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Fully automated version management and generator of release notes

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Intelligent AI automation examples using Bito CLI and tools

# XFEM_Fracture2D ### Description This is a Matlab program that can be used to solve fracture problems involving arbitrary multiple crack propagations in a 2D linear-elastic solid based on the principle of minimum potential energy. The extended finite element method is used to discretise the solid continuum considering cracks as discontinuities in the displacement field. To this end, a strong discontinuity enrichment and a square-root singular crack tip enrichment are used to describe each crack. Several crack growth criteria are available to determine the evolution of cracks over time; apart from the classic maximum tension (or hoop-stress) criterion, the minimum total energy criterion and the local symmetry criterion are implemented implicitly with respect to the discrete time-stepping. ### Key features * *Fast:* The stiffness matrix and the force vector (i.e. the equations' system) and the enrichment tracking data structures are updated at each time step only with respect to the changes in the fracture topology. This ultimately results in the major part of the computational expense in the solution to the linear system of equations rather than in the post-processing of the solution or in the assembly and updating of the equations. As Matlab offers fast and robust direct solvers, the computational times are reasonably fast. * *Robust.* Suitable for multiple crack propagations with intersections. Furthermore, the stress intensity factors are computed robustly via the interaction integral approach (with the inclusion of the terms to account for crack surface pressure, residual stresses or strains). The minimum total energy criterion and the principle of local symmetry are implemented implicitly in time. The energy release rates are computed based on the stiffness derivative approach using algebraic differentiation (rather than finite differencing of the potential energy). On the other hand, the crack growth direction based on the local symmetry criterion is determined such that the local mode-II stress intensity factor vanishes; the change in a crack tip kink angle is approximated using the ratio of the crack tip stress intensity factors. * *Easy to run.* Each job has its own input files which are independent form those of all other jobs. The code especially lends itself to running parametric studies. Various results can be saved relating to the fracture geometry, fracture mechanics parameters, and the elastic fields in the solid domain. Extensive visualisation library is available for plotting results. ### Instructions 1. Get started by running the demo to showcase some of the capabilities of the program and to determine if it can be useful for you. At the Matlab's command line enter: ```Matlab >> RUN_JOBS.m ``` This will execute a series of jobs located inside the *jobs directory* `./JOBS_LIBRARY/`. These jobs do not take very long to execute (around 5 minutes in total). 2. Subsequently, you can pick one of the jobs inside `./JOBS_LIBRARY/` by defining the job title: ```Matlab >> job_title = 'several_cracks/edge/vertical_tension' ``` 3. Then you can open all the relevant scripts for this job as follows: ```Matlab >> open_job ``` The following input scripts for the *job* will be open in the Matlab's editor: 1. `JOB_MAIN.m`: This is the job's main script. It is called when executing `RUN_JOB` (or `RUN_JOBS`) and acts like a wrapper. Notably, it can serve as a convenient interface to run parametric studies and to save intermediate simulation results. 2. `Input_Scope.m`: This defines the scope of the simulation. From which crack growth criteria to use, to what to compute and what results to show via plots and/or movies. To put it simply, the script is a bunch of "switches" that tell the program what the user wants to be done. 3. `Input_Material.m`: Defines the material's elastic properties in different regions or layers (called "phases") of the computational domain. Moreover, it defines the fracture toughness of the material (assumed to be constant in all material phases). 4. `Input_Crack.m`: Defines the initial crack geometry. 5. `Input_BC.m`: Defines boundary conditions, such as displacements, tractions, crack surface pressure (assumed to be constant in all cracks), body loads (e.g. gravity, pre-stress or pre-strain). 6. `Mesh_make.m`: In-house structured mesh generator for rectangular domains using either linear triangle or bilinear quadrilateral elements. It is possible to mesh horizontal layers using different mesh sizes. 7. `Mesh_read.m`: Gmsh based mesh reader for version-1 mesh files. Of course you can use your own mesh reader provided the output variables are of the correct format (see later). 8. `Mesh_file.m`: Specifies the mesh input file (.msh). At the moment, only Gmsh mesh files of version-1 are allowed. ### Mesh_file.m A mesh file needs to be able to output the following data or variables: * `mNdCrd`: Node coordinates, size = `[nNdStd, 2]` * `mLNodS`: Element connectivities, size = `[nElemn,nLNodS]` * `vElPhz`: Element material phase (or region) ID's, size = `[nElemn,1]` * `cBCNod`: cell of boundary nodes, cell size = `{nBound,1}`, cell element size = `[nBnNod,2]` Example mesh files are located in `./JOBS_LIBRARY/`. Gmsh version-1 file format is described [here](http://www.manpagez.com/info/gmsh/gmsh-2.4.0/gmsh_60.php). ### Additional notes * global variables are defined in `.\Routines_AuxInput\Declare_Global.m` * External libraries are `.\Other_Libs\distmesh` and `.\Other_Libs\mesh2d` ### References Two external meshing libraries are used for the local mesh refinement and remeshing at the crack tip during crack propagation or prior to a crack intersection with another crack or with a boundary of the domain. Specifically, these libraries, which are located in `.\Other_Libs\`, are the following: * [*mesh2d*](https://people.sc.fsu.edu/~jburkardt/m_src/mesh2d/mesh2d.html) by Darren Engwirda * [*distmesh*](http://persson.berkeley.edu/distmesh/) by Per-Olof Persson and Gilbert Strang. ### Issues and Support For support or questions please email [sutula.danas@gmail.com](mailto:sutula.danas@gmail.com). ### Authors Danas Sutula, University of Luxembourg, Luxembourg. If you find this code useful, we kindly ask that you consider citing us. * [Minimum energy multiple crack propagation](http://hdl.handle.net/10993/29414)

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Semver utility for Unity projects with changelog / release notes generator

A fully configurable release note generation framework. Allow you to automatically generate a beautiful release note from commit messages and pull requests.

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A release note generator that reads and parses git commits and retrieves issue links from GitHub.

Quickstart tutorial Prerequisites Before reading this tutorial you should know a bit of Python. If you would like to refresh your memory, take a look at the Python tutorial. If you wish to work the examples in this tutorial, you must also have some software installed on your computer. Please see https://scipy.org/install.html for instructions. Learner profile This tutorial is intended as a quick overview of algebra and arrays in NumPy and want to understand how n-dimensional (n>=2) arrays are represented and can be manipulated. In particular, if you don’t know how to apply common functions to n-dimensional arrays (without using for-loops), or if you want to understand axis and shape properties for n-dimensional arrays, this tutorial might be of help. Learning Objectives After this tutorial, you should be able to: Understand the difference between one-, two- and n-dimensional arrays in NumPy; Understand how to apply some linear algebra operations to n-dimensional arrays without using for-loops; Understand axis and shape properties for n-dimensional arrays. The Basics NumPy’s main object is the homogeneous multidimensional array. It is a table of elements (usually numbers), all of the same type, indexed by a tuple of non-negative integers. In NumPy dimensions are called axes. For example, the coordinates of a point in 3D space [1, 2, 1] has one axis. That axis has 3 elements in it, so we say it has a length of 3. In the example pictured below, the array has 2 axes. The first axis has a length of 2, the second axis has a length of 3. [[ 1., 0., 0.], [ 0., 1., 2.]] NumPy’s array class is called ndarray. It is also known by the alias array. Note that numpy.array is not the same as the Standard Python Library class array.array, which only handles one-dimensional arrays and offers less functionality. The more important attributes of an ndarray object are: ndarray.ndim the number of axes (dimensions) of the array. ndarray.shape the dimensions of the array. This is a tuple of integers indicating the size of the array in each dimension. For a matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the number of axes, ndim. ndarray.size the total number of elements of the array. This is equal to the product of the elements of shape. ndarray.dtype an object describing the type of the elements in the array. One can create or specify dtype’s using standard Python types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.float64 are some examples. ndarray.itemsize the size in bytes of each element of the array. For example, an array of elements of type float64 has itemsize 8 (=64/8), while one of type complex32 has itemsize 4 (=32/8). It is equivalent to ndarray.dtype.itemsize. ndarray.data the buffer containing the actual elements of the array. Normally, we won’t need to use this attribute because we will access the elements in an array using indexing facilities. An example >>> import numpy as np a = np.arange(15).reshape(3, 5) a array([[ 0, 1, 2, 3, 4], [ 5, 6, 7, 8, 9], [10, 11, 12, 13, 14]]) a.shape (3, 5) a.ndim 2 a.dtype.name 'int64' a.itemsize 8 a.size 15 type(a) <class 'numpy.ndarray'> b = np.array([6, 7, 8]) b array([6, 7, 8]) type(b) <class 'numpy.ndarray'> Array Creation There are several ways to create arrays. For example, you can create an array from a regular Python list or tuple using the array function. The type of the resulting array is deduced from the type of the elements in the sequences. >>> >>> import numpy as np >>> a = np.array([2,3,4]) >>> a array([2, 3, 4]) >>> a.dtype dtype('int64') >>> b = np.array([1.2, 3.5, 5.1]) >>> b.dtype dtype('float64') A frequent error consists in calling array with multiple arguments, rather than providing a single sequence as an argument. >>> >>> a = np.array(1,2,3,4) # WRONG Traceback (most recent call last): ... TypeError: array() takes from 1 to 2 positional arguments but 4 were given >>> a = np.array([1,2,3,4]) # RIGHT array transforms sequences of sequences into two-dimensional arrays, sequences of sequences of sequences into three-dimensional arrays, and so on. >>> >>> b = np.array([(1.5,2,3), (4,5,6)]) >>> b array([[1.5, 2. , 3. ], [4. , 5. , 6. ]]) The type of the array can also be explicitly specified at creation time: >>> >>> c = np.array( [ [1,2], [3,4] ], dtype=complex ) >>> c array([[1.+0.j, 2.+0.j], [3.+0.j, 4.+0.j]]) Often, the elements of an array are originally unknown, but its size is known. Hence, NumPy offers several functions to create arrays with initial placeholder content. These minimize the necessity of growing arrays, an expensive operation. The function zeros creates an array full of zeros, the function ones creates an array full of ones, and the function empty creates an array whose initial content is random and depends on the state of the memory. By default, the dtype of the created array is float64. >>> >>> np.zeros((3, 4)) array([[0., 0., 0., 0.], [0., 0., 0., 0.], [0., 0., 0., 0.]]) >>> np.ones( (2,3,4), dtype=np.int16 ) # dtype can also be specified array([[[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]], [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]], dtype=int16) >>> np.empty( (2,3) ) # uninitialized array([[ 3.73603959e-262, 6.02658058e-154, 6.55490914e-260], # may vary [ 5.30498948e-313, 3.14673309e-307, 1.00000000e+000]]) To create sequences of numbers, NumPy provides the arange function which is analogous to the Python built-in range, but returns an array. >>> >>> np.arange( 10, 30, 5 ) array([10, 15, 20, 25]) >>> np.arange( 0, 2, 0.3 ) # it accepts float arguments array([0. , 0.3, 0.6, 0.9, 1.2, 1.5, 1.8]) When arange is used with floating point arguments, it is generally not possible to predict the number of elements obtained, due to the finite floating point precision. For this reason, it is usually better to use the function linspace that receives as an argument the number of elements that we want, instead of the step: >>> >>> from numpy import pi >>> np.linspace( 0, 2, 9 ) # 9 numbers from 0 to 2 array([0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75, 2. ]) >>> x = np.linspace( 0, 2*pi, 100 ) # useful to evaluate function at lots of points >>> f = np.sin(x) See also array, zeros, zeros_like, ones, ones_like, empty, empty_like, arange, linspace, numpy.random.Generator.rand, numpy.random.Generator.randn, fromfunction, fromfile Printing Arrays When you print an array, NumPy displays it in a similar way to nested lists, but with the following layout: the last axis is printed from left to right, the second-to-last is printed from top to bottom, the rest are also printed from top to bottom, with each slice separated from the next by an empty line. One-dimensional arrays are then printed as rows, bidimensionals as matrices and tridimensionals as lists of matrices. >>> >>> a = np.arange(6) # 1d array >>> print(a) [0 1 2 3 4 5] >>> >>> b = np.arange(12).reshape(4,3) # 2d array >>> print(b) [[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11]] >>> >>> c = np.arange(24).reshape(2,3,4) # 3d array >>> print(c) [[[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]] [[12 13 14 15] [16 17 18 19] [20 21 22 23]]] See below to get more details on reshape. If an array is too large to be printed, NumPy automatically skips the central part of the array and only prints the corners: >>> >>> print(np.arange(10000)) [ 0 1 2 ... 9997 9998 9999] >>> >>> print(np.arange(10000).reshape(100,100)) [[ 0 1 2 ... 97 98 99] [ 100 101 102 ... 197 198 199] [ 200 201 202 ... 297 298 299] ... [9700 9701 9702 ... 9797 9798 9799] [9800 9801 9802 ... 9897 9898 9899] [9900 9901 9902 ... 9997 9998 9999]] To disable this behaviour and force NumPy to print the entire array, you can change the printing options using set_printoptions. >>> >>> np.set_printoptions(threshold=sys.maxsize) # sys module should be imported Basic Operations Arithmetic operators on arrays apply elementwise. A new array is created and filled with the result. >>> >>> a = np.array( [20,30,40,50] ) >>> b = np.arange( 4 ) >>> b array([0, 1, 2, 3]) >>> c = a-b >>> c array([20, 29, 38, 47]) >>> b**2 array([0, 1, 4, 9]) >>> 10*np.sin(a) array([ 9.12945251, -9.88031624, 7.4511316 , -2.62374854]) >>> a<35 array([ True, True, False, False]) Unlike in many matrix languages, the product operator * operates elementwise in NumPy arrays. The matrix product can be performed using the @ operator (in python >=3.5) or the dot function or method: >>> >>> A = np.array( [[1,1], ... [0,1]] ) >>> B = np.array( [[2,0], ... [3,4]] ) >>> A * B # elementwise product array([[2, 0], [0, 4]]) >>> A @ B # matrix product array([[5, 4], [3, 4]]) >>> A.dot(B) # another matrix product array([[5, 4], [3, 4]]) Some operations, such as += and *=, act in place to modify an existing array rather than create a new one. >>> >>> rg = np.random.default_rng(1) # create instance of default random number generator >>> a = np.ones((2,3), dtype=int) >>> b = rg.random((2,3)) >>> a *= 3 >>> a array([[3, 3, 3], [3, 3, 3]]) >>> b += a >>> b array([[3.51182162, 3.9504637 , 3.14415961], [3.94864945, 3.31183145, 3.42332645]]) >>> a += b # b is not automatically converted to integer type Traceback (most recent call last): ... numpy.core._exceptions.UFuncTypeError: Cannot cast ufunc 'add' output from dtype('float64') to dtype('int64') with casting rule 'same_kind' When operating with arrays of different types, the type of the resulting array corresponds to the more general or precise one (a behavior known as upcasting). >>> >>> a = np.ones(3, dtype=np.int32) >>> b = np.linspace(0,pi,3) >>> b.dtype.name 'float64' >>> c = a+b >>> c array([1. , 2.57079633, 4.14159265]) >>> c.dtype.name 'float64' >>> d = np.exp(c*1j) >>> d array([ 0.54030231+0.84147098j, -0.84147098+0.54030231j, -0.54030231-0.84147098j]) >>> d.dtype.name 'complex128' Many unary operations, such as computing the sum of all the elements in the array, are implemented as methods of the ndarray class. >>> >>> a = rg.random((2,3)) >>> a array([[0.82770259, 0.40919914, 0.54959369], [0.02755911, 0.75351311, 0.53814331]]) >>> a.sum() 3.1057109529998157 >>> a.min() 0.027559113243068367 >>> a.max() 0.8277025938204418 By default, these operations apply to the array as though it were a list of numbers, regardless of its shape. However, by specifying the axis parameter you can apply an operation along the specified axis of an array: >>> >>> b = np.arange(12).reshape(3,4) >>> b array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> b.sum(axis=0) # sum of each column array([12, 15, 18, 21]) >>> >>> b.min(axis=1) # min of each row array([0, 4, 8]) >>> >>> b.cumsum(axis=1) # cumulative sum along each row array([[ 0, 1, 3, 6], [ 4, 9, 15, 22], [ 8, 17, 27, 38]]) Universal Functions NumPy provides familiar mathematical functions such as sin, cos, and exp. In NumPy, these are called “universal functions”(ufunc). Within NumPy, these functions operate elementwise on an array, producing an array as output. >>> >>> B = np.arange(3) >>> B array([0, 1, 2]) >>> np.exp(B) array([1. , 2.71828183, 7.3890561 ]) >>> np.sqrt(B) array([0. , 1. , 1.41421356]) >>> C = np.array([2., -1., 4.]) >>> np.add(B, C) array([2., 0., 6.]) See also all, any, apply_along_axis, argmax, argmin, argsort, average, bincount, ceil, clip, conj, corrcoef, cov, cross, cumprod, cumsum, diff, dot, floor, inner, invert, lexsort, max, maximum, mean, median, min, minimum, nonzero, outer, prod, re, round, sort, std, sum, trace, transpose, var, vdot, vectorize, where Indexing, Slicing and Iterating One-dimensional arrays can be indexed, sliced and iterated over, much like lists and other Python sequences. >>> >>> a = np.arange(10)**3 >>> a array([ 0, 1, 8, 27, 64, 125, 216, 343, 512, 729]) >>> a[2] 8 >>> a[2:5] array([ 8, 27, 64]) # equivalent to a[0:6:2] = 1000; # from start to position 6, exclusive, set every 2nd element to 1000 >>> a[:6:2] = 1000 >>> a array([1000, 1, 1000, 27, 1000, 125, 216, 343, 512, 729]) >>> a[ : :-1] # reversed a array([ 729, 512, 343, 216, 125, 1000, 27, 1000, 1, 1000]) >>> for i in a: ... print(i**(1/3.)) ... 9.999999999999998 1.0 9.999999999999998 3.0 9.999999999999998 4.999999999999999 5.999999999999999 6.999999999999999 7.999999999999999 8.999999999999998 Multidimensional arrays can have one index per axis. These indices are given in a tuple separated by commas: >>> >>> def f(x,y): ... return 10*x+y ... >>> b = np.fromfunction(f,(5,4),dtype=int) >>> b array([[ 0, 1, 2, 3], [10, 11, 12, 13], [20, 21, 22, 23], [30, 31, 32, 33], [40, 41, 42, 43]]) >>> b[2,3] 23 >>> b[0:5, 1] # each row in the second column of b array([ 1, 11, 21, 31, 41]) >>> b[ : ,1] # equivalent to the previous example array([ 1, 11, 21, 31, 41]) >>> b[1:3, : ] # each column in the second and third row of b array([[10, 11, 12, 13], [20, 21, 22, 23]]) When fewer indices are provided than the number of axes, the missing indices are considered complete slices: >>> >>> b[-1] # the last row. Equivalent to b[-1,:] array([40, 41, 42, 43]) The expression within brackets in b[i] is treated as an i followed by as many instances of : as needed to represent the remaining axes. NumPy also allows you to write this using dots as b[i,...]. The dots (...) represent as many colons as needed to produce a complete indexing tuple. For example, if x is an array with 5 axes, then x[1,2,...] is equivalent to x[1,2,:,:,:], x[...,3] to x[:,:,:,:,3] and x[4,...,5,:] to x[4,:,:,5,:]. >>> >>> c = np.array( [[[ 0, 1, 2], # a 3D array (two stacked 2D arrays) ... [ 10, 12, 13]], ... [[100,101,102], ... [110,112,113]]]) >>> c.shape (2, 2, 3) >>> c[1,...] # same as c[1,:,:] or c[1] array([[100, 101, 102], [110, 112, 113]]) >>> c[...,2] # same as c[:,:,2] array([[ 2, 13], [102, 113]]) Iterating over multidimensional arrays is done with respect to the first axis: >>> >>> for row in b: ... print(row) ... [0 1 2 3] [10 11 12 13] [20 21 22 23] [30 31 32 33] [40 41 42 43] However, if one wants to perform an operation on each element in the array, one can use the flat attribute which is an iterator over all the elements of the array: >>> >>> for element in b.flat: ... print(element) ... 0 1 2 3 10 11 12 13 20 21 22 23 30 31 32 33 40 41 42 43 See also Indexing, Indexing (reference), newaxis, ndenumerate, indices Shape Manipulation Changing the shape of an array An array has a shape given by the number of elements along each axis: >>> >>> a = np.floor(10*rg.random((3,4))) >>> a array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) >>> a.shape (3, 4) The shape of an array can be changed with various commands. Note that the following three commands all return a modified array, but do not change the original array: >>> >>> a.ravel() # returns the array, flattened array([3., 7., 3., 4., 1., 4., 2., 2., 7., 2., 4., 9.]) >>> a.reshape(6,2) # returns the array with a modified shape array([[3., 7.], [3., 4.], [1., 4.], [2., 2.], [7., 2.], [4., 9.]]) >>> a.T # returns the array, transposed array([[3., 1., 7.], [7., 4., 2.], [3., 2., 4.], [4., 2., 9.]]) >>> a.T.shape (4, 3) >>> a.shape (3, 4) The order of the elements in the array resulting from ravel() is normally “C-style”, that is, the rightmost index “changes the fastest”, so the element after a[0,0] is a[0,1]. If the array is reshaped to some other shape, again the array is treated as “C-style”. NumPy normally creates arrays stored in this order, so ravel() will usually not need to copy its argument, but if the array was made by taking slices of another array or created with unusual options, it may need to be copied. The functions ravel() and reshape() can also be instructed, using an optional argument, to use FORTRAN-style arrays, in which the leftmost index changes the fastest. The reshape function returns its argument with a modified shape, whereas the ndarray.resize method modifies the array itself: >>> >>> a array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) >>> a.resize((2,6)) >>> a array([[3., 7., 3., 4., 1., 4.], [2., 2., 7., 2., 4., 9.]]) If a dimension is given as -1 in a reshaping operation, the other dimensions are automatically calculated: >>> >>> a.reshape(3,-1) array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) See also ndarray.shape, reshape, resize, ravel Stacking together different arrays Several arrays can be stacked together along different axes: >>> >>> a = np.floor(10*rg.random((2,2))) >>> a array([[9., 7.], [5., 2.]]) >>> b = np.floor(10*rg.random((2,2))) >>> b array([[1., 9.], [5., 1.]]) >>> np.vstack((a,b)) array([[9., 7.], [5., 2.], [1., 9.], [5., 1.]]) >>> np.hstack((a,b)) array([[9., 7., 1., 9.], [5., 2., 5., 1.]]) The function column_stack stacks 1D arrays as columns into a 2D array. It is equivalent to hstack only for 2D arrays: >>> >>> from numpy import newaxis >>> np.column_stack((a,b)) # with 2D arrays array([[9., 7., 1., 9.], [5., 2., 5., 1.]]) >>> a = np.array([4.,2.]) >>> b = np.array([3.,8.]) >>> np.column_stack((a,b)) # returns a 2D array array([[4., 3.], [2., 8.]]) >>> np.hstack((a,b)) # the result is different array([4., 2., 3., 8.]) >>> a[:,newaxis] # view `a` as a 2D column vector array([[4.], [2.]]) >>> np.column_stack((a[:,newaxis],b[:,newaxis])) array([[4., 3.], [2., 8.]]) >>> np.hstack((a[:,newaxis],b[:,newaxis])) # the result is the same array([[4., 3.], [2., 8.]]) On the other hand, the function row_stack is equivalent to vstack for any input arrays. In fact, row_stack is an alias for vstack: >>> >>> np.column_stack is np.hstack False >>> np.row_stack is np.vstack True In general, for arrays with more than two dimensions, hstack stacks along their second axes, vstack stacks along their first axes, and concatenate allows for an optional arguments giving the number of the axis along which the concatenation should happen. Note In complex cases, r_ and c_ are useful for creating arrays by stacking numbers along one axis. They allow the use of range literals (“:”) >>> >>> np.r_[1:4,0,4] array([1, 2, 3, 0, 4]) When used with arrays as arguments, r_ and c_ are similar to vstack and hstack in their default behavior, but allow for an optional argument giving the number of the axis along which to concatenate. See also hstack, vstack, column_stack, concatenate, c_, r_ Splitting one array into several smaller ones Using hsplit, you can split an array along its horizontal axis, either by specifying the number of equally shaped arrays to return, or by specifying the columns after which the division should occur: >>> >>> a = np.floor(10*rg.random((2,12))) >>> a array([[6., 7., 6., 9., 0., 5., 4., 0., 6., 8., 5., 2.], [8., 5., 5., 7., 1., 8., 6., 7., 1., 8., 1., 0.]]) # Split a into 3 >>> np.hsplit(a,3) [array([[6., 7., 6., 9.], [8., 5., 5., 7.]]), array([[0., 5., 4., 0.], [1., 8., 6., 7.]]), array([[6., 8., 5., 2.], [1., 8., 1., 0.]])] # Split a after the third and the fourth column >>> np.hsplit(a,(3,4)) [array([[6., 7., 6.], [8., 5., 5.]]), array([[9.], [7.]]), array([[0., 5., 4., 0., 6., 8., 5., 2.], [1., 8., 6., 7., 1., 8., 1., 0.]])] vsplit splits along the vertical axis, and array_split allows one to specify along which axis to split. Copies and Views When operating and manipulating arrays, their data is sometimes copied into a new array and sometimes not. This is often a source of confusion for beginners. There are three cases: No Copy at All Simple assignments make no copy of objects or their data. >>> >>> a = np.array([[ 0, 1, 2, 3], ... [ 4, 5, 6, 7], ... [ 8, 9, 10, 11]]) >>> b = a # no new object is created >>> b is a # a and b are two names for the same ndarray object True Python passes mutable objects as references, so function calls make no copy. >>> >>> def f(x): ... print(id(x)) ... >>> id(a) # id is a unique identifier of an object 148293216 # may vary >>> f(a) 148293216 # may vary View or Shallow Copy Different array objects can share the same data. The view method creates a new array object that looks at the same data. >>> >>> c = a.view() >>> c is a False >>> c.base is a # c is a view of the data owned by a True >>> c.flags.owndata False >>> >>> c = c.reshape((2, 6)) # a's shape doesn't change >>> a.shape (3, 4) >>> c[0, 4] = 1234 # a's data changes >>> a array([[ 0, 1, 2, 3], [1234, 5, 6, 7], [ 8, 9, 10, 11]]) Slicing an array returns a view of it: >>> >>> s = a[ : , 1:3] # spaces added for clarity; could also be written "s = a[:, 1:3]" >>> s[:] = 10 # s[:] is a view of s. Note the difference between s = 10 and s[:] = 10 >>> a array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]]) Deep Copy The copy method makes a complete copy of the array and its data. >>> >>> d = a.copy() # a new array object with new data is created >>> d is a False >>> d.base is a # d doesn't share anything with a False >>> d[0,0] = 9999 >>> a array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]]) Sometimes copy should be called after slicing if the original array is not required anymore. For example, suppose a is a huge intermediate result and the final result b only contains a small fraction of a, a deep copy should be made when constructing b with slicing: >>> >>> a = np.arange(int(1e8)) >>> b = a[:100].copy() >>> del a # the memory of ``a`` can be released. If b = a[:100] is used instead, a is referenced by b and will persist in memory even if del a is executed. Functions and Methods Overview Here is a list of some useful NumPy functions and methods names ordered in categories. See Routines for the full list. Array Creation arange, array, copy, empty, empty_like, eye, fromfile, fromfunction, identity, linspace, logspace, mgrid, ogrid, ones, ones_like, r_, zeros, zeros_like Conversions ndarray.astype, atleast_1d, atleast_2d, atleast_3d, mat Manipulations array_split, column_stack, concatenate, diagonal, dsplit, dstack, hsplit, hstack, ndarray.item, newaxis, ravel, repeat, reshape, resize, squeeze, swapaxes, take, transpose, vsplit, vstack Questions all, any, nonzero, where Ordering argmax, argmin, argsort, max, min, ptp, searchsorted, sort Operations choose, compress, cumprod, cumsum, inner, ndarray.fill, imag, prod, put, putmask, real, sum Basic Statistics cov, mean, std, var Basic Linear Algebra cross, dot, outer, linalg.svd, vdot Less Basic Broadcasting rules Broadcasting allows universal functions to deal in a meaningful way with inputs that do not have exactly the same shape. The first rule of broadcasting is that if all input arrays do not have the same number of dimensions, a “1” will be repeatedly prepended to the shapes of the smaller arrays until all the arrays have the same number of dimensions. The second rule of broadcasting ensures that arrays with a size of 1 along a particular dimension act as if they had the size of the array with the largest shape along that dimension. The value of the array element is assumed to be the same along that dimension for the “broadcast” array. After application of the broadcasting rules, the sizes of all arrays must match. More details can be found in Broadcasting. Advanced indexing and index tricks NumPy offers more indexing facilities than regular Python sequences. In addition to indexing by integers and slices, as we saw before, arrays can be indexed by arrays of integers and arrays of booleans. Indexing with Arrays of Indices >>> >>> a = np.arange(12)**2 # the first 12 square numbers >>> i = np.array([1, 1, 3, 8, 5]) # an array of indices >>> a[i] # the elements of a at the positions i array([ 1, 1, 9, 64, 25]) >>> >>> j = np.array([[3, 4], [9, 7]]) # a bidimensional array of indices >>> a[j] # the same shape as j array([[ 9, 16], [81, 49]]) When the indexed array a is multidimensional, a single array of indices refers to the first dimension of a. The following example shows this behavior by converting an image of labels into a color image using a palette. >>> >>> palette = np.array([[0, 0, 0], # black ... [255, 0, 0], # red ... [0, 255, 0], # green ... [0, 0, 255], # blue ... [255, 255, 255]]) # white >>> image = np.array([[0, 1, 2, 0], # each value corresponds to a color in the palette ... [0, 3, 4, 0]]) >>> palette[image] # the (2, 4, 3) color image array([[[ 0, 0, 0], [255, 0, 0], [ 0, 255, 0], [ 0, 0, 0]], [[ 0, 0, 0], [ 0, 0, 255], [255, 255, 255], [ 0, 0, 0]]]) We can also give indexes for more than one dimension. The arrays of indices for each dimension must have the same shape. >>> >>> a = np.arange(12).reshape(3,4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> i = np.array([[0, 1], # indices for the first dim of a ... [1, 2]]) >>> j = np.array([[2, 1], # indices for the second dim ... [3, 3]]) >>> >>> a[i, j] # i and j must have equal shape array([[ 2, 5], [ 7, 11]]) >>> >>> a[i, 2] array([[ 2, 6], [ 6, 10]]) >>> >>> a[:, j] # i.e., a[ : , j] array([[[ 2, 1], [ 3, 3]], [[ 6, 5], [ 7, 7]], [[10, 9], [11, 11]]]) In Python, arr[i, j] is exactly the same as arr[(i, j)]—so we can put i and j in a tuple and then do the indexing with that. >>> >>> l = (i, j) # equivalent to a[i, j] >>> a[l] array([[ 2, 5], [ 7, 11]]) However, we can not do this by putting i and j into an array, because this array will be interpreted as indexing the first dimension of a. >>> >>> s = np.array([i, j]) # not what we want >>> a[s] Traceback (most recent call last): File "<stdin>", line 1, in <module> IndexError: index 3 is out of bounds for axis 0 with size 3 # same as a[i, j] >>> a[tuple(s)] array([[ 2, 5], [ 7, 11]]) Another common use of indexing with arrays is the search of the maximum value of time-dependent series: >>> >>> time = np.linspace(20, 145, 5) # time scale >>> data = np.sin(np.arange(20)).reshape(5,4) # 4 time-dependent series >>> time array([ 20. , 51.25, 82.5 , 113.75, 145. ]) >>> data array([[ 0. , 0.84147098, 0.90929743, 0.14112001], [-0.7568025 , -0.95892427, -0.2794155 , 0.6569866 ], [ 0.98935825, 0.41211849, -0.54402111, -0.99999021], [-0.53657292, 0.42016704, 0.99060736, 0.65028784], [-0.28790332, -0.96139749, -0.75098725, 0.14987721]]) # index of the maxima for each series >>> ind = data.argmax(axis=0) >>> ind array([2, 0, 3, 1]) # times corresponding to the maxima >>> time_max = time[ind] >>> >>> data_max = data[ind, range(data.shape[1])] # => data[ind[0],0], data[ind[1],1]... >>> time_max array([ 82.5 , 20. , 113.75, 51.25]) >>> data_max array([0.98935825, 0.84147098, 0.99060736, 0.6569866 ]) >>> np.all(data_max == data.max(axis=0)) True You can also use indexing with arrays as a target to assign to: >>> >>> a = np.arange(5) >>> a array([0, 1, 2, 3, 4]) >>> a[[1,3,4]] = 0 >>> a array([0, 0, 2, 0, 0]) However, when the list of indices contains repetitions, the assignment is done several times, leaving behind the last value: >>> >>> a = np.arange(5) >>> a[[0,0,2]]=[1,2,3] >>> a array([2, 1, 3, 3, 4]) This is reasonable enough, but watch out if you want to use Python’s += construct, as it may not do what you expect: >>> >>> a = np.arange(5) >>> a[[0,0,2]]+=1 >>> a array([1, 1, 3, 3, 4]) Even though 0 occurs twice in the list of indices, the 0th element is only incremented once. This is because Python requires “a+=1” to be equivalent to “a = a + 1”. Indexing with Boolean Arrays When we index arrays with arrays of (integer) indices we are providing the list of indices to pick. With boolean indices the approach is different; we explicitly choose which items in the array we want and which ones we don’t. The most natural way one can think of for boolean indexing is to use boolean arrays that have the same shape as the original array: >>> >>> a = np.arange(12).reshape(3,4) >>> b = a > 4 >>> b # b is a boolean with a's shape array([[False, False, False, False], [False, True, True, True], [ True, True, True, True]]) >>> a[b] # 1d array with the selected elements array([ 5, 6, 7, 8, 9, 10, 11]) This property can be very useful in assignments: >>> >>> a[b] = 0 # All elements of 'a' higher than 4 become 0 >>> a array([[0, 1, 2, 3], [4, 0, 0, 0], [0, 0, 0, 0]]) You can look at the following example to see how to use boolean indexing to generate an image of the Mandelbrot set: >>> import numpy as np import matplotlib.pyplot as plt def mandelbrot( h,w, maxit=20 ): """Returns an image of the Mandelbrot fractal of size (h,w).""" y,x = np.ogrid[ -1.4:1.4:h*1j, -2:0.8:w*1j ] c = x+y*1j z = c divtime = maxit + np.zeros(z.shape, dtype=int) for i in range(maxit): z = z**2 + c diverge = z*np.conj(z) > 2**2 # who is diverging div_now = diverge & (divtime==maxit) # who is diverging now divtime[div_now] = i # note when z[diverge] = 2 # avoid diverging too much return divtime plt.imshow(mandelbrot(400,400)) ../_images/quickstart-1.png The second way of indexing with booleans is more similar to integer indexing; for each dimension of the array we give a 1D boolean array selecting the slices we want: >>> >>> a = np.arange(12).reshape(3,4) >>> b1 = np.array([False,True,True]) # first dim selection >>> b2 = np.array([True,False,True,False]) # second dim selection >>> >>> a[b1,:] # selecting rows array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> a[b1] # same thing array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> a[:,b2] # selecting columns array([[ 0, 2], [ 4, 6], [ 8, 10]]) >>> >>> a[b1,b2] # a weird thing to do array([ 4, 10]) Note that the length of the 1D boolean array must coincide with the length of the dimension (or axis) you want to slice. In the previous example, b1 has length 3 (the number of rows in a), and b2 (of length 4) is suitable to index the 2nd axis (columns) of a. The ix_() function The ix_ function can be used to combine different vectors so as to obtain the result for each n-uplet. For example, if you want to compute all the a+b*c for all the triplets taken from each of the vectors a, b and c: >>> >>> a = np.array([2,3,4,5]) >>> b = np.array([8,5,4]) >>> c = np.array([5,4,6,8,3]) >>> ax,bx,cx = np.ix_(a,b,c) >>> ax array([[[2]], [[3]], [[4]], [[5]]]) >>> bx array([[[8], [5], [4]]]) >>> cx array([[[5, 4, 6, 8, 3]]]) >>> ax.shape, bx.shape, cx.shape ((4, 1, 1), (1, 3, 1), (1, 1, 5)) >>> result = ax+bx*cx >>> result array([[[42, 34, 50, 66, 26], [27, 22, 32, 42, 17], [22, 18, 26, 34, 14]], [[43, 35, 51, 67, 27], [28, 23, 33, 43, 18], [23, 19, 27, 35, 15]], [[44, 36, 52, 68, 28], [29, 24, 34, 44, 19], [24, 20, 28, 36, 16]], [[45, 37, 53, 69, 29], [30, 25, 35, 45, 20], [25, 21, 29, 37, 17]]]) >>> result[3,2,4] 17 >>> a[3]+b[2]*c[4] 17 You could also implement the reduce as follows: >>> >>> def ufunc_reduce(ufct, *vectors): ... vs = np.ix_(*vectors) ... r = ufct.identity ... for v in vs: ... r = ufct(r,v) ... return r and then use it as: >>> >>> ufunc_reduce(np.add,a,b,c) array([[[15, 14, 16, 18, 13], [12, 11, 13, 15, 10], [11, 10, 12, 14, 9]], [[16, 15, 17, 19, 14], [13, 12, 14, 16, 11], [12, 11, 13, 15, 10]], [[17, 16, 18, 20, 15], [14, 13, 15, 17, 12], [13, 12, 14, 16, 11]], [[18, 17, 19, 21, 16], [15, 14, 16, 18, 13], [14, 13, 15, 17, 12]]]) The advantage of this version of reduce compared to the normal ufunc.reduce is that it makes use of the Broadcasting Rules in order to avoid creating an argument array the size of the output times the number of vectors. Indexing with strings See Structured arrays. Linear Algebra Work in progress. Basic linear algebra to be included here. Simple Array Operations See linalg.py in numpy folder for more. >>> >>> import numpy as np >>> a = np.array([[1.0, 2.0], [3.0, 4.0]]) >>> print(a) [[1. 2.] [3. 4.]] >>> a.transpose() array([[1., 3.], [2., 4.]]) >>> np.linalg.inv(a) array([[-2. , 1. ], [ 1.5, -0.5]]) >>> u = np.eye(2) # unit 2x2 matrix; "eye" represents "I" >>> u array([[1., 0.], [0., 1.]]) >>> j = np.array([[0.0, -1.0], [1.0, 0.0]]) >>> j @ j # matrix product array([[-1., 0.], [ 0., -1.]]) >>> np.trace(u) # trace 2.0 >>> y = np.array([[5.], [7.]]) >>> np.linalg.solve(a, y) array([[-3.], [ 4.]]) >>> np.linalg.eig(j) (array([0.+1.j, 0.-1.j]), array([[0.70710678+0.j , 0.70710678-0.j ], [0. -0.70710678j, 0. +0.70710678j]])) Parameters: square matrix Returns The eigenvalues, each repeated according to its multiplicity. The normalized (unit "length") eigenvectors, such that the column ``v[:,i]`` is the eigenvector corresponding to the eigenvalue ``w[i]`` . Tricks and Tips Here we give a list of short and useful tips. “Automatic” Reshaping To change the dimensions of an array, you can omit one of the sizes which will then be deduced automatically: >>> >>> a = np.arange(30) >>> b = a.reshape((2, -1, 3)) # -1 means "whatever is needed" >>> b.shape (2, 5, 3) >>> b array([[[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8], [ 9, 10, 11], [12, 13, 14]], [[15, 16, 17], [18, 19, 20], [21, 22, 23], [24, 25, 26], [27, 28, 29]]]) Vector Stacking How do we construct a 2D array from a list of equally-sized row vectors? In MATLAB this is quite easy: if x and y are two vectors of the same length you only need do m=[x;y]. In NumPy this works via the functions column_stack, dstack, hstack and vstack, depending on the dimension in which the stacking is to be done. For example: >>> >>> x = np.arange(0,10,2) >>> y = np.arange(5) >>> m = np.vstack([x,y]) >>> m array([[0, 2, 4, 6, 8], [0, 1, 2, 3, 4]]) >>> xy = np.hstack([x,y]) >>> xy array([0, 2, 4, 6, 8, 0, 1, 2, 3, 4]) The logic behind those functions in more than two dimensions can be strange. See also NumPy for Matlab users Histograms The NumPy histogram function applied to an array returns a pair of vectors: the histogram of the array and a vector of the bin edges. Beware: matplotlib also has a function to build histograms (called hist, as in Matlab) that differs from the one in NumPy. The main difference is that pylab.hist plots the histogram automatically, while numpy.histogram only generates the data. >>> import numpy as np rg = np.random.default_rng(1) import matplotlib.pyplot as plt # Build a vector of 10000 normal deviates with variance 0.5^2 and mean 2 mu, sigma = 2, 0.5 v = rg.normal(mu,sigma,10000) # Plot a normalized histogram with 50 bins plt.hist(v, bins=50, density=1) # matplotlib version (plot) # Compute the histogram with numpy and then plot it (n, bins) = np.histogram(v, bins=50, density=True) # NumPy version (no plot) plt.plot(.5*(bins[1:]+bins[:-1]), n) ../_images/quickstart-2.png Further reading The Python tutorial NumPy Reference SciPy Tutorial SciPy Lecture Notes A matlab, R, IDL, NumPy/SciPy dictionary © Copyright 2008-2020, The SciPy community. Last updated on Jun 29, 2020. Created using Sphinx 2.4.4.

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CC-FlexiMIDI-V1R0-03.09.2009 and CC-FlexiMIDI-V1R1-03.09.2009 : Updated to CC-FlexiMIDI-V1R2-12.29.2019 on December 29, 2019 ================================ BACKGROUND: CC-FlexiMIDI-V1R0-03.09.2009 - A Hardware M.I.D.I. Interface Program Pak Cartridge for the Tandy Radio Shack TRS-80 Color Computer 1, 2 and 3, including clones and compatibles (Tano Dragon 64, Dragon Data D32, D64 and D200, Tandy Data Products TDP-100, etcetera) by "Little" John Eric Turner and his father "Big" John Robert (J.R.) Turner. Copyright 09 March 2009. Originally released as Open-Source Hardware on March 9, 2009. Subsequently released under a Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) License on 21 May 2019. ENJOY! Note that the original design is crap, however, a debugged version is forthcoming from "Uncle" Robert "The R.A.T." Allen Turner. CC-FlexiMIDI-V1R0-03.09.2009 has been updated to CC-FlexiMIDI-V1R1-03.09.2009 by R.A. Turner on May 21, 2019, just over ten years after the initial release of Version 1, Revision 0. Version 1, Revision 1 is Copyright (C) 2019 by the above mentioned parties and is released under a Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) License on 21 May 2019. =============================== DESCRIPTION: This project is an updated version of the "CC-FlexiMIDI-V1R0-03.09.2009", a hardware MIDI Interface Card for the Tandy Radio Shack TRS-80 Color Computer 1,2 and 3, Dragon Data Dragon D32, D64 and D200, Tandy Data Products TDP-100, Tano Dragon 64 and other clones and compatibles. The original "CC-FlexiMIDI-V1R0-03.09.2009" was designed by my nephew, "Little John", on March 8-9, 2009 as a learning excercise. He was teaching himself to use E.A.G.L.E. in order to design products for the TRS-80 Color Computer line of computers, with the help of his father, my brother, "Big John" or "J.R." as he is known to me. The "CC-FlexiMIDI-V1R0-03.09.2009" was among his very first (learning the art of circuit design) works. It is a terrible design only because he knew nothing about circuit design at the time and it does not appear that his father, "Big John" (J.R.) offered any input in regards to this particular design. I, "Uncle" Robert "The R.A.T." Allen Turner, have decided to polish up the design a bit and lay out a manufacturable Printed Circuit Board which I will release under a Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) License. As such, I will analyze "Little John's" original design and then provide my improved version. The original "CC-FlexiMIDI-V1R0-03.09.2009" design files, as provided by "Little John" and his father (J.R.) are contained in the "Original (Deprecated)" folder of this archive and should be referenced for this initial analysis of the design. ================================ ANALYSIS OF ORIGINAL DESIGN: Load up the "CC-FlexiMIDI-V1R0-03.09.2009.sch" schematic file and have it handy for this discussion. Starting with Page 1 of the schematic, we see the expected cartridge (program pak) plug followed by an oddly interesting series of "purported" interrupts, labeled IRQ0* and IRQ1* (the "*" indicates low-level triggering, or active low). These "Interrupts", IRQ0* and IRQ1* appear to go, through disable jumpers, to Pins 1 and 2 of the CoCo Cartridge (Program PAK) Connector. This is both ODD and INTERESTING because Pins 1 and 2 of that connector are -12V and +12V, respectively, on ALL CoCo 1's, TDP-100's and ALL Multi-Pak Interfaces. Both of these pins are +12V on the Dragon computers. Those self-same pins, however, are NOT connected to anything on ANY stock, unmodified, CoCo 2 or 3 computers. I am thus forced to draw the following conclusion: "Little John" apparently allowed for using Pins 1 and 2 of a CoCo 2 or 3 Cartridge Slot to connect to any desired interrupt within the CoCo 2 or 3. That is, a CoCo 2 or 3 might be modified to connect Pins 1 and/or 2 of the Cartridge Slot to any of the CPU Interrupts, the PIA Interrupt (CART*), G.I.M.E. (A.C.V.C.) Interrupts (CoCo 3 only), etcetera. This is an UNECCESSARY feature of the "FlexiMIDI" design and my initial inclination was to omit it from the design. However, since there are jumpers that allow these "hacked in" custom interrupts to be disabled (removed) via JP1 and/or JP2 or connected together (wire or'ed) via JP3, I have decided to leave them in the design should anyone be so inclined as to use this custom interrupt scheme for experimentation or otherwise. Also on Page 1 is a fairly standard RESET switch which I would imagine could prove to be quite convenient but potentially problematic if the device is plugged into a Multi-Pak Interface (RESET* is buffered in a single direction in the M.P.I. and should not be triggered from any cartridge plugged into the M.P.I.), Power ON L.E.D. (which I assume might be quite distracting) and some pull-up resistors for the interrupts, custom and legit. Lastly, there is a 220uF Electrolytic Capacitor for Vcc (+5V) filtering. Ideally, a low ESR Electrolytic should be used, however, paralleling a 220uF Electrolytic with a .1uF Ceramic Disc should provide approximately the same result as a single Low ESR type. Moving on to Page 2, we see a crystal oscillator comprised of three inverters, three resistors and a crystal rated at 1 to 2 MHz. The third inverter actually acts as a buffer and "shaper". Schmitt Trigger inverters are used, although this is not actually necessary it does provide a nice, sharp square wave. Without the hysteresis provided by the schmitt triggers the waveform would appear quasi-sinusoidal at the crystal frequency if viewed on an oscilloscope, but would still function just fine. The output of that third inverter, the buffer stage, is fed into a pair of toggling D type Flip-Flops which provide a divide by two output and a divide by four output, either of which may be selected by jumper JP4. Ideally, we want a solid 500KHz squarewave as the ACIA Clock (which "Little John" labeled "MIDICLOCK" or "MIDICLK"). If a 1MHz crystal is used we would place JP4 on Pins 1 and 2. With a 2MHz crystal we would connect JP4 Pins 2 and 3. This is flexible in that it allows the use of either a 1MHz or 2MHz crystal, whichever might be handy. In my case, and for the redesign, I have a large stock of 16MHz half-can oscillators and so this is what I will be using in the redesign. The 500KHz then, will be derived from the 16MHz oscillator by using the 16MHz to clock a binary counter. At the bottom left of Page 2, we also see three inverters used to invert A7, A4 and A3. This appears to be part of the "address decoding" scheme. Lastly, we see the decoupling capacitors for the inverters and "d-flops". This page (page 2) of the design is fairly solid and well designed. Moving on to page 3, we see the "heart" of the "CC-FlexiMIDI-V1R0-03.09.2009" MIDI Interface Pak. A 74LS133 13-Input NAND is used for address decoding. The 74LS133 in conjunction with the aforementioned inverters and the ACIA enable lines fully decode the ACIA into two consectutive memory addresses. With this, we can now decipher the addressing of the device. This will be done by writing A15 - A0 and filling in the "bit status" required to enable the ACIA, as follows: ========================================================================= | A15 A14 A13 A12 | A11 A10 A09 A08 | A07 A06 A05 A04 | A03 A02 A01 A00 | |=================|=================|=================|=================| | 1 1 1 1 | 1 1 1 1 | 0 1 1 0 | 0 1 1 x | |=================|=================|=================|================== | F | F | 6 | x | ========================================================================= Looking at the above table and noting that A0 selects one of the two internal ACIA registers, it is clear that "Little John" mapped the ACIA to 0xFF66 and 0xFF67. This seems ODD because the most popular MIDI Packs designed for use with the Tandy Radio Shack TRS-80 Color Computer decode the ACIA to 0xFF6E and 0xFF6F. A bit of research, however, led to the discovery that the original CoCo MIDI Pack, "The Colorchestra", mapped the ACIA at 0xFF66 and 0xFF67. The "Colorchestra" was released in 1985 by "Color Horizons" and I own two of them. The aforementioned "research" was simply me looking at the "Colorchestra" P.C.B. and deciphering the address decoding which turns out to be 0xFF66-67. I assume that "Little John" arrived at the 0xFF66-67 addressing in a similar manner as to that just mentioned. It would be relatively easy to redesign the "FlexiMIDI" to respond to both sets of addresses thus guaranteeing compatibility with everything. I have decided, however, that the redesign will feature a semi-programmable address decoder allowing the ACIA to be mapped to any two consecutive addresses within the 0xFF6n area. This will allow the "Flexi-MIDI" to be even more flexible. Setting the address decoder to respond to 0xFF66-67 will make the device "Colorchestra" compatible, whilst setting the decoder to respond to 0xFF6E-6F will make it compatible with the MIDI Interfaces produced by Speech Systems, MusicWare, Rulaford Research, Glenside CoCo Club and other CoCo MIDI Packs. As mentioned, it would be relatively easy to hardwire the decoder to respond to both the 0xFF66-67 and the 0xFF6E-6F address ranges, but I feel that this is unneccesary. Next, we see the 6850 ACIA. This is the "true heart" of the device - a hardware serial port. Looking at the 6850 section of this page of the schematic, we see yet another oddly interesting Interrupt Selection circuit. It is in the form of a 2x4 Jumper Block. This appears to allow selection of any 1 of 4 interrupts to be triggered by the ACIA. IRQ0* and IRQ1* are the previously mentioned "custom" interrupts. NMI* is the 6809 or G.I.M.E./A.C.V.C. Non-Maskable Interrupt Input. The last interrupt on the 2x4 block is the CART* interrupt. This is actually the 6809 or G.I.M.E. IRQ* line that is passed through a PIA inside the CoCo/Dragon. This, the CART* interrupt is the one that should be used for compatibility. The remaining circuitry on Page 3 are fairly standard circuits for MIDI IN, OUT and THROUGH. These go to 5-pin headers. It appears that "Little John" intended for MIDI Cable ends to be soldered to these headers. The redesign will feature 5-pin DIN MIDI connectors. I do see some potential problems with these MIDI IN, OUT and THRU connections on "Little John's" original design. The first problem that I notice is that the MIDI Ground Pins are connected to the same Ground (common or GND) as the computer and MIDI Pack circuitry. This is no good as it violates the MIDI specification and defeats the purpose of the opto-isolator. Thus, the redesign will sever the ground connection of the DIN connectors from the ground connection of the MIDI Interface Pak circuitry. Next, the 330 Ohm (330R) pull-up resistor connected to the output of the opto-isolator should probably be 270R, however, the device should work fine with the 330R resistor. The redesign will have this changed to 270R. The 10K resistor connected to the "BASE" of the opto-isolator darlington-transistor pair should not be needed. I will allow for it in the redesign for testing purposes. The output of the opto-isolator is sent through two schmitt trigger inverters before being applied to the "Receive Data" input of the ACIA. I am drawing the following conclusion in regards to those two inverters: It seems the design was originally intended for use with a Sharp PC-900 or PC-900V digital opto-isolator which has an internal schmitt trigger, the hysteresis of which provides nice, sharp waveform edges. It appears that "Little John" decided, instead, to use a 6N138 opto-isolator, which does not have hysteresis (schmitt triggering) and thus he must have included the two inverters to alleviate this perceived problem. I am relatively certain, however, that these two inverters are unneccessary and thus I will remove them in the redesign. Had I not used two of the inverters in the hex-inverter package for address decoding, I might have left these two inverters in the redesign, however, I decided the savings of one chip was worth eliminating these two inverters. Hopefully, results will be satisfactory. That is about it for the initial analysis of "Little John's" original design. I shall now proceed to design a slightly improved and, hopefully, manufacturable version of "Little John's CC-FlexiMIDI-V1R0-03.09.2009" Hardware M.I.D.I. Interface Pack. This redesign will be titled: "CC-FlexiMIDI-V1R1-03.09.2009". ================================ THE REDESIGN: Load up the NEW design from the CURRENT folder in the archive and use it to follow this discussion. Starting with Page 1 of the schematic, I will start the redesign with the Cartridge Program Pak Slot Plug (Edge-Card or Edge-Fingers). This is what will actually plug into the cartridge port on the computer or Multi-Pak Interface (M.P.I.). Next, I will add an edge card socket wired in parallel to the edge-fingers. This is based on "Little John's" Universal Footprint which means that you can fit either a 40-pin card socket or a 40-pin header. This will allow an additional cartridge or other hardware to be plugged directly into the MIDI Interface, thus eliminating the need for a "y-cable" or Multi-Pak Interface. The +5V is filtered with a 220uF Electrolytic Capacitor in parallel with a .1uF Ceramic Disc or Dacron/Polyester/Mylar capacitor. A Power ON L.E.D. indicator is included here, along with an enable/disable jumper. Removing the jumper disables the Power ON L.E.D. should it become a distraction. Next, I'll add in the "CUSTOM" Interrupts, including their jumpers. The jumpers should be REMOVED from all of these if the device is to be used with a CoCo 1 and/or M.P.I. (Multi-Pak Interface) or with ANY of the CoCo Clones and/or compatibles, including the Dragon. In actuality, these jumpers should never be needed and thus should never be installed - they are for experimental purposes only. Removing the jumpers prevents the accidental application of +/-12V to the IRQ* output pin of the ACIA which would fry the ACIA. I have included 680R "failsafe" resistors, but it is likely that they would not prevent a fried ACIA. Lastly, I have included the RESET Switch for convenience. The RESET switch should NEVER be pressed if the device is inserted in a Multi-Pak Interface as you may blow the 74LS367 in the M.P.I. That is about it for Page 1 of the redesign. Moving on to Page 2: This page is exclusively dedicated to the Baud Rate Generator for the ACIA. Starting at the left, we see the bypass capacitors for the 74LS590 counter. I have used both a 10uF Electrolytic and a .1uF (100nF) Ceramic Disc. This would be important for a ripple counter, however, the LS590 is a synchronous counter and so the Electrolytic could be omitted. I chose to leave it in. There is also a bypass capacitor for the 16MHz oscillator can. I created a dual-footprint for the oscillator can which allows the use of a full or half can oscillator. The 16MHz is fed into the LS590 counter which provides a choice of ten different clocks for the ACIA. For compatibility with existing standard MIDI packs for the CoCo, the 500KHz clock should be selected. The LS590 has an output register which is clocked by the same 16MHz that clocks the counter section. The enable pin of the oscillator is connected to system RESET* which prevents it from oscillating when the system is in a reset state. This pin could have been left floating causing the oscillator to always oscillate. It will work either way. Page 3 is the semi-programmable address decoder. The 74LS133 in conjunction with the two inverters decodes 0xFF6n - the output will go low on any access to the 0xFF6x range. Only 12 of the 13 inputs to the LS133 were needed. The unused input could be connected to Vcc, E or RESET*. It is important to gate the E Clock in at some point and it could have been done here. I chose to connect the input to RESET*. The ACIA actually has an E Clock input which gates it with the E-Clock so it probably does not need to be gated to the address decoder, though, as you'll see, I gated the E-Clock into the next stage. The 74LS138 decodes 1 of 8 sets of even/odd addresses in the 0xFF6n range (it is enabled by the output of the LS133 and the E-Clock).) So, when any address in the 0xFF6n range appears on the address buss during the high time of the E-clock, the LS138 is enabled and decodes A1-A3 into 1-of-8 chip selects. For maximum compatibility, the 0xFF6E-F output should be selected. Page 4: This is the 6850 ACIA. This should be either a 68B50 or a 63B50 or 63C50 for operation at up to 2MHz CPU Clocks. This should be pretty self-explanatory. The 6850 datasheet can fill in any necessary details. Page 5: This is a fairly standard MIDI IN circuit. There are two optocouplers here: a 6N138 and a PC-900 - You should use ONLY ONE, not both. R9 is only needed if you use the 6N138. The diode is a 1N4148 or 1N914A. Page 6: This is a fairly standard MIDI Out circuit. Page 7: This is the final page and is a fairly standard MIDI Thru circuit. It simply echoes the MIDI In. Well, that's about it for a redesign of "Little John's" original. I am ordering some prototype boards to see if this thing will work. Updated to CC-FlexiMIDI-V1R2-12.29.2019 on December 29, 2019 - This minor update: A Universal 5-Pin DIN component was created and the GND Connection was reconnected to MIDI OUT and MIDI THRU. NO GND connection was made to MIDI IN. This should now create a proper MIDI Interface.

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