#LyX 2.3 created this file. For more info see http://www.lyx.org/ \lyxformat 544 \begin_document \begin_header \save_transient_properties true \origin unavailable \textclass book \use_default_options true \maintain_unincluded_children false \language spanish \language_package default \inputencoding auto \fontencoding global \font_roman "default" "default" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default \use_non_tex_fonts false \font_sc false \font_osf false \font_sf_scale 100 100 \font_tt_scale 100 100 \use_microtype false \use_dash_ligatures true \graphics default \default_output_format default \output_sync 0 \bibtex_command default \index_command default \paperfontsize default \spacing single \use_hyperref false \papersize default \use_geometry false \use_package amsmath 1 \use_package amssymb 1 \use_package cancel 1 \use_package esint 1 \use_package mathdots 1 \use_package mathtools 1 \use_package mhchem 1 \use_package stackrel 1 \use_package stmaryrd 1 \use_package undertilde 1 \cite_engine basic \cite_engine_type default \biblio_style plain \use_bibtopic false \use_indices false \paperorientation portrait \suppress_date false \justification true \use_refstyle 1 \use_minted 0 \index Index \shortcut idx \color #008000 \end_index \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \paragraph_indentation default \is_math_indent 0 \math_numbering_side default \quotes_style french \dynamic_quotes 0 \papercolumns 1 \papersides 1 \paperpagestyle default \tracking_changes false \output_changes false \html_math_output 0 \html_css_as_file 0 \html_be_strict false \end_header \begin_body \begin_layout Standard Los ficheros de código de Octave tienen extensión \family typewriter .m \family default y pueden contener un \emph on script \emph default o una función. Los \emph on scripts \emph default contienen una secuencia de órdenes y se invocan con \family typewriter \emph on nombre \family default \emph default (el nombre del fichero sin la extensión). Las funciones tienen forma: \end_layout \begin_layout Standard \begin_inset Box Frameless position "t" hor_pos "c" has_inner_box 1 inner_pos "t" use_parbox 0 use_makebox 0 width "100col%" special "none" height "1in" height_special "totalheight" thickness "0.4pt" separation "3pt" shadowsize "4pt" framecolor "black" backgroundcolor "none" status open \begin_layout Plain Layout \family typewriter function \family default ( \family typewriter \emph on val \family default \emph default | \family typewriter [ \emph on val \emph default , \family default ... \family typewriter ] \family default ) \family typewriter = \emph on nombre \emph default ( \emph on par \emph default , \family default ... \family typewriter ) \end_layout \begin_layout Plain Layout \family typewriter \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \emph on stmt \end_layout \begin_layout Plain Layout \family typewriter \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \family default ... \end_layout \begin_layout Plain Layout \family typewriter endfunction \end_layout \end_inset \end_layout \begin_layout Standard Donde \family typewriter \emph on nombre \family default \emph default debe coincidir con el nombre del fichero, los parámetros ( \family typewriter \emph on par \family default \emph default ) se pueden usar como variables, y los valores de retorno ( \family typewriter \emph on val \family default \emph default ) se usan como variables inicialmente no definidas, de modo que su valor al final de la función es el valor devuelto. La función se invoca con la expresión \family typewriter \emph on nombre \emph default ( \emph on arg \emph default , \family default ... \family typewriter ) \family default si devuelve un solo valor o con la sentencia \family typewriter [ \emph on var \emph default , \family default ... \family typewriter ] = \emph on nombre \emph default ( \emph on arg \emph default , \family default ... \family typewriter ) \family default si devuelve varios. Por defecto, Octave busca los \emph on scripts \emph default y funciones en el directorio actual (que se puede cambiar en la interfaz gráfica) y en la biblioteca estándar. \end_layout \begin_layout Standard Las sentencias terminan con salto de línea o con \family typewriter ; \family default (normalmente seguido de salto de línea), pero si termina en salto de línea, el valor devuelto se imprime, bien como \family typewriter ans = \emph on valor \family default \emph default si la sentencia es una expresión \family typewriter \emph on expr \family default \emph default que devuelve un \family typewriter \emph on valor \family default \emph default , o como \family typewriter \emph on A \emph default = \emph on valor \family default \emph default si la sentencia es una asignación \family typewriter \emph on A \emph default = \emph on expr \family default \emph default . Las variables se definen en su primera asignación. \end_layout \begin_layout Standard Los comentarios empiezan por \family typewriter % \family default o \family typewriter # \family default y terminan al final de la línea. \end_layout \begin_layout Standard Las variables de las funciones tienen ámbito local y las de los \emph on scripts \emph default tienen como ámbito el intérprete de comandos. Existe un ámbito global, y para indicar que una variable pertenece a este, se añade el comando \family typewriter global \emph on variable \family default \emph default en cada ámbito en que se vaya a usar (en el intérprete, normalmente dentro de un \emph on script \emph default , y en las funciones). \end_layout \begin_layout Section Tipos de datos \end_layout \begin_layout Subsection Matrices \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{sloppypar} \end_layout \end_inset En Octave, los números (con sintaxis \family typewriter [-+]?(( \backslash d+ \backslash .?| \backslash d* \backslash . \backslash d+)([eE][-+]? \backslash d+)?|[Ii]nf) \family default o \family typewriter ( \family default {número} \family typewriter \backslash +)? \family default {número} \family typewriter ?i \family default ) representan matrices \begin_inset Formula $1\times1$ \end_inset de números de doble precisión, y las cadenas de caracteres (con sintaxis \family typewriter '([^']|'')*' \family default o \family typewriter "([^ \backslash \backslash ']| \backslash \backslash \family default {escape} \family typewriter )*" \family default ) representan matrices fila de caracteres. En estas, \family typewriter \backslash n \family default indica un salto de línea y \family typewriter \backslash t \family default un tabulador. \begin_inset ERT status open \begin_layout Plain Layout \backslash end{sloppypar} \end_layout \end_inset \end_layout \begin_layout Standard La expresión \family typewriter [ \begin_inset Formula $a_{1}$ \end_inset , \family default ... \family typewriter , \begin_inset Formula $a_{p}$ \end_inset ] \family default concatena horizontalmente las matrices \begin_inset Formula $a_{1}\in{\cal M}_{m\times n_{1}}(S)$ \end_inset hasta \begin_inset Formula $a_{p}\in{\cal M}_{m\times n_{p}}(S)$ \end_inset en una matriz en \begin_inset Formula ${\cal M}_{m\times\sum_{k=1}^{p}n_{k}}(S)$ \end_inset , y la sintaxis \family typewriter [ \begin_inset Formula $a_{11}$ \end_inset , \family default ... \family typewriter , \begin_inset Formula $a_{1p_{1}}$ \end_inset ; \family default ... \family typewriter ; \begin_inset Formula $a_{q1}$ \end_inset , \family default ... \family typewriter , \begin_inset Formula $a_{qp_{q}}$ \end_inset ] \family default hace esto en cada parte, resultando en \begin_inset Formula $q$ \end_inset matrices \begin_inset Formula $b_{k}\in{\cal M}_{m_{k}\times n}(S)$ \end_inset , y las concatena verticalmente en una \begin_inset Formula ${\cal M}_{\sum_{k=1}^{q}m_{k}\times n}(S)$ \end_inset . \end_layout \begin_layout Standard Si una operación \begin_inset Formula $*$ \end_inset actúa sobre matrices, \begin_inset Formula $\mathtt{.}*$ \end_inset actúa sobre cada elemento. Si se aplica a dos matrices de igual tamaño, se aplica a cada elemento de una con el correspondiente de la otra para obtener un elemento \begin_inset Formula $1\times1$ \end_inset que se sitúa en la posición correspondiente de la matriz de salida. Si una de las dos es de un elemento, se extiende a una de igual tamaño que la otra con todos los elementos iguales al original. \end_layout \begin_layout Standard \family typewriter \emph on A \emph default ( \emph on x \emph default , \emph on y \emph default ) \family default es la submatriz de \family typewriter \emph on A \family default \emph default formada por las columnas con índice en el vector \family typewriter \emph on x \family default \emph default y las filas con índice en el vector \family typewriter \emph on y \family default \emph default , y \family typewriter \emph on A \emph default ( \emph on x \emph default ) \family default convierte la matriz en un vector concatenando las traspuestas de sus columnas y toma los elementos del vector con índice en \family typewriter \emph on x \family default \emph default . Los vectores de índice se pueden sustituir por \family typewriter : \family default para tomar todas las filas o columnas. Los índices empiezan por 1. \end_layout \begin_layout Standard \family typewriter \emph on A \emph default ( \emph on x \emph default , \emph on y \emph default ) = \emph on expr \family default \emph default o \family typewriter \emph on A \emph default ( \emph on x \emph default ) = \emph on expr \family default \emph default asigna los elementos de la submatriz a la izquierda del \family typewriter = \family default a los de la devuelta por la expresión, que debe ser del mismo tamaño. Si la variable no existe, se crea, y si la submatriz indicada supone que \family typewriter \emph on A \family default \emph default es más grande de lo que es, esta se amplía y se rellena con ceros. \end_layout \begin_layout Subsection Números \end_layout \begin_layout Standard El operador \family typewriter + \family default suma matrices numéricas de igual tamaño, \family typewriter - \family default las resta y \family typewriter * \family default multiplica matrices o una matriz por un escalar. Si \family typewriter \emph on a \family default \emph default y \family typewriter \emph on b \family default \emph default son escalares con \begin_inset Formula $\text{\emph{\texttt{b}}}\neq0$ \end_inset , \family typewriter \emph on a \emph default / \emph on b \family default \emph default es su cociente. \end_layout \begin_layout Standard Llamamos vector a una matriz fila. Entonces \family typewriter \emph on a \emph default : \emph on b \family default \emph default genera el vector \begin_inset Formula $(\text{\emph{\texttt{a}}},\text{\emph{\texttt{a}}}+1,\dots,\text{\emph{\texttt{b}}})$ \end_inset y \family typewriter \emph on a \emph default : \emph on t \emph default : \emph on b \family default \emph default genera el vector \begin_inset Formula $(\text{\emph{\texttt{a}}},\text{\emph{\texttt{a}}}+\text{\emph{\texttt{t}}},\dots,\text{\emph{\texttt{b}}})$ \end_inset . Cuando es posible, \family typewriter A \backslash \emph on B \family default \emph default devuelve una matriz \begin_inset Formula $X$ \end_inset tal que \begin_inset Formula $\text{\emph{\texttt{A}}}X=\text{\emph{\texttt{B}}}$ \end_inset . \family typewriter \begin_inset Formula $\text{\emph{\texttt{A}}}\mathtt{'}$ \end_inset \family default es \begin_inset Formula $\text{\emph{\texttt{A}}}^{*}$ \end_inset . \end_layout \begin_layout Subsection Booleanos \end_layout \begin_layout Standard Los booleanos son números: 0 para falso, cualquier otro número (normalmente 1) para verdadero. Entonces \family typewriter | \family default o \family typewriter || \family default es el operador disyunción; \family typewriter & \family default o \family typewriter && \family default es la conjunción. Los operadores de comparación \family typewriter == \family default , \family typewriter != \family default (o \family typewriter ~= \family default ), \family typewriter < \family default , \family typewriter <= \family default , \family typewriter > \family default y \family typewriter >= \family default hacen lo que se esperaría. \end_layout \begin_layout Subsection Listas \end_layout \begin_layout Standard Las listas pueden contener elementos de distintos tipos. No se asigna a una lista, sino a sus elementos, a los que se hace referencia por \family typewriter \emph on lista \emph default { \emph on índice \emph default } \family default . Los índices empiezan por 1. Si se asigna a un índice mayor que el tamaño de la lista, esta se amplía y se rellena con matrices numéricas \begin_inset Formula $0\times0$ \end_inset . \end_layout \begin_layout Subsection Funciones anónimas \end_layout \begin_layout Standard Una función anónima se expresa como \family typewriter @( \emph on par \emph default , \family default ... \family typewriter ) \emph on expr \family default \emph default , puede asignarse y puede usarse como una función normal. Solo puede devolver un elemento. \end_layout \begin_layout Standard \begin_inset Newpage pagebreak \end_inset \end_layout \begin_layout Section Control de flujo \end_layout \begin_layout Standard La sentencia \end_layout \begin_layout Standard \begin_inset Box Frameless position "t" hor_pos "c" has_inner_box 1 inner_pos "t" use_parbox 0 use_makebox 0 width "100col%" special "none" height "1in" height_special "totalheight" thickness "0.4pt" separation "3pt" shadowsize "4pt" framecolor "black" backgroundcolor "none" status open \begin_layout Plain Layout \family typewriter for \emph on var \emph default = \emph on vector \end_layout \begin_layout Plain Layout \family typewriter \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \emph on stmt \family default \emph default ... \end_layout \begin_layout Plain Layout \family typewriter endfor \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash noindent \end_layout \end_inset evalúa los \family typewriter \emph on stmt \family default \emph default una vez por cada elemento del \family typewriter \emph on vector \family default \emph default con \family typewriter \emph on var \family default \emph default tomando el valor del elemento. El \family typewriter \emph on vector \family default \emph default también puede ser una lista, pero entonces devuelve listas de un elemento a las que hay que acceder con el índice 1. \end_layout \begin_layout Standard \begin_inset Box Frameless position "t" hor_pos "c" has_inner_box 1 inner_pos "t" use_parbox 0 use_makebox 0 width "100col%" special "none" height "1in" height_special "totalheight" thickness "0.4pt" separation "3pt" shadowsize "4pt" framecolor "black" backgroundcolor "none" status open \begin_layout Plain Layout \family typewriter while \emph on condición \end_layout \begin_layout Plain Layout \family typewriter \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \emph on stmt \emph default \family default ... \end_layout \begin_layout Plain Layout \family typewriter endwhile \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash noindent \end_layout \end_inset evalúa los \family typewriter \emph on stmt \family default \emph default repetidamente mientras la \family typewriter \emph on condición \family default \emph default se cumpla, comprobándola al principio de cada iteración. \end_layout \begin_layout Standard \begin_inset Box Frameless position "t" hor_pos "c" has_inner_box 1 inner_pos "t" use_parbox 0 use_makebox 0 width "100col%" special "none" height "1in" height_special "totalheight" thickness "0.4pt" separation "3pt" shadowsize "4pt" framecolor "black" backgroundcolor "none" status open \begin_layout Plain Layout \family typewriter do \end_layout \begin_layout Plain Layout \family typewriter \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \emph on stmt \family default \emph default ... \end_layout \begin_layout Plain Layout \family typewriter until \emph on condición \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash noindent \end_layout \end_inset evalúa los \family typewriter \emph on stmt \family default \emph default repetidamente mientras la \family typewriter \emph on condición \family default \emph default no se cumpla, comprobándola al principio de cada iteración salvo la primera. \end_layout \begin_layout Standard \begin_inset Box Frameless position "t" hor_pos "c" has_inner_box 1 inner_pos "t" use_parbox 0 use_makebox 0 width "100col%" special "none" height "1in" height_special "totalheight" thickness "0.4pt" separation "3pt" shadowsize "4pt" framecolor "black" backgroundcolor "none" status open \begin_layout Plain Layout \family typewriter if \emph on condición \end_layout \begin_layout Plain Layout \family typewriter \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \emph on then-stmts \end_layout \begin_layout Plain Layout [ \family typewriter else \end_layout \begin_layout Plain Layout \family typewriter \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \emph on else-stmts \family default \emph default ] \end_layout \begin_layout Plain Layout \family typewriter endif \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash noindent \end_layout \end_inset evalúa \family typewriter \emph on condición \family default \emph default y, si se cumple, ejecuta \family typewriter \emph on then-stmts \family default \emph default , y de lo contrario, si está, ejecuta \family typewriter \emph on else-stmts \family default \emph default . \end_layout \begin_layout Standard La sentencia \family typewriter break \family default sale del bucle ( \family typewriter for \family default o \family typewriter while \family default ) más interno en que se encuentra, \family typewriter continue \family default pasa a su siguiente iteración y \family typewriter return \family default sale de la función. \end_layout \begin_layout Standard \begin_inset Box Frameless position "t" hor_pos "c" has_inner_box 1 inner_pos "t" use_parbox 0 use_makebox 0 width "100col%" special "none" height "1in" height_special "totalheight" thickness "0.4pt" separation "3pt" shadowsize "4pt" framecolor "black" backgroundcolor "none" status open \begin_layout Plain Layout \family typewriter try \end_layout \begin_layout Plain Layout \family typewriter \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \emph on stmts \end_layout \begin_layout Plain Layout \family typewriter catch \end_layout \begin_layout Plain Layout \family typewriter \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \emph on handle-stmts \end_layout \begin_layout Plain Layout \family typewriter end_try_catch \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash noindent \end_layout \end_inset ejecuta los \family typewriter \emph on stmts \family default \emph default y, si hay una excepción, la captura y ejecuta los \family typewriter \emph on handle-stmts \family default \emph default . \end_layout \begin_layout Section Biblioteca estándar \end_layout \begin_layout Standard La mayoría de funciones que reciben un número y devuelven otro también funcionan elemento a elemento con matrices. \end_layout \begin_layout Description \family typewriter \series bold abs( \emph on z \emph default ) \family default \series default \begin_inset Formula $|\text{\emph{\texttt{z}}}|$ \end_inset . \end_layout \begin_layout Description \family typewriter addpath( \emph on dir \emph default , \family default ... \family typewriter ) \family default Añade los directorios indicados a la lista de rutas donde buscar \emph on scripts \emph default y funciones. \end_layout \begin_layout Description \family typewriter and( \emph on x1 \emph default , \emph on x2 \emph default , \family default \series bold ... \family typewriter ) \family default \series default \family typewriter \emph on x1 \emph default & \emph on x2 \emph default & \family default ... \end_layout \begin_layout Description \family typewriter \series bold clc \family default \series default Limpia la pantalla de la \emph on shell \emph default . \end_layout \begin_layout Description \family typewriter \series bold clear \family default \series default Borra todas las variables. \end_layout \begin_layout Description \family typewriter clf \family default Vacía la ventana de gráficas, creándola si no existía ya. \end_layout \begin_layout Description \family typewriter cond( \series bold \emph on A \series default \emph default , \emph on p \emph default ) \family default \family typewriter norm( \emph on A \emph default , \emph on p \emph default ) * norm(inv( \emph on A \emph default ), \emph on p \emph default ) \family default . \end_layout \begin_layout Description \family typewriter cond( \series bold \emph on A \series default \emph default ) \family default \family typewriter cond( \emph on A \emph default ,2) \family default . \end_layout \begin_layout Description \family typewriter contour( \emph on x \emph default , \emph on y \emph default , \emph on v \emph default , \emph on h \emph default , \emph on style \emph default ) \family default Si a cada par formado por un elemento de \family typewriter \emph on x \family default \emph default y el correspondiente de \family typewriter \emph on y \family default \emph default se le asigna el elemento correspondiente de \family typewriter \emph on v \family default \emph default , dibuja la curva de nivel (aproximada) de la gráfica a la altura \family typewriter \emph on h \family default \emph default . El parámetro \family typewriter \emph on style \family default \emph default es una cadena donde cada caracter indica una propiedad: \family typewriter r \family default rojo, \family typewriter b \family default azul, \family typewriter m \family default magenta, etc. \end_layout \begin_layout Description \family typewriter contour( \series bold \emph on x \emph default , \emph on y \emph default , \emph on z \emph default , \emph on h \emph default ) \family default \series default Como la anterior, con el estilo por defecto. \end_layout \begin_layout Description \family typewriter diag( \emph on A \emph default , \emph on k \emph default ) \family default Si \family typewriter \emph on A \family default \emph default es vector, devuelve una matriz diagonal con elementos del vector en la diagonal \begin_inset Formula $\{(i,j)\mid i+k=j\}$ \end_inset , y de lo contrario devuelve un vector con los elementos de dicha diagonal de \family typewriter \emph on A \family default \emph default . \end_layout \begin_layout Description \family typewriter diag( \emph on A \series bold \emph default ) \family default \series default \family typewriter diag( \emph on A \emph default ,0) \family default . \end_layout \begin_layout Description \family typewriter disp( \emph on x \emph default ) \family default Imprime el valor de \family typewriter \emph on x \family default \emph default . \end_layout \begin_layout Description \family typewriter dot( \emph on x \emph default , \emph on y \emph default ) \family default Producto escalar hermitiano \begin_inset Formula $\langle\text{\emph{\texttt{y}}},\text{\emph{\texttt{x}}}\rangle$ \end_inset . \end_layout \begin_layout Description \family typewriter [ \emph on V \emph default , \emph on lambda \emph default ]=eig( \emph on A \emph default ) \family default Devuelve una matriz diagonal \family typewriter \emph on lambda \family default \emph default en la que los elementos de las diagonal son los valores propios de \family typewriter \emph on A \family default \emph default y una matriz \family typewriter \emph on V \family default \emph default cuyas columnas son los vectores propios correspondientes. \end_layout \begin_layout Description \family typewriter eps \family default Menor \begin_inset Formula $\epsilon$ \end_inset tal que \begin_inset Formula $1+\epsilon>1$ \end_inset con la precisión de la máquina. \end_layout \begin_layout Description \family typewriter error( \emph on text \emph default ) \family default Lanza una excepción con un cierto texto. \end_layout \begin_layout Description \family typewriter exp( \series bold \emph on z \emph default ) \family default \series default \begin_inset Formula $e^{\text{\emph{\texttt{z}}}}$ \end_inset . \end_layout \begin_layout Description \family typewriter eye( \emph on n \emph default ) \family default Matriz identidad de tamaño \family typewriter \emph on n \family default \emph default . \end_layout \begin_layout Description \family typewriter feval( \emph on función \series bold \emph default , \family default ... \family typewriter ) \family default \family typewriter \series default \emph on función \emph default ( \family default ... \family typewriter ) \family default . \end_layout \begin_layout Description \family typewriter figure( \emph on n \emph default ) \family default \series medium Crea una ventana para gráficas identificada por \family typewriter \series default \emph on n \family default \emph default si esta no existe, y la usa para los dibujos posteriores. \end_layout \begin_layout Description \family typewriter fminunc( \emph on f \emph default , \emph on x0 \emph default ) \family default Busca un mínimo local de \family typewriter \emph on f \family default \emph default partiendo de una aproximación inicial \family typewriter \emph on x0 \family default \emph default . \end_layout \begin_layout Description \family typewriter format \begin_inset space ~ \end_inset \emph on opción \family default \emph default Cambia el formato en que se imprimen los números por defecto. Posibles valores son \family typewriter short \family default o \family typewriter long \family default para la cantidad de decimales (pocos o muchos), seguido opcionalmente por \family typewriter e \family default para notación científica o \family typewriter g \family default para elegir en cada caso si es mejor usar notación científica o normal. \end_layout \begin_layout Description \family typewriter fprintf( \emph on fmt \emph default , \family default ... \family typewriter ) \family default \family typewriter printf( \emph on fmt \emph default , \family default ... \family typewriter ) \family default . \end_layout \begin_layout Description \family typewriter inv( \emph on A \emph default ) \family default Inversa de la matriz cuadrada no singular \family typewriter \emph on A \family default \emph default . \end_layout \begin_layout Description \family typewriter isosurface( \series bold \emph on x \emph default , \emph on y \emph default , \emph on z \emph default , \emph on v \emph default , \emph on val \emph default ) \family default \series default Como \family typewriter contour \family default para funciones de 3 variables \begin_inset Formula $(\text{\emph{\texttt{x}}},\text{\emph{\texttt{y}}},\text{\emph{\texttt{z}}})$ \end_inset . \end_layout \begin_layout Description \family typewriter length( \emph on A \emph default ) \family default \family typewriter max(size( \emph on A \emph default )) \family default . \end_layout \begin_layout Description \family typewriter linspace( \emph on start \emph default , \emph on end \emph default , \emph on n \emph default ) \family default Vector de \family typewriter \emph on n \family default \emph default puntos equiespaciados de \family typewriter \emph on start \family default \emph default a \family typewriter \emph on end \family default \emph default . \end_layout \begin_layout Description \family typewriter [ \series bold \emph on L \emph default , \emph on U \emph default , \emph on P \emph default , \series default \emph on Q \series bold \emph default ]=lu( \series default \emph on A \emph default ) \family default Descomposición de Gauss de \family typewriter \series bold \emph on A \family default \series default \emph default con elección de pivote total. \end_layout \begin_layout Description \family typewriter [ \emph on L \emph default , \emph on U \emph default , \emph on P \emph default ]=lu( \emph on A \emph default ) \family default Descomposición de Gauss de \family typewriter \emph on A \family default \emph default con elección de pivote parcial. \end_layout \begin_layout Description \family typewriter max( \emph on x \emph default , \series bold \emph on y \emph default ) \family default \series default \begin_inset Formula $\max\{\text{\emph{\texttt{x}}},\text{\emph{\texttt{y}}}\}$ \end_inset . \end_layout \begin_layout Description \family typewriter [ \emph on w \emph default , \emph on iw \emph default ]=max( \emph on v \emph default ) \family default Obtiene \begin_inset Formula $\text{\emph{\texttt{w}}}=\max\text{\emph{\texttt{v}}}_{i}$ \end_inset e \family typewriter \emph on iw \family default \emph default con \begin_inset Formula $\text{\emph{\texttt{w}}}=v_{\text{\emph{\texttt{iw}}}}$ \end_inset . \end_layout \begin_layout Description \family typewriter max( \emph on A \emph default ) \family default \begin_inset Formula $\max\text{\emph{\texttt{A}}}_{ij}$ \end_inset . \end_layout \begin_layout Description \family typewriter [ \emph on xx \emph default , \emph on yy \emph default ]=meshgrid( \emph on x \emph default , \series bold \emph on y \emph default ) \family default \series default Si \family typewriter \emph on x \family default \emph default es un vector de \begin_inset Formula $m$ \end_inset elementos e \family typewriter \emph on y \family default \emph default es un vector de \begin_inset Formula $y$ \end_inset elementos, \family typewriter \emph on xx \family default \emph default e \family typewriter \emph on yy \family default \emph default son matrices \begin_inset Formula $m\times n$ \end_inset donde las filas de \family typewriter \emph on xx \family default \emph default son copias de \family typewriter \emph on x \family default \emph default y las columnas de \family typewriter \emph on yy \family default \emph default son copias de \family typewriter \emph on y \family default \emph default . \end_layout \begin_layout Description \family typewriter min( \emph on x \emph default , \series bold \emph on y \emph default ) \family default \series default \begin_inset Formula $\min\{\text{\emph{\texttt{x}}},\text{\emph{\texttt{y}}}\}$ \end_inset . \end_layout \begin_layout Description \family typewriter [ \emph on w \emph default , \emph on iw \emph default ]=min( \emph on v \emph default ) \family default Obtiene \begin_inset Formula $\text{\emph{\texttt{w}}}=\min\text{\emph{\texttt{v}}}_{i}$ \end_inset e \family typewriter \emph on iw \family default \emph default con \begin_inset Formula $\text{\emph{\texttt{w}}}=v_{\text{\emph{\texttt{iw}}}}$ \end_inset . \end_layout \begin_layout Description \family typewriter min( \emph on A \emph default ) \family default \begin_inset Formula $\min\text{\emph{\texttt{A}}}_{ij}$ \end_inset . \end_layout \begin_layout Description \family typewriter norm( \series bold \emph on A \emph default , \series default \emph on p \emph default , \emph on opt \series bold \emph default ) \family default \series default Si \family typewriter \series bold opt \family default \series default es \family typewriter \begin_inset Quotes qld \end_inset columns \begin_inset Quotes qrd \end_inset \family default o \family typewriter \begin_inset Quotes qld \end_inset cols \begin_inset Quotes qrd \end_inset \family default , vector fila con la norma \family typewriter \emph on p \family default \emph default de cada vector columna en \family typewriter \emph on A \family default \emph default . Si es \family typewriter \begin_inset Quotes qld \end_inset rows \begin_inset Quotes qrd \end_inset \family default , vector columna con la norma \family typewriter \emph on p \family default \emph default de cada vector fila en \family typewriter \emph on A \family default \emph default . \end_layout \begin_layout Description \family typewriter norm( \emph on A \series medium \emph default , \emph on p \emph default ) \family default Norma \family typewriter \series default \emph on p \family default \emph default de \family typewriter \emph on A \family default \emph default , matricial o vectorial según corresponda, donde \family typewriter \emph on p \family default \emph default es un entero positivo o \family typewriter Inf \family default . \end_layout \begin_layout Description \family typewriter norm( \emph on A \emph default ) \family default \family typewriter norm( \emph on A \emph default ,2) \family default . \end_layout \begin_layout Description \family typewriter ones( \emph on m \emph default , \emph on n \emph default ) \family default Matriz \begin_inset Formula $m\times n$ \end_inset formada por unos. \end_layout \begin_layout Description \family typewriter or( \emph on x1 \emph default , \emph on x2 \emph default , \family default ... \family typewriter ) \family default \family typewriter \emph on x1 \emph default | \emph on x2 \emph default | \family default ... \end_layout \begin_layout Description \family typewriter printf( \emph on fmt \emph default , \family default ... \family typewriter ) \family default Imprime los argumentos con un cierto formato \family typewriter \emph on fmt \family default \emph default , una cadena con caracteres normales que se representan a sí mismos y secuencias de escape que empiezan por \family typewriter % \family default . Por ejemplo, \family typewriter %f \family default imprime el siguiente argumento como número de punto flotante con varios decimales, \family typewriter %e \family default también pero con notación científica, \family typewriter %d \family default también pero con pocos decimales, \family typewriter %s \family default como cadena y \family typewriter %% \family default representa un caracter \family typewriter % \family default . \end_layout \begin_layout Description \family typewriter rand( \emph on m \emph default , \emph on n \emph default ) \family default Matriz de \family typewriter \emph on m \family default \emph default filas y \family typewriter \emph on n \family default \emph default columnas con elementos aleatorios entre 0 y 1. \end_layout \begin_layout Description \family typewriter rmpath( \emph on dir \emph default , \family default ... \family typewriter ) \family default Elimina los directorios indicados de la lista de directorios donde buscar \emph on scripts \emph default y funciones. \end_layout \begin_layout Description \family typewriter size( \emph on A \emph default ) \family default Devuelve un vector con el número de elementos en cada dimensión de \family typewriter \emph on A \family default \emph default . Las matrices tienen dos dimensiones, y las listas también con primera dimensión de tamaño 1. \end_layout \begin_layout Description \family typewriter sign( \emph on z \emph default ) \family default Si \begin_inset Formula $\text{\emph{\texttt{z}}}=0$ \end_inset , 0, de lo contrario \begin_inset Formula $\frac{\text{\emph{\texttt{z}}}}{|\text{\emph{\texttt{z}}}|}$ \end_inset . \end_layout \begin_layout Description \family typewriter sort( \emph on v \emph default ) \family default Copia del vector \family typewriter \emph on v \family default \emph default con sus elementos en orden creciente. \end_layout \begin_layout Description \family typewriter sortrows( \emph on A \emph default ) \family default Copia de la matriz \family typewriter \emph on A \family default \emph default con sus filas en orden de menor a mayor primer elemento, o segundo en caso de empate, etc. \end_layout \begin_layout Description \family typewriter sqrt( \emph on z \emph default ) \family default \begin_inset Formula $\sqrt{\text{\emph{\texttt{z}}}}$ \end_inset . \end_layout \begin_layout Description \family typewriter sum( \emph on A \emph default ) \family default \begin_inset Formula $\sum\text{\emph{\texttt{A}}}_{ij}$ \end_inset . \end_layout \begin_layout Description \family typewriter [ \emph on U \emph default , \emph on S \emph default , \emph on V \emph default ]=svd( \emph on A \emph default ) \family default Devuelve dos matriz ortogonales \family typewriter \emph on U \family default \emph default y \family typewriter \emph on V \family default \emph default y una diagonal \family typewriter \emph on S \family default \emph default tales que \begin_inset Formula $\text{\emph{\texttt{A}}}=\text{\emph{\texttt{U}}}\text{\emph{\texttt{S}}}\text{\emph{\texttt{V}}}^{*}$ \end_inset . \end_layout \begin_layout Description \family typewriter title( \emph on str \emph default ) \family default Da un título a la gráfica. \end_layout \begin_layout Description \family typewriter trace( \emph on A \emph default ) \family default Traza de \family typewriter \emph on A \family default \emph default . \end_layout \begin_layout Description \family typewriter transpose( \series medium \emph on A \series default \emph default ) \family default \series medium \begin_inset Formula $\text{\emph{\texttt{A}}}^{t}$ \end_inset . \end_layout \begin_layout Description \family typewriter tril( \emph on A \emph default , \emph on k \emph default ) \family default Matriz como \family typewriter \emph on A \family default \emph default pero con los elementos \begin_inset Formula $(i,j)$ \end_inset con \begin_inset Formula $j-i>\text{\emph{\texttt{k}}}$ \end_inset a 0. \end_layout \begin_layout Description \family typewriter tril( \emph on A \emph default ) \family default \family typewriter tril( \emph on A \emph default ,0) \family default , matriz triangular inferior. \end_layout \begin_layout Description \family typewriter triu( \emph on A \emph default , \emph on k \emph default ) \family default Matriz como \family typewriter \emph on A \family default \emph default pero con los elementos \begin_inset Formula $(i,j)$ \end_inset con \begin_inset Formula $i-j>\text{\emph{\texttt{k}}}$ \end_inset a 0. \end_layout \begin_layout Description \family typewriter triu( \emph on A \series bold \emph default ) \family default \series default \family typewriter triu( \emph on A \emph default ,0) \family default , matriz triangular superior. \end_layout \begin_layout Description \family typewriter vander( \emph on c \emph default , \emph on n \emph default ) \family default \begin_inset Formula $(\text{\emph{\texttt{c}}}_{i}^{n-j})_{ij}\in{\cal M}_{\mathtt{size(\text{\emph{\texttt{c}}})}\times n}$ \end_inset . \end_layout \begin_layout Description \family typewriter warning( \emph on text \emph default ) \family default Muestra un texto a modo de alerta. \end_layout \begin_layout Description \family typewriter xlabel( \emph on str \emph default ) \family default Indica la leyenda del eje X de la gráfica. \end_layout \begin_layout Description \family typewriter ylabel( \series bold \emph on str \emph default ) \family default \series default Indica la leyenda del eje Y de la gráfica. \end_layout \begin_layout Description \family typewriter zeros( \emph on m \emph default , \emph on n \emph default ) \family default Matriz nula de \family typewriter \emph on m \family default \emph default filas y \family typewriter \emph on n \family default \emph default columnas. \end_layout \begin_layout Description \family typewriter zlabel( \emph on str \emph default ) \family default Indica la leyenda del eje Z de la gráfica. \end_layout \end_body \end_document