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10 Sparse Matrix Handling
These sections outline the functionality available for sparse matrix
handling included with TOMVIEW.
The following functions are available to create sparse matrices.
Purpose
Initiate a sparse matrix from three arrays and two integers. One array with matrix element values, one array with row index and the third array with column index. The integers describe the number of rows and number of columns in the matrix.
Description of Inputs
| value |
Array value. The array contains matrix element values. |
| |
| row |
Array row index. The array contains row index corresponding to the array of values. |
| |
| col |
Array column index. The array contains column index corresponding to the array of values. |
| |
| m |
An integer equal to the number of rows in A. |
| |
| n |
An integer equal to the number of columns in A. |
| |
Description of Outputs
| A |
A sparse matrix described by the inputs. |
Description
The routine sparse_init.vi initiates a sparse matrix from the inputs. The length of all the three input arrays must be equal. The indexing starts with 0 and must be less then the size of the matrix (
m resp.
n).
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If the minimum value in
row or
col is less then zero the errorcode 6522 is returned. If the three input vectors differ in length or
m or
n is less then zero the errorcode 6521 is returned.
Purpose
Initiate an empty sparse matrix.
Description of Inputs
| m |
An integer equal to the number of rows in A. |
| |
| n |
An integer equal to the number of columns in A. |
Description of Outputs
| A |
A sparse matrix with all elements equal to zero. |
Description
The routine sparse_empty.vi initiates a sparse matrix from the inputs.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If
m or
n is less then zero the errorcode 6521 is returned.
Purpose
Initiate a matrix in sparse format with all element equal.
Description of Inputs
| m |
An integer equal to the number of rows in the output matrix A. |
| |
| n |
An integer equal to the number of columns in the output matrix A. |
| |
| element |
A real number. element is the value all the elements matrix A will have. |
Description of Outputs
| A |
A sparse matrix described by the inputs. |
Description
The routine sparse_fill.vi initiates a sparse matrix from the inputs with all elements equal to the input variable element.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If
m or
n is less or equal to zero the errorcode 6521 is returned.
Purpose
Initiate a sparse identity matrix from two integers. The integers describe the number of rows and number of columns in the identity matrix.
Description of Inputs
| m |
An integer equal to the number of rows in matrix I. |
| |
| n |
An integer equal to the number of columns in matrix I. |
Description of Outputs
| I |
A sparse identity matrix with size described by the inputs. |
Description
The routine sparse_eye.vi initiates a sparse identity matrix from the inputs. If only one input is given the function will return a quadratic identity matrix of size as the nonzero input.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If
m or
n is less or equal to zero the errorcode 6521 is returned.
Purpose
Returns matrix triplet components from a sparse matrix.
Description of Inputs
Description of Outputs
| value |
Array value. The array contains matrix element values. |
| |
| row |
Array row index. The array contains row index corresponding to the array of values. |
| |
| col |
Array column index. The array contains column index corresponding to the array of values. |
| |
| m |
An integer equal to the number of rows in A. |
| |
| n |
An integer equal to the number of columns in A. |
Description
The routine sparse_toTriplet.vi returns triplet components from a sparse matrix.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. Errorcode
6521 is returned if the matrix is corrupt.
The following functions are available to merge and modify existing
sparse matrices.
Purpose
The function returns the transpose of the input matrix.
where
B 
Rn × m,
A Rm × n.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
Description of Outputs
| B |
Sparse matrix B. The transpose of the input matrix. |
Description
The routine sparse_transpose.vi uses optimal data handling and structures to return the transpose of a matrix.
Examples
usersguide_sparse.
Purpose
Concats two sparse matrices either rowwise or columnwise.
where
C RmA × (nA+nB) or
C R(mA+mB) × nA,
A RmA × nA,
B RmB × nB.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| B |
Sparse matrix B. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| dim |
Integer dim. Eighter 0 (default) or 1. 0 for rowwise concatation or 1 for columnwise concatation. |
Description of Outputs
Description
The routine sparse_concat.vi uses optimal data handling and structures to concate two sparse matrices eighter rowwise or columnwise.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If the two matrices has different number of rows/columns (depending on what dimensions that will be concate) the errorcode 6521 is returned.
Purpose
Add more rows or columns filled with zeros to a sparse matrix.
|
B = |
[ |
|
] |
(dim = 0 order = 0)
|
|
B = |
[ |
|
] |
(dim = 0 order = 1)
|
where
B Rm × (n+n0) or
B R(m+m0) × n,
A Rm × n.
Description of Inputs
| A |
Sparse matrix. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| dim |
An integer. Eighter 0 (default) or 1. 0 for rowwise concatation or 1 for columnwise concatation. |
| |
| order |
An integer. Eighter 0 (default) or 1. 0 for A to be the first matrix and 1 for the zero matrix to be the first matrix to concat. |
| |
| m0/n0 |
An integer equal to the number of rows/columns to concat. |
Description of Outputs
Description
The routine sparse_concateZeros.vi uses optimal data handling and structures to add more rows/columns filled with zeros to a matrix.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If the input matrix has one of its dimension less than zero the errorcode 6521 is returned.
Purpose
Returns a sub matrix of the input matrix.
|
|
| B=A(:,index) |
|
| B=A(index,:) |
|
|
where
B Rm× length(index) or
B Rlength(index) × n,
A Rm × n.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| index |
Integer vector with index that will be in the submatrix. |
| |
| dim |
Integer dim. Eighter 0 (default) or 1. 0 to get columns or 1 for get rows. |
Description of Outputs
| B |
Sparse matrix B. A sub matrix to the input matrix A. |
Description
The routine sparse_subMatrix.vi uses optimal data handling and structures to return a sub matrix of the input matrix.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If the index in the index vector is out of matrix dimension the errorcode 6522 is returned.
Purpose
Set a matrix element to a given value.
where
A Rm × n,
i integer,
j integer,
val is a scalar.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| i |
Integer equal to the row index. |
| |
| j |
Integer equal to the column index. |
| |
| val |
The new element in A. |
Description of Outputs
| A new |
The modified sparse matrix. |
Description
The routine sparse_setVal.vi sets a sparse matrix element value in the i:th row and j:th column to a given value.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If
i or
j is out of matrix dimension the errorcode 6522 is returned.
Purpose
Set a matrix column to given values.
where
A Rm × n,
row integer vector,
j integer,
val is a value vector.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| row |
Integer vector equal to the row indices. |
| |
| j |
Integer equal to the column index. |
| |
| val |
A vector with the new elements in A. |
Description of Outputs
| A new |
The modified sparse matrix. |
Description
The routine sparse_setCol.vi sets row element values in a sparse matrix to given values.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If
j or the indices in
row is out of matrix dimension the errorcode 6522 is returned. If the two input vectors have different size the errorcode -23036 is returned.
Purpose
Set a matrix row to given values.
where
A Rm × n,
i integer,
col integer vector,
val is a value vector.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| i |
Integer equal to the row index. |
| |
| col |
Integer vector equal to the column indices. |
| |
| val |
A vector with the new elements in A. |
Description of Outputs
| A new |
The modified sparse matrix. |
Description
The routine sparse_setRow.vi sets column element values in a sparse matrix to given values.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If
i or the indices in
col is out of matrix dimension the errorcode 6522 is returned. If the two input vectors have different size the errorcode -23036 is returned.
10.3 Functions
The following functions are available to obtain information about
the sparse matrices.
Purpose
Get the size of a sparse 2-D matrix.
|
|
| m |
= |
number of rows in A |
| n |
= |
number of columns in A |
|
where
A Rm × n.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
Description of Outputs
| m |
An integer equal to the number of rows in A. |
| |
| n |
An integer equal to the number of columns in A. |
Description
The routine sparse_size.vi gives the size of a sparse matrix.
Examples
usersguide_sparse.
Purpose
Get the number of non zeros in a sparse 2-D matrix.
|
|
| nnz= number of nonzeros in A |
|
where
A Rm × n.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
Description of Outputs
| nnz |
An integer equal to the number of non zeros in A. |
Description
The routine sparse_nnz.vi gives the number of non zeros in a sparse matrix.
Examples
usersguide_sparse.
Purpose
Get a matrix element value from a sparse 2-D matrix.
where
val is a scalar,
A Rm × n,
i integer,
j integer.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| i |
Integer equal to the row index. |
| |
| j |
Integer equal to the column index. |
Description of Outputs
| val |
The element in A in the i:th row and j:th column. |
Description
The routine sparse_getVal.vi gives the matrix element value in the i:th row and j:th column of the sparse matrix A.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If
i or
j is out of matrix dimension the errorcode 6522 is returned.
Purpose
Get a matrix column from a sparse 2-D matrix.
where
col Rm × 1 ,
A Rm × n,
j integer.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| j |
Integer equal to the column index. |
Description of Outputs
| col |
The j:th column in A. |
Description
The routine sparse_getCol.vi gives an array equal to the j:th column of the sparse matrix A.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If
j is out of matrix dimension the errorcode 6522 is returned.
Purpose
Get a matrix row from a sparse 2-D matrix.
where
row R1 × n ,
A Rm × n,
i integer.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| i |
Integer equal to the row index. |
Description of Outputs
Description
The routine sparse_getRow.vi gives an array equal to the i:th row of the sparse matrix A.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If
i is out of matrix dimension the errorcode 6522 is returned.
10.4 Operators
The following functions are available to perform calculations with
sparse matrices.
Purpose
Mutliplies a sparse 2-D matrix with a scalar c.
where
B Rm × n,
A Rm × n, and
c is scalar.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| c |
A scalar c. |
Description of Outputs
| B |
A sparse matrix containing each element in A multiplied by c. |
Description
The routine sparse_cA.vi uses optimal data handling and structures to
multiply a sparse LabVIEW matrix by a scalar.
Examples
usersguide_sparse.
Purpose
Mutliplies a sparse 2-D matrix with a dense vector x.
where
y Rm × 1,
A Rm × n, and
x
Rn × 1.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| x |
A dense vector (array) x. |
Description of Outputs
| y |
An array containing each row in A multiplied by x. |
Description
The routine sparse_Ax.vi uses optimal data handling and structures to
multiply a sparse LabVIEW matrix by a dense array.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If length of x is not equal to the number of columns in A the errorcode -20039 is returned.
If the dimensions of all the input variables is equal to zero the errorcode -20003 is returned.
Purpose
Mutliplies the transpose of a sparse 2-D matrix with a dense vector x.
where
y Rn × 1,
A Rm × n, and
x
Rm × 1.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| x |
A dense vector (array) x. |
Description of Outputs
| y |
An array containing each column in A multiplied by x. |
Description
The routine sparse_ATx.vi uses optimal data handling and structures to
multiply a sparse LabVIEW matrix by a dense array.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If length of x is not equal to the number of rows in A the errorcode -20039 is returned.
If the dimensions of all the input variables is equal to zero the errorcode -20003 is returned.
Purpose
Mutliplies two sparse 2-D matrices.
where
C RmA × nB,
A RmA × nA and
B RmB × nB.
Description of Inputs
| A |
Sparse matrix A. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| B |
Sparse matrix B. Defined by sparse_init or by converting a dense matrix to a sparse. |
Description of Outputs
Description
The routine sparse_mult.vi uses optimal data handling and structures to
multiply two sparse LabVIEW matrices.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If the number of columns in
A is different from the number of rows in
B the errorcode -20039 is returned.
If some of the dimensions to the input variables is equal to zero the errorcode -20003 is returned.
Purpose
Returns the function value of each nonzero element in a sparse 2-D matrix.
where
B Rm × n,
A Rm × n, and
func is a mathematical function given as a number in the input.
Description of Inputs
| A |
A sparse matrix. Defined by sparse_init or by converting a dense matrix to a sparse. |
| |
| func |
An integer describing what matematical function to be used (defalult =1) (see list below). |
| |
| n |
(optional) An integer used in some matematical function (default=3). |
Table 10:
The different types of optimization problems defined in TOMVIEW.
|
| func |
|
function |
|
| 1 |
|
cos |
| 2 |
|
sin |
| 3 |
|
tan |
| 4 |
|
acos |
| 5 |
|
asin |
| 6 |
|
atan |
| 7 |
|
cosh |
| 8 |
|
sinh |
| 9 |
|
tanh |
| 10 |
|
acosh |
| 11 |
|
asinh |
| 12 |
|
atanh |
| 13 |
|
ln |
| 14 |
|
exp |
| 15 |
|
log10 |
| 16 |
|
power of 10 |
| 17 |
|
log2 |
| 18 |
|
power of 2 |
| 19 |
|
power of n |
| 20 |
|
abs |
| 21 |
|
round to nearest |
| 22 |
|
round to −∞ |
| 23 |
|
round to +∞ |
| 24 |
|
sqrt |
| 25 |
|
to the power of 2 |
| 26 |
|
to the power of n |
|
Description of Outputs
| B |
A sparse matrix containing the function value of each nonzero element. |
Description
The routine sparse_mathFunc.vi uses optimal data handling and structures to return the function value of each
nonzero element.
Examples
usersguide_sparse.
Error codes
An integer error code is returned for various scenarios. If the function number (
func) is not included in the list above the errorcode -23095 is returned.
10.5 Examples
In the following sub-sections are some examples of how to use the
sparse matrix library included with TOMVIEW.
The first exemplified VI is sparse_init.vi. It initiates a sparse
matrix in TOMVIEW using values and row/column position. The
following figure illustrates a Front Panel where a small sparse
matrix is created.
Figure 11:
Creating a sparse matrix.
The values 3, 1.9, -5.7, 0.8 are inserted into a matrix in positions
(2,1), (0,0), (1,2), (2,2). The indices start with 0.
m (number of
rows) and
n (number of columns) are not given. They will get the
default value 3, which is the largest value in
row and
col plus
one. The output is a matrix in sparse form. It is possible to view
the dense version of the matrix and the sparse matrix cluster
component vectors
pr,
ir and
jc.
Next figure displays how the block sparse_init.vi is called.
Figure 12:
Block Diagram for creating a
sparse matrix.
The inputs are inserted into the block. The output from
sparse_init.vi is a sparse matrix (as a cluster). The cluster
components are unbundled as seen in Front Panel figure.
The VI sparse_concat.vi concatenates two sparse matrices either row
or column wise. When dim is set to 0 the VI concatenates row wise
and column wise for 1. The following two figures illustrates the
difference.
Figure 13:
Front Panel illustrating a row wise
concatenation.
Figure 14:
Front Panel illustrating a column wise
concatenation.
The input matrices are viewed in dense form to get an better
overview. The output is viewed in both dense and sparse formats.
The block diagram shows how to connect the inputs to the
sparse_concat block.
Figure 15:
Block Diagram illustrating
sparse_concat.
The dense matrices are first converted to the sparse format. The
output from concat is also a sparse matrix. In this example the
output cluster is unbundled into its components. Also a dense
version of the output is displayed (as seen on the Front Panel).
sparse_Ax.vi is a function which multiplies a sparse matrix with a
vector (in LabVIEW an array). The front panel is shown in the next
figure.
Figure 16:
Front Panel illustrating a sparse matrix
vector multiplication.
The matrix is displayed in a dense format to get a better overview.
The VI sparse_Ax.vi accepts a sparse matrix as input which can be
seen in the Block Diagram.
The Block Diagram shows how to connect the input to sparse_Ax.vi.
Figure 17:
Block Diagram for illustration of sparse matrix vector multiplication.
sparse_example.vi is an example VI where all the sparse functions are examplified. A sparse matrix is initiated by sparse_init which is used in many of the examples. In the Block Diagram all the sparse functions are called.
The next two figures show how to call the sparse functions.
Figure 18:
Block Diagram for illustration of the functions in the sparse library.
Figure 19:
Block Diagram for illustration of the functions in the sparse library.
The inputs and the outputs are dispayed in the Front Panel which is shown in the next figure.
Figure 20:
Front Panel to sparse_example. All inputs and outputs are displayed.
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