## all functions - r

random

random(dimension_list) random_seed, seed returns an array of random double values with the given DIMENSION_LIST (nil for a scalar result), uniformly distributed on the interval from 0.0 to 1.0. The algorithm is from Press and Teukolsky, Computers in Physics, vol. 6, no. 5, Sep/Oct 1992 (ran2). They offer a reward of $1000 to anyone who can exhibit a statistical test that this random number generator fails in a "non-trivial" way. The random_seed call reinitializes the random number sequence; SEED should be between 0.0 and 1.0 non-inclusive; if SEED is omitted, nil, or out of range, the sequence is reinitialized as when Yorick starts. The numbers are actually at the centers of 2147483562 equal width bins on the interval [0,1]. Although only these 2 billion numbers are possible, the period of the generator is roughly 2.3e18. Builtin function, documented at i0/std.i line 758SEE ALSO: randomize

random_ipq

random_ipq(ipq_model, dimlist) returns an array of double values with the given DIMLIST (see array function, nil for a scalar result). The numbers are distributed according to a piecewise linear function (possibly with power law or exponential tails) specified by the IPQ_MODEL. The "IPQ" stands for "inverse piecewise quadratic", which the type of function required to transform a uniform random deviate into the piecewise linear distribution. Use the ipq_setup function to compute IPQ_MODEL. Interpreted function, defined at i/random.i line 179SEE ALSO: random, random_x, random_u, random_n, random_rej, ipq_setup

random_n

random_n(dimlist) returns an array of normally distributed random double values with the given DIMLIST (see array function, nil for a scalar result). The mean is 0.0 and the standard deviation is 1.0. The algorithm follows the Box-Muller method (see Numerical Recipes by Press et al.). Interpreted function, defined at i/random.i line 130SEE ALSO: random, random_x, random_u, random_ipq, random_rej, poisson

random_rej

random_rej(target_dist, ipq_model, dimlist) or random_rej(target_dist, bounding_dist, bounding_rand, dimlist) returns an array of double values with the given DIMLIST (see array function, nil for a scalar result). The numbers are distributed according to the TARGET_DIST function: func target_dist(x) returning u(x)>=0 of same number and dimensionality as x, normalized so that the integral of target_dist(x) from -infinity to +infinity is 1.0. The BOUNDING_DIST function must have the same calling sequence as TARGET_DIST: func bounding_dist(x) returning b(x)>=u(x) everywhere. Since u(x) is normalized, the integral of b(x) must be >=1.0. Finally, BOUNDING_RAND is a function which converts an array of uniformly distributed random numbers on (0,1) -- as returned by random -- into an array distributed according to BOUNDING_DIST: func bounding_rand(uniform_x_01) Mathematically, BOUNDING_RAND is the inverse of the integral of BOUNDING_DIST from -infinity to x, with its input scaled to (0,1). If BOUNDING_DIST is not a function, then it must be an IPQ_MODEL returned by the ipq_setup function. In this case BOUNDING_RAND is omitted -- ipq_compute will be used automatically. Interpreted function, defined at i/random.i line 199SEE ALSO: random, random_x, random_u, random_n, random_ipq, ipq_setup

random_seed

random_seed Builtin function, documented at i0/std.i line 758SEE random

random_u

random_u(a, b, dimlist) return uniformly distributed random numbers between A and B. (Will never exactly equal A or B.) The DIMLIST is as for the array function. Same as (b-a)*random(dimlist)+a. If A==0, you are better off just writing B*random(dimlist). Interpreted function, defined at i/random.i line 113SEE ALSO: random, random_x, random_n, random_ipq, random_rej

random_x

random_x(dimlist) same as random(DIMLIST), except that random_x calls random twice at each point, to avoid the defect that random only can produce about 2.e9 numbers on the interval (0.,1.) (see random for an explanation of these bins). You may set random=random_x to get these "better" random numbers in every call to random. Unlike random, there is a chance in 1.e15 or so that random_x may return exactly 1.0 or 0.0 (the latter may not be possible with IEEE standard arithmetic, while the former apparently is). Since cosmic rays are far more likely, you may as well not worry about this. Also, because of rounding errors, some bit patterns may still be more likely than others, but the 0.5e-9 wide bins of random will be absent. Interpreted function, defined at i/random.i line 74SEE ALSO: random

randomize

randomize randomize() set the seed for random "randomly" (based on the timer clock and the current state of random). As a function, returns the value of the seed passed to random_seed. Interpreted function, defined at i0/std.i line 780SEE ALSO: random, random_seed

range

range, ymin, ymax sets the y-axis plot limits in the current coordinate system to YMIN, YMAX, which may be nil or omitted to leave the corresponding limit unchanged, a number to fix the corresponding limit to a specified value, or the string "e" to make the corresponding limit take on the extreme value of the currently displayed data. Use limits, xmin, xmin to accomplish the same function for the x-axis plot limits. Interpreted function, defined at i0/graph.i line 836SEE ALSO: plsys, limits, logxy, plg

range3

range3, zmin,zmax Set the 3D axis z limits for use with the cage. Use keyword aspect=[ax,ay,az] to set the aspect ratios of the cage to ax:ay:az -- that is, the ratios of the lengths of the cage axes will become ax:ay:az. Interpreted function, defined at i/pl3d.i line 221SEE ALSO: cage3, limit3, plwf, plwf, orient3

raw_not_cdf

raw_not_cdf Interpreted function, defined at i/netcdf.i line 57

raw_style

raw_style: get_style, set_style, read_style, write_style #include "style.i" alternatives to the style= keyword of the window command which allow the interpreter to set or get all the details of the window style. Include "style.i" and read the help for get_style. Builtin function, documented at i0/graph.i line 1515

rdfile

rdfile(f) or rdfile(f, nmax) reads all remaining lines (or at most NMAX lines) from file F. If NMAX is omitted, it defaults to 2^20 lines (about a million). The result is an array of strings, one per line of F. Interpreted function, defined at i0/std.i line 2110SEE ALSO: rdline

rdline

rdline(f) or rdline(f, n, prompt= pstring) returns next line from stream F (stdin if F nil). If N is non-nil, returns a string array containing the next N lines of F. If end-of-file occurs, rdline returns nil strings. If F is nil, uses the PSTRING to prompt for input (default "read> "). Builtin function, documented at i0/std.i line 2100SEE ALSO: read, open, close, bookmark, backup, read_n, rdfile

read

n= read(f, format=fstring, obj1, obj2, ...) or n= read(prompt= pstring, format=fstring, obj1, obj2, ...) or n= sread(source, format=fstring, obj1, obj2, ...) reads text from I/O stream F (1st form), or from the keyboard (2nd form), or from the string or string array SOURCE (3rd form), interprets it according to the optional FSTRING, and uses that interpretation to assign values to OBJ1, OBJ2, ... If the input is taken from the keyboard, the optional prompt PSTRING (default "read> ") is printed before each line is read. The Yorick write function does not interact with the read function -- writes are always to end-of-file, and do not affect the sequence of lines returned by read. The backup (and bookmark) function is the only way to change the sequence of lines returned by read. There must be one non-supressed conversion specifier (see below) in FSTRING for each OBJ to be read; the type of the conversion specifier must generally match the type of the OBJ. That is, an integer OBJ requires an integer specifier (d, i, o, u, or x) in FSTRING, a real OBJ requires a real specifier (e, f, or g), and a string OBJ requires a string specifier (s or []). An OBJ may not be complex, a pointer, a structure instance, or any non- array Yorick object. If FSTRING is not supplied, or if it has fewer conversion specifiers than the number of OBJ arguments, then Yorick supplies default specifiers ("%ld" for integers, "%lg" for reals, and "%s" for strings). If FSTRING contains more specifiers than there are OBJ arguments, the part of FSTRING beginning with the first specifier with no OBJ is ignored. The OBJ may be scalar or arrays, but the dimensions of every OBJ must be identical. If the OBJ are arrays, Yorick behaves as if the read were called in a loop numberof(OBJ1) times, filling one array element of each of the OBJ according to FSTRING on each pass through the loop. (Note that this behavior includes the case of reading columns of numbers by a single call to read.) The return value N is the total number of scalar assignments which were made as a result of this call. (If there were 4 OBJ arguments, and each was an array with 17 elements, a return value of N==35 would mean the following: The first 8 elements of OBJ1, OBJ2, OBJ3, and OBJ4 were read, and the 9th element of OBJ1, OBJ2, and OBJ3 was read.) The read function sets any elements of the OBJ which were not read to zero -- hence, independent of the returned N, the all of the old data in the OBJ arguments is overwritten. The read or sread functions continue reading until either: (1) all elements of all OBJ have been filled, or (2) end-of-file (or end of SOURCE for sread) is reached ("input failure"), or (3) part of FSTRING or a conversion specifier supplied by default fails to match the source text ("matching failure"). The FSTRING is composed of a series of "directives" which are (1) whitespace -- means to skip any amount of whitespace in the source text (2) characters other than whitespace and % -- must match the characters in the source text exactly, or matching failure occurs and the read operation stops (3) conversion specifiers beginning with % and ending with a character specifying the type of conversion -- optionally skip whitespace, then convert as many characters as continue to "look like" the conversion type, possibly producing a matching failure The conversion specifier is of the form %*WSC, where: is either the character '*' or not present A specifier beginning with %* does not correspond to any of the OBJ; the converted value will be discarded. W is either a positive decimal integer specifying the maximum field width (not including any skipped leading whitespace), or not present if any number of characters up to end-of-line is acceptable. S is either one of the characters 'h', 'l', or 'L', or not present. Yorick allows this for compatibility with the C library functions, but ignores it. C is a character specifying the type of conversion: d - decimal integer i - decimal, octal (leading 0), or hex (leading 0x) integer o - octal integer u - unsigned decimal integer (same as d for Yorick) x, X - hex integer e, f, g, E, G - floating point real s - string of non-whitespace characters [xxx] - (xxx is any sequence of characters) longest string of characters matching those in the list [^xxx] - longest string of characters NOT matching those in the list (this is how you can extend %s to be delimited by something other than whitespace) % - the ordinary % character; complete conversion specification must be "%%" The read function is modeled on the ANSI standard C library fscanf and sscanf functions, but differs in several respects: (1) Yorick's read cannot handle the %c, %p, or %n conversion specifiers in FSTRING. (2) Yorick's read never results in a portion of a line being read -- any unused part of a line is simply discarded (end FSTRING with "%[^\n]" if you want to save the trailing part of an input line). (3) As a side effect of (2), there are some differences between fscanf and Yorick's read in how whitespace extending across newlines is handled. Builtin function, documented at i0/std.i line 1994SEE ALSO: rdline, write, open, close, bookmark, backup, save, restore, read_n

read_clog

file= read_clog(file, clog_name) raw routine to set the binary data structure of FILE according to the text description in the Contents Log file CLOG_NAME. Builtin function, documented at i0/std.i line 2649

read_otable

read_otable Interpreted function, defined at i/ylmdec.i line 372

read_state

read_state Interpreted function, defined at i/ylmdec.i line 259

read_style

read_style, file, landscape, systems, legends, clegends read a Gist style sheet (.gs file), and return the data structures as described in the get_style function. The FILE can be a filename or a text file stream. Interpreted function, defined at i/style.i line 312SEE ALSO: get_style, set_style, write_style

recover_file

recover_file, filename or recover_file, filename, clogfile writes the descriptive information at the end of a corrupted binary file FILENAME from its Contents Log file CLOGFILE, which is FILENAME+"L" by default. Interpreted function, defined at i0/std.i line 2655

redraw

redraw redraws the X window associated with the current graphics window. Builtin function, documented at i0/graph.i line 334SEE ALSO: window, fma, hcp, plg

reform

reform(x, dimlist) returns array X reshaped according to dimension list DIMLIST. Interpreted function, defined at i0/std.i line 301SEE ALSO: array, dimsof

reg_track

c= reg_track(x, y, z, rays, s) track RAYS through regular mesh defined by the 1D coordinate arrays X, Y, and Z. Return values S and C are as for hex5_track, where the mesh is numberof(X) by numberof(Y) by numberof(Z). Builtin function, documented at i0/hex.i line 85SEE ALSO: hex5_track, track_reduce

remove

remove Builtin function, documented at i0/std.i line 1986SEE rename

rename

rename, old_filename, new_filename remove filename rename or remove a file. Builtin function, documented at i0/std.i line 1986SEE ALSO: open, close, openb

require

require Builtin function, documented at i0/std.i line 2254SEE include

reset

reset Interpreted function, defined at i/demo1.i line 37

reset_options

reset_options resets all options for the streak, snap, and streak_save functions to their default values. Interpreted function, defined at i0/drat.i line 856

reshape

reshape, reference, address, type, dimension_list or reshape, reference, type, dimension_list or reshape, reference The REFERENCE must be an unadorned variable, not an expression; reshape sets this variable to an LValue at the specified ADDRESS with the specified TYPE and DIMENSION_LIST. (See the array function documentation for acceptable DIMENSION_LIST formats.) If ADDRESS is an integer (e.g.- a long), the programmer is responsible for assuring that the data at ADDRESS is valid. If ADDRESS is a (Yorick) pointer, Yorick will assure that the data pointed to will not be discarded, and the reshape will fail if TYPE and DIMENSION_LIST extend beyond the pointee bounds. In the second form, ADDRESS is taken to be &REFERENCE; that is, the TYPE and DIMENSION_LIST of the variable are changed without doing any type conversion. In the third form, REFERENCE is set to nil ([]). (Simple redefinition will not work on a variable defined using reshape.) WARNING: There are almost no situations for which reshape is the correct operation. Use reform instead. Builtin function, documented at i0/std.i line 278SEE ALSO: reform, array, dimsof, numberof, is_array, eq_nocopy

restore

restore Builtin function, documented at i0/std.i line 3080SEE save

restore3

restore3, view Restore a previously saved 3D viewing transformation and lighting. If VIEW is nil, rotate object to viewer's coordinate system. Interpreted function, defined at i/pl3d.i line 242SEE ALSO: restore3, rot3, mov3, aim3, light3

rez_adjust_mesh

rez_adjust_mesh is an optional hook function which is called after any change to the mesh (e.g.- by dragging points) has been made. If it is defined, it may modify the external variables rez_rt and rez_zt. This hook can be used, for example, to force points along some k or l line to lie along a symmetry line. Builtin function, documented at i/rezone.i line 130SEE ALSO: rezone, rez_all, rez_mesh

rez_all

rez_all Click on [Drag Points] to drag points around with the mouse with rez_drag. Click on [Adjust Line] to adjust points along a line segment with rez_ladj. Click on [Adjust Region] to adjust points in a rectangular region with rez_radj. Click on the [Undo] button to undo the previous change. Click on the [Redo] button to redo the previous undo. Click on the [Revert] to return to the original mesh. When you are finished moving points around, click on [OK]. Click on [Escape] to exit with a non-zero return value. Click on [Zoom or Pan] to change the plot limits (see rez_zoom). Click on [Set Styles] to change the line styles or colors (see rez_style). Interpreted function, defined at i/rezone.i line 423SEE ALSO: rez_ladj, rez_mesh, rez_zoom, rez_style, rez_adjust_mesh

rez_chk_palette

rez_chk_palette Interpreted function, defined at i/rezone.i line 98

rez_color

rez_color Builtin function, documented at i/rezone.i line 39SEE rez_kstyle

rez_ding

rez_ding Interpreted function, defined at i/rezone.i line 1517

rez_drag

rez_drag Allow points in the rezone mesh to be dragged around with the mouse. Press mouse button near a vertex, move mouse to desired position of that vertex, and release button. If the point where you click is less than twice the distance to the second closest point than to the nearest point, the point will not be moved (you will hear a beep when you release the button). Click on the [Undo] button to undo the previous move; you can undo up to 100 previous moves by successive [Undo] clicks. When you are finished moving points around, click on [OK]. Click on [Zoom or Pan] to change the plot limits (see rez_zoom). Click on [Set Styles] to change the line styles or colors (see rez_style). Interpreted function, defined at i/rezone.i line 532SEE ALSO: rez_ladj, rez_radj, rez_mesh, rez_zoom, rez_style

rez_find

rez_find Interpreted function, defined at i/rezone.i line 1493

rez_getrz

rez_getrz Interpreted function, defined at i/rezone.i line 1451

rez_getvar

rez_getvar Interpreted function, defined at i/rezone.i line 1506

rez_kstyle

rez_kstyle, rez_lstyle, rez_color is a vector of three longs: [type,width,color] type MUST be 1, 2, 3, 4, or 5, width MUST be 1, 2, 3, 4, 5, 6, 7, or 8, and color MUST be -1, -2, -3, -4, -5, -6, -7, -8, -9, or -10 Either or both parameters may be set before or after including rez.i; by default: rez_kstyle= [4, 1, -2] (dashdot, thin, foreground color) rez_lstyle= [1, 1, -2] (solid, thin, foreground color) To distinguish K and L by color instead of type, try: rez_kstyle= [1, 1, -7] (dashdot, thin, blue) rez_lstyle= [1, 1, -5] (solid, thin, red) If the variable rez_color is true (non-nil and non-zero) when this file is included, then these will be the default. Builtin function, documented at i/rezone.i line 39SEE ALSO: rez_load_hook

rez_ladj

rez_ladj Adjust the points along a logical line segment PQ: Click on [Set P] or [Set Q] to set the endpoints of the segment. When P and Q have been set, click [OK]; this button will read [Cancel] if P and Q do not have either the same K or the same L index. Click on [Smooth] to smooth the points along PQ. Click on [Equal Space] to make the points along PQ equally spaced. This forces PQ to be a straight line. Drag any point between P and Q to get equal ratio spacing of all the points between P and Q. This also forces PQ to be a straight line; if PQ is initially curved, you may want to click on [Equal Space] before you attempt to drag points. Click on the [Undo] button to undo the previous adjustment; you can undo up to 20 previous adjustments by successive [Undo] clicks. When you are finished adjusting lines, click on [OK]. Click on [Zoom or Pan] to change the plot limits (see rez_zoom). Click on [Set Styles] to change the line styles or colors (see rez_style). Hint: You can select a center point as the second point during rez_ladj. When you do this, the K (or L) value of this second point will be the same as that of the first point -- otherwise there is no way to distinguish among all of the logical points at the center. Interpreted function, defined at i/rezone.i line 615SEE ALSO: rez_drag, rez_radj, rez_mesh, rez_zoom, rez_style

rez_load_hook

rez_load_hook If non-nil, filename to be included immediately after rez.i. This file can be used to set personalized default values for the many parameters. Some parameters may be set before loading rez.i, as well Builtin function, documented at i/rezone.i line 30SEE ALSO: rez_kstyle, rez_lstyle

rez_lstyle

rez_lstyle Builtin function, documented at i/rezone.i line 39SEE rez_kstyle

rez_mark

rez_mark Causes rezone functions to mark bowtied or chevroned (boomeranged) zones when the mesh is plotted. MUST have one of the following values: 0 to not mark bowtied or chevroned zones 1 to put a B at the center of the positive triangle of bowtied zones 2 to put a C at the center of the larger wing of chevroned zones 3 to mark both bowtied and chevroned zones By default, rez_mark is 3; you may set it to a different value either before or after including rez.i. Builtin function, documented at i/rezone.i line 66SEE ALSO: rez_mesh, rez_next, rez_prev, rez_drag

rez_mesh

rez_mesh, rt, zt, ireg -or- rez_mesh, rt, zt -or- rez_mesh, zfile set mesh for rez_... commands. If ZFILE is specified, it must be a binary file containing variables RT, ZT, and (optionally) IREG. Interpreted function, defined at i/rezone.i line 1373SEE ALSO: rez_all, rez_adjust_mesh

rez_next

rez_next zoom in on next bowtied (or chevroned) zone (after rez_mesh). With numeric argument, zooms to that bowtie (or chevron). With numeric argument 0, zooms to current bowtie (or chevron). Interpreted function, defined at i/rezone.i line 1410SEE ALSO: rez_prev, rez_mark, rez_drag

rez_palette

rez_palette 3-by-ncolors array used as a palette when rez_regs region coloring is set. The index in rez_regs is the second index into rez_palette. The length 3 first index is [r,g,b]. The default is 15 pastels. Builtin function, documented at i/rezone.i line 84SEE ALSO: rez_regs

rez_plm

rez_plm Interpreted function, defined at i/rezone.i line 140

rez_prev

rez_prev zoom in on previous bowtied (or chevroned) zone (after rez_mesh). Interpreted function, defined at i/rezone.i line 1442SEE ALSO: rez_next, rez_mark, rez_drag

rez_ptexist

rez_ptexist Interpreted function, defined at i/rezone.i line 1474

rez_qrt

rez_qrt, rez_qzt, rez_qireg are the names of the mesh variables for rez_mesh, "rt", "zt", and "ireg" by default. Note that ireg is optional. Builtin function, documented at i/rezone.i line 1364

rez_radj

rez_radj Adjust the points in a logical rectangle PQRS: Click on [Set P] or [Set R] to set the endpoints of the segment. When P and R have been set, click [OK]; this button will read [Cancel] if P and R have the same K or the same L index. Click on a point on any edge of PQRS (but not one of the corners) to copy the spacings on that edge throughout the entire region. All of the lines of the same type (K-line or L-line) as the edge you clicked on will become straight lines. Click on [Smooth] to smooth the points interior to PQRS. Click on [Smooth 4] to perform the smooth operation four times. Click on the [Undo] button to undo the previous adjustment; you can undo up to 10 previous adjustments by successive [Undo] clicks. When you are finished adjusting regions, click on [OK]. Click on [Zoom or Pan] to change the plot limits (see rez_zoom). Click on [Set Styles] to change the line styles or colors (see rez_style). Hint: You can select a center point as the second point during rez_radj. When you do this, the K (or L) value of this second point will be the same as that of the first point -- otherwise there is no way to distinguish among all of the logical points at the center. The center point will be labeled Q instead of R as usual, and you will need to choose a third point (S) to complete the rectangle PQRS. Interpreted function, defined at i/rezone.i line 865SEE ALSO: rez_drag, rez_ladj, rez_mesh, rez_zoom, rez_style

rez_range

rez_range Interpreted function, defined at i/rezone.i line 1515

rez_regs

rez_regs is a vector of region numbers which are to be drawn in the colors specified in rez_palette. Thus: rez_regs= [3,5] causes regions 3 and 5 to be drawn in colors. All other regions have white backgrounds. Hilighting too many regions in this way may slow down the redraws unacceptably. To highlight all regions, use: rez_regs= indgen(max(rez_ireg)) This won't work on monochrome monitors, of course. The default is rez_regs=[]. Builtin function, documented at i/rezone.i line 116SEE ALSO: rez_palette

rez_solve

rez_solve Interpreted function, defined at i/rezone.i line 1522

rez_style

rez_style Interpreted function, defined at i/rezone.i line 1258

rez_toggle

rez_toggle Interpreted function, defined at i/rezone.i line 261

rez_zoom

rez_zoom Change limits after setting rez_mesh. There are two modes of operation: (1) P-mode: Click on a point to magnify or demagnify about that point. Drag the point to move it to a different position in the viewport. The left button zooms in (magnifies by 1.5), the right button zooms out (demagnifies by 1.5), and the middle button pans (no magnification change). If you click just below or just above the tick marks, only the x coordinate is changed; clicking just to the left or just to the right of the viewport changes only the y coordinate. (2) R-mode: Left drag out a rectangle to set the limits to that rectangle. Right drag out a rectangle to cram the entire current viewport into that rectangle (an analog to zooming out). Middle drag to pan as in P-mode (the rubber band rectangle is meaningless in this case). Click the [R-mode] (or [P-mode]) button to change modes. Click the [OK] button when you are satisfied with the limits. Click the [Undo] button to remove the effect of the previous zoom-click. Up to 100 successive undo operations are allowed. Click the [Polar] button to toggle polar coordinates. The vertical axis will be theta, and the horizontal axis radius. The polar coordinate origin will be at (zt,rt) = (0,0). Click the [Next], [Prev], or [First] buttons to focus in on zones which are bowtied or chevroned. These zones are marked by a B or a C, respectively (if rez_mark is set). Interpreted function, defined at i/rezone.i line 1113SEE ALSO: rez_mesh

rezone

rezone, filename -or- rezone Invoke the mouse-driven rezoner. Input is taken from variables rt, zt, and ireg in the file FILENAME (which is prompted for if omitted). Output is written to a different file as rt, zt, and ireg. The output file also contains copies rez_rt, rez_zt, and rez_ireg in case the mesh under a different name is desirable, as well as rez_rt0, rez_zt0, and rez_ireg0, which are the original mesh. If you click on [Escape], you may continue rezoning where you left off by typing rezone with no arguments. When you are finished, click [OK] to write the output file. Use [Zoom or Pan] and [Set Styles] to change the plot limits or line colors and styles. The [Zoom or Pan] screen has buttons which "warp" you to each bowtied or chevroned "problem" zone, as well as a button to toggle between rectangular and polar coordinates. Click [Drag Points] to drag points one at a time with the mouse. Click [Adjust Line] to smooth the points on logical line segments. You first click on the endpoints P and Q, then click a button to smooth or equal space the poionts between P and Q, or drag any point between P and Q to establish equal ratio zones ("ER" operation). Click [Adjust Region] to smooth the points in logically rectangular regions. You first click on the opposite corners P and R of the rectangle PQRS, then click a button to smooth the interior points, or click on a point on one of the four edges to transfer the spacing on that edge throughout the region PQRS ("EQ" operation). The [Undo] (or [Redo]) button removes the effect of the most recent drag points, adjust line, or adjust region operation. Hints: (0) After [Escape], the current mesh is in the variables rez_zt, rez_rt, and rez_ireg. You can change these variables "by hand" before restarting rezone to make algebraic adjustments. (1) Switch to polar coordinates during an [Adjust Line] or [Adjust Region] in order to get points to lie along a circular arc. If your center point is not (0,0), you will need to [Escape] and subtract your center point from the rez_zt and rez_rt variables yourself, then [Escape] a second time to restore the proper coordinates before you write the output file. (2) You can select a center point as the second point during [Adjust Line] or [Adjust Region]. When you do this, the K (or L) value of this second point will be the same as that of the first point -- otherwise there is no way to distinguish among all of the logical points at the center. In an [Adjust Region], the center point will be labeled Q instead of R as usual, and you will need to choose a third point (S) to complete the rectangle PQRS. (3) If you set the variable rez_color=1 before you include rezone.i, you will get K lines and L lines drawn in different colors instead of the default (which is K lines dashdot and L lines solid). (4) If you have a color monitor, you can set rez_regs before invoking rezone in order to highlight a list of regions. The ALL keyword will be passed to the nbow function, which will not be called if the QUIET keyword is non-nil and non-zero. By default, a short summary of bowtied and chevroned zones is printed. If you need help on how to use one of the screens, try getting help on the appropriate on of these see-also topics, e.g.- help, rez_style to get help on the [Set Styles] screen. Interpreted function, defined at i/rezone.i line 294SEE ALSO: rez_all, rez_drag, rez_ladj, rez_radj, rez_zoom, rez_style,

rez_color, rez_regs, rez_adjust_mesh, toy_mesh

rgb_read

rgb = rgb_read() or rgb = rgb_read(n) Read contents of current graphics window, or of graphics window N. RGB is a 3xNXxNY array of char where NXxNY is the current shape of the window in pixels. RGB(1,,) is the red component, RGB(2,,) is the green component, and RGB(3,,) is the blue component, with 0 black and 255 full intensity. RGB(,,1) is the top row of the window, RGB(,,2) the second row, and so on to RGB(,,0), which is the bottom row. (So RGB(,,::-1) to pli redraws a copy.) Builtin function, documented at i0/graph.i line 1452

rk4

y_at_x_plus_dx= rk4(y,dydx, x,dx, derivative) takes a single 4th order Runge-Kutta step from X to X+DX. DERIVATIVE(y,x) is a function returning dydx; the input DYDX is DERIVATIVE(y,x) at the input (X,Y). This fourth evaluation of DERIVATIVE must be performed by the caller of rk4. Interpreted function, defined at i/rkutta.i line 233

rk_integrate

y= rk_integrate(derivative, y1, x, epsilon, dx1) integrates dydx= DERIVATIVE(y,x) beginning at (X(1),Y1) and going to X(0) with fractional error EPSILON. The result is the value of y at each value in the list X. If non-nil, DX1 will be used as initial guess for the first step size. Otherwise, X(2)-X(1) will be the first step size guess. The list of X values must be monotone -- strictly increasing or strictly decreasing; the Runge-Kutta step sizes are selected adaptively until the next X value would be passed, when the step size is adjusted to complete the step exactly. The external variable rk_maxits (default 10000) is the maximum number of steps rk_integrate will take. If a function rk_yscale(y,dydx,x,dx) exists, it is used to compute an appropriate yscale to give the EPSILON error criterion meaning. Otherwise, yscale is taken to be: abs(y)+abs(dydx*dx)+1.e-30 Based on odeint from Numerical Recipes (Press, et.al.). If the function you are trying to integrate is very smooth, and your X values are fairly far apart, bs_integrate may work better than rk_integrate. Interpreted function, defined at i/rkutta.i line 14SEE ALSO: rkutta, bs_integrate, rk_maxits, rk_minstep, rk_maxstep, rk_ngood,

rk_nbad, rkdumb, rk4

rk_store

rk_store Interpreted function, defined at i/rkutta.i line 163

rkdumb

y_of_x= rkdumb(derivative, y0,x0, x1,nsteps) integrates dydx= DERIVATIVE(y,x) beginning at (X0,Y0) and going to X1 in NSTEPS 4th order Runge-Kutta steps. The result is dimsof(Y0)-by-(NSTEPS+1) values of y at the points span(X0, X1, NSTEPS+1). If the nosave= keyword is non-zero, the returned value will simply be the final y value. Interpreted function, defined at i/rkutta.i line 184

rkqc

rkqc Interpreted function, defined at i/rkutta.i line 205

rkutta

y1= rkutta(derivative, y0,x0, x1,epsilon, dx0) integrates dydx= DERIVATIVE(y,x) beginning at (X0,Y0) and going to X1 with fractional error EPSILON. The result is the value of y at X1. DX0 will be used as the initial guess for a step size. If the external variable rk_nstore is >0, rk_y and rk_x will contain up to rk_nstore intermediate values after the call to rkutta. Consider using rk_integrate if you need this feature; using rk_nstore gives you the results at intermediate values which will tend to be closer where the Runge-Kutta step size was smaller, while rk_integrate forces you to specify precisely which x values you want. The external variable rk_maxits (default 10000) is the maximum number of steps rkutta will take. The variable rk_minstep (default 0.0) is the minimum step size. The variable rk_maxstep (default 1.e35) is the maximum step size, which you may need if you are storing intermediate values (particularly with bstoer). If a function rk_yscale(y,dydx,x,dx) exists, it is used to compute an appropriate yscale to give the EPSILON error criterion meaning. Otherwise, yscale is taken to be: abs(y)+abs(dydx*dx)+1.e-30 Based on odeint from Numerical Recipes (Press, et.al.). If the function you are trying to integrate is very smooth, bstoer will probably work better than rkutta. Interpreted function, defined at i/rkutta.i line 52SEE ALSO: rk_integrate, bstoer, rk_nstore, rk_maxits, rk_minstep, rk_maxstep,

rk_ngood, rk_nbad, rkdumb, rk4

rmdir

rmdir Builtin function, documented at i0/std.i line 2478SEE mkdir

roll

roll(x, ljoff, rjoff) or roll, x, ljoff, rjoff or roll(x) or roll, x "rolls" selected dimensions of the array X. The roll offsets LJOFF and RJOFF (both optional) work in the same fashion as the LJDIR and RJDIR arguments to the fft function: A scalar LJDIR (and nil RJDIR) rolls all dimensions of X by the specified offset. Otherwise, the elements of the LJDIR vector [ljoff1, ljoff2, ...] are used as the roll offsets for the first, second, etc. dimensions of X. Similarly, the elements of the RJDIR vector [..., rjoff1, rjoff0] are matched to the final dimensions of X, so the next to last dimension is rolled by rjoff1 and the last dimension by rjoff0. As a special case (mostly for use with the fft function), if both LJDIR and RJDIR are nil, every dimension is rolled by half of its length. Thus, roll(x) it equivalent to roll(x, dimsof(x)(2:0)/2) The result of the roll function is complex if X is complex, otherwise double (i.e.- any other array type is promoted to type double). If roll is invoked as a subroutine, the operation is performed in place. Interpreted function, defined at i0/fft.i line 254SEE ALSO: fft

romberg

integral= romberg(function, a, b) or integral= romberg(function, a, b, epsilon) returns the integral of FUNCTION(x) from A to B. If EPSILON is given, Simpson's rule is refined until that fractional accuracy is obtained. EPSILON defaults to 1.e-6. If the notvector= keyword is supplied and non-zero, then FUNCTION may not be called with a list of x values to return a list of results. By default, FUNCTION is assumed to be a vector function. If the function is not very smooth, simpson may work better. Interpreted function, defined at i/romberg.i line 10SEE ALSO: simpson, max_doublings

rot3

rot3, xa,ya,za rotate the current 3D plot by XA about viewer's x-axis, YA about viewer's y-axis, and ZA about viewer's z-axis. Interpreted function, defined at i/pl3d.i line 57SEE ALSO: orient3, mov3, aim3, setz3, undo3, save3, restore3, light3

rotext

plt, rotext(text,path), x, y return TEXT string as is (PATH=0), reversed (PATH=1), reversed and with a '\n' between each character, or with '\n' between characters (PATH=3). When plotted, these strings correspond to the original meaning of the text path= keyword. That is, successive characters will appear to the right, left, up, or down according to whether PATH is 0, 1, 2, or 3 Interpreted function, defined at i/txpath.i line 12SEE ALSO: plt

rzextr

rzextr Interpreted function, defined at i/rkutta.i line 338