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

Latest revision as of 12:23, 21 April 2011

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

Usage 1

yint(y_vector {, dx_scalar=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(y_vector , dx_scalar, c_scalar)

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(y_vector, dx_vector)

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(y_vector, dx_vector, c_scalar)

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(y_vector, x_vector)

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(y_vector, x_vector, c_scalar)

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

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:{{SUBPAGENAME}}}}
-=====yint=====
+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})</code>
+;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''[i]=''r''[i-1]+''y''[i-1]*''dx''; with: i=1..nrow(''y'')</code>
+----
+;Usage 3: <code>yint(<var>y<sub>vector</sub></var>, <var>dx<sub>vector</sub></var>)</code>
+;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''[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 6: <code>yint(<var>y<sub>vector</sub></var>, <var>x<sub>vector</sub></var>, <var>c<sub>scalar</sub></var>)</code>
+;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''[i]=''r''[i-1]+''y''[i-1]*(''x''[i]-''x''[i-1]); with: i=1..nrow(''y'')</code>
+----
+;See also: [[../ydiff|ydiff]]
-Calculates the integration <code>r</code> of the vector <var>y</var> with <code>nrow(y)+1</code> elements.
+[[../#Functions|<function list>]]
-=====Usage:=====
-<code>yint(<var>y</var>,<var>dx</var>,<var>c</var>)</code>
-=====Parameters:=====
-;<var>y</var>
-:The y data vector.
-;<var>dx</var>
-:The x increment. If <var>dx</var> is not specified, the default value of <code>1</code> is used.
-;<var>c</var>
-:The start value (default = 0).
-=====Result:=====
-<code>r[0] =</code> <var>c</var><code>, r[i+1] = r[i] +</code> <var>y</var><code>[i]*</code><var>dx</var>
-with: <code>i = 0</code> .. <code>nrow(y)-1</code>
-=====Usage:=====
-<code>yint(<var>y</var>,<var>x</var>,<var>c</var>)</code>
-=====Parameters:=====
-;<var>y</var>
-:The y data vector.
-;<var>x</var>
-:The x data vector with <code>nrow(</code><var>y</var><code>)+1</code> elements.
-;<var>c</var>
-:The start value (default = 0).
-=====Result:=====
-<code>r[0] =</code> <var>c</var><code>, r[i+1] = r[i] +</code> <var>y</var><code>[i]*(</code><var>x</var><code>[i+1]-</code><var>x</var><code>[i])</code>
-with: <code>i = 0</code> .. <code>nrow(</code><var>y</var><code>)-1</code>

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

Latest revision as of 12:23, 21 April 2011

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