Difference between revisions of "Manuals/calci/PENTADIAGONAL"

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<div style="font-size:30px">'''PENTADIAGONAL'''</div><br/>
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<div style="font-size:30px">'''MATRIX("PENTADIAGONAL",order)'''</div><br/>
 +
*<math>order</math> is the size of the Pentadiagonal matrix.
 +
 
 +
==Description==
 +
*This function gives the pentadiagonal matrix of order 3.
 +
*A pentadiagonal matrix is a matrix that is nearly diagonal.
 +
*So it is a matrix in which the only nonzero entries are on the main diagonal, and the first two diagonals above and below it.
 +
*The form of pentadiagonal matrix is:
 +
<math>A=\begin{pmatrix}
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c_1 & d_1 & e_1 & 0 & \cdots & \cdots & 0 \\
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b_1 & c_2 & d_2 & e_2 & \ddots &\cdots & \vdots \\
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a_1 & b_2 & \cdots & \ddots & \ddots & \ddots & \vdots \\
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0 & a_2 & \cdots & \ddots & \ddots & e_{n-3} & 0 \\
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\vdots & \ddots & \ddots & \ddots & \ddots & d_{n-2} & e_{n-2} \\
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\vdots &\cdots& \ddots & a_{n-3} & b_{n-2} & c_{n-1} & d_{n-1} \\
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0 & \cdots & \cdots & 0 & a_{n-2} & b_{n-1} & c_n
 +
\end{pmatrix}</math>.
 +
*When n is the size of the matrix, a pentadiagonal matrix has atmost 5n-6 nonzero entries.
 +
*Here MATIRX("pentadiagonal") is showing the penta diagonal matrix of order 3 with the integer numbers.
 +
*Also in Calci users can get a deimal values with positive and negative numbers.
 +
*The syntax  is to get  the decimal penta diagonal matrix is  MATRIX("pentadiagonal:negative") and MATRIX(pentadiagonal:positive")
 +
 
 +
==Examples==
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*1.MATRIX("pentadiagonal") =22
 +
*2.MATRIX("pentadiagonal",3)
 +
{| class="wikitable"
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|-
 +
| -58 || 15 || -4
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|-
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| -54 || 55 || -75
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|-
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| 21 || -25 || -64
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|}
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*3.MATRIX("pentadiagonal",6)
 +
{| class="wikitable"
 +
|-
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| 54 || -56 || -28 || 0 || 0 || 0
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|-
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| 62 || -96 || -82 || -49 || 0 || 0
 +
|-
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| 15 || 23 || 20 || 30 || 94 || 0
 +
|-
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| 0 || 80 || 95 || 76 || -82 || 66
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|-
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| 0 || 0 || -60 || -27 || -82 || -87
 +
|-
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| 0 || 0 || 0 || -43 || 19 || 89
 +
|}
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*4.MATRIX("pentadiagonal:negative",4)
 +
{| class="wikitable"
 +
|-
 +
| -59.92012487258762 || -79.75753229111433 || -20.13208125717938 || 0 
 +
|-
 +
| -47.0609312877059 || -7.832704461179674 || -29.973211092874408 || -12.44902245234698 
 +
|-
 +
| -47.85296192858368 || -67.0970072504133 || -53.094227402471006 || -84.4662182033062
 +
|-
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| 0 || -12.941046571359038 || -31.090207281522453 || -52.342877350747585
 +
|}
 +
*5.MATRIX("pentadiagonal:positive",5)
 +
{| class="wikitable"
 +
|-
 +
| 86.68749532662332 || 69.28418821189553 || 15.4073191806674 || 0  || 0
 +
|-
 +
| 35.21442376077175 || 31.06112303212285 || 35.75007226318121 || 77.74382838979363 || 0 
 +
|-
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| 24.096227367408574 || 42.69053868483752 || 98.5696179093793 || 5.866385693661869 || 81.69623236171901
 +
|-
 +
| 0 || 80.96880922093987 || 67.79956801328808 || 45.05093654152006 || 71.03362120687962
 +
|-
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| 0 || 0 || 32.176876766607165 || 47.92787255719304 || 48.10425683390349
 +
|}
 +
 
 +
==See Also==
 +
*[[Manuals/calci/SYMMETRIC| SYMMETRIC]]
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*[[Manuals/calci/BIDIAGONAL| BIDIAGONAL]]
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*[[Manuals/calci/TRIANGULAR| TRIANGULAR]]
 +
 
 +
==References==
 +
*[http://en.wikipedia.org/wiki/Pentadiagonal_matrix Pentadiagonal Matrix]

Latest revision as of 02:33, 26 October 2015

MATRIX("PENTADIAGONAL",order)


  • is the size of the Pentadiagonal matrix.

Description

  • This function gives the pentadiagonal matrix of order 3.
  • A pentadiagonal matrix is a matrix that is nearly diagonal.
  • So it is a matrix in which the only nonzero entries are on the main diagonal, and the first two diagonals above and below it.
  • The form of pentadiagonal matrix is:

.

  • When n is the size of the matrix, a pentadiagonal matrix has atmost 5n-6 nonzero entries.
  • Here MATIRX("pentadiagonal") is showing the penta diagonal matrix of order 3 with the integer numbers.
  • Also in Calci users can get a deimal values with positive and negative numbers.
  • The syntax is to get the decimal penta diagonal matrix is MATRIX("pentadiagonal:negative") and MATRIX(pentadiagonal:positive")

Examples

  • 1.MATRIX("pentadiagonal") =22
  • 2.MATRIX("pentadiagonal",3)
-58 15 -4
-54 55 -75
21 -25 -64
  • 3.MATRIX("pentadiagonal",6)
54 -56 -28 0 0 0
62 -96 -82 -49 0 0
15 23 20 30 94 0
0 80 95 76 -82 66
0 0 -60 -27 -82 -87
0 0 0 -43 19 89
  • 4.MATRIX("pentadiagonal:negative",4)
-59.92012487258762 -79.75753229111433 -20.13208125717938 0
-47.0609312877059 -7.832704461179674 -29.973211092874408 -12.44902245234698
-47.85296192858368 -67.0970072504133 -53.094227402471006 -84.4662182033062
0 -12.941046571359038 -31.090207281522453 -52.342877350747585
  • 5.MATRIX("pentadiagonal:positive",5)
86.68749532662332 69.28418821189553 15.4073191806674 0 0
35.21442376077175 31.06112303212285 35.75007226318121 77.74382838979363 0
24.096227367408574 42.69053868483752 98.5696179093793 5.866385693661869 81.69623236171901
0 80.96880922093987 67.79956801328808 45.05093654152006 71.03362120687962
0 0 32.176876766607165 47.92787255719304 48.10425683390349

See Also

References