Difference between revisions of "Manuals/calci/PENTADIAGONAL"
Jump to navigation
Jump to search
| (4 intermediate revisions by the same user not shown) | |||
| Line 9: | Line 9: | ||
<math>A=\begin{pmatrix} | <math>A=\begin{pmatrix} | ||
c_1 & d_1 & e_1 & 0 & \cdots & \cdots & 0 \\ | c_1 & d_1 & e_1 & 0 & \cdots & \cdots & 0 \\ | ||
| − | b_1 & c_2 & d_2 & e_2 & \ddots & & \vdots \\ | + | b_1 & c_2 & d_2 & e_2 & \ddots &\cdots & \vdots \\ |
a_1 & b_2 & \cdots & \ddots & \ddots & \ddots & \vdots \\ | a_1 & b_2 & \cdots & \ddots & \ddots & \ddots & \vdots \\ | ||
0 & a_2 & \cdots & \ddots & \ddots & e_{n-3} & 0 \\ | 0 & a_2 & \cdots & \ddots & \ddots & e_{n-3} & 0 \\ | ||
\vdots & \ddots & \ddots & \ddots & \ddots & d_{n-2} & e_{n-2} \\ | \vdots & \ddots & \ddots & \ddots & \ddots & d_{n-2} & e_{n-2} \\ | ||
| − | \vdots & & \ddots & a_{n-3} & b_{n-2} & c_{n-1} & d_{n-1} \\ | + | \vdots &\cdots& \ddots & a_{n-3} & b_{n-2} & c_{n-1} & d_{n-1} \\ |
0 & \cdots & \cdots & 0 & a_{n-2} & b_{n-1} & c_n | 0 & \cdots & \cdots & 0 & a_{n-2} & b_{n-1} & c_n | ||
\end{pmatrix}</math>. | \end{pmatrix}</math>. | ||
| Line 20: | Line 20: | ||
*Also in Calci users can get a deimal values with positive and negative 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") | *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) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | -58 || 15 || -4 | ||
| + | |- | ||
| + | | -54 || 55 || -75 | ||
| + | |- | ||
| + | | 21 || -25 || -64 | ||
| + | |} | ||
| + | *3.MATRIX("pentadiagonal",6) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 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) | ||
| + | {| 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 | ||
| + | |- | ||
| + | | 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 | ||
| + | |- | ||
| + | | 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== | ||
| + | *[[Manuals/calci/SYMMETRIC| SYMMETRIC]] | ||
| + | *[[Manuals/calci/BIDIAGONAL| BIDIAGONAL]] | ||
| + | *[[Manuals/calci/TRIANGULAR| TRIANGULAR]] | ||
| + | |||
| + | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Pentadiagonal_matrix Pentadiagonal Matrix] | ||
Latest revision as of 01:33, 26 October 2015
MATRIX("PENTADIAGONAL",order)
- is the size of the Pentadiagonal matrix.
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 |