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Assigning a matrix value to a variable or retrieving a value from a matrix
I am trying to put values determined by matrix operations, thus in a matrix, as values in a separate function.
I just need a way to get out the x and y values to use them.
- Are you trying to sub them in to solve the equation? How is t defined? Is Function a string? – Freddy Mcloughlan Mar 24, 2022 at 0:57
2 Answers 2
If you just want x and y from your matrix and assign them to a variable that you can use in your equation
If you actually have a matrix like with numpy then maybe the following question may be more what you are looking for.
If you want to access the x and y values from Matrix
If you want to sub in those values:
If you are trying to sub in the equations, you may like the sympy library
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You can declare an array to work with a set of values of the same data type . An array is a single variable with many compartments to store values, while a typical variable has only one storage compartment in which it can store only one value. Refer to the array as a whole when you want to refer to all the values it holds, or you can refer to its individual elements.
For example, to store daily expenses for each day of the year, you can declare one array variable with 365 elements, rather than declaring 365 variables. Each element in an array contains one value. The following statement declares the array variable with 365 elements. By default, an array is indexed beginning with zero, so the upper bound of the array is 364 rather than 365.
To set the value of an individual element, you specify the element's index. The following example assigns an initial value of 20 to each element in the array.
Changing the lower bound
Use the Option Base statement at the top of a module to change the default index of the first element from 0 to 1. In the following example, the Option Base statement changes the index for the first element, and the Dim statement declares the array variable with 365 elements.
You can also explicitly set the lower bound of an array by using a To clause, as shown in the following example.
Storing Variant values in arrays
There are two ways to create arrays of Variant values. One way is to declare an array of Variant data type , as shown in the following example:
The other way is to assign the array returned by the Array function to a Variant variable, as shown in the following example.
You identify the elements in an array of Variant values by index, no matter which technique you use to create the array. For example, the following statement can be added to either of the preceding examples.
Using multidimensional arrays
In Visual Basic, you can declare arrays with up to 60 dimensions. For example, the following statement declares a 2-dimensional, 5-by-10 array.
If you think of the array as a matrix, the first argument represents the rows and the second argument represents the columns.
Use nested For...Next statements to process multidimensional arrays. The following procedure fills a two-dimensional array with Single values.
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Indexing on ndarrays #
ndarrays can be indexed using the standard Python x[obj] syntax, where x is the array and obj the selection. There are different kinds of indexing available depending on obj : basic indexing, advanced indexing and field access.
Most of the following examples show the use of indexing when referencing data in an array. The examples work just as well when assigning to an array. See Assigning values to indexed arrays for specific examples and explanations on how assignments work.
Note that in Python, x[(exp1, exp2, ..., expN)] is equivalent to x[exp1, exp2, ..., expN] ; the latter is just syntactic sugar for the former.
Basic indexing #
Single element indexing #.
Single element indexing works exactly like that for other standard Python sequences. It is 0-based, and accepts negative indices for indexing from the end of the array.
It is not necessary to separate each dimension’s index into its own set of square brackets.
Note that if one indexes a multidimensional array with fewer indices than dimensions, one gets a subdimensional array. For example:
That is, each index specified selects the array corresponding to the rest of the dimensions selected. In the above example, choosing 0 means that the remaining dimension of length 5 is being left unspecified, and that what is returned is an array of that dimensionality and size. It must be noted that the returned array is a view , i.e., it is not a copy of the original, but points to the same values in memory as does the original array. In this case, the 1-D array at the first position (0) is returned. So using a single index on the returned array, results in a single element being returned. That is:
So note that x[0, 2] == x though the second case is more inefficient as a new temporary array is created after the first index that is subsequently indexed by 2.
NumPy uses C-order indexing. That means that the last index usually represents the most rapidly changing memory location, unlike Fortran or IDL, where the first index represents the most rapidly changing location in memory. This difference represents a great potential for confusion.
Slicing and striding #
Basic slicing extends Python’s basic concept of slicing to N dimensions. Basic slicing occurs when obj is a slice object (constructed by start:stop:step notation inside of brackets), an integer, or a tuple of slice objects and integers. Ellipsis and newaxis objects can be interspersed with these as well.
The simplest case of indexing with N integers returns an array scalar representing the corresponding item. As in Python, all indices are zero-based: for the i -th index \(n_i\) , the valid range is \(0 \le n_i < d_i\) where \(d_i\) is the i -th element of the shape of the array. Negative indices are interpreted as counting from the end of the array ( i.e. , if \(n_i < 0\) , it means \(n_i + d_i\) ).
All arrays generated by basic slicing are always views of the original array.
NumPy slicing creates a view instead of a copy as in the case of built-in Python sequences such as string, tuple and list. Care must be taken when extracting a small portion from a large array which becomes useless after the extraction, because the small portion extracted contains a reference to the large original array whose memory will not be released until all arrays derived from it are garbage-collected. In such cases an explicit copy() is recommended.
The standard rules of sequence slicing apply to basic slicing on a per-dimension basis (including using a step index). Some useful concepts to remember include:
The basic slice syntax is i:j:k where i is the starting index, j is the stopping index, and k is the step ( \(k\neq0\) ). This selects the m elements (in the corresponding dimension) with index values i , i + k , …, i + (m - 1) k where \(m = q + (r\neq0)\) and q and r are the quotient and remainder obtained by dividing j - i by k : j - i = q k + r , so that i + (m - 1) k < j . For example:
Negative i and j are interpreted as n + i and n + j where n is the number of elements in the corresponding dimension. Negative k makes stepping go towards smaller indices. From the above example:
Assume n is the number of elements in the dimension being sliced. Then, if i is not given it defaults to 0 for k > 0 and n - 1 for k < 0 . If j is not given it defaults to n for k > 0 and -n-1 for k < 0 . If k is not given it defaults to 1. Note that :: is the same as : and means select all indices along this axis. From the above example:
If the number of objects in the selection tuple is less than N , then : is assumed for any subsequent dimensions. For example:
An integer, i , returns the same values as i:i+1 except the dimensionality of the returned object is reduced by 1. In particular, a selection tuple with the p -th element an integer (and all other entries : ) returns the corresponding sub-array with dimension N - 1 . If N = 1 then the returned object is an array scalar. These objects are explained in Scalars .
If the selection tuple has all entries : except the p -th entry which is a slice object i:j:k , then the returned array has dimension N formed by concatenating the sub-arrays returned by integer indexing of elements i , i+k , …, i + (m - 1) k < j ,
Basic slicing with more than one non- : entry in the slicing tuple, acts like repeated application of slicing using a single non- : entry, where the non- : entries are successively taken (with all other non- : entries replaced by : ). Thus, x[ind1, ..., ind2,:] acts like x[ind1][..., ind2, :] under basic slicing.
The above is not true for advanced indexing.
You may use slicing to set values in the array, but (unlike lists) you can never grow the array. The size of the value to be set in x[obj] = value must be (broadcastable to) the same shape as x[obj] .
A slicing tuple can always be constructed as obj and used in the x[obj] notation. Slice objects can be used in the construction in place of the [start:stop:step] notation. For example, x[1:10:5, ::-1] can also be implemented as obj = (slice(1, 10, 5), slice(None, None, -1)); x[obj] . This can be useful for constructing generic code that works on arrays of arbitrary dimensions. See Dealing with variable numbers of indices within programs for more information.
Dimensional indexing tools #
There are some tools to facilitate the easy matching of array shapes with expressions and in assignments.
Ellipsis expands to the number of : objects needed for the selection tuple to index all dimensions. In most cases, this means that the length of the expanded selection tuple is x.ndim . There may only be a single ellipsis present. From the above example:
This is equivalent to:
Each newaxis object in the selection tuple serves to expand the dimensions of the resulting selection by one unit-length dimension. The added dimension is the position of the newaxis object in the selection tuple. newaxis is an alias for None , and None can be used in place of this with the same result. From the above example:
This can be handy to combine two arrays in a way that otherwise would require explicit reshaping operations. For example:
Advanced indexing #
Advanced indexing is triggered when the selection object, obj , is a non-tuple sequence object, an ndarray (of data type integer or bool), or a tuple with at least one sequence object or ndarray (of data type integer or bool). There are two types of advanced indexing: integer and Boolean.
Advanced indexing always returns a copy of the data (contrast with basic slicing that returns a view ).
The definition of advanced indexing means that x[(1, 2, 3),] is fundamentally different than x[(1, 2, 3)] . The latter is equivalent to x[1, 2, 3] which will trigger basic selection while the former will trigger advanced indexing. Be sure to understand why this occurs.
Also recognize that x[[1, 2, 3]] will trigger advanced indexing, whereas due to the deprecated Numeric compatibility mentioned above, x[[1, 2, slice(None)]] will trigger basic slicing.
Integer array indexing #
Integer array indexing allows selection of arbitrary items in the array based on their N -dimensional index. Each integer array represents a number of indices into that dimension.
Negative values are permitted in the index arrays and work as they do with single indices or slices:
If the index values are out of bounds then an IndexError is thrown:
When the index consists of as many integer arrays as dimensions of the array being indexed, the indexing is straightforward, but different from slicing.
Advanced indices always are broadcast and iterated as one :
Note that the resulting shape is identical to the (broadcast) indexing array shapes ind_1, ..., ind_N . If the indices cannot be broadcast to the same shape, an exception IndexError: shape mismatch: indexing arrays could not be broadcast together with shapes... is raised.
Indexing with multidimensional index arrays tend to be more unusual uses, but they are permitted, and they are useful for some problems. We’ll start with the simplest multidimensional case:
In this case, if the index arrays have a matching shape, and there is an index array for each dimension of the array being indexed, the resultant array has the same shape as the index arrays, and the values correspond to the index set for each position in the index arrays. In this example, the first index value is 0 for both index arrays, and thus the first value of the resultant array is y[0, 0] . The next value is y[2, 1] , and the last is y[4, 2] .
If the index arrays do not have the same shape, there is an attempt to broadcast them to the same shape. If they cannot be broadcast to the same shape, an exception is raised:
The broadcasting mechanism permits index arrays to be combined with scalars for other indices. The effect is that the scalar value is used for all the corresponding values of the index arrays:
Jumping to the next level of complexity, it is possible to only partially index an array with index arrays. It takes a bit of thought to understand what happens in such cases. For example if we just use one index array with y:
It results in the construction of a new array where each value of the index array selects one row from the array being indexed and the resultant array has the resulting shape (number of index elements, size of row).
In general, the shape of the resultant array will be the concatenation of the shape of the index array (or the shape that all the index arrays were broadcast to) with the shape of any unused dimensions (those not indexed) in the array being indexed.
From each row, a specific element should be selected. The row index is just [0, 1, 2] and the column index specifies the element to choose for the corresponding row, here [0, 1, 0] . Using both together the task can be solved using advanced indexing:
To achieve a behaviour similar to the basic slicing above, broadcasting can be used. The function ix_ can help with this broadcasting. This is best understood with an example.
From a 4x3 array the corner elements should be selected using advanced indexing. Thus all elements for which the column is one of [0, 2] and the row is one of [0, 3] need to be selected. To use advanced indexing one needs to select all elements explicitly . Using the method explained previously one could write:
However, since the indexing arrays above just repeat themselves, broadcasting can be used (compare operations such as rows[:, np.newaxis] + columns ) to simplify this:
This broadcasting can also be achieved using the function ix_ :
Note that without the np.ix_ call, only the diagonal elements would be selected:
This difference is the most important thing to remember about indexing with multiple advanced indices.
A real-life example of where advanced indexing may be useful is for a color lookup table where we want to map the values of an image into RGB triples for display. The lookup table could have a shape (nlookup, 3). Indexing such an array with an image with shape (ny, nx) with dtype=np.uint8 (or any integer type so long as values are with the bounds of the lookup table) will result in an array of shape (ny, nx, 3) where a triple of RGB values is associated with each pixel location.
Boolean array indexing #
This advanced indexing occurs when obj is an array object of Boolean type, such as may be returned from comparison operators. A single boolean index array is practically identical to x[obj.nonzero()] where, as described above, obj.nonzero() returns a tuple (of length obj.ndim ) of integer index arrays showing the True elements of obj . However, it is faster when obj.shape == x.shape .
If obj.ndim == x.ndim , x[obj] returns a 1-dimensional array filled with the elements of x corresponding to the True values of obj . The search order will be row-major , C-style. If obj has True values at entries that are outside of the bounds of x , then an index error will be raised. If obj is smaller than x it is identical to filling it with False .
A common use case for this is filtering for desired element values. For example, one may wish to select all entries from an array which are not NaN :
Or wish to add a constant to all negative elements:
In general if an index includes a Boolean array, the result will be identical to inserting obj.nonzero() into the same position and using the integer array indexing mechanism described above. x[ind_1, boolean_array, ind_2] is equivalent to x[(ind_1,) + boolean_array.nonzero() + (ind_2,)] .
If there is only one Boolean array and no integer indexing array present, this is straightforward. Care must only be taken to make sure that the boolean index has exactly as many dimensions as it is supposed to work with.
In general, when the boolean array has fewer dimensions than the array being indexed, this is equivalent to x[b, ...] , which means x is indexed by b followed by as many : as are needed to fill out the rank of x. Thus the shape of the result is one dimension containing the number of True elements of the boolean array, followed by the remaining dimensions of the array being indexed:
Here the 4th and 5th rows are selected from the indexed array and combined to make a 2-D array.
From an array, select all rows which sum up to less or equal two:
Combining multiple Boolean indexing arrays or a Boolean with an integer indexing array can best be understood with the obj.nonzero() analogy. The function ix_ also supports boolean arrays and will work without any surprises.
Use boolean indexing to select all rows adding up to an even number. At the same time columns 0 and 2 should be selected with an advanced integer index. Using the ix_ function this can be done with:
Without the np.ix_ call, only the diagonal elements would be selected.
Or without np.ix_ (compare the integer array examples):
Use a 2-D boolean array of shape (2, 3) with four True elements to select rows from a 3-D array of shape (2, 3, 5) results in a 2-D result of shape (4, 5):
Combining advanced and basic indexing #
When there is at least one slice ( : ), ellipsis ( ... ) or newaxis in the index (or the array has more dimensions than there are advanced indices), then the behaviour can be more complicated. It is like concatenating the indexing result for each advanced index element.
In the simplest case, there is only a single advanced index combined with a slice. For example:
In effect, the slice and index array operation are independent. The slice operation extracts columns with index 1 and 2, (i.e. the 2nd and 3rd columns), followed by the index array operation which extracts rows with index 0, 2 and 4 (i.e the first, third and fifth rows). This is equivalent to:
A single advanced index can, for example, replace a slice and the result array will be the same. However, it is a copy and may have a different memory layout. A slice is preferable when it is possible. For example:
The easiest way to understand a combination of multiple advanced indices may be to think in terms of the resulting shape. There are two parts to the indexing operation, the subspace defined by the basic indexing (excluding integers) and the subspace from the advanced indexing part. Two cases of index combination need to be distinguished:
The advanced indices are separated by a slice, Ellipsis or newaxis . For example x[arr1, :, arr2] .
The advanced indices are all next to each other. For example x[..., arr1, arr2, :] but not x[arr1, :, 1] since 1 is an advanced index in this regard.
In the first case, the dimensions resulting from the advanced indexing operation come first in the result array, and the subspace dimensions after that. In the second case, the dimensions from the advanced indexing operations are inserted into the result array at the same spot as they were in the initial array (the latter logic is what makes simple advanced indexing behave just like slicing).
Suppose x.shape is (10, 20, 30) and ind is a (2, 3, 4)-shaped indexing intp array, then result = x[..., ind, :] has shape (10, 2, 3, 4, 30) because the (20,)-shaped subspace has been replaced with a (2, 3, 4)-shaped broadcasted indexing subspace. If we let i, j, k loop over the (2, 3, 4)-shaped subspace then result[..., i, j, k, :] = x[..., ind[i, j, k], :] . This example produces the same result as x.take(ind, axis=-2) .
Let x.shape be (10, 20, 30, 40, 50) and suppose ind_1 and ind_2 can be broadcast to the shape (2, 3, 4). Then x[:, ind_1, ind_2] has shape (10, 2, 3, 4, 40, 50) because the (20, 30)-shaped subspace from X has been replaced with the (2, 3, 4) subspace from the indices. However, x[:, ind_1, :, ind_2] has shape (2, 3, 4, 10, 30, 50) because there is no unambiguous place to drop in the indexing subspace, thus it is tacked-on to the beginning. It is always possible to use .transpose() to move the subspace anywhere desired. Note that this example cannot be replicated using take .
Slicing can be combined with broadcasted boolean indices:
Field access #
If the ndarray object is a structured array the fields of the array can be accessed by indexing the array with strings, dictionary-like.
Indexing x['field-name'] returns a new view to the array, which is of the same shape as x (except when the field is a sub-array) but of data type x.dtype['field-name'] and contains only the part of the data in the specified field. Also, record array scalars can be “indexed” this way.
Indexing into a structured array can also be done with a list of field names, e.g. x[['field-name1', 'field-name2']] . As of NumPy 1.16, this returns a view containing only those fields. In older versions of NumPy, it returned a copy. See the user guide section on Structured arrays for more information on multifield indexing.
If the accessed field is a sub-array, the dimensions of the sub-array are appended to the shape of the result. For example:
Flat Iterator indexing #
x.flat returns an iterator that will iterate over the entire array (in C-contiguous style with the last index varying the fastest). This iterator object can also be indexed using basic slicing or advanced indexing as long as the selection object is not a tuple. This should be clear from the fact that x.flat is a 1-dimensional view. It can be used for integer indexing with 1-dimensional C-style-flat indices. The shape of any returned array is therefore the shape of the integer indexing object.
Assigning values to indexed arrays #
As mentioned, one can select a subset of an array to assign to using a single index, slices, and index and mask arrays. The value being assigned to the indexed array must be shape consistent (the same shape or broadcastable to the shape the index produces). For example, it is permitted to assign a constant to a slice:
or an array of the right size:
Note that assignments may result in changes if assigning higher types to lower types (like floats to ints) or even exceptions (assigning complex to floats or ints):
Unlike some of the references (such as array and mask indices) assignments are always made to the original data in the array (indeed, nothing else would make sense!). Note though, that some actions may not work as one may naively expect. This particular example is often surprising to people:
Where people expect that the 1st location will be incremented by 3. In fact, it will only be incremented by 1. The reason is that a new array is extracted from the original (as a temporary) containing the values at 1, 1, 3, 1, then the value 1 is added to the temporary, and then the temporary is assigned back to the original array. Thus the value of the array at x + 1 is assigned to x three times, rather than being incremented 3 times.
Dealing with variable numbers of indices within programs #
The indexing syntax is very powerful but limiting when dealing with a variable number of indices. For example, if you want to write a function that can handle arguments with various numbers of dimensions without having to write special case code for each number of possible dimensions, how can that be done? If one supplies to the index a tuple, the tuple will be interpreted as a list of indices. For example:
So one can use code to construct tuples of any number of indices and then use these within an index.
Slices can be specified within programs by using the slice() function in Python. For example:
Likewise, ellipsis can be specified by code by using the Ellipsis object:
For this reason, it is possible to use the output from the np.nonzero() function directly as an index since it always returns a tuple of index arrays.
Because of the special treatment of tuples, they are not automatically converted to an array as a list would be. As an example:
Detailed notes #
These are some detailed notes, which are not of importance for day to day indexing (in no particular order):
The native NumPy indexing type is intp and may differ from the default integer array type. intp is the smallest data type sufficient to safely index any array; for advanced indexing it may be faster than other types.
For advanced assignments, there is in general no guarantee for the iteration order. This means that if an element is set more than once, it is not possible to predict the final result.
An empty (tuple) index is a full scalar index into a zero-dimensional array. x[()] returns a scalar if x is zero-dimensional and a view otherwise. On the other hand, x[...] always returns a view.
If a zero-dimensional array is present in the index and it is a full integer index the result will be a scalar and not a zero-dimensional array. (Advanced indexing is not triggered.)
When an ellipsis ( ... ) is present but has no size (i.e. replaces zero : ) the result will still always be an array. A view if no advanced index is present, otherwise a copy.
The nonzero equivalence for Boolean arrays does not hold for zero dimensional boolean arrays.
When the result of an advanced indexing operation has no elements but an individual index is out of bounds, whether or not an IndexError is raised is undefined (e.g. x[, ] with 123 being out of bounds).
When a casting error occurs during assignment (for example updating a numerical array using a sequence of strings), the array being assigned to may end up in an unpredictable partially updated state. However, if any other error (such as an out of bounds index) occurs, the array will remain unchanged.
The memory layout of an advanced indexing result is optimized for each indexing operation and no particular memory order can be assumed.
When using a subclass (especially one which manipulates its shape), the default ndarray.__setitem__ behaviour will call __getitem__ for basic indexing but not for advanced indexing. For such a subclass it may be preferable to call ndarray.__setitem__ with a base class ndarray view on the data. This must be done if the subclasses __getitem__ does not return views.
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The Object.assign() static method copies all enumerable own properties from one or more source objects to a target object . It returns the modified target object.
The target object — what to apply the sources' properties to, which is returned after it is modified.
The source object(s) — objects containing the properties you want to apply.
The target object.
Properties in the target object are overwritten by properties in the sources if they have the same key . Later sources' properties overwrite earlier ones.
The Object.assign() method only copies enumerable and own properties from a source object to a target object. It uses [[Get]] on the source and [[Set]] on the target, so it will invoke getters and setters . Therefore it assigns properties, versus copying or defining new properties. This may make it unsuitable for merging new properties into a prototype if the merge sources contain getters.
For copying property definitions (including their enumerability) into prototypes, use Object.getOwnPropertyDescriptor() and Object.defineProperty() instead.
Both String and Symbol properties are copied.
In case of an error, for example if a property is non-writable, a TypeError is raised, and the target object is changed if any properties are added before the error is raised.
Note: Object.assign() does not throw on null or undefined sources.
Cloning an object
Warning for deep clone.
For deep cloning , we need to use alternatives, because Object.assign() copies property values.
If the source value is a reference to an object, it only copies the reference value.
Merging objects with same properties.
The properties are overwritten by other objects that have the same properties later in the parameters order.
Copying symbol-typed properties
Properties on the prototype chain and non-enumerable properties cannot be copied, primitives will be wrapped to objects, exceptions will interrupt the ongoing copying task, copying accessors, specifications, browser compatibility.
- Polyfill of Object.assign in core-js
- Enumerability and ownership of properties
- Spread in object literals
The most basic method of assigning matrix values is to assign a value for a specific row and column element of the matrix. Simply enter the matrix name, followed by the row and column indices, in parentheses, and then an assignment to a scalar value.
1 If you just want x and y from your matrix and assign them to a variable that you can use in your equation Matrix = [10,11] # What is typically referred to as a list x = Matrix  y = Matrix  print (x) 10 print (y) 11 If you actually have a matrix like with numpy then maybe the following question may be more what you are looking for. Share
numpy.put. #. Replaces specified elements of an array with given values. The indexing works on the flattened target array. put is roughly equivalent to: Target array. Target indices, interpreted as integers. Values to place in a at target indices. If v is shorter than ind it will be repeated as necessary. Specifies how out-of-bounds indices ...
I want the first element of the matrix to have the value of 25, and then I will define the other elements to have different values in subsequent loops. This is the section of code that isn't working. Theme Copy T=ones (t,1); T (1,1)=25; Does anyone have a simple fix to this? Thanks! Dr. Kelsey Joy on 27 Nov 2021 Your code looks good to me.
Trial software assigning values to a matrix Follow 568 views (last 30 days) Show older comments William Hou on 6 Jan 2021 Vote 0 Link Commented: Walter Roberson on 6 Jan 2021 so I have this matrix,and I want everything on the 4th row to become 4s. a=zeros (10,10)
To set the value of an individual element, you specify the element's index. The following example assigns an initial value of 20 to each element in the array. VB Sub FillArray () Dim curExpense (364) As Currency Dim intI As Integer For intI = 0 to 364 curExpense (intI) = 20 Next End Sub Changing the lower bound
Assigning values to indexed arrays# As mentioned, one can select a subset of an array to assign to using a single index, slices, and index and mask arrays. The value being assigned to the indexed array must be shape consistent (the same shape or broadcastable to the shape the index produces).
Description. Properties in the target object are overwritten by properties in the sources if they have the same key. Later sources' properties overwrite earlier ones. The Object.assign () method only copies enumerable and own properties from a source object to a target object. It uses [ [Get]] on the source and [ [Set]] on the target, so it ...