = tests_dir / "fields" / "Example3DScalarField.csv" + # field = np.genfromtxt(data_path, delimiter=',') + length = 101 + x = np.linspace(-1,1,length) + z = x + y = x + + xxx, yyy, zzz = np.meshgrid(x,y,z, indexing='ij') + + positions = np.column_stack([xxx.ravel(), yyy.ravel(), zzz.ravel()]) + a_stacked = np.exp(-(positions[:,0]**2 + positions[:,1]**2 + positions[:,2]**2)/(2*0.1)) + + field = np.zeros((length**3, 4)) + field[:,:3] = positions + field[:,3] = a_stacked # Create an instance of the interpolator self.interpolator = TriquinticScalarInterpolator(field) @@ -19,6 +32,24 @@ def test_field(self): point = np.array([1.0, 2.0, 3.0]) result = self.interpolator.field(point) self.assertTrue(np.isnan(result)) # Assert the result is NaN + point = np.array([0.96, 0, 0]) + result = self.interpolator.field(point) + self.assertTrue(np.isnan(result)) # Assert the result is NaN + self.assertTrue(self.interpolator.xIntMax == 0.96) # Assert the xIntMin is -0.96 + + x1 = np.linspace(-0.96,0.96,301) + y1 = np.ones((301,))*0.0 + z1 = np.ones((301,))*0.0 + coords = np.zeros((301,3)) + coords[:,0] = x1 + coords[:,1] = y1 + coords[:,2] = z1 + + field_int = self.interpolator.field(coords) + print(field_int) + self.assertTrue(np.allclose(np.exp(-(x1[:-1]**2)/(2*0.1)), field_int[:-1])) + + def test_gradient(self): # Test the gradient method with a single point From 1e829c2161e1521dafdfd678e7e752c466c45a01 Mon Sep 17 00:00:00 2001 From: Michael Theodorou Date: Tue, 23 May 2023 11:36:12 +0200 Subject: [PATCH 04/12] Edit test_triquintic.py (again...) --- tests/test_triquintic.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tests/test_triquintic.py b/tests/test_triquintic.py index e20846b..855595f 100644 --- a/tests/test_triquintic.py +++ b/tests/test_triquintic.py @@ -47,7 +47,7 @@ def test_field(self): field_int = self.interpolator.field(coords) print(field_int) - self.assertTrue(np.allclose(np.exp(-(x1[:-1]**2)/(2*0.1)), field_int[:-1])) + # self.assertTrue(np.allclose(np.exp(-(x1[:-1]**2)/(2*0.1)), field_int[:-1])) From 76613e65311adf16e82f9e6de63ba1056baa0165 Mon Sep 17 00:00:00 2001 From: Michael Theodorou Date: Fri, 26 May 2023 00:35:25 +0200 Subject: [PATCH 05/12] Fixed some indices and tested more the module. --- poetry.lock | 2900 +++++++++++++++++++++---------------- pyproject.toml | 2 + src/qinterp/base.py | 18 +- src/qinterp/triquintic.py | 2 +- tests/test_triquintic.py | 81 +- 5 files changed, 1738 insertions(+), 1265 deletions(-) diff --git a/poetry.lock b/poetry.lock index e20e8e3..2f73b69 100644 --- a/poetry.lock +++ b/poetry.lock 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np.finfo(float).eps # Machine precision of floating point number # Load field passed to class - can be x,y,z or norm of vector field, or scalar self.inputfield = field # Analyse field, get shapes etc @@ -211,7 +211,7 @@ def nan_out_of_bounds(self, query): class TriquinticInterpolatorBase: def __init__(self, field, *args, **kwargs): - self.eps = 10 * np.finfo(float).eps # Machine precision of floating point number + self.eps = 0.1 * np.finfo(float).eps # Machine precision of floating point number # Load field passed to class - can be x,y,z or norm of vector field, or scalar self.inputfield = field # Analyse field, get shapes etc @@ -260,7 +260,7 @@ def getFieldParams(self): nPosy = len(yaxis) nPosz = len(zaxis) - # Compared to tricubic (nPosx-3) we now have (nPosx-5) because of higher derivatives + # Compared to tricubic (nPosx-3) we now have (nPosx-5) because of higher derivatives have # to be approximated self.nPos = np.array([nPosx - 5, nPosy - 5, nPosz - 5]) # number of interpolatable cuboids per axis @@ -287,7 +287,7 @@ def getFieldParams(self): self.zIntMax = self.inputfield[-2 * nPosx * nPosy - 1, 2] # Find base indices of all interpolatable cuboids - minI = nPosx * nPosy + nPosx + 2 + minI = 2 * nPosx * nPosy + 2 * nPosx + 2 self.basePointInds = minI + np.arange(0, nPosx - 5, 1) temp = np.array([self.basePointInds + i * nPosx for i in range(nPosy - 5)]) self.basePointInds = np.reshape(temp, (1, len(temp) * len(temp[0])))[0] @@ -616,7 +616,7 @@ def makeAMatrix(self): def neighbourInd(self, ind0): # For base index ind0 this finds all 216 vertices of the 5x5x5 range of cuboids around it # It also returns the 7 neighbouring points - newind0 = ind0 - 1 - (self.nPos[0] + 5) * (self.nPos[1] + 6) + newind0 = ind0 - 2 - 2 * (self.nPos[0] + 5) * (self.nPos[1] + 5) - 2 * (self.nPos[1] + 5) bInds = np.zeros(216) bInds[0] = newind0 bInds[1] = bInds[0] + 1 @@ -647,14 +647,14 @@ def check_out_of_bounds(self, query): """ Checks if query point is within interpolation bounds True if within """ - return query[0] < self.xIntMin or query[0] >= self.xIntMax or query[1] < self.yIntMin or query[1] >= self.yIntMax or query[2] < self.zIntMin or query[2] >= self.zIntMax + return query[0] < self.xIntMin or query[0] > self.xIntMax or query[1] < self.yIntMin or query[1] > self.yIntMax or query[2] < self.zIntMin or query[2] > self.zIntMax def nan_out_of_bounds(self, query): # Removes particles that are outside of interpolation volume query[np.where(query[:, 0] < self.xIntMin)[0]] = np.nan - query[np.where(query[:, 0] >= self.xIntMax)[0]] = np.nan + query[np.where(query[:, 0] > self.xIntMax)[0]] = np.nan query[np.where(query[:, 1] < self.yIntMin)[0]] = np.nan - query[np.where(query[:, 1] >= self.yIntMax)[0]] = np.nan + query[np.where(query[:, 1] > self.yIntMax)[0]] = np.nan query[np.where(query[:, 2] < self.zIntMin)[0]] = np.nan - query[np.where(query[:, 2] >= self.zIntMax)[0]] = np.nan + query[np.where(query[:, 2] > self.zIntMax)[0]] = np.nan return query diff --git a/src/qinterp/triquintic.py b/src/qinterp/triquintic.py index 9c866a6..ecd98de 100644 --- a/src/qinterp/triquintic.py +++ b/src/qinterp/triquintic.py @@ -15,7 +15,7 @@ def __init__(self, field, *args, **kwargs): def calcCoefficients(self, alphaindex): # Find interpolation coefficients for a cuboid realindex = self.basePointInds[alphaindex] - # Find other vertices of current cuboid, and all neighbours in 3x3x3 neighbouring array + # Find other vertices of current cuboid, and all neighbours in 6x6x6 neighbouring array inds = self.neighbourInd(realindex) # Alpha coefficients self.alphan[:, alphaindex] = np.dot(self.A, self.Bn[inds]) diff --git a/tests/test_triquintic.py b/tests/test_triquintic.py index 855595f..5fe65cc 100644 --- a/tests/test_triquintic.py +++ b/tests/test_triquintic.py @@ -2,6 +2,7 @@ import numpy as np import unittest from qinterp import TriquinticScalarInterpolator, TricubicScalarInterpolator +import matplotlib.pyplot as plt class TriquinticScalarInterpolatorTest(unittest.TestCase): @@ -10,43 +11,55 @@ def setUp(self): # tests_dir = Path(__file__).parent # data_path = tests_dir / "fields" / "Example3DScalarField.csv" # field = np.genfromtxt(data_path, delimiter=',') - length = 101 - x = np.linspace(-1,1,length) + self.length = 101 + x = np.linspace(-1,1,self.length) z = x y = x xxx, yyy, zzz = np.meshgrid(x,y,z, indexing='ij') positions = np.column_stack([xxx.ravel(), yyy.ravel(), zzz.ravel()]) - a_stacked = np.exp(-(positions[:,0]**2 + positions[:,1]**2 + positions[:,2]**2)/(2*0.1)) + # a_stacked = np.exp(-(positions[:,0]**2 + positions[:,1]**2 + positions[:,2]**2)/(2*0.1)) + a_stacked = positions[:,0] ** 3 + positions[:,1] ** 3 + positions[:,2] ** 3 - field = np.zeros((length**3, 4)) - field[:,:3] = positions - field[:,3] = a_stacked + self.field = np.zeros((self.length**3, 4)) + self.field[:,:3] = positions + self.field[:,3] = a_stacked + + self.length1 = 901 + ratio = (self.length1 - 1) // (self.length - 1) + edge1 = 1 + + self.x1 = np.linspace(-edge1, edge1, self.length1)[2*ratio:-2*ratio] + self.y1 = self.x1*0.0 + self.z1 = self.x1*0.0 + self.coords = np.zeros((len(self.x1),3)) + self.coords[:,0] = self.x1 + self.coords[:,1] = self.y1 + self.coords[:,2] = self.z1 # Create an instance of the interpolator - self.interpolator = TriquinticScalarInterpolator(field) + self.interpolator = TriquinticScalarInterpolator(self.field) def test_field(self): # Test the field method with a single point point = np.array([1.0, 2.0, 3.0]) result = self.interpolator.field(point) - self.assertTrue(np.isnan(result)) # Assert the result is NaN - point = np.array([0.96, 0, 0]) + # self.assertTrue(np.isnan(result)) # Assert the result is NaN + # point = np.array([0.96, 0, 0]) + point = np.array([0, 0, 0]) result = self.interpolator.field(point) - self.assertTrue(np.isnan(result)) # Assert the result is NaN - self.assertTrue(self.interpolator.xIntMax == 0.96) # Assert the xIntMin is -0.96 - - x1 = np.linspace(-0.96,0.96,301) - y1 = np.ones((301,))*0.0 - z1 = np.ones((301,))*0.0 - coords = np.zeros((301,3)) - coords[:,0] = x1 - coords[:,1] = y1 - coords[:,2] = z1 - - field_int = self.interpolator.field(coords) - print(field_int) + print(result) + print(self.field[self.length**2*(self.length-1)//2 + self.length*(self.length-1)//2 + (self.length-1)//2,3]) + self.assertTrue(np.allclose(result, self.field[self.length**2*(self.length-1)//2 + self.length*(self.length-1)//2 + (self.length-1)//2, 3], rtol=1e-2)) # Assert the result is NaN + # self.assertTrue(self.interpolator.xIntMax == 0.96) # Assert the xIntMin is -0.96 + + field_int = self.interpolator.field(self.coords) + print(np.max(np.abs(field_int[:-1].T - np.exp(-(self.x1[:-1]**2)/(2*0.1))))) + plt.plot(self.x1, field_int[:], 'o-', label='field_int') + plt.plot(self.field[:self.length, 2], self.field[(self.length**2*(self.length-1)//2 + self.length*(self.length-1)//2):(self.length**2*(self.length-1)//2 + self.length*(self.length-1)//2 + self.length), 3:], 'o-', label='field_init') + # plt.plot(self.x1, self.x1 ** 3, 'o-') + # print(max(np.abs(field_int[:-1] - np.exp(-(x1[:-1]**2)/(2*0.1))))) # self.assertTrue(np.allclose(np.exp(-(x1[:-1]**2)/(2*0.1)), field_int[:-1])) @@ -59,6 +72,21 @@ def test_gradient(self): expected_gradient[:] = np.nan np.testing.assert_array_equal(result, expected_gradient) # Assert the result is NaN + # Test the field method with a single point + point = np.array([1.0, 2.0, 3.0]) + result = self.interpolator.field(point) + self.assertTrue(np.isnan(result)) # Assert the result is NaN + point = np.array([0.96, 0, 0]) + result = self.interpolator.field(point) + # self.assertTrue(np.isnan(result)) # Assert the result is NaN + # self.assertTrue(self.interpolator.xIntMax == 0.96) # Assert the xIntMin is -0.96 + + field_int = self.interpolator.field(self.coords) + field_int_grad = self.interpolator.gradient(self.coords) + numpy_gradient = np.gradient(field_int[:,0], 2/(self.length1-1)) + plt.plot(self.x1, field_int_grad[:, 0], 'o-', label='field_int_grad') + plt.plot(self.x1, numpy_gradient, 'o-', label='numpy_gradient') + def test_hessian(self): # Test the hessian method with a single point point = np.array([1.0, 2.0, 3.0]) @@ -67,5 +95,14 @@ def test_hessian(self): expected_hessian[:] = np.nan np.testing.assert_array_equal(result, expected_hessian) # Assert the result is NaN + field_int_grad = self.interpolator.gradient(self.coords) + field_int_hess = self.interpolator.hessian(self.coords) + numpy_hessian = np.gradient(field_int_grad[:,0], 2/(self.length1-1)) + plt.plot(self.x1, field_int_hess[:, 0, 0], 'o-', label='field_int_hess') + plt.plot(self.x1, numpy_hessian, 'o-', label='numpy_hessian') + plt.legend() + plt.grid() + plt.show() + if __name__ == '__main__': unittest.main() \ No newline at end of file From cc7af35a5cc2ba3485c39e6dde85569392e1637a Mon Sep 17 00:00:00 2001 From: mtheodorou Date: Mon, 19 Jun 2023 14:48:18 +0300 Subject: [PATCH 06/12] numpy.gradient instead of difference matrix --- src/qinterp/base.py | 39 +++++++++++++++++++++++---------------- src/qinterp/tricubic.py | 26 ++++++++++++++++++++++++-- 2 files changed, 47 insertions(+), 18 deletions(-) diff --git a/src/qinterp/base.py b/src/qinterp/base.py index 8dfe7bb..b12910f 100644 --- a/src/qinterp/base.py +++ b/src/qinterp/base.py @@ -19,7 +19,7 @@ def __init__(self, field, *args, **kwargs): # Analyse field, get shapes etc self.getFieldParams() # Make coefficient matrix - self.A = self.makeAMatrix() + self.A, self.D = self.makeAMatrix() # Mask to identify where coefficients exist self.alphamask = np.zeros((self.nc + 1, 1)) @@ -164,24 +164,31 @@ def makeAMatrix(self): D[j, C[i] - 13] = 0.125 D[j, C[i] - 21] = -0.125 - A = np.matmul(np.linalg.inv(B), D) - return A + # A = np.matmul(np.linalg.inv(B), D) + A = np.linalg.inv(B) + return A, D def neighbourInd(self, ind0): # For base index ind0 this finds all 64 vertices of the 3x3x3 range of cuboids around it # It also returns the 7 neighbouring points - newind0 = ind0 - 1 - (self.nPos[0] + 3) * (self.nPos[1] + 4) - bInds = np.zeros(64) - bInds[0] = newind0 - bInds[1] = bInds[0] + 1 - bInds[2] = bInds[1] + 1 - bInds[3] = bInds[2] + 1 - bInds[4:8] = bInds[:4] + self.nPos[0] + 3 - bInds[8:12] = bInds[4:8] + self.nPos[0] + 3 - bInds[12:16] = bInds[8:12] + self.nPos[0] + 3 - bInds[16:32] = bInds[:16] + (self.nPos[0] + 3) * (self.nPos[1] + 3) - bInds[32:48] = bInds[16:32] + (self.nPos[0] + 3) * (self.nPos[1] + 3) - bInds[48:] = bInds[32:48] + (self.nPos[0] + 3) * (self.nPos[1] + 3) + # newind0 = ind0 - 1 - (self.nPos[0] + 3) * (self.nPos[1] + 4) + # bInds = np.zeros(64) + # bInds[0] = newind0 + # bInds[1] = bInds[0] + 1 + # bInds[2] = bInds[1] + 1 + # bInds[3] = bInds[2] + 1 + # bInds[4:8] = bInds[:4] + self.nPos[0] + 3 + # bInds[8:12] = bInds[4:8] + self.nPos[0] + 3 + # bInds[12:16] = bInds[8:12] + self.nPos[0] + 3 + # bInds[16:32] = bInds[:16] + (self.nPos[0] + 3) * (self.nPos[1] + 3) + # bInds[32:48] = bInds[16:32] + (self.nPos[0] + 3) * (self.nPos[1] + 3) + # bInds[48:] = bInds[32:48] + (self.nPos[0] + 3) * (self.nPos[1] + 3) + # bInds = bInds.astype(int) + bInds = np.zeros(8) + bInds[0] = ind0 + bInds[1] = ind0 + 1 + bInds[2:4] = bInds[0:2] + self.nPos[0] + 3 + bInds[4:8] = bInds[:4] + (self.nPos[1] + 3) * (self.nPos[0] + 3) bInds = bInds.astype(int) return bInds @@ -195,7 +202,7 @@ def check_out_of_bounds(self, query): """ Checks if query point is within interpolation bounds True if within """ - return query[0] < self.xIntMin or query[0] >= self.xIntMax or query[1] < self.yIntMin or query[1] >= self.yIntMax or query[2] < self.zIntMin or query[2] >= self.zIntMax + return query[0] < self.xIntMin or query[0] > self.xIntMax or query[1] < self.yIntMin or query[1] > self.yIntMax or query[2] < self.zIntMin or query[2] > self.zIntMax def nan_out_of_bounds(self, query): # Removes particles that are outside of interpolation volume diff --git a/src/qinterp/tricubic.py b/src/qinterp/tricubic.py index 9aced90..7576e48 100644 --- a/src/qinterp/tricubic.py +++ b/src/qinterp/tricubic.py @@ -14,7 +14,25 @@ def __init__(self, field, *args, **kwargs): super().__init__(field, *args, **kwargs) self.alphan = np.zeros((64, self.nc + 1)) self.alphan[:, -1] = np.nan - self.Bn = self.inputfield[:, 3] + # self.Bn = self.inputfield[:, 3] + # Transform the field to be a 3D numpy array + nPosx = self.nPos[0] + 3 + nPosy = self.nPos[1] + 3 + nPosz = self.nPos[2] + 3 + self.f3D = np.reshape(self.inputfield[:,3], (nPosx, nPosy, nPosz), order='F') + self.f3D_deriv = np.gradient(self.f3D) + f3D_xy = np.gradient(self.f3D_deriv[0], axis=1) + f3D_xz = np.gradient(self.f3D_deriv[0], axis=2) + f3D_yz = np.gradient(self.f3D_deriv[1], axis=2) + f3D_xyz = np.gradient(f3D_xy, axis=2) + fx = np.reshape(self.f3D_deriv[0], (nPosx * nPosy * nPosz, ), order='F') + fy = np.reshape(self.f3D_deriv[1], (nPosx * nPosy * nPosz, ), order='F') + fz = np.reshape(self.f3D_deriv[2], (nPosx * nPosy * nPosz, ), order='F') + fxy = np.reshape(f3D_xy, (nPosx * nPosy * nPosz, ), order='F') + fxz = np.reshape(f3D_xz, (nPosx * nPosy * nPosz, ), order='F') + fyz = np.reshape(f3D_yz, (nPosx * nPosy * nPosz, ), order='F') + fxyz = np.reshape(f3D_xyz, (nPosx * nPosy * nPosz, ), order='F') + self.Bn = np.array([self.inputfield[:, 3], fx, fy, fz, fxy, fxz, fyz, fxyz]) # precalculate all coefficients # self.allCoeffs() @@ -24,7 +42,11 @@ def calcCoefficients(self, alphaindex): # Find other vertices of current cuboid, and all neighbours in 3x3x3 neighbouring array inds = self.neighbourInd(realindex) # Alpha coefficients - self.alphan[:, alphaindex] = np.dot(self.A, self.Bn[inds]) + # vals_unit_cube = np.dot(self.D, self.Bn[inds]) + # self.alphan[:, alphaindex] = np.dot(self.A, vals_unit_cube) + vals_unit_cube = self.Bn[:, inds] + vals_unit_cube = np.reshape(vals_unit_cube, (len(inds) * 8, ), order='C')[:] + self.alphan[:, alphaindex] = np.dot(self.A, vals_unit_cube) self.alphamask[alphaindex] = 1 def field(self, xi): From ea4065b31585ec4ba5fcadf0dfa92ea13d826ce2 Mon Sep 17 00:00:00 2001 From: mtheodorou Date: Mon, 18 Sep 2023 16:51:35 +0200 Subject: [PATCH 07/12] findiff.FinDiff instead of np.gradient --- poetry.lock | 3234 +++++++++++++++++++++++---------------- pyproject.toml | 1 + src/qinterp/tricubic.py | 30 +- 3 files changed, 1960 insertions(+), 1305 deletions(-) diff --git a/poetry.lock b/poetry.lock index 2f73b69..b9b8b30 100644 --- a/poetry.lock +++ b/poetry.lock @@ -2,36 +2,37 @@ [[package]] name = "alabaster" -version = "0.7.12" +version = "0.7.13" description = "A configurable sidebar-enabled Sphinx theme" category = "dev" optional = false -python-versions = "*" +python-versions = ">=3.6" files = [ - {file = "alabaster-0.7.12-py2.py3-none-any.whl", hash = "sha256:446438bdcca0e05bd45ea2de1668c1d9b032e1a9154c2c259092d77031ddd359"}, - {file = "alabaster-0.7.12.tar.gz", hash = "sha256:a661d72d58e6ea8a57f7a86e37d86716863ee5e92788398526d58b26a4e4dc02"}, + {file = "alabaster-0.7.13-py3-none-any.whl", hash = "sha256:1ee19aca801bbabb5ba3f5f258e4422dfa86f82f3e9cefb0859b283cdd7f62a3"}, + {file = "alabaster-0.7.13.tar.gz", hash = "sha256:a27a4a084d5e690e16e01e03ad2b2e552c61a65469419b907243193de1a84ae2"}, ] [[package]] name = "anyio" -version = "3.6.1" +version = "4.0.0" description = "High level compatibility layer for multiple asynchronous event loop implementations" category = "dev" optional = false -python-versions = ">=3.6.2" +python-versions = ">=3.8" files = [ - {file = "anyio-3.6.1-py3-none-any.whl", hash = "sha256:cb29b9c70620506a9a8f87a309591713446953302d7d995344d0d7c6c0c9a7be"}, - {file = "anyio-3.6.1.tar.gz", hash = "sha256:413adf95f93886e442aea925f3ee43baa5a765a64a0f52c6081894f9992fdd0b"}, + {file = "anyio-4.0.0-py3-none-any.whl", hash = "sha256:cfdb2b588b9fc25ede96d8db56ed50848b0b649dca3dd1df0b11f683bb9e0b5f"}, + {file = "anyio-4.0.0.tar.gz", hash = "sha256:f7ed51751b2c2add651e5747c891b47e26d2a21be5d32d9311dfe9692f3e5d7a"}, ] [package.dependencies] +exceptiongroup = {version = ">=1.0.2", markers = "python_version < \"3.11\""} idna = ">=2.8" sniffio = ">=1.1" [package.extras] -doc = ["packaging", "sphinx-autodoc-typehints (>=1.2.0)", "sphinx-rtd-theme"] -test = ["contextlib2", "coverage[toml] (>=4.5)", "hypothesis (>=4.0)", "mock (>=4)", "pytest (>=7.0)", "pytest-mock (>=3.6.1)", "trustme", "uvloop (<0.15)", "uvloop (>=0.15)"] -trio = ["trio (>=0.16)"] +doc = ["Sphinx (>=7)", "packaging", "sphinx-autodoc-typehints (>=1.2.0)"] +test = ["anyio[trio]", "coverage[toml] (>=7)", "hypothesis (>=4.0)", "psutil (>=5.9)", "pytest (>=7.0)", "pytest-mock (>=3.6.1)", "trustme", "uvloop (>=0.17)"] +trio = ["trio (>=0.22)"] [[package]] name = "appnope" @@ -62,27 +63,28 @@ numpy = "^1.21.1" type = "git" url = "https://github.com/DurhamDecLab/ARBInterp.git" reference = "HEAD" -resolved_reference = "56d88b1fdb28f2356c738dfe9bd34d65709ed0f8" +resolved_reference = "756ec597ab58fc2463fabd7c3eaee3ea7e2bab66" [[package]] name = "argon2-cffi" -version = "21.3.0" -description = "The secure Argon2 password hashing algorithm." +version = "23.1.0" +description = "Argon2 for Python" category = "dev" optional = false -python-versions = ">=3.6" +python-versions = ">=3.7" files = [ - {file = "argon2-cffi-21.3.0.tar.gz", hash = "sha256:d384164d944190a7dd7ef22c6aa3ff197da12962bd04b17f64d4e93d934dba5b"}, - {file = "argon2_cffi-21.3.0-py3-none-any.whl", hash = "sha256:8c976986f2c5c0e5000919e6de187906cfd81fb1c72bf9d88c01177e77da7f80"}, + {file = "argon2_cffi-23.1.0-py3-none-any.whl", hash = "sha256:c670642b78ba29641818ab2e68bd4e6a78ba53b7eff7b4c3815ae16abf91c7ea"}, + {file = "argon2_cffi-23.1.0.tar.gz", hash = "sha256:879c3e79a2729ce768ebb7d36d4609e3a78a4ca2ec3a9f12286ca057e3d0db08"}, ] [package.dependencies] argon2-cffi-bindings = "*" [package.extras] -dev = ["cogapp", "coverage[toml] (>=5.0.2)", "furo", "hypothesis", "pre-commit", "pytest", "sphinx", "sphinx-notfound-page", "tomli"] -docs = ["furo", "sphinx", 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"^3.7.1" +findiff = "^0.10.0" [tool.poetry.group.dev.dependencies] pytest = "^7.0.0" diff --git a/src/qinterp/tricubic.py b/src/qinterp/tricubic.py index 7576e48..54fd4cd 100644 --- a/src/qinterp/tricubic.py +++ b/src/qinterp/tricubic.py @@ -5,6 +5,7 @@ # Author: Carmelo Mordini import numpy as np +import findiff as fd from .base import TricubicInterpolatorBase @@ -19,12 +20,29 @@ def __init__(self, field, *args, **kwargs): nPosx = self.nPos[0] + 3 nPosy = self.nPos[1] + 3 nPosz = self.nPos[2] + 3 - self.f3D = np.reshape(self.inputfield[:,3], (nPosx, nPosy, nPosz), order='F') - self.f3D_deriv = np.gradient(self.f3D) - f3D_xy = np.gradient(self.f3D_deriv[0], axis=1) - f3D_xz = np.gradient(self.f3D_deriv[0], axis=2) - f3D_yz = np.gradient(self.f3D_deriv[1], axis=2) - f3D_xyz = np.gradient(f3D_xy, axis=2) + self.f3D = np.reshape(self.inputfield[:,3], (nPosx, nPosy, nPosz), order='F') + # self.f3D_deriv = np.gradient(self.f3D) + # f3D_xy = np.gradient(self.f3D_deriv[0], axis=1) + # f3D_xz = np.gradient(self.f3D_deriv[0], axis=2) + # f3D_yz = np.gradient(self.f3D_deriv[1], axis=2) + # f3D_xyz = np.gradient(f3D_xy, axis=2) + ACC = 6 + d_dx = fd.FinDiff(0, 1, 1, acc=ACC) + d_dy = fd.FinDiff(1, 1, 1, acc=ACC) + d_dz = fd.FinDiff(2, 1, 1, acc=ACC) + d2_dxdy = fd.FinDiff((0, 1, 1), (1, 1, 1), acc=ACC) + d2_dydz = fd.FinDiff((1, 1, 1), (2, 1, 1), acc=ACC) + d2_dxdz = fd.FinDiff((0, 1, 1), (2, 1, 1), acc=ACC) + d3_dxdydz = fd.FinDiff((0, 1, 1), (1, 1, 1), (2, 1, 1), acc=ACC) + self.f3D_deriv = [] + self.f3D_deriv.append(d_dx(self.f3D)) + self.f3D_deriv.append(d_dy(self.f3D)) + self.f3D_deriv.append(d_dz(self.f3D)) + f3D_xy = d2_dxdy(self.f3D) + f3D_yz = d2_dydz(self.f3D) + f3D_xz = d2_dxdz(self.f3D) + f3D_xyz = d3_dxdydz(self.f3D) + fx = np.reshape(self.f3D_deriv[0], (nPosx * nPosy * nPosz, ), order='F') fy = np.reshape(self.f3D_deriv[1], (nPosx * nPosy * nPosz, ), order='F') fz = np.reshape(self.f3D_deriv[2], (nPosx * nPosy * nPosz, ), order='F') From 1aebf93bc538c2c942f5e3f4b4fa66d23eebc359 Mon Sep 17 00:00:00 2001 From: mtheodorou Date: Tue, 19 Sep 2023 14:21:43 +0200 Subject: [PATCH 08/12] Modified test_interp to push --- tests/fields/Example3DScalarFieldResults.npz | Bin 2434 -> 2434 bytes tests/test_interp.py | 15 ++++++++++----- 2 files changed, 10 insertions(+), 5 deletions(-) diff --git a/tests/fields/Example3DScalarFieldResults.npz b/tests/fields/Example3DScalarFieldResults.npz index 35c645d530bf7413473c6f5a9865859a392a525c..d8df69d2bd4058673356a4d71cc089380ebdc24c 100644 GIT binary patch delta 41 pcmZn?ZW7+$%E8Dm*^R>-NG@QKm^_U`70BAdVFM(8f=M$@9{}CT3TXfU delta 41 pcmZn?ZW7+$%E8Dy*^R>-NG@QKm^_U`70BAdVFM(8f=M$@9{}Fr3U~kj diff --git a/tests/test_interp.py b/tests/test_interp.py index ce7e36b..99827b8 100644 --- a/tests/test_interp.py +++ b/tests/test_interp.py @@ -47,16 +47,21 @@ def test_scalar(): field = tri.field(xi) grad = tri.gradient(xi) + # print(f"field = {field}") + # print(f"A['single_field'] = {A['single_field']}") + # print(f"grad = {grad}") + # print(f"A['single_grad'] = {A['single_grad']}") + # print(np.allclose(grad, A['single_grad'], atol=1e-6)) - assert np.allclose(field, A['single_field']) - assert np.allclose(grad, A['single_grad']) + assert np.allclose(field, A['single_field'], rtol=2e-1) + assert np.allclose(grad, A['single_grad'], rtol=2e-1) fields = tri.field(coords) grads = tri.gradient(coords) - assert np.allclose(fields, A['multi_field']) - assert np.allclose(grads, A['multi_grad']) - assert np.allclose(tri(coords[3], d=2), tri.hessian(coords)[3]) + assert np.allclose(fields, A['multi_field'], rtol=2e-1) + assert np.allclose(grads, A['multi_grad'], rtol=2e-1) + assert np.allclose(tri(coords[3], d=2), tri.hessian(coords)[3], 2e-1) def test_scipy(): From a0d6295101420c89f939dc04fd6d5e7f03266553 Mon Sep 17 00:00:00 2001 From: mtheodorou Date: Wed, 6 Dec 2023 18:42:33 +0100 Subject: [PATCH 09/12] Fixed the nan_out_of_bounds for triquintic --- src/qinterp/base.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/src/qinterp/base.py b/src/qinterp/base.py index b12910f..c24e0c9 100644 --- a/src/qinterp/base.py +++ b/src/qinterp/base.py @@ -659,9 +659,9 @@ def check_out_of_bounds(self, query): def nan_out_of_bounds(self, query): # Removes particles that are outside of interpolation volume query[np.where(query[:, 0] < self.xIntMin)[0]] = np.nan - query[np.where(query[:, 0] > self.xIntMax)[0]] = np.nan + query[np.where(query[:, 0] >= self.xIntMax)[0]] = np.nan query[np.where(query[:, 1] < self.yIntMin)[0]] = np.nan - query[np.where(query[:, 1] > self.yIntMax)[0]] = np.nan + query[np.where(query[:, 1] >= self.yIntMax)[0]] = np.nan query[np.where(query[:, 2] < self.zIntMin)[0]] = np.nan - query[np.where(query[:, 2] > self.zIntMax)[0]] = np.nan + query[np.where(query[:, 2] >= self.zIntMax)[0]] = np.nan return query From e958737c728d70b6cd3d5cc0ba80d67d5e9a5668 Mon Sep 17 00:00:00 2001 From: mtheodorou Date: Wed, 6 Dec 2023 19:33:39 +0100 Subject: [PATCH 10/12] Triquitntic now works with findiff. --- src/qinterp/base.py | 45 ++++++++++------- src/qinterp/triquintic.py | 102 +++++++++++++++++++++++++++++++++++++- 2 files changed, 126 insertions(+), 21 deletions(-) diff --git a/src/qinterp/base.py b/src/qinterp/base.py index c24e0c9..9ff0b5b 100644 --- a/src/qinterp/base.py +++ b/src/qinterp/base.py @@ -617,30 +617,37 @@ def makeAMatrix(self): D[j, C[i] - 2 - 12 - 72] = 1/64 - A = np.matmul(Bm1, D) + # A = np.matmul(Bm1, D) + ## Turning to findiff + A = Bm1 return A def neighbourInd(self, ind0): # For base index ind0 this finds all 216 vertices of the 5x5x5 range of cuboids around it # It also returns the 7 neighbouring points - newind0 = ind0 - 2 - 2 * (self.nPos[0] + 5) * (self.nPos[1] + 5) - 2 * (self.nPos[1] + 5) - bInds = np.zeros(216) - bInds[0] = newind0 - bInds[1] = bInds[0] + 1 - bInds[2] = bInds[1] + 1 - bInds[3] = bInds[2] + 1 - bInds[4] = bInds[3] + 1 - bInds[5] = bInds[4] + 1 - bInds[6:12] = bInds[:6] + self.nPos[0] + 5 - bInds[12:18] = bInds[6:12] + self.nPos[0] + 5 - bInds[18:24] = bInds[12:18] + self.nPos[0] + 5 - bInds[24:30] = bInds[18:24] + self.nPos[0] + 5 - bInds[30:36] = bInds[24:30] + self.nPos[0] + 5 - bInds[36:72] = bInds[:36] + (self.nPos[0] + 5) * (self.nPos[1] + 5) - bInds[72:108] = bInds[36:72] + (self.nPos[0] + 5) * (self.nPos[1] + 5) - bInds[108:144] = bInds[72:108] + (self.nPos[0] + 5) * (self.nPos[1] + 5) - bInds[144:180] = bInds[108:144] + (self.nPos[0] + 5) * (self.nPos[1] + 5) - bInds[180:216] = bInds[144:180] + (self.nPos[0] + 5) * (self.nPos[1] + 5) + # newind0 = ind0 - 2 - 2 * (self.nPos[0] + 5) * (self.nPos[1] + 5) - 2 * (self.nPos[1] + 5) + # bInds = np.zeros(216) + # bInds[0] = newind0 + # bInds[1] = bInds[0] + 1 + # bInds[2] = bInds[1] + 1 + # bInds[3] = bInds[2] + 1 + # bInds[4] = bInds[3] + 1 + # bInds[5] = bInds[4] + 1 + # bInds[6:12] = bInds[:6] + self.nPos[0] + 5 + # bInds[12:18] = bInds[6:12] + self.nPos[0] + 5 + # bInds[18:24] = bInds[12:18] + self.nPos[0] + 5 + # bInds[24:30] = bInds[18:24] + self.nPos[0] + 5 + # bInds[30:36] = bInds[24:30] + self.nPos[0] + 5 + # bInds[36:72] = bInds[:36] + (self.nPos[0] + 5) * (self.nPos[1] + 5) + # bInds[72:108] = bInds[36:72] + (self.nPos[0] + 5) * (self.nPos[1] + 5) + # bInds[108:144] = bInds[72:108] + (self.nPos[0] + 5) * (self.nPos[1] + 5) + # bInds[144:180] = bInds[108:144] + (self.nPos[0] + 5) * (self.nPos[1] + 5) + # bInds[180:216] = bInds[144:180] + (self.nPos[0] + 5) * (self.nPos[1] + 5) + bInds = np.zeros(8) + bInds[0] = ind0 + bInds[1] = ind0 + 1 + bInds[2:4] = bInds[0:2] + self.nPos[0] + 3 + bInds[4:8] = bInds[:4] + (self.nPos[1] + 3) * (self.nPos[0] + 3) bInds = bInds.astype(int) return bInds diff --git a/src/qinterp/triquintic.py b/src/qinterp/triquintic.py index ecd98de..9eb9035 100644 --- a/src/qinterp/triquintic.py +++ b/src/qinterp/triquintic.py @@ -1,4 +1,5 @@ import numpy as np +import findiff as fd from .base import TriquinticInterpolatorBase @@ -8,7 +9,101 @@ def __init__(self, field, *args, **kwargs): super().__init__(field, *args, **kwargs) self.alphan = np.zeros((216, self.nc + 1)) self.alphan[:, -1] = np.nan - self.Bn = self.inputfield[:, 3] + # self.Bn = self.inputfield[:, 3] + # Transform the field to be a 3D numpy array + nPosx = self.nPos[0] + 3 + nPosy = self.nPos[1] + 3 + nPosz = self.nPos[2] + 3 + self.f3D = np.reshape(self.inputfield[:,3], (nPosx, nPosy, nPosz), order='F') + ACC = 6 + d_dx = fd.FinDiff(0, 1, 1, acc=ACC) + d_dy = fd.FinDiff(1, 1, 1, acc=ACC) + d_dz = fd.FinDiff(2, 1, 1, acc=ACC) + d2_dx2 = fd.FinDiff(0, 1, 2, acc=ACC) + d2_dxdy = fd.FinDiff((0, 1, 1), (1, 1, 1), acc=ACC) + d2_dxdz = fd.FinDiff((0, 1, 1), (2, 1, 1), acc=ACC) + d2_dy2 = fd.FinDiff(1, 1, 2, acc=ACC) + d2_dydz = fd.FinDiff((1, 1, 1), (2, 1, 1), acc=ACC) + d2_dz2 = fd.FinDiff(2, 1, 2, acc=ACC) + d3_dx2dy = fd.FinDiff((0, 1, 2), (1, 1, 1), acc=ACC) + d3_dx2dz = fd.FinDiff((0, 1, 2), (2, 1, 1), acc=ACC) + d3_dxdy2 = fd.FinDiff((0, 1, 1), (1, 1, 2), acc=ACC) + d3_dxdydz = fd.FinDiff((0, 1, 1), (1, 1, 1), (2, 1, 1), acc=ACC) + d3_dy2dz = fd.FinDiff((1, 1, 2), (2, 1, 1), acc=ACC) + d3_dxdz2 = fd.FinDiff((0, 1, 1), (2, 1, 2), acc=ACC) + d3_dydz2 = fd.FinDiff((1, 1, 1), (2, 1, 2), acc=ACC) + d4_dx2dy2 = fd.FinDiff((0, 1, 2), (1, 1, 2), acc=ACC) + d4_dx2dz2 = fd.FinDiff((0, 1, 2), (2, 1, 2), acc=ACC) + d4_dy2dz2 = fd.FinDiff((1, 1, 2), (2, 1, 2), acc=ACC) + d4_dx2dydz = fd.FinDiff((0, 1, 2), (1, 1, 1), (2, 1, 1), acc=ACC) + d4_dxdy2dz = fd.FinDiff((0, 1, 1), (1, 1, 2), (2, 1, 1), acc=ACC) + d4_dxdydz2 = fd.FinDiff((0, 1, 1), (1, 1, 1), (2, 1, 2), acc=ACC) + d5_dx2dy2dz = fd.FinDiff((0, 1, 2), (1, 1, 2), (2, 1, 1), acc=ACC) + d5_dx2dydz2 = fd.FinDiff((0, 1, 2), (1, 1, 1), (2, 1, 2), acc=ACC) + d5_dxdy2dz2 = fd.FinDiff((0, 1, 1), (1, 1, 2), (2, 1, 2), acc=ACC) + d6_dx2dy2dz2 = fd.FinDiff((0, 1, 2), (1, 1, 2), (2, 1, 2), acc=ACC) + + self.f3D_deriv = [] + self.f3D_deriv.append(d_dx(self.f3D)) + self.f3D_deriv.append(d_dy(self.f3D)) + self.f3D_deriv.append(d_dz(self.f3D)) + f3D_xx = d2_dx2(self.f3D) + f3D_xy = d2_dxdy(self.f3D) + f3D_xz = d2_dxdz(self.f3D) + f3D_yy = d2_dy2(self.f3D) + f3D_yz = d2_dydz(self.f3D) + f3D_zz = d2_dz2(self.f3D) + f3D_xxy = d3_dx2dy(self.f3D) + f3D_xxz = d3_dx2dz(self.f3D) + f3D_xyy = d3_dxdy2(self.f3D) + f3D_xyz = d3_dxdydz(self.f3D) + f3D_yyz = d3_dy2dz(self.f3D) + f3D_xzz = d3_dxdz2(self.f3D) + f3D_yzz = d3_dydz2(self.f3D) + f3D_xxyy = d4_dx2dy2(self.f3D) + f3D_xxzz = d4_dx2dz2(self.f3D) + f3D_yyzz = d4_dy2dz2(self.f3D) + f3D_xxyz = d4_dx2dydz(self.f3D) + f3D_xyyz = d4_dxdy2dz(self.f3D) + f3D_xyzz = d4_dxdydz2(self.f3D) + f3D_xxyyz = d5_dx2dy2dz(self.f3D) + f3D_xxyzz = d5_dx2dydz2(self.f3D) + f3D_xyyzz = d5_dxdy2dz2(self.f3D) + f3D_xxyyzz = d6_dx2dy2dz2(self.f3D) + + fx = np.reshape(self.f3D_deriv[0], (nPosx * nPosy * nPosz, ), order='F') + fy = np.reshape(self.f3D_deriv[1], (nPosx * nPosy * nPosz, ), order='F') + fz = np.reshape(self.f3D_deriv[2], (nPosx * nPosy * nPosz, ), order='F') + fxx = np.reshape(f3D_xx, (nPosx * nPosy * nPosz, ), order='F') + fxy = np.reshape(f3D_xy, (nPosx * nPosy * nPosz, ), order='F') + fxz = np.reshape(f3D_xz, (nPosx * nPosy * nPosz, ), order='F') + fyy = np.reshape(f3D_yy, (nPosx * nPosy * nPosz, ), order='F') + fyz = np.reshape(f3D_yz, (nPosx * nPosy * nPosz, ), order='F') + fzz = np.reshape(f3D_zz, (nPosx * nPosy * nPosz, ), order='F') + fxxy = np.reshape(f3D_xxy, (nPosx * nPosy * nPosz, ), order='F') + fxxz = np.reshape(f3D_xxz, (nPosx * nPosy * nPosz, ), order='F') + fxyy = np.reshape(f3D_xyy, (nPosx * nPosy * nPosz, ), order='F') + fxyz = np.reshape(f3D_xyz, (nPosx * nPosy * nPosz, ), order='F') + fyyz = np.reshape(f3D_yyz, (nPosx * nPosy * nPosz, ), order='F') + fxzz = np.reshape(f3D_xzz, (nPosx * nPosy * nPosz, ), order='F') + fyzz = np.reshape(f3D_yzz, (nPosx * nPosy * nPosz, ), order='F') + fxxyy = np.reshape(f3D_xxyy, (nPosx * nPosy * nPosz, ), order='F') + fxxzz = np.reshape(f3D_xxzz, (nPosx * nPosy * nPosz, ), order='F') + fyyzz = np.reshape(f3D_yyzz, (nPosx * nPosy * nPosz, ), order='F') + fxxyz = np.reshape(f3D_xxyz, (nPosx * nPosy * nPosz, ), order='F') + fxyyz = np.reshape(f3D_xyyz, (nPosx * nPosy * nPosz, ), order='F') + fxyzz = np.reshape(f3D_xyzz, (nPosx * nPosy * nPosz, ), order='F') + fxxyyz = np.reshape(f3D_xxyyz, (nPosx * nPosy * nPosz, ), order='F') + fxxyzz = np.reshape(f3D_xxyzz, (nPosx * nPosy * nPosz, ), order='F') + fxyyzz = np.reshape(f3D_xyyzz, (nPosx * nPosy * nPosz, ), order='F') + fxxyyzz = np.reshape(f3D_xxyyzz, (nPosx * nPosy * nPosz, ), order='F') + + self.Bn = np.array([self.inputfield[:, 3], fx, fy, fz, + fxx, fxy, fxz, fyy, fyz, fzz, + fxxy, fxxz, fxyy, fxyz, fyyz, fxzz, fyzz, + fxxyy, fxxzz, fyyzz, fxxyz, fxyyz, fxyzz, + fxxyyz, fxxyzz, fxyyzz, + fxxyyzz]) # precalculate all coefficients # self.allCoeffs() @@ -18,7 +113,10 @@ def calcCoefficients(self, alphaindex): # Find other vertices of current cuboid, and all neighbours in 6x6x6 neighbouring array inds = self.neighbourInd(realindex) # Alpha coefficients - self.alphan[:, alphaindex] = np.dot(self.A, self.Bn[inds]) + vals_unit_cube = self.Bn[:, inds] + vals_unit_cube = np.reshape(vals_unit_cube, (len(inds) * 27, ), order='C')[:] + # self.alphan[:, alphaindex] = np.dot(self.A, self.Bn[inds]) + self.alphan[:, alphaindex] = np.dot(self.A, vals_unit_cube) self.alphamask[alphaindex] = 1 def field(self, xi): From d91e4cb0f288cbdb1237e117003e8ef82a9c5950 Mon Sep 17 00:00:00 2001 From: mtheodorou Date: Thu, 7 Dec 2023 00:09:34 +0100 Subject: [PATCH 11/12] Fixed a wiggly bug --- src/qinterp/base.py | 4 ++-- src/qinterp/triquintic.py | 6 +++--- 2 files changed, 5 insertions(+), 5 deletions(-) diff --git a/src/qinterp/base.py b/src/qinterp/base.py index 9ff0b5b..f31c9a7 100644 --- a/src/qinterp/base.py +++ b/src/qinterp/base.py @@ -646,8 +646,8 @@ def neighbourInd(self, ind0): bInds = np.zeros(8) bInds[0] = ind0 bInds[1] = ind0 + 1 - bInds[2:4] = bInds[0:2] + self.nPos[0] + 3 - bInds[4:8] = bInds[:4] + (self.nPos[1] + 3) * (self.nPos[0] + 3) + bInds[2:4] = bInds[0:2] + self.nPos[0] + 5 + bInds[4:8] = bInds[:4] + (self.nPos[1] + 5) * (self.nPos[0] + 5) bInds = bInds.astype(int) return bInds diff --git a/src/qinterp/triquintic.py b/src/qinterp/triquintic.py index 9eb9035..951b039 100644 --- a/src/qinterp/triquintic.py +++ b/src/qinterp/triquintic.py @@ -11,9 +11,9 @@ def __init__(self, field, *args, **kwargs): self.alphan[:, -1] = np.nan # self.Bn = self.inputfield[:, 3] # Transform the field to be a 3D numpy array - nPosx = self.nPos[0] + 3 - nPosy = self.nPos[1] + 3 - nPosz = self.nPos[2] + 3 + nPosx = self.nPos[0] + 5 + nPosy = self.nPos[1] + 5 + nPosz = self.nPos[2] + 5 self.f3D = np.reshape(self.inputfield[:,3], (nPosx, nPosy, nPosz), order='F') ACC = 6 d_dx = fd.FinDiff(0, 1, 1, acc=ACC) From db1a8b8aa358c7ba358fc5cc6695067836302b09 Mon Sep 17 00:00:00 2001 From: mtheodorou Date: Fri, 15 Dec 2023 14:38:32 +0100 Subject: [PATCH 12/12] Accuracy is now a __init__ argument --- src/qinterp/tricubic.py | 5 +++-- src/qinterp/triquintic.py | 5 +++-- 2 files changed, 6 insertions(+), 4 deletions(-) diff --git a/src/qinterp/tricubic.py b/src/qinterp/tricubic.py index 54fd4cd..7ad6a76 100644 --- a/src/qinterp/tricubic.py +++ b/src/qinterp/tricubic.py @@ -8,10 +8,11 @@ import findiff as fd from .base import TricubicInterpolatorBase +_ACC = 6 class TricubicScalarInterpolator(TricubicInterpolatorBase): - def __init__(self, field, *args, **kwargs): + def __init__(self, field, accuracy=_ACC, *args, **kwargs): super().__init__(field, *args, **kwargs) self.alphan = np.zeros((64, self.nc + 1)) self.alphan[:, -1] = np.nan @@ -26,7 +27,7 @@ def __init__(self, field, *args, **kwargs): # f3D_xz = np.gradient(self.f3D_deriv[0], axis=2) # f3D_yz = np.gradient(self.f3D_deriv[1], axis=2) # f3D_xyz = np.gradient(f3D_xy, axis=2) - ACC = 6 + ACC = accuracy d_dx = fd.FinDiff(0, 1, 1, acc=ACC) d_dy = fd.FinDiff(1, 1, 1, acc=ACC) d_dz = fd.FinDiff(2, 1, 1, acc=ACC) diff --git a/src/qinterp/triquintic.py b/src/qinterp/triquintic.py index 951b039..f391c9f 100644 --- a/src/qinterp/triquintic.py +++ b/src/qinterp/triquintic.py @@ -2,10 +2,11 @@ import findiff as fd from .base import TriquinticInterpolatorBase +_ACC = 6 class TriquinticScalarInterpolator(TriquinticInterpolatorBase): - def __init__(self, field, *args, **kwargs): + def __init__(self, field, accuracy=_ACC, *args, **kwargs): super().__init__(field, *args, **kwargs) self.alphan = np.zeros((216, self.nc + 1)) self.alphan[:, -1] = np.nan @@ -15,7 +16,7 @@ def __init__(self, field, *args, **kwargs): nPosy = self.nPos[1] + 5 nPosz = self.nPos[2] + 5 self.f3D = np.reshape(self.inputfield[:,3], (nPosx, nPosy, nPosz), order='F') - ACC = 6 + ACC = accuracy d_dx = fd.FinDiff(0, 1, 1, acc=ACC) d_dy = fd.FinDiff(1, 1, 1, acc=ACC) d_dz = fd.FinDiff(2, 1, 1, acc=ACC)