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#The Nerv Matrix Package#
Part of the [Nerv](../README.md) toolkit.
##Description##
###Underlying structure###
In the begining is could be useful to know something about the underlying structure of a __Nerv__ matrix. Please keep in mind that matrice in __Nerv__ is row-major.
Every matrix object is a encapsulation of a C struct that describes the attributes of this matrix.
```
typedef struct Matrix {
size_t stride; /* size of a row */
long ncol, nrow, nmax; /* dimension of the matrix, nmax is simply nrow * ncol */
union {
float *f;
double *d;
long *i;
} data; /* pointer to actual storage */
long *data_ref;
} Matrix;
```
It is worth mentioning that that `data_ref` is a counter which counts the number of references to its memory space, mind that it will also be increased when a row of the matrix is referenced(`col = m[2]`). A __Nerv__ matrix will deallocate its space when this counter is decreased to zero.
Also note that all assigning operation in __Nerv__ is reference copy, you can use `copy_tod` or `copy_toh` method to copy value. Also, row assigning operations like `m1[2]=m2[3]` is forbidden in __Nerv__.
###Class hierarchy###
The class hierarchy of the matrix classes can be clearly observed in `matrix/init.c`.
First there is a abstract base class __Nerv.Matrix__, which is inherited by __Nerv.CuMatrix__ and __Nerv.MMatrix__(also abstract).
Finally, there is __Nerv.CuMatrixFloat__, __Nerv.CuMatrixDouble__, inheriting __Nerv.CuMatrix__, and __Nerv.MMatrixFloat__, __Nerv.MMatrixDouble__, __Nerv.MMatrixInt__ , inheriting __Nerv.MMatrix__.
##Methods##
Mind that usually a matrix object can only do calculation with matrix of its own type(a __Nerv.CuMatrixFloat__ matrix can only do add operation with a __Nerv.CuMatrixFloat__).
In the methods description below, __Matrix__ could be __Nerv.CuMatrixFloat__, __Nerv.CuMatrixDouble__, __Nerv.MMatrixFloat__ or __Nerv.MMatrixDouble__. __Element_type__ could be `float` or `double`, respectively.
* __Matrix = Matrix(int nrow, int ncol)__
Returns a __Matrix__ object of `nrow` rows and `ncol` columns.
* __Element_type = Matrix.get_elem(Matrix self, int index)__
Returns the element value at the specific index(treating the matrix as a vector). The index should be less than `nmax` of the matrix.
* __void Matrix.set_elem(Matrix self, int index, Element_type value)__
Set the value at `index` to be `value`.
* __int Matrix.ncol(Matrix self)__
Get `ncol`, the number of columns.
* __int Matrix.nrow(Matrix self)__
Get `nrow`, the number of rows.
* __int Matrix.get_dataref_value(Matrix self)__
Returns the value(not a pointer) of space the `data_ref` pointer pointed to. This function is mainly for debugging.
* __Matrix/Element\_type, boolean Matrix.\_\_index\_\_(Matrix self, int index)__
If the matrix has more than one row, will return the row at `index` as a __Matrix__ . Otherwise it will return the value at `index`.
* __void Matrix.\_\_newindex\_\_(Matrix self, int index, Element_type value)__
Set the element at `index` to be `value`.
---
* __Matrix Matrix.create(Matrix a)__
Return a new __Matrix__ of `a`'s size(of the same number of rows and columns).
* __Matrix Matrix.colsum(Matrix self)__
Return a new __Matrix__ of size (1,`self.ncol`), which stores the sum of all columns of __Matrix__ `self`.
* __Matrix Matrix.rowsum(Matrix self)__
Return a new __Matrix__ of size (`self.nrow`,1), which stores the sum of all rows of __Matrix__ `self`.
* __Matrix Matrix.rowmax(Matrix self)__
Return a new __Matrix__ of size (`self.nrow`,1), which stores the max value of all rows of __Matrix__ `self`.
* __Matrix Matrix.trans(Matrix self)__
Return a new __Matrix__ of size (`self.ncol`,`self.nrow`), which stores the transpose of __Matrix__ `self`.
* __void Matrix.copy_fromh(Matrix self, MMatrix a)__
Copy the content of a __MMatrix__ `a` to __Matrix__ `self`, they should be of the same size.
* __void Matrix.copy_fromd(Matrix self, CuMatrix a)__
Copy the content of a __CuMatrix__ `a` to __Matrix__ `self`, they should be of the same size.
* __void Matrix.copy_toh(Matrix self, MMatrix a)__
Copy the content of the __Matrix__ `self` to a __MMatrix__ `a`.
* __void Matrix.copy_tod(Matrix self, CuMatrix a)__
Copy the content of the __Matrix__ `self` to a __CuMatrix__ `a`.
* __void Matrix.add(Matrix self, Matrix ma, Matrix mb, Element_type alpha, Element_type beta)__
It sets the content of __Matrix__ `self` to be `alpha * ma + beta * mb`.__Matrix__ `ma,mb,self` should be of the same size.
* __void Matrix.mul(Matrix self, Matrix ma, Matrix mb, Element_type alpha, Element_type beta, [string ta, string tb])__
It sets the content of __Matrix__ `self` to be `beta * self + alpha * ma * mb`. `ta` and `tb` is optional, if `ta` is 'T', then `ma` will be transposed, also if `tb` is 'T', `mb` will be transposed.
* __void Matrix.add_row(Matrix self, Matrix va, Element_type beta)__
Add `beta * va` to every row of __Matrix__ `self`.
* __void Matrix.fill(Matrix self, Element_type value)__
Fill the content of __Matrix__ `self` to be `value`.
* __void Matrix.sigmoid(Matrix self, Matrix ma)__
Set the element of __Matrix__ `self` to be elementwise-sigmoid of `ma`.
* __void Matrix.sigmoid_grad(Matrix self, Matrix err, Matrix output)__
Set the element of __Matrix__ `self`, to be `self[i][j]=err[i][j]*output[i][j]*(1-output[i][j])`. This function is used to propagate sigmoid layer error.
* __void Matrix.softmax(Matrix self, Matrix a)__
Calculate a row-by-row softmax of __Matrix__ `a` and save the result in `self`.
* __void Matrix.mul_elem(Matrix self, Matrix ma, Matrix mb)__
Calculate element-wise multiplication of __Matrix__ `ma` and `mb`, store the result in `self`.
* __void Matrix.log_elem(Matrix self, Matrix ma)__
Calculate element-wise log of __Matrix__ `ma`, store the result in `self`.
* __void Matrix.copy_rows_fromh_by_idx(Matrix self, MMatrix ma, MMatrixInt idx)__
`idx` should be a row vector. This function copy the rows of `ma` to `self` according to `idx`, in other words, it assigns `ma[idx[i]]` to `self[i]`.
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