diff --git a/simpegPF/Magnetics.py b/simpegPF/Magnetics.py
index b44c7fc9..e727d3b3 100644
--- a/simpegPF/Magnetics.py
+++ b/simpegPF/Magnetics.py
@@ -39,11 +39,11 @@ class MagneticIntegral(Problem.BaseProblem):
# return self.G.dot(self.mapping*(m))
- def Jvec(self, m, v, u=None):
+ def Jvec(self, m, v, f=None):
dmudm = self.mapping.deriv(m)
return self.G.dot(dmudm*v)
- def Jtvec(self, m, v, u=None):
+ def Jtvec(self, m, v, f=None):
dmudm = self.mapping.deriv(m)
return dmudm.T * (self.G.T.dot(v))
@@ -706,139 +706,139 @@ def Intgrl_Fwr_Data(mesh,B,M,rxLoc,model,actv,flag):
return d
-def Intrgl_Fwr_Op(mesh,B,M,rxLoc,actv,flag):
- """
-
- Magnetic forward operator in integral form
-
- INPUT:
- mesh = Mesh in SimPEG format
- B = Inducing field parameter [Binc, Bdecl, B0]
- M = Magnetization information
- [OPTIONS]
- 1- [Minc, Mdecl] : Assumes uniform magnetization orientation
- 2- [mx1,mx2,..., my1,...,mz1] : cell-based defined magnetization direction
- 3- diag(M): Block diagonal matrix with [Mx, My, Mz] along the diagonal
-
- rxLox = Observation location informat [obsx, obsy, obsz]
-
- flag = 'tmi' | 'xyz' | 'full'
- [OPTIONS]
- 1- tmi : Magnetization direction used and data are projected onto the
- inducing field direction F.shape([ndata, nc])
-
- 2- xyz : Magnetization direction used and data are given in 3-components
- F.shape([3*ndata, nc])
-
- 3- full: Full tensor matrix stored with shape([3*ndata, 3*nc])
-
- OUTPUT:
- F = Linear forward modeling operation
-
- Created on Dec, 20th 2015
-
- @author: dominiquef
-
- """
- # Find non-zero cells
- #inds = np.nonzero(actv)[0]
- if actv.dtype=='bool':
- inds = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem], dtype = int) - 1
- else:
- inds = actv
-
- nC = len(inds)
-
- # Create active cell projector
- P = sp.csr_matrix((np.ones(nC),(inds, range(nC))),
- shape=(mesh.nC, nC))
-
- # Create vectors of nodal location (lower and upper coners for each cell)
- xn = mesh.vectorNx;
- yn = mesh.vectorNy;
- zn = mesh.vectorNz;
-
- yn2,xn2,zn2 = np.meshgrid(yn[1:], xn[1:], zn[1:])
- yn1,xn1,zn1 = np.meshgrid(yn[0:-1], xn[0:-1], zn[0:-1])
-
- Yn = P.T*np.c_[mkvc(yn1), mkvc(yn2)]
- Xn = P.T*np.c_[mkvc(xn1), mkvc(xn2)]
- Zn = P.T*np.c_[mkvc(zn1), mkvc(zn2)]
-
- ndata = rxLoc.shape[0]
-
- # Convert Bdecination from north to cartesian
- D = (450.-float(B[1]))%360.
-
-
- # Pre-allocate space and create magnetization matrix if required
- if (flag=='tmi') | (flag == 'xyz'):
- # If assumes uniform magnetization direction
- if M.shape != (nC,3):
-
- print 'Magnetization vector must be Nc x 3'
- return
-
-
- Mx = Utils.sdiag(M[:,0]*B[2])
- My = Utils.sdiag(M[:,1]*B[2])
- Mz = Utils.sdiag(M[:,2]*B[2])
-
- Mxyz = sp.vstack((Mx,My,Mz))
-
-
-
- if flag == 'tmi':
- F = np.zeros((ndata, nC))
-
- # Projection matrix
- Ptmi = mkvc(np.r_[np.cos(np.deg2rad(B[0]))*np.cos(np.deg2rad(D)),
- np.cos(np.deg2rad(B[0]))*np.sin(np.deg2rad(D)),
- np.sin(np.deg2rad(B[0]))],2).T;
-
- elif flag == 'xyz':
-
- F = np.zeros((int(3*ndata), nC))
-
- elif flag == 'full':
- F = np.zeros((int(3*ndata), int(3*nC)))
-
-
- else:
- print """Flag must be either 'tmi' | 'xyz' | 'full', please revised"""
- return
-
-
- # Loop through all observations and create forward operator (ndata-by-nC)
- print "Begin calculation of forward operator: " + flag
-
- # Add counter to dsiplay progress. Good for large problems
- count = -1;
- for ii in range(ndata):
-
-
- tx, ty, tz = get_T_mat(Xn,Yn,Zn,rxLoc[ii,:])
-
- if flag=='tmi':
- F[ii,:] = Ptmi.dot(np.vstack((tx,ty,tz)))*Mxyz
-
- elif flag == 'xyz':
- F[ii,:] = tx*Mxyz
- F[ii+ndata,:] = ty*Mxyz
- F[ii+2*ndata,:] = tz*Mxyz
-
- elif flag == 'full':
- F[ii,:] = tx
- F[ii+ndata,:] = ty
- F[ii+2*ndata,:] = tz
-
-
- # Display progress
- count = progress(ii,count,ndata)
-
- print "Done 100% ...forward operator completed!!\n"
-
- return F
+#def Intrgl_Fwr_Op(mesh,B,M,rxLoc,actv,flag):
+# """
+#
+# Magnetic forward operator in integral form
+#
+# INPUT:
+# mesh = Mesh in SimPEG format
+# B = Inducing field parameter [Binc, Bdecl, B0]
+# M = Magnetization information
+# [OPTIONS]
+# 1- [Minc, Mdecl] : Assumes uniform magnetization orientation
+# 2- [mx1,mx2,..., my1,...,mz1] : cell-based defined magnetization direction
+# 3- diag(M): Block diagonal matrix with [Mx, My, Mz] along the diagonal
+#
+# rxLox = Observation location informat [obsx, obsy, obsz]
+#
+# flag = 'tmi' | 'xyz' | 'full'
+# [OPTIONS]
+# 1- tmi : Magnetization direction used and data are projected onto the
+# inducing field direction F.shape([ndata, nc])
+#
+# 2- xyz : Magnetization direction used and data are given in 3-components
+# F.shape([3*ndata, nc])
+#
+# 3- full: Full tensor matrix stored with shape([3*ndata, 3*nc])
+#
+# OUTPUT:
+# F = Linear forward modeling operation
+#
+# Created on Dec, 20th 2015
+#
+# @author: dominiquef
+#
+# """
+# # Find non-zero cells
+# #inds = np.nonzero(actv)[0]
+# if actv.dtype=='bool':
+# inds = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem], dtype = int) - 1
+# else:
+# inds = actv
+#
+# nC = len(inds)
+#
+# # Create active cell projector
+# P = sp.csr_matrix((np.ones(nC),(inds, range(nC))),
+# shape=(mesh.nC, nC))
+#
+# # Create vectors of nodal location (lower and upper coners for each cell)
+# xn = mesh.vectorNx;
+# yn = mesh.vectorNy;
+# zn = mesh.vectorNz;
+#
+# yn2,xn2,zn2 = np.meshgrid(yn[1:], xn[1:], zn[1:])
+# yn1,xn1,zn1 = np.meshgrid(yn[0:-1], xn[0:-1], zn[0:-1])
+#
+# Yn = P.T*np.c_[mkvc(yn1), mkvc(yn2)]
+# Xn = P.T*np.c_[mkvc(xn1), mkvc(xn2)]
+# Zn = P.T*np.c_[mkvc(zn1), mkvc(zn2)]
+#
+# ndata = rxLoc.shape[0]
+#
+# # Convert Bdecination from north to cartesian
+# D = (450.-float(B[1]))%360.
+#
+#
+# # Pre-allocate space and create magnetization matrix if required
+# if (flag=='tmi') | (flag == 'xyz'):
+# # If assumes uniform magnetization direction
+# if M.shape != (nC,3):
+#
+# print 'Magnetization vector must be Nc x 3'
+# return
+#
+#
+# Mx = Utils.sdiag(M[:,0]*B[2])
+# My = Utils.sdiag(M[:,1]*B[2])
+# Mz = Utils.sdiag(M[:,2]*B[2])
+#
+# Mxyz = sp.vstack((Mx,My,Mz))
+#
+#
+#
+# if flag == 'tmi':
+# F = np.zeros((ndata, nC))
+#
+# # Projection matrix
+# Ptmi = mkvc(np.r_[np.cos(np.deg2rad(B[0]))*np.cos(np.deg2rad(D)),
+# np.cos(np.deg2rad(B[0]))*np.sin(np.deg2rad(D)),
+# np.sin(np.deg2rad(B[0]))],2).T;
+#
+# elif flag == 'xyz':
+#
+# F = np.zeros((int(3*ndata), nC))
+#
+# elif flag == 'full':
+# F = np.zeros((int(3*ndata), int(3*nC)))
+#
+#
+# else:
+# print """Flag must be either 'tmi' | 'xyz' | 'full', please revised"""
+# return
+#
+#
+# # Loop through all observations and create forward operator (ndata-by-nC)
+# print "Begin calculation of forward operator: " + flag
+#
+# # Add counter to dsiplay progress. Good for large problems
+# count = -1;
+# for ii in range(ndata):
+#
+#
+# tx, ty, tz = get_T_mat(Xn,Yn,Zn,rxLoc[ii,:])
+#
+# if flag=='tmi':
+# F[ii,:] = Ptmi.dot(np.vstack((tx,ty,tz)))*Mxyz
+#
+# elif flag == 'xyz':
+# F[ii,:] = tx*Mxyz
+# F[ii+ndata,:] = ty*Mxyz
+# F[ii+2*ndata,:] = tz*Mxyz
+#
+# elif flag == 'full':
+# F[ii,:] = tx
+# F[ii+ndata,:] = ty
+# F[ii+2*ndata,:] = tz
+#
+#
+# # Display progress
+# count = progress(ii,count,ndata)
+#
+# print "Done 100% ...forward operator completed!!\n"
+#
+# return F
def get_T_mat(Xn,Yn,Zn,rxLoc):
"""
@@ -1193,7 +1193,7 @@ def getActiveTopo(mesh,topo,flag):
return inds
-def plot_obs_2D(rxLoc,d = None ,varstr = 'Mag Obs', vmin = None, vmax = None):
+def plot_obs_2D(rxLoc,d = None ,varstr = 'Mag Obs', vmin = None, vmax = None, levels = None):
""" Function plot_obs(rxLoc,d)
Generate a 2d interpolated plot from scatter points of data
@@ -1238,8 +1238,12 @@ def plot_obs_2D(rxLoc,d = None ,varstr = 'Mag Obs', vmin = None, vmax = None):
d_grid = griddata(rxLoc[:,0:2],d,(X,Y), method ='linear')
plt.imshow(d_grid, extent=[x.min(), x.max(), y.min(), y.max()],origin = 'lower', vmin = vmin, vmax = vmax)
plt.colorbar(fraction=0.02)
- plt.contour(X,Y, d_grid,10,vmin = vmin, vmax = vmax)
-
+
+ if levels is None:
+ plt.contour(X,Y, d_grid,10,vmin = vmin, vmax = vmax)
+ else:
+ plt.contour(X,Y, d_grid,levels = levels,colors = 'r', vmin = vmin, vmax = vmax)
+
plt.title(varstr)
plt.gca().set_aspect('equal', adjustable='box')
diff --git a/simpegPF/notebooks/SimPEG Tutorial - MAG Linear Problem.ipynb b/simpegPF/notebooks/SimPEG Tutorial - MAG Linear Problem.ipynb
index 169b3cfc..d504509e 100644
--- a/simpegPF/notebooks/SimPEG Tutorial - MAG Linear Problem.ipynb
+++ b/simpegPF/notebooks/SimPEG Tutorial - MAG Linear Problem.ipynb
@@ -69,7 +69,8 @@
"%matplotlib notebook\n",
"%pylab\n",
"from SimPEG import *\n",
- "import simpegPF as PF"
+ "import simpegPF as PF\n",
+ "from simpegPF import BaseMag as MAG\n"
]
},
{
@@ -79,16 +80,23 @@
"collapsed": false,
"scrolled": true
},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\dominiquef.MIRAGEOSCIENCE\\Documents\\GIT\\SimPEG\\simpeg\\SimPEG\\Maps.py:533: FutureWarning: `ActiveCells` is deprecated and will be removed in future versions. Use `InjectActiveCells` instead\n",
+ " FutureWarning)\n"
+ ]
+ }
+ ],
"source": [
"# First we need to define the direction of the inducing field\n",
"# As a simple case, we pick a vertical inducing field of magnitude 50,000nT. \n",
"# From old convention, field orientation is given as an azimuth from North \n",
"# (positive clockwise) and dip from the horizontal (positive downward).\n",
- "H0 = np.array(([90.,0.,50000.]))\n",
+ "H0 = (50000.,90.,0.)\n",
"\n",
- "# Assume all induced so the magnetization M is also in the same direction\n",
- "M = np.array([90,0])\n",
"\n",
"# Create a mesh\n",
"dx = 5.\n",
@@ -126,7 +134,11 @@
"# Let just put the observation above the topo\n",
"Z = -np.exp( ( X**2 + Y**2 )/ 75**2 ) + mesh.vectorNz[-1] + 5. \n",
"\n",
- "rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]\n"
+ "# Create a MAGsurvey\n",
+ "rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]\n",
+ "rxLoc = MAG.RxObs(rxLoc)\n",
+ "srcField = MAG.SrcField([rxLoc],H0)\n",
+ "survey = MAG.LinearSurvey(srcField) \n"
]
},
{
@@ -164,7 +176,7 @@
},
{
"cell_type": "code",
- "execution_count": 6,
+ "execution_count": 7,
"metadata": {
"collapsed": false
},
@@ -173,7 +185,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "Begin calculation of forward operator: tmi\n",
+ "Begin calculation of forward operator: ind\n",
"Done 0.0 %\n",
"Done 10.0 %\n",
"Done 20.0 %\n",
@@ -190,802 +202,27 @@
}
],
"source": [
- "# First, convert the magnetization direction to Cartesian\n",
- "mi = np.ones(nC) * M[0]\n",
- "md = np.ones(nC) * M[1]\n",
- "M_xyz = PF.Magnetics.dipazm_2_xyz( mi , md ) # Ouputs an nc x 3 array\n",
+ "# We can now create a susceptibility model and generate data\n",
+ "# Lets start with a simple block in half-space\n",
+ "model = np.zeros((mesh.nCx,mesh.nCy,mesh.nCz))\n",
+ "model[(midx-2):(midx+2),(midy-2):(midy+2),-6:-2] = 0.01\n",
+ "model = mkvc(model)\n",
+ "model = model[actv]\n",
+ "\n",
+ "# Create active map to go from reduce set to full\n",
+ "actvMap = Maps.InjectActiveCells(mesh, actv, -100)\n",
+ "\n",
+ "# Creat reduced identity map\n",
+ "idenMap = Maps.IdentityMap(nP = len(actv))\n",
"\n",
"# Create the forward model operator\n",
- "F = PF.Magnetics.Intrgl_Fwr_Op(mesh,H0,M_xyz,rxLoc,actv,'tmi')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Begin calculation of distance weighting for R= 3.0\n",
- "Done 0.0 %\n",
- "Done 10.0 %\n",
- "Done 20.0 %\n",
- "Done 30.0 %\n",
- "Done 40.0 %\n",
- "Done 50.0 %\n",
- "Done 60.0 %\n",
- "Done 70.0 %\n",
- "Done 80.0 %\n",
- "Done 90.0 %\n",
- "Done 100% ...distance weighting completed!!\n",
- "\n"
- ]
- },
- {
- "data": {
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- "\n",
- " // Disable right mouse context menu.\n",
- " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
- " return false;\n",
- " });\n",
- "\n",
- " function set_focus () {\n",
- " canvas.focus();\n",
- " canvas_div.focus();\n",
- " }\n",
- "\n",
- " window.setTimeout(set_focus, 100);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._init_toolbar = function() {\n",
- " var fig = this;\n",
- "\n",
- " var nav_element = $('')\n",
- " nav_element.attr('style', 'width: 100%');\n",
- " this.root.append(nav_element);\n",
- "\n",
- " // Define a callback function for later on.\n",
- " function toolbar_event(event) {\n",
- " return fig.toolbar_button_onclick(event['data']);\n",
- " }\n",
- " function toolbar_mouse_event(event) {\n",
- " return fig.toolbar_button_onmouseover(event['data']);\n",
- " }\n",
- "\n",
- " for(var toolbar_ind in mpl.toolbar_items) {\n",
- " var name = mpl.toolbar_items[toolbar_ind][0];\n",
- " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
- " var image = mpl.toolbar_items[toolbar_ind][2];\n",
- " var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
- "\n",
- " if (!name) {\n",
- " // put a spacer in here.\n",
- " continue;\n",
- " }\n",
- " var button = $('');\n",
- " button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
- " 'ui-button-icon-only');\n",
- " button.attr('role', 'button');\n",
- " button.attr('aria-disabled', 'false');\n",
- " button.click(method_name, toolbar_event);\n",
- " button.mouseover(tooltip, toolbar_mouse_event);\n",
- "\n",
- " var icon_img = $('');\n",
- " icon_img.addClass('ui-button-icon-primary ui-icon');\n",
- " icon_img.addClass(image);\n",
- " icon_img.addClass('ui-corner-all');\n",
- "\n",
- " var tooltip_span = $('');\n",
- " tooltip_span.addClass('ui-button-text');\n",
- " tooltip_span.html(tooltip);\n",
- "\n",
- " button.append(icon_img);\n",
- " button.append(tooltip_span);\n",
- "\n",
- " nav_element.append(button);\n",
- " }\n",
- "\n",
- " var fmt_picker_span = $('');\n",
- "\n",
- " var fmt_picker = $('');\n",
- " fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
- " fmt_picker_span.append(fmt_picker);\n",
- " nav_element.append(fmt_picker_span);\n",
- " this.format_dropdown = fmt_picker[0];\n",
- "\n",
- " for (var ind in mpl.extensions) {\n",
- " var fmt = mpl.extensions[ind];\n",
- " var option = $(\n",
- " '', {selected: fmt === mpl.default_extension}).html(fmt);\n",
- " fmt_picker.append(option)\n",
- " }\n",
- "\n",
- " // Add hover states to the ui-buttons\n",
- " $( \".ui-button\" ).hover(\n",
- " function() { $(this).addClass(\"ui-state-hover\");},\n",
- " function() { $(this).removeClass(\"ui-state-hover\");}\n",
- " );\n",
- "\n",
- " var status_bar = $('');\n",
- " nav_element.append(status_bar);\n",
- " this.message = status_bar[0];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
- " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
- " // which will in turn request a refresh of the image.\n",
- " this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.send_message = function(type, properties) {\n",
- " properties['type'] = type;\n",
- " properties['figure_id'] = this.id;\n",
- " this.ws.send(JSON.stringify(properties));\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.send_draw_message = function() {\n",
- " if (!this.waiting) {\n",
- " this.waiting = true;\n",
- " this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
- " }\n",
- "}\n",
- "\n",
- "\n",
- "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
- " var format_dropdown = fig.format_dropdown;\n",
- " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
- " fig.ondownload(fig, format);\n",
- "}\n",
- "\n",
- "\n",
- "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
- " var size = msg['size'];\n",
- " if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
- " fig._resize_canvas(size[0], size[1]);\n",
- " fig.send_message(\"refresh\", {});\n",
- " };\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
- " var x0 = msg['x0'];\n",
- " var y0 = fig.canvas.height - msg['y0'];\n",
- " var x1 = msg['x1'];\n",
- " var y1 = fig.canvas.height - msg['y1'];\n",
- " x0 = Math.floor(x0) + 0.5;\n",
- " y0 = Math.floor(y0) + 0.5;\n",
- " x1 = Math.floor(x1) + 0.5;\n",
- " y1 = Math.floor(y1) + 0.5;\n",
- " var min_x = Math.min(x0, x1);\n",
- " var min_y = Math.min(y0, y1);\n",
- " var width = Math.abs(x1 - x0);\n",
- " var height = Math.abs(y1 - y0);\n",
- "\n",
- " fig.rubberband_context.clearRect(\n",
- " 0, 0, fig.canvas.width, fig.canvas.height);\n",
- "\n",
- " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
- " // Updates the figure title.\n",
- " fig.header.textContent = msg['label'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
- " var cursor = msg['cursor'];\n",
- " switch(cursor)\n",
- " {\n",
- " case 0:\n",
- " cursor = 'pointer';\n",
- " break;\n",
- " case 1:\n",
- " cursor = 'default';\n",
- " break;\n",
- " case 2:\n",
- " cursor = 'crosshair';\n",
- " break;\n",
- " case 3:\n",
- " cursor = 'move';\n",
- " break;\n",
- " }\n",
- " fig.rubberband_canvas.style.cursor = cursor;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
- " fig.message.textContent = msg['message'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
- " // Request the server to send over a new figure.\n",
- " fig.send_draw_message();\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
- " fig.image_mode = msg['mode'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.updated_canvas_event = function() {\n",
- " // Called whenever the canvas gets updated.\n",
- " this.send_message(\"ack\", {});\n",
- "}\n",
- "\n",
- "// A function to construct a web socket function for onmessage handling.\n",
- "// Called in the figure constructor.\n",
- "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
- " return function socket_on_message(evt) {\n",
- " if (evt.data instanceof Blob) {\n",
- " /* FIXME: We get \"Resource interpreted as Image but\n",
- " * transferred with MIME type text/plain:\" errors on\n",
- " * Chrome. But how to set the MIME type? It doesn't seem\n",
- " * to be part of the websocket stream */\n",
- " evt.data.type = \"image/png\";\n",
- "\n",
- " /* Free the memory for the previous frames */\n",
- " if (fig.imageObj.src) {\n",
- " (window.URL || window.webkitURL).revokeObjectURL(\n",
- " fig.imageObj.src);\n",
- " }\n",
- "\n",
- " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
- " evt.data);\n",
- " fig.updated_canvas_event();\n",
- " return;\n",
- " }\n",
- " else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
- " fig.imageObj.src = evt.data;\n",
- " fig.updated_canvas_event();\n",
- " return;\n",
- " }\n",
- "\n",
- " var msg = JSON.parse(evt.data);\n",
- " var msg_type = msg['type'];\n",
- "\n",
- " // Call the \"handle_{type}\" callback, which takes\n",
- " // the figure and JSON message as its only arguments.\n",
- " try {\n",
- " var callback = fig[\"handle_\" + msg_type];\n",
- " } catch (e) {\n",
- " console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
- " return;\n",
- " }\n",
- "\n",
- " if (callback) {\n",
- " try {\n",
- " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
- " callback(fig, msg);\n",
- " } catch (e) {\n",
- " console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
- " }\n",
- " }\n",
- " };\n",
- "}\n",
- "\n",
- "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
- "mpl.findpos = function(e) {\n",
- " //this section is from http://www.quirksmode.org/js/events_properties.html\n",
- " var targ;\n",
- " if (!e)\n",
- " e = window.event;\n",
- " if (e.target)\n",
- " targ = e.target;\n",
- " else if (e.srcElement)\n",
- " targ = e.srcElement;\n",
- " if (targ.nodeType == 3) // defeat Safari bug\n",
- " targ = targ.parentNode;\n",
- "\n",
- " // jQuery normalizes the pageX and pageY\n",
- " // pageX,Y are the mouse positions relative to the document\n",
- " // offset() returns the position of the element relative to the document\n",
- " var x = e.pageX - $(targ).offset().left;\n",
- " var y = e.pageY - $(targ).offset().top;\n",
- "\n",
- " return {\"x\": x, \"y\": y};\n",
- "};\n",
- "\n",
- "mpl.figure.prototype.mouse_event = function(event, name) {\n",
- " var canvas_pos = mpl.findpos(event)\n",
- "\n",
- " if (name === 'button_press')\n",
- " {\n",
- " this.canvas.focus();\n",
- " this.canvas_div.focus();\n",
- " }\n",
- "\n",
- " var x = canvas_pos.x;\n",
- " var y = canvas_pos.y;\n",
- "\n",
- " this.send_message(name, {x: x, y: y, button: event.button,\n",
- " step: event.step});\n",
- "\n",
- " /* This prevents the web browser from automatically changing to\n",
- " * the text insertion cursor when the button is pressed. We want\n",
- " * to control all of the cursor setting manually through the\n",
- " * 'cursor' event from matplotlib */\n",
- " event.preventDefault();\n",
- " return false;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
- " // Handle any extra behaviour associated with a key event\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.key_event = function(event, name) {\n",
- "\n",
- " // Prevent repeat events\n",
- " if (name == 'key_press')\n",
- " {\n",
- " if (event.which === this._key)\n",
- " return;\n",
- " else\n",
- " this._key = event.which;\n",
- " }\n",
- " if (name == 'key_release')\n",
- " this._key = null;\n",
- "\n",
- " var value = '';\n",
- " if (event.ctrlKey && event.which != 17)\n",
- " value += \"ctrl+\";\n",
- " if (event.altKey && event.which != 18)\n",
- " value += \"alt+\";\n",
- " if (event.shiftKey && event.which != 16)\n",
- " value += \"shift+\";\n",
- "\n",
- " value += 'k';\n",
- " value += event.which.toString();\n",
- "\n",
- " this._key_event_extra(event, name);\n",
- "\n",
- " this.send_message(name, {key: value});\n",
- " return false;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
- " if (name == 'download') {\n",
- " this.handle_save(this, null);\n",
- " } else {\n",
- " this.send_message(\"toolbar_button\", {name: name});\n",
- " }\n",
- "};\n",
- "\n",
- "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
- " this.message.textContent = tooltip;\n",
- "};\n",
- "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
- "\n",
- "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
- "\n",
- "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
- " // Create a \"websocket\"-like object which calls the given IPython comm\n",
- " // object with the appropriate methods. Currently this is a non binary\n",
- " // socket, so there is still some room for performance tuning.\n",
- " var ws = {};\n",
- "\n",
- " ws.close = function() {\n",
- " comm.close()\n",
- " };\n",
- " ws.send = function(m) {\n",
- " //console.log('sending', m);\n",
- " comm.send(m);\n",
- " };\n",
- " // Register the callback with on_msg.\n",
- " comm.on_msg(function(msg) {\n",
- " //console.log('receiving', msg['content']['data'], msg);\n",
- " // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
- " ws.onmessage(msg['content']['data'])\n",
- " });\n",
- " return ws;\n",
- "}\n",
- "\n",
- "mpl.mpl_figure_comm = function(comm, msg) {\n",
- " // This is the function which gets called when the mpl process\n",
- " // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
- "\n",
- " var id = msg.content.data.id;\n",
- " // Get hold of the div created by the display call when the Comm\n",
- " // socket was opened in Python.\n",
- " var element = $(\"#\" + id);\n",
- " var ws_proxy = comm_websocket_adapter(comm)\n",
- "\n",
- " function ondownload(figure, format) {\n",
- " window.open(figure.imageObj.src);\n",
- " }\n",
- "\n",
- " var fig = new mpl.figure(id, ws_proxy,\n",
- " ondownload,\n",
- " element.get(0));\n",
- "\n",
- " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
- " // web socket which is closed, not our websocket->open comm proxy.\n",
- " ws_proxy.onopen();\n",
- "\n",
- " fig.parent_element = element.get(0);\n",
- " fig.cell_info = mpl.find_output_cell(\"\");\n",
- " if (!fig.cell_info) {\n",
- " console.error(\"Failed to find cell for figure\", id, fig);\n",
- " return;\n",
- " }\n",
- "\n",
- " var output_index = fig.cell_info[2]\n",
- " var cell = fig.cell_info[0];\n",
- "\n",
- "};\n",
- "\n",
- "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
- " // Update the output cell to use the data from the current canvas.\n",
- " fig.push_to_output();\n",
- " var dataURL = fig.canvas.toDataURL();\n",
- " // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
- " // the notebook keyboard shortcuts fail.\n",
- " IPython.keyboard_manager.enable()\n",
- " $(fig.parent_element).html('
');\n",
- " fig.send_message('closing', {});\n",
- " fig.ws.close()\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
- " // Turn the data on the canvas into data in the output cell.\n",
- " var dataURL = this.canvas.toDataURL();\n",
- " this.cell_info[1]['text/html'] = '
';\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.updated_canvas_event = function() {\n",
- " // Tell IPython that the notebook contents must change.\n",
- " IPython.notebook.set_dirty(true);\n",
- " this.send_message(\"ack\", {});\n",
- " var fig = this;\n",
- " // Wait a second, then push the new image to the DOM so\n",
- " // that it is saved nicely (might be nice to debounce this).\n",
- " setTimeout(function () { fig.push_to_output() }, 1000);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._init_toolbar = function() {\n",
- " var fig = this;\n",
- "\n",
- " var nav_element = $('')\n",
- " nav_element.attr('style', 'width: 100%');\n",
- " this.root.append(nav_element);\n",
- "\n",
- " // Define a callback function for later on.\n",
- " function toolbar_event(event) {\n",
- " return fig.toolbar_button_onclick(event['data']);\n",
- " }\n",
- " function toolbar_mouse_event(event) {\n",
- " return fig.toolbar_button_onmouseover(event['data']);\n",
- " }\n",
- "\n",
- " for(var toolbar_ind in mpl.toolbar_items){\n",
- " var name = mpl.toolbar_items[toolbar_ind][0];\n",
- " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
- " var image = mpl.toolbar_items[toolbar_ind][2];\n",
- " var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
- "\n",
- " if (!name) { continue; };\n",
- "\n",
- " var button = $('');\n",
- " button.click(method_name, toolbar_event);\n",
- " button.mouseover(tooltip, toolbar_mouse_event);\n",
- " nav_element.append(button);\n",
- " }\n",
- "\n",
- " // Add the status bar.\n",
- " var status_bar = $('');\n",
- " nav_element.append(status_bar);\n",
- " this.message = status_bar[0];\n",
- "\n",
- " // Add the close button to the window.\n",
- " var buttongrp = $('');\n",
- " var button = $('');\n",
- " button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
- " button.mouseover('Close figure', toolbar_mouse_event);\n",
- " buttongrp.append(button);\n",
- " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
- " titlebar.prepend(buttongrp);\n",
- "}\n",
- "\n",
- "\n",
- "mpl.figure.prototype._canvas_extra_style = function(el){\n",
- " // this is important to make the div 'focusable\n",
- " el.attr('tabindex', 0)\n",
- " // reach out to IPython and tell the keyboard manager to turn it's self\n",
- " // off when our div gets focus\n",
- "\n",
- " // location in version 3\n",
- " if (IPython.notebook.keyboard_manager) {\n",
- " IPython.notebook.keyboard_manager.register_events(el);\n",
- " }\n",
- " else {\n",
- " // location in version 2\n",
- " IPython.keyboard_manager.register_events(el);\n",
- " }\n",
- "\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
- " var manager = IPython.notebook.keyboard_manager;\n",
- " if (!manager)\n",
- " manager = IPython.keyboard_manager;\n",
- "\n",
- " // Check for shift+enter\n",
- " if (event.shiftKey && event.which == 13) {\n",
- " this.canvas_div.blur();\n",
- " event.shiftKey = false;\n",
- " // Send a \"J\" for go to next cell\n",
- " event.which = 74;\n",
- " event.keyCode = 74;\n",
- " manager.command_mode();\n",
- " manager.handle_keydown(event);\n",
- " }\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
- " fig.ondownload(fig, null);\n",
- "}\n",
- "\n",
- "\n",
- "mpl.find_output_cell = function(html_output) {\n",
- " // Return the cell and output element which can be found *uniquely* in the notebook.\n",
- " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
- " // IPython event is triggered only after the cells have been serialised, which for\n",
- " // our purposes (turning an active figure into a static one), is too late.\n",
- " var cells = IPython.notebook.get_cells();\n",
- " var ncells = cells.length;\n",
- " for (var i=0; i= 3 moved mimebundle to data attribute of output\n",
- " data = data.data;\n",
- " }\n",
- " if (data['text/html'] == html_output) {\n",
- " return [cell, data, j];\n",
- " }\n",
- " }\n",
- " }\n",
- " }\n",
- "}\n",
- "\n",
- "// Register the function which deals with the matplotlib target/channel.\n",
- "// The kernel may be null if the page has been refreshed.\n",
- "if (IPython.notebook.kernel != null) {\n",
- " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
- "}\n"
- ],
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "data": {
- "text/html": [
- "
"
- ],
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# Generate a distance weighting\n",
- "wr = PF.Magnetics.get_dist_wgt(mesh,rxLoc,actv,3.,np.min(mesh.hx)/4)\n",
- "wrMap = PF.BaseMag.WeightMap(nC, wr)\n",
+ "prob = PF.Magnetics.MagneticIntegral(mesh, mapping = idenMap, actInd = actv)\n",
"\n",
- "wr_FULL = actvMap * wr\n",
- "plt.figure()\n",
- "ax = subplot()\n",
- "mesh.plotSlice(wr_FULL, ax = ax, normal = 'Y', ind=midx, grid=True, clim = (0, wr.max()))\n",
- "title('Distance weighting')\n",
- "xlabel('x');ylabel('z')\n",
- "plt.gca().set_aspect('equal', adjustable='box')"
+ "# Pair the survey and problem\n",
+ "survey.pair(prob)\n",
+ "\n",
+ "# Compute linear forward operator and compute some data\n",
+ "d = prob.fields(model)"
]
},
{
@@ -1734,7 +971,7 @@
{
"data": {
"text/html": [
- "
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+ "
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"text/plain": [
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@@ -1746,7 +983,7 @@
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"text/plain": [
- ""
+ ""
]
},
"execution_count": 8,
@@ -1755,12 +992,7 @@
}
],
"source": [
- "# We can now create a susceptibility model and generate data\n",
- "# Lets start with a simple block in half-space\n",
- "model = np.zeros((mesh.nCx,mesh.nCy,mesh.nCz))\n",
- "model[(midx-2):(midx+2),(midy-2):(midy+2),-6:-2] = 0.01\n",
- "model = mkvc(model)\n",
- "model = model[actv]\n",
+ "\n",
"\n",
"# Plot the model\n",
"figure()\n",
@@ -1771,7 +1003,6 @@
"plt.gca().set_aspect('equal', adjustable='box')\n",
"\n",
"# We can now generate data\n",
- "d = F.dot(model) #: this is matrix multiplication!!\n",
"data = d + randn(len(d)) # We add some random Gaussian noise (1nT)\n",
"wd = np.ones(len(data))*1. # Assign flat uncertainties\n",
"\n",
@@ -1791,135 +1022,7 @@
},
{
"cell_type": "code",
- "execution_count": null,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Once we have our problem, we can use the inversion tools in SimPEG to run our inversion:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
- "source": [
- "beta_in = 1e+4\n",
- "\n",
- "# Creat reduced identity map for topography\n",
- "idenMap = Maps.IdentityMap(nP = nC)\n",
- "\n",
- "prob = PF.Magnetics.MagneticIntegral(mesh, F, mapping = idenMap)\n",
- "prob.solverOpts['accuracyTol'] = 1e-4\n",
- "survey = Survey.LinearSurvey()\n",
- "survey.pair(prob)\n",
- "survey.dobs=data\n",
- "\n",
- "# Initiate a simple Tikonov regularization\n",
- "reg = Regularization.Simple(mesh, indActive = actv, mapping=wrMap)\n",
- "reg.mref = np.zeros(nC)\n",
- "reg.alpha_s = 1.\n",
- "\n",
- "# Create pre-conditioner \n",
- "diagA = np.sum(F**2.,axis=0) + beta_in*(reg.W.T*reg.W).diagonal()*(wr**2.0)\n",
- "PC = Utils.sdiag(diagA**-1.)\n",
- "\n",
- "# Creat reduced identity map\n",
- "idenMap = Maps.IdentityMap(nP = nC)\n",
- "\n",
- "# Set up the misfit function and pre-conditioner\n",
- "dmis = DataMisfit.l2_DataMisfit(survey)\n",
- "dmis.Wd = wd\n",
- "opt = Optimization.ProjectedGNCG(maxIter=10,lower=0.,upper=1.)\n",
- "opt.approxHinv = PC\n",
- "\n",
- "# Set up directives for the inverse problem\n",
- "invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta = beta_in)\n",
- "beta = Directives.BetaSchedule(coolingFactor=2, coolingRate=1)\n",
- "target = Directives.TargetMisfit()\n",
- "\n",
- "# The final inversion object controling all the parts above\n",
- "inv = Inversion.BaseInversion(invProb, directiveList=[beta, target])\n",
- "\n",
- "# Define a starting model (small)\n",
- "m0 = np.ones(nC) * 1e-4"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "True"
- ]
- },
- "execution_count": 10,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "prob.ispaired"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "SimPEG.InvProblem is setting bfgsH0 to the inverse of the eval2Deriv.\n",
- " ***Done using same Solver and solverOpts as the problem***\n",
- "=============================== Projected GNCG ===============================\n",
- " # beta phi_d phi_m f |proj(x-g)-x| LS Comment \n",
- "-----------------------------------------------------------------------------\n",
- " 0 1.00e+04 6.76e+04 3.37e-04 6.76e+04 8.30e+01 0 \n",
- " 1 5.00e+03 2.79e+03 3.20e-02 2.95e+03 6.89e+01 0 \n",
- " 2 2.50e+03 4.04e+02 5.56e-02 5.43e+02 7.04e+01 0 \n",
- " 3 1.25e+03 2.16e+02 5.78e-02 2.88e+02 7.02e+01 0 Skip BFGS \n",
- "------------------------- STOP! -------------------------\n",
- "1 : |fc-fOld| = 0.0000e+00 <= tolF*(1+|f0|) = 6.7632e+03\n",
- "1 : |xc-x_last| = 5.8532e-03 <= tolX*(1+|x0|) = 1.0111e-01\n",
- "0 : |proj(x-g)-x| = 7.0238e+01 <= tolG = 1.0000e-01\n",
- "0 : |proj(x-g)-x| = 7.0238e+01 <= 1e3*eps = 1.0000e-02\n",
- "0 : maxIter = 10 <= iter = 4\n",
- "------------------------- DONE! -------------------------\n"
- ]
- }
- ],
- "source": [
- "mrec = inv.run(m0)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Inversion has converged. We can plot sections through the model."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
+ "execution_count": 25,
"metadata": {
"collapsed": false
},
@@ -2663,7 +1766,870 @@
{
"data": {
"text/html": [
- "
"
+ "
"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Create distance weights from our linera forward operator\n",
+ "wr = np.sum(prob.G**2.,axis=0)**0.5\n",
+ "wr = ( wr/np.max(wr) )\n",
+ "\n",
+ "\n",
+ "wr_FULL = actvMap * wr\n",
+ "plt.figure()\n",
+ "ax = subplot()\n",
+ "mesh.plotSlice(wr_FULL, ax = ax, normal = 'Y', ind=midx, grid=True, clim = (0, wr.max()))\n",
+ "title('Distance weighting')\n",
+ "xlabel('x');ylabel('z')\n",
+ "plt.gca().set_aspect('equal', adjustable='box')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Once we have our problem, we can use the inversion tools in SimPEG to run our inversion:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "#survey.makeSyntheticData(data, std=0.01)\n",
+ "survey.dobs=data\n",
+ "survey.std = np.ones(len(data))\n",
+ "survey.mtrue = model\n",
+ "\n",
+ "# Create a regularization\n",
+ "reg = Regularization.Simple(mesh, indActive = actv, mapping = idenMap)\n",
+ "reg.wght = wr\n",
+ "\n",
+ "# Directive to cool the trade-off parameter beta\n",
+ "beta = Directives.BetaSchedule(coolingFactor=2, coolingRate=1)\n",
+ "beta_in = 1e+4\n",
+ "\n",
+ "# Create a jacobi pre-conditioner\n",
+ "diagA = np.sum(prob.G**2.,axis=0) + beta_in*(reg.W.T*reg.W).diagonal()*wr\n",
+ "PC = Utils.sdiag(diagA**-1.)\n",
+ "\n",
+ "# Define the misfit function\n",
+ "dmis = DataMisfit.l2_DataMisfit(survey)\n",
+ "dmis.Wd = 1./survey.std\n",
+ "\n",
+ "\n",
+ "# Solver for the optimization problem\n",
+ "opt = Optimization.ProjectedGNCG(maxIter=10, lower=0.,upper=1., maxIterCG= 30, tolCG = 1e-3)\n",
+ "opt.approxHinv = PC\n",
+ "\n",
+ "# Put everything together\n",
+ "invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta = beta_in)\n",
+ "target = Directives.TargetMisfit()\n",
+ "\n",
+ "inv = Inversion.BaseInversion(invProb, directiveList=[beta,target])\n",
+ "m0 = np.ones(mesh.nC)*1e-4\n",
+ "m0 = m0[actv]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "SimPEG.InvProblem will set Regularization.mref to m0.\n",
+ "SimPEG.InvProblem is setting bfgsH0 to the inverse of the eval2Deriv.\n",
+ " ***Done using same Solver and solverOpts as the problem***\n",
+ "=============================== Projected GNCG ===============================\n",
+ " # beta phi_d phi_m f |proj(x-g)-x| LS Comment \n",
+ "-----------------------------------------------------------------------------\n",
+ " 0 1.00e+04 6.70e+04 0.00e+00 6.70e+04 8.30e+01 0 \n",
+ " 1 5.00e+03 2.94e+03 4.20e-02 3.15e+03 6.89e+01 0 \n",
+ " 2 2.50e+03 3.61e+02 6.08e-02 5.13e+02 7.04e+01 0 \n",
+ " 3 1.25e+03 2.58e+02 5.84e-02 3.31e+02 8.36e+01 0 Skip BFGS \n",
+ "------------------------- STOP! -------------------------\n",
+ "1 : |fc-fOld| = 0.0000e+00 <= tolF*(1+|f0|) = 6.6998e+03\n",
+ "1 : |xc-x_last| = 8.5475e-03 <= tolX*(1+|x0|) = 1.0111e-01\n",
+ "0 : |proj(x-g)-x| = 8.3598e+01 <= tolG = 1.0000e-01\n",
+ "0 : |proj(x-g)-x| = 8.3598e+01 <= 1e3*eps = 1.0000e-02\n",
+ "0 : maxIter = 10 <= iter = 4\n",
+ "------------------------- DONE! -------------------------\n"
+ ]
+ }
+ ],
+ "source": [
+ "mrec = inv.run(m0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Inversion has converged. We can plot sections through the model."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ " // put a spacer in here.\n",
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+ "\n",
+ "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
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+ " fig._resize_canvas(size[0], size[1]);\n",
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+ " };\n",
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+ "\n",
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+ " var x0 = msg['x0'];\n",
+ " var y0 = fig.canvas.height - msg['y0'];\n",
+ " var x1 = msg['x1'];\n",
+ " var y1 = fig.canvas.height - msg['y1'];\n",
+ " x0 = Math.floor(x0) + 0.5;\n",
+ " y0 = Math.floor(y0) + 0.5;\n",
+ " x1 = Math.floor(x1) + 0.5;\n",
+ " y1 = Math.floor(y1) + 0.5;\n",
+ " var min_x = Math.min(x0, x1);\n",
+ " var min_y = Math.min(y0, y1);\n",
+ " var width = Math.abs(x1 - x0);\n",
+ " var height = Math.abs(y1 - y0);\n",
+ "\n",
+ " fig.rubberband_context.clearRect(\n",
+ " 0, 0, fig.canvas.width, fig.canvas.height);\n",
+ "\n",
+ " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
+ " // Updates the figure title.\n",
+ " fig.header.textContent = msg['label'];\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
+ " var cursor = msg['cursor'];\n",
+ " switch(cursor)\n",
+ " {\n",
+ " case 0:\n",
+ " cursor = 'pointer';\n",
+ " break;\n",
+ " case 1:\n",
+ " cursor = 'default';\n",
+ " break;\n",
+ " case 2:\n",
+ " cursor = 'crosshair';\n",
+ " break;\n",
+ " case 3:\n",
+ " cursor = 'move';\n",
+ " break;\n",
+ " }\n",
+ " fig.rubberband_canvas.style.cursor = cursor;\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
+ " fig.message.textContent = msg['message'];\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
+ " // Request the server to send over a new figure.\n",
+ " fig.send_draw_message();\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
+ " fig.image_mode = msg['mode'];\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.updated_canvas_event = function() {\n",
+ " // Called whenever the canvas gets updated.\n",
+ " this.send_message(\"ack\", {});\n",
+ "}\n",
+ "\n",
+ "// A function to construct a web socket function for onmessage handling.\n",
+ "// Called in the figure constructor.\n",
+ "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
+ " return function socket_on_message(evt) {\n",
+ " if (evt.data instanceof Blob) {\n",
+ " /* FIXME: We get \"Resource interpreted as Image but\n",
+ " * transferred with MIME type text/plain:\" errors on\n",
+ " * Chrome. But how to set the MIME type? It doesn't seem\n",
+ " * to be part of the websocket stream */\n",
+ " evt.data.type = \"image/png\";\n",
+ "\n",
+ " /* Free the memory for the previous frames */\n",
+ " if (fig.imageObj.src) {\n",
+ " (window.URL || window.webkitURL).revokeObjectURL(\n",
+ " fig.imageObj.src);\n",
+ " }\n",
+ "\n",
+ " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
+ " evt.data);\n",
+ " fig.updated_canvas_event();\n",
+ " return;\n",
+ " }\n",
+ " else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
+ " fig.imageObj.src = evt.data;\n",
+ " fig.updated_canvas_event();\n",
+ " return;\n",
+ " }\n",
+ "\n",
+ " var msg = JSON.parse(evt.data);\n",
+ " var msg_type = msg['type'];\n",
+ "\n",
+ " // Call the \"handle_{type}\" callback, which takes\n",
+ " // the figure and JSON message as its only arguments.\n",
+ " try {\n",
+ " var callback = fig[\"handle_\" + msg_type];\n",
+ " } catch (e) {\n",
+ " console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
+ " return;\n",
+ " }\n",
+ "\n",
+ " if (callback) {\n",
+ " try {\n",
+ " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
+ " callback(fig, msg);\n",
+ " } catch (e) {\n",
+ " console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
+ " }\n",
+ " }\n",
+ " };\n",
+ "}\n",
+ "\n",
+ "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
+ "mpl.findpos = function(e) {\n",
+ " //this section is from http://www.quirksmode.org/js/events_properties.html\n",
+ " var targ;\n",
+ " if (!e)\n",
+ " e = window.event;\n",
+ " if (e.target)\n",
+ " targ = e.target;\n",
+ " else if (e.srcElement)\n",
+ " targ = e.srcElement;\n",
+ " if (targ.nodeType == 3) // defeat Safari bug\n",
+ " targ = targ.parentNode;\n",
+ "\n",
+ " // jQuery normalizes the pageX and pageY\n",
+ " // pageX,Y are the mouse positions relative to the document\n",
+ " // offset() returns the position of the element relative to the document\n",
+ " var x = e.pageX - $(targ).offset().left;\n",
+ " var y = e.pageY - $(targ).offset().top;\n",
+ "\n",
+ " return {\"x\": x, \"y\": y};\n",
+ "};\n",
+ "\n",
+ "mpl.figure.prototype.mouse_event = function(event, name) {\n",
+ " var canvas_pos = mpl.findpos(event)\n",
+ "\n",
+ " if (name === 'button_press')\n",
+ " {\n",
+ " this.canvas.focus();\n",
+ " this.canvas_div.focus();\n",
+ " }\n",
+ "\n",
+ " var x = canvas_pos.x;\n",
+ " var y = canvas_pos.y;\n",
+ "\n",
+ " this.send_message(name, {x: x, y: y, button: event.button,\n",
+ " step: event.step});\n",
+ "\n",
+ " /* This prevents the web browser from automatically changing to\n",
+ " * the text insertion cursor when the button is pressed. We want\n",
+ " * to control all of the cursor setting manually through the\n",
+ " * 'cursor' event from matplotlib */\n",
+ " event.preventDefault();\n",
+ " return false;\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
+ " // Handle any extra behaviour associated with a key event\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.key_event = function(event, name) {\n",
+ "\n",
+ " // Prevent repeat events\n",
+ " if (name == 'key_press')\n",
+ " {\n",
+ " if (event.which === this._key)\n",
+ " return;\n",
+ " else\n",
+ " this._key = event.which;\n",
+ " }\n",
+ " if (name == 'key_release')\n",
+ " this._key = null;\n",
+ "\n",
+ " var value = '';\n",
+ " if (event.ctrlKey && event.which != 17)\n",
+ " value += \"ctrl+\";\n",
+ " if (event.altKey && event.which != 18)\n",
+ " value += \"alt+\";\n",
+ " if (event.shiftKey && event.which != 16)\n",
+ " value += \"shift+\";\n",
+ "\n",
+ " value += 'k';\n",
+ " value += event.which.toString();\n",
+ "\n",
+ " this._key_event_extra(event, name);\n",
+ "\n",
+ " this.send_message(name, {key: value});\n",
+ " return false;\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
+ " if (name == 'download') {\n",
+ " this.handle_save(this, null);\n",
+ " } else {\n",
+ " this.send_message(\"toolbar_button\", {name: name});\n",
+ " }\n",
+ "};\n",
+ "\n",
+ "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
+ " this.message.textContent = tooltip;\n",
+ "};\n",
+ "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
+ "\n",
+ "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
+ "\n",
+ "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
+ " // Create a \"websocket\"-like object which calls the given IPython comm\n",
+ " // object with the appropriate methods. Currently this is a non binary\n",
+ " // socket, so there is still some room for performance tuning.\n",
+ " var ws = {};\n",
+ "\n",
+ " ws.close = function() {\n",
+ " comm.close()\n",
+ " };\n",
+ " ws.send = function(m) {\n",
+ " //console.log('sending', m);\n",
+ " comm.send(m);\n",
+ " };\n",
+ " // Register the callback with on_msg.\n",
+ " comm.on_msg(function(msg) {\n",
+ " //console.log('receiving', msg['content']['data'], msg);\n",
+ " // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
+ " ws.onmessage(msg['content']['data'])\n",
+ " });\n",
+ " return ws;\n",
+ "}\n",
+ "\n",
+ "mpl.mpl_figure_comm = function(comm, msg) {\n",
+ " // This is the function which gets called when the mpl process\n",
+ " // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
+ "\n",
+ " var id = msg.content.data.id;\n",
+ " // Get hold of the div created by the display call when the Comm\n",
+ " // socket was opened in Python.\n",
+ " var element = $(\"#\" + id);\n",
+ " var ws_proxy = comm_websocket_adapter(comm)\n",
+ "\n",
+ " function ondownload(figure, format) {\n",
+ " window.open(figure.imageObj.src);\n",
+ " }\n",
+ "\n",
+ " var fig = new mpl.figure(id, ws_proxy,\n",
+ " ondownload,\n",
+ " element.get(0));\n",
+ "\n",
+ " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
+ " // web socket which is closed, not our websocket->open comm proxy.\n",
+ " ws_proxy.onopen();\n",
+ "\n",
+ " fig.parent_element = element.get(0);\n",
+ " fig.cell_info = mpl.find_output_cell(\"\");\n",
+ " if (!fig.cell_info) {\n",
+ " console.error(\"Failed to find cell for figure\", id, fig);\n",
+ " return;\n",
+ " }\n",
+ "\n",
+ " var output_index = fig.cell_info[2]\n",
+ " var cell = fig.cell_info[0];\n",
+ "\n",
+ "};\n",
+ "\n",
+ "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
+ " // Update the output cell to use the data from the current canvas.\n",
+ " fig.push_to_output();\n",
+ " var dataURL = fig.canvas.toDataURL();\n",
+ " // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
+ " // the notebook keyboard shortcuts fail.\n",
+ " IPython.keyboard_manager.enable()\n",
+ " $(fig.parent_element).html('
');\n",
+ " fig.send_message('closing', {});\n",
+ " fig.ws.close()\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
+ " // Turn the data on the canvas into data in the output cell.\n",
+ " var dataURL = this.canvas.toDataURL();\n",
+ " this.cell_info[1]['text/html'] = '
';\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.updated_canvas_event = function() {\n",
+ " // Tell IPython that the notebook contents must change.\n",
+ " IPython.notebook.set_dirty(true);\n",
+ " this.send_message(\"ack\", {});\n",
+ " var fig = this;\n",
+ " // Wait a second, then push the new image to the DOM so\n",
+ " // that it is saved nicely (might be nice to debounce this).\n",
+ " setTimeout(function () { fig.push_to_output() }, 1000);\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._init_toolbar = function() {\n",
+ " var fig = this;\n",
+ "\n",
+ " var nav_element = $('')\n",
+ " nav_element.attr('style', 'width: 100%');\n",
+ " this.root.append(nav_element);\n",
+ "\n",
+ " // Define a callback function for later on.\n",
+ " function toolbar_event(event) {\n",
+ " return fig.toolbar_button_onclick(event['data']);\n",
+ " }\n",
+ " function toolbar_mouse_event(event) {\n",
+ " return fig.toolbar_button_onmouseover(event['data']);\n",
+ " }\n",
+ "\n",
+ " for(var toolbar_ind in mpl.toolbar_items){\n",
+ " var name = mpl.toolbar_items[toolbar_ind][0];\n",
+ " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
+ " var image = mpl.toolbar_items[toolbar_ind][2];\n",
+ " var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
+ "\n",
+ " if (!name) { continue; };\n",
+ "\n",
+ " var button = $('');\n",
+ " button.click(method_name, toolbar_event);\n",
+ " button.mouseover(tooltip, toolbar_mouse_event);\n",
+ " nav_element.append(button);\n",
+ " }\n",
+ "\n",
+ " // Add the status bar.\n",
+ " var status_bar = $('');\n",
+ " nav_element.append(status_bar);\n",
+ " this.message = status_bar[0];\n",
+ "\n",
+ " // Add the close button to the window.\n",
+ " var buttongrp = $('');\n",
+ " var button = $('');\n",
+ " button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
+ " button.mouseover('Close figure', toolbar_mouse_event);\n",
+ " buttongrp.append(button);\n",
+ " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
+ " titlebar.prepend(buttongrp);\n",
+ "}\n",
+ "\n",
+ "\n",
+ "mpl.figure.prototype._canvas_extra_style = function(el){\n",
+ " // this is important to make the div 'focusable\n",
+ " el.attr('tabindex', 0)\n",
+ " // reach out to IPython and tell the keyboard manager to turn it's self\n",
+ " // off when our div gets focus\n",
+ "\n",
+ " // location in version 3\n",
+ " if (IPython.notebook.keyboard_manager) {\n",
+ " IPython.notebook.keyboard_manager.register_events(el);\n",
+ " }\n",
+ " else {\n",
+ " // location in version 2\n",
+ " IPython.keyboard_manager.register_events(el);\n",
+ " }\n",
+ "\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
+ " var manager = IPython.notebook.keyboard_manager;\n",
+ " if (!manager)\n",
+ " manager = IPython.keyboard_manager;\n",
+ "\n",
+ " // Check for shift+enter\n",
+ " if (event.shiftKey && event.which == 13) {\n",
+ " this.canvas_div.blur();\n",
+ " event.shiftKey = false;\n",
+ " // Send a \"J\" for go to next cell\n",
+ " event.which = 74;\n",
+ " event.keyCode = 74;\n",
+ " manager.command_mode();\n",
+ " manager.handle_keydown(event);\n",
+ " }\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
+ " fig.ondownload(fig, null);\n",
+ "}\n",
+ "\n",
+ "\n",
+ "mpl.find_output_cell = function(html_output) {\n",
+ " // Return the cell and output element which can be found *uniquely* in the notebook.\n",
+ " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
+ " // IPython event is triggered only after the cells have been serialised, which for\n",
+ " // our purposes (turning an active figure into a static one), is too late.\n",
+ " var cells = IPython.notebook.get_cells();\n",
+ " var ncells = cells.length;\n",
+ " for (var i=0; i= 3 moved mimebundle to data attribute of output\n",
+ " data = data.data;\n",
+ " }\n",
+ " if (data['text/html'] == html_output) {\n",
+ " return [cell, data, j];\n",
+ " }\n",
+ " }\n",
+ " }\n",
+ " }\n",
+ "}\n",
+ "\n",
+ "// Register the function which deals with the matplotlib target/channel.\n",
+ "// The kernel may be null if the page has been refreshed.\n",
+ "if (IPython.notebook.kernel != null) {\n",
+ " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
+ "}\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "
"
],
"text/plain": [
""
@@ -2703,7 +2669,7 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 29,
"metadata": {
"collapsed": false
},
@@ -3447,7 +3413,7 @@
{
"data": {
"text/html": [
- "
"
+ "
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],
"text/plain": [
""
@@ -3459,10 +3425,10 @@
{
"data": {
"text/plain": [
- ""
+ ""
]
},
- "execution_count": 19,
+ "execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
@@ -3470,7 +3436,7 @@
"source": [
"# Plot predicted data and residual\n",
"plt.figure()\n",
- "pred = F.dot(mrec) #: this is matrix multiplication!!\n",
+ "pred = prob.fields(mrec) #: this is matrix multiplication!!\n",
"\n",
"subplot(221)\n",
"imshow(data.reshape(X.shape))\n",