Programmer Guide/Command Reference/EVAL/yint: Difference between revisions

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Calculates the integration (differnce quotients) of the vector ''y'' = f(''x'').
Calculates the integration of the vector ''y'' = f(''x'').
----
----
;Usage 1: <code>yint(<var>y<sub>vector</sub></var> {, <var>dx<sub>scalar</sub></var>=1 {, <var>c<sub>scalar</sub></var>=0}})</code>
;Usage 1: <code>yint(<var>y<sub>vector</sub></var> {, <var>dx<sub>scalar</sub></var>=1})</code>
;Result 1: The result is the vector ''r'' with <code>nrow(''y'')+1</code> elements.  
;Result 1: The result is the vector ''r'' with <code>nrow(''y'')</code> elements.
::<code>''r''[0]=''y''[0]*''dx''</code>
::<code>''r''[i]=''r''[i-1]+''y''[i]*''dx''; with: i=1..nrow(''y'')-1</code>
----
;Usage 2: <code>yint(<var>y<sub>vector</sub></var> , <var>dx<sub>scalar</sub></var>, <var>c<sub>scalar</sub></var>)</code>
;Result 2: The result is the vector ''r'' with <code>nrow(''y'')+1</code> elements.  
::<code>''r''[0]=''c''</code>
::<code>''r''[0]=''c''</code>
::<code>''r''[i+1]=''r''[i]+''y''[i]*''dx''; with: i=0..nrow(''y'')-1</code>
::<code>''r''[i]=''r''[i-1]+''y''[i-1]*''dx''; with: i=1..nrow(''y'')</code>
----
----
;Usage 2: <code>yint(<var>y<sub>vector</sub></var>, <var>dx<sub>vector</sub></var> {, <var>c<sub>scalar</sub></var>=0})</code>
;Usage 3: <code>yint(<var>y<sub>vector</sub></var>, <var>dx<sub>vector</sub></var>)</code>
;Result 2: The result is the vector ''r'' with <code>nrow(''y'')+1</code> elements. The argument ''dx'' contains the differences of the x values and is a vector with <code>nrow(''y'')</code> elements.
;Result 3: The result is the vector ''r'' with <code>nrow(''y'')</code> elements. The argument ''dx'' contains the differences of the x values and is a vector with <code>nrow(''y'')</code> elements.
::<code>''r''[0]=''y''[0]*''dx''[0]</code>
::<code>''r''[i]=''r''[i-1]+''y''[i]*''dx''[i]; with: i=1..nrow(''y'')-1</code>
----
;Usage 4: <code>yint(<var>y<sub>vector</sub></var>, <var>dx<sub>vector</sub></var>, <var>c<sub>scalar</sub></var>)</code>
;Result 4: The result is the vector ''r'' with <code>nrow(''y'')+1</code> elements. The argument ''dx'' contains the differences of the x values and is a vector with <code>nrow(''y'')</code> elements.
::<code>''r''[0]=''c''</code>
::<code>''r''[0]=''c''</code>
::<code>''r''[i+1]=''r''[i]+''y''[i]*''dx''[i]; with: i=0..nrow(''y'')-1</code>
::<code>''r''[i]=''r''[i-1]+''y''[i-1]*''dx''[i-1]; with: i=1..nrow(''y'')</code>
----
;Usage 5: <code>yint(<var>y<sub>vector</sub></var>, <var>x<sub>vector</sub></var>)</code>
;Result 5: The result is the vector ''r'' with <code>nrow(''y'')</code> elements. The argument ''x'' contains the x values and is a vector with <code>nrow(''y'')+1</code> elements.
::<code>''r''[0]=''y''[0]*(''x''[1]-''x''[0])</code>
::<code>''r''[i]=''r''[i-1]+''y''[i]*(''x''[i+1]-''x''[i]); with: i=1..nrow(''y'')-1</code>
----
----
;Usage 2: <code>yint(<var>y<sub>vector</sub></var>, <var>x<sub>vector</sub></var>=1 {, <var>c<sub>scalar</sub></var>=0})</code>
;Usage 6: <code>yint(<var>y<sub>vector</sub></var>, <var>x<sub>vector</sub></var>, <var>c<sub>scalar</sub></var>)</code>
;Result 2: The result is the vector ''r'' with <code>nrow(''y'')+1</code> elements. The argument ''x'' contains the x values and is a vector with <code>nrow(''y'')+1</code> elements.
;Result 6: The result is the vector ''r'' with <code>nrow(''y'')+1</code> elements. The argument ''x'' contains the x values and is a vector with <code>nrow(''y'')+1</code> elements.
::<code>''r''[0]=''c''</code>
::<code>''r''[0]=''c''</code>
::<code>''r''[i+1]=''r''[i]+''y''[i]*(''x''[i+1]-''x''[i]); with: i=0..nrow(''y'')-1</code>
::<code>''r''[i]=''r''[i-1]+''y''[i-1]*(''x''[i]-''x''[i-1]); with: i=1..nrow(''y'')</code>
----
----
;See also: [[Programmer_Guide/Command_Reference/EVAL/ydiff|ydiff]]
;See also: [[../ydiff|ydiff]]


[[Programmer_Guide/Command_Reference/EVAL#Functions|<function list>]]
[[../#Functions|<function list>]]

Latest revision as of 12:23, 21 April 2011

Calculates the integration of the vector y = f(x).

Usage 1
yint(yvector {, dxscalar=1})
Result 1
The result is the vector r with nrow(y) elements.
r[0]=y[0]*dx
r[i]=r[i-1]+y[i]*dx; with: i=1..nrow(y)-1
Usage 2
yint(yvector , dxscalar, cscalar)
Result 2
The result is the vector r with nrow(y)+1 elements.
r[0]=c
r[i]=r[i-1]+y[i-1]*dx; with: i=1..nrow(y)
Usage 3
yint(yvector, dxvector)
Result 3
The result is the vector r with nrow(y) elements. The argument dx contains the differences of the x values and is a vector with nrow(y) elements.
r[0]=y[0]*dx[0]
r[i]=r[i-1]+y[i]*dx[i]; with: i=1..nrow(y)-1
Usage 4
yint(yvector, dxvector, cscalar)
Result 4
The result is the vector r with nrow(y)+1 elements. The argument dx contains the differences of the x values and is a vector with nrow(y) elements.
r[0]=c
r[i]=r[i-1]+y[i-1]*dx[i-1]; with: i=1..nrow(y)
Usage 5
yint(yvector, xvector)
Result 5
The result is the vector r with nrow(y) elements. The argument x contains the x values and is a vector with nrow(y)+1 elements.
r[0]=y[0]*(x[1]-x[0])
r[i]=r[i-1]+y[i]*(x[i+1]-x[i]); with: i=1..nrow(y)-1
Usage 6
yint(yvector, xvector, cscalar)
Result 6
The result is the vector r with nrow(y)+1 elements. The argument x contains the x values and is a vector with nrow(y)+1 elements.
r[0]=c
r[i]=r[i-1]+y[i-1]*(x[i]-x[i-1]); with: i=1..nrow(y)
See also
ydiff

<function list>

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