This is an automated email from the ASF dual-hosted git repository.
janardhan pushed a commit to branch master
in repository https://gitbox.apache.org/repos/asf/systemds.git
The following commit(s) were added to refs/heads/master by this push:
new caa0ca9 [SYSTEMDS-2842][DOC] cspline builtin doc (#1265)
caa0ca9 is described below
commit caa0ca94ebb5d2f3504ba59fe44616a425ed11df
Author: j143 <[email protected]>
AuthorDate: Fri May 7 11:42:05 2021 +0530
[SYSTEMDS-2842][DOC] cspline builtin doc (#1265)
cspline builtin has two modes CG, DS - correspondingly named as
`csplineCG` and `csplineDS`.
---
docs/site/builtins-reference.md | 119 ++++++++++++++++++++++++++++++++++++++++
1 file changed, 119 insertions(+)
diff --git a/docs/site/builtins-reference.md b/docs/site/builtins-reference.md
index 784b067..bb8bb93 100644
--- a/docs/site/builtins-reference.md
+++ b/docs/site/builtins-reference.md
@@ -28,6 +28,9 @@ limitations under the License.
* [`tensor`-Function](#tensor-function)
* [DML-Bodied Built-In functions](#dml-bodied-built-in-functions)
* [`confusionMatrix`-Function](#confusionmatrix-function)
+ * [`cspline`-Function](#cspline-function)
+ * [`csplineCG`-Function](#csplineCG-function)
+ * [`csplineDS`-Function](#csplineDS-function)
* [`cvlm`-Function](#cvlm-function)
* [`DBSCAN`-Function](#DBSCAN-function)
* [`discoverFD`-Function](#discoverFD-function)
@@ -187,6 +190,122 @@ y = toOneHot(X, numClasses)
[ConfusionSum, ConfusionAvg] = confusionMatrix(P=z, Y=y)
```
+## `cspline`-Function
+
+This `cspline`-function solves Cubic spline interpolation. The function usages
natural spline with $$ q_1''(x_0) == q_n''(x_n) == 0.0 $$.
+By default, it calculates via `csplineDS`-function.
+
+Algorithm reference:
https://en.wikipedia.org/wiki/Spline_interpolation#Algorithm_to_find_the_interpolating_cubic_spline
+
+### Usage
+```r
+[result, K] = cspline(X, Y, inp_x, tol, maxi)
+```
+
+### Arguments
+
+| Name | Type | Default | Description |
+| :--- | :------------- | :------ | :---------- |
+| X | Matrix[Double] | --- | 1-column matrix of x values knots. It is
assumed that x values are monotonically increasing and there is no duplicate
points in X |
+| Y | Matrix[Double] | --- | 1-column matrix of corresponding y values
knots |
+| inp_x | Double | --- | the given input x, for which the cspline
will find predicted y |
+| mode | String | `DS` | Specifies that method for cspline (DS -
Direct Solve, CG - Conjugate Gradient) |
+| tol | Double | `-1.0` | Tolerance (epsilon); conjugate gradient
procedure terminates early if L2 norm of the beta-residual is less than
tolerance * its initial norm |
+| maxi | Integer | `-1` | Maximum number of conjugate gradient
iterations, 0 = no maximum |
+
+### Returns
+
+| Name | Type | Description |
+| :----------- | :------------- | :---------- |
+| pred_Y | Matrix[Double] | Predicted values |
+| K | Matrix[Double] | Matrix of k parameters |
+
+### Example
+
+```r
+num_rec = 100 # Num of records
+X = matrix(seq(1,num_rec), num_rec, 1)
+Y = round(rand(rows = 100, cols = 1, min = 1, max = 5))
+inp_x = 4.5
+tolerance = 0.000001
+max_iter = num_rec
+[result, K] = cspline(X=X, Y=Y, inp_x=inp_x, tol=tolerance, maxi=max_iter)
+```
+
+## `csplineCG`-Function
+
+This `csplineCG`-function solves Cubic spline interpolation with conjugate
gradient method. Usage will be same as `cspline`-function.
+
+### Usage
+```r
+[result, K] = csplineCG(X, Y, inp_x, tol, maxi)
+```
+
+### Arguments
+
+| Name | Type | Default | Description |
+| :--- | :------------- | :------ | :---------- |
+| X | Matrix[Double] | --- | 1-column matrix of x values knots. It is
assumed that x values are monotonically increasing and there is no duplicate
points in X |
+| Y | Matrix[Double] | --- | 1-column matrix of corresponding y values
knots |
+| inp_x | Double | --- | the given input x, for which the cspline
will find predicted y |
+| tol | Double | `-1.0` | Tolerance (epsilon); conjugate gradient
procedure terminates early if L2 norm of the beta-residual is less than
tolerance * its initial norm |
+| maxi | Integer | `-1` | Maximum number of conjugate gradient
iterations, 0 = no maximum |
+
+### Returns
+
+| Name | Type | Description |
+| :----------- | :------------- | :---------- |
+| pred_Y | Matrix[Double] | Predicted values |
+| K | Matrix[Double] | Matrix of k parameters |
+
+### Example
+
+```r
+num_rec = 100 # Num of records
+X = matrix(seq(1,num_rec), num_rec, 1)
+Y = round(rand(rows = 100, cols = 1, min = 1, max = 5))
+inp_x = 4.5
+tolerance = 0.000001
+max_iter = num_rec
+[result, K] = csplineCG(X=X, Y=Y, inp_x=inp_x, tol=tolerance, maxi=max_iter)
+```
+
+## `csplineDS`-Function
+
+This `csplineDS`-function solves Cubic spline interpolation with direct solver
method.
+
+### Usage
+```r
+[result, K] = csplineDS(X, Y, inp_x)
+```
+
+### Arguments
+
+| Name | Type | Default | Description |
+| :--- | :------------- | :------ | :---------- |
+| X | Matrix[Double] | --- | 1-column matrix of x values knots. It is
assumed that x values are monotonically increasing and there is no duplicate
points in X |
+| Y | Matrix[Double] | --- | 1-column matrix of corresponding y values
knots |
+| inp_x | Double | --- | the given input x, for which the cspline
will find predicted y |
+
+### Returns
+
+| Name | Type | Description |
+| :----------- | :------------- | :---------- |
+| pred_Y | Matrix[Double] | Predicted values |
+| K | Matrix[Double] | Matrix of k parameters |
+
+### Example
+
+```r
+num_rec = 100 # Num of records
+X = matrix(seq(1,num_rec), num_rec, 1)
+Y = round(rand(rows = 100, cols = 1, min = 1, max = 5))
+inp_x = 4.5
+
+[result, K] = csplineDS(X=X, Y=Y, inp_x=inp_x)
+```
+
+
## `cvlm`-Function
The `cvlm`-function is used for cross-validation of the provided data model.
This function follows a non-exhaustive
