Piece Wise Linear Fitting
 

Another dawning while doodling at the beauty shop...

http://www.analog-innovations.com/SED/PieceWiseLinearThoughts_2013_12_12.pdf

.... a way to join line segments easily to form PWL's, while
maintaining all derivatives at the joining points.

(Using my TANH version of greater than, less than... I'm working on
refining its coefficients to match segment slopes so there's no
"peaking" :-)

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

Piece Wise Linear Fitting
 

On Thu, 12 Dec 2013 09:50:47 -0700, Jim Thompson wrote:

Another dawning while doodling at the beauty shop...

http://www.analog-innovations.com/SED/PieceWiseLinearThoughts_2013_12_12.pdf

... a way to join line segments easily to form PWL's, while
maintaining all derivatives at the joining points.

(Using my TANH version of greater than, less than... I'm working on
refining its coefficients to match segment slopes so there's no
"peaking" :-)

...Jim Thompson

How important is the continuity of higher order derivatives? Cubic
B-splines are continuous to the second order, becoming discontinuous
at the third, but are much easier/faster to calculate:
http://en.wikipedia.org/wiki/Spline_%28mathematics%29

Piece Wise Linear Fitting
 

On Thu, 12 Dec 2013 17:16:09 +0000 (UTC), Frank Miles
wrote:

On Thu, 12 Dec 2013 09:50:47 -0700, Jim Thompson wrote:

Another dawning while doodling at the beauty shop...

http://www.analog-innovations.com/SED/PieceWiseLinearThoughts_2013_12_12.pdf

... a way to join line segments easily to form PWL's, while
maintaining all derivatives at the joining points.

(Using my TANH version of greater than, less than... I'm working on
refining its coefficients to match segment slopes so there's no
"peaking" :-)

...Jim Thompson

How important is the continuity of higher order derivatives? Cubic
B-splines are continuous to the second order, becoming discontinuous
at the third, but are much easier/faster to calculate:
http://en.wikipedia.org/wiki/Spline_%28mathematics%29

There's no calculation involved here... just straight line segments
joined by greater-than/less-than TANH "devices".

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

Piece Wise Linear Fitting
 

On Thu, 12 Dec 2013 12:45:52 -0700, Jim Thompson
wrote:

On Thu, 12 Dec 2013 17:16:09 +0000 (UTC), Frank Miles
wrote:

On Thu, 12 Dec 2013 09:50:47 -0700, Jim Thompson wrote:

Another dawning while doodling at the beauty shop...

http://www.analog-innovations.com/SED/PieceWiseLinearThoughts_2013_12_12.pdf

... a way to join line segments easily to form PWL's, while
maintaining all derivatives at the joining points.

(Using my TANH version of greater than, less than... I'm working on
refining its coefficients to match segment slopes so there's no
"peaking" :-)

...Jim Thompson

How important is the continuity of higher order derivatives? Cubic
B-splines are continuous to the second order, becoming discontinuous
at the third, but are much easier/faster to calculate:
http://en.wikipedia.org/wiki/Spline_%28mathematics%29

There's no calculation involved here... just straight line segments
joined by greater-than/less-than TANH "devices".

...Jim Thompson

Softened...


http://www.analog-innovations.com/SED/PieceWiseLinearThoughts_2013_12_12-2.pdf

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

Piece Wise Linear Fitting
 

Try regular hyperbolae. The derivatives exist... just take care not to
divide by zero (which can happen with tanh too, and probably at analogous
points, for analogous reasons).

Tim

--
Seven Transistor Labs
Electrical Engineering Consultation
Website: http://seventransistorlabs.com

"Jim Thompson" wrote
in message ...
Another dawning while doodling at the beauty shop...

http://www.analog-innovations.com/SED/PieceWiseLinearThoughts_2013_12_12.pdf

... a way to join line segments easily to form PWL's, while
maintaining all derivatives at the joining points.

(Using my TANH version of greater than, less than... I'm working on
refining its coefficients to match segment slopes so there's no
"peaking" :-)

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

Piece Wise Linear Fitting
 

On 12/12/2013 10:27 PM, Tim Williams wrote:
Try regular hyperbolae. The derivatives exist... just take care not to
divide by zero (which can happen with tanh too, and probably at analogous
points, for analogous reasons).

Division by zero computing tanh of a real number? That would take
talent. Care to elaborate?

Cheers

Phil Hobbs

Piece Wise Linear Fitting
 

"Phil Hobbs" wrote in message
m...
On 12/12/2013 10:27 PM, Tim Williams wrote:
Try regular hyperbolae. The derivatives exist... just take care not to
divide by zero (which can happen with tanh too, and probably at analogous
points, for analogous reasons).

Division by zero computing tanh of a real number? That would take talent.
Care to elaborate?

Maybe it was atanh, but it's not the function of a real number, it's the
derivative that causes problems. Certain people here swear by this for
continuous limiter functions in SPICE, but I've found they can go batty
rather often.

Incidentally, The Internet doesn't know that degenerate circuits aren't the
only condition that can create singular matrices.

Tim

--
Seven Transistor Labs
Electrical Engineering Consultation
Website: http://seventransistorlabs.com

Piece Wise Linear Fitting
 

On Fri, 13 Dec 2013 14:31:22 -0600, "Tim Williams"
wrote:


"Phil Hobbs" wrote in message
om...
On 12/12/2013 10:27 PM, Tim Williams wrote:
Try regular hyperbolae. The derivatives exist... just take care not to
divide by zero (which can happen with tanh too, and probably at analogous
points, for analogous reasons).

Division by zero computing tanh of a real number? That would take talent.
Care to elaborate?

Maybe it was atanh, but it's not the function of a real number, it's the
derivative that causes problems. Certain people here swear by this for
continuous limiter functions in SPICE, but I've found they can go batty
rather often.

Incidentally, The Internet doesn't know that degenerate circuits aren't the
only condition that can create singular matrices.

Tim

All derivatives of TANH exist and don't go "batty". You must be
thinking of some other function.

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.