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LIST OF FEATURES EQUIPIMENT: IBM-PC, CGA, EGA, or Hercules Card, 512K memory OUTPUT: Printers--Epson FX-LQ, HP LaserJet Files--HP LaserJet file, Lotus PIC file GRAPH TYPES: Line, XY, Scatter, Needle, Bar GRAPH SCALES: Linear, Log, Probability, Time Series, or mixed MAIN FUNCTIONS: 1)--READ DATA FROM FILE: 32,000 x,y pairs ASCII Columnar, Lotus WK1, 'SHELL' to DOS 2)--ENTER, EDIT, SORT OR SAVE DATA: Enter or edit, swap & copy, insert & delete X values not required for time series Choose Y2 values as labels Sort data on X 3)--SPLINE CURVE FITTING: Smoother interpolated values at user specified intervals 4)--STATISTICS & OTHER DISTRIBUTIONS: Sample size, Mean, Median, Min & Max, Variance, Std. Deviation, Std. Error of Mean, Skewness, Kurtosis Other Distributions: Frequency Histogram, Cumulative %, Mass, Double Mass, Moving Average (centered or lagged) 5)--REGRESSION: Y=a+bX, Y=a+bX+cX^2, Y=a+bLogX, LogY=a+bX, Y=aX^b, Y=a(X+e)^b, Plot regression or errors 6)--PROBABILITY: Compute probability of Y values or user probability as X Add Pearson III or Log-Pearson III (normal & log normal) 7)--TIME SERIES: General-give starting X value and interval between Y values Daily w/monthly or yearly labels, Monthly w/yearly labels 8)--REPLOT Make corrections to labels, line and marker type, scales... 1 MANUAL SCALING OPTIONS: Suppress X scale labels (user may interactively add) Second Y axis Set X & Y graphing range Reverse Y scale Set Y2 line color and marker type 14 colors, 14 marker types, or user text as markers Set # of blank rows to begin new Y2 line and marker type Set restart of Y2 time series values on X scale Turn Y markers off and line on after blank value INTERACTIVE SCREEN EDITING: Add markers, lines, curves and text Display cursor coordinates Change editing color UTILITY PROGRAMS: CONTOUR.exe--generates contour data file for EGRAPH using randomly spaced X-Y values and associated Z value PRNWHAT.exe--Extracts data from columnar ASCII files. Sequential data on rows may be stacked into columns NOTABS.exe--Replaces tabs in ASCII files with 8 spaces for proper reading by EGRAPH. 2 ENGINEERING GRAPHICS Copyright (c) 1987-90 by Great Basin Associates 12990 W. Grand Place Morrison, CO 80465 EGRAPH is an engineering graphics program for the IBM-PC with a CGA, EGA, VGA (ega mode), or Hercules graphics card. LINEAR, LOG, PROBABILITY, and TIME SERIES axis scaling may be mixed. Over 32,000 x,y data pairs may be graphed. Descriptive Statistics, Cumulative & Frequency Distributions, Regression, Pearson III, Splines, and Contours can be added. Text, lines, curves, and points can be interactively placed on graph. Data can be read directly form Lotus worksheet files, PRN, columnar ASCII files or keyboard. Graphs may be printed directly on an Epson or HP LaserJet printer or saved as a Lotus PIC file. High resolution graphs can be printed or plotted using all the printers and plotters supported by Lotus 123 or Symphony. The PIC file can also be imported into other programs such as Freelance, Word Perfect, Word and desktop publishers for editing and printing. It is menu driven with prompts for required input. After reading the command line section below, most users will probably not need to read the rest of this manual. EGRAPH COMMAND LINE: Options can be set when starting EGRAPH by including values for setting screen foreground and background colors or auto selection of graphics adapter. The command line format is: EGRAPH,a,b,c (command line format) The default values used when only EGRAPH is entered from the DOS prompt is: a= 7 color white foreground b= 1 color blue background c= 0 auto selection of graphics adapter, 1 for manual For example, EGRAPH,4,7 would set red on white screen colors with auto select type of graphics adapter. 3 Color numbers are: 0-Black, 1-Blue, 2-Green, 3-Light Blue, 4-Red, 5-Violet, 6-Brown, 7-White: Add 8 to these values for brighter foreground color. EGRAPH MENU OPTIONS READ DATA FROM FILE: Input data files can be created from any program that creates ASCII files or from Lotus Worksheet files (WKS, WK1). Most word processor programs can create ASCII files but usually is not the format in which they normally save files. Each line of data is terminated by the carriage return (ascii 13) and linefeed (ascii 10) sequence. These terminate each row of data but will not be displayed when using the TYPE filename DOS command. TAB's(ascii 9) are read as 1 character and not expanded into 8 spaces as displayed using the TYPE command. You can check for TAB's using the DOS command COPY /B filename CON. This displays the file in binary format on the screen and TAB's show up as little circles. This should be kept in mind when telling EGRAPH where data columns are located. The included utility program NOTABS will read a file and replace the tabs with 8 spaces. To use NOTABS type NOTABS infilename outfilename. Below are data files in EGRAPH's default data locations of 9 characters wide starting in column 1. If your data is not in this format answer "N" to the auto format prompt and enter your formats data width, starting column, and number of variables (1- 4). A data file can have as many title lines as desired. EGRAPH will detect the start of data lines when the line contains no letters. Lotus 123 users can create columnar ASCII files by using \Print File Range Options Margins Left 1 Other Unformatted. EGRAPH DATA FILES Example of 1 Y variable data file Title lines are ok. Y1 'Y1 is not required and is used for clarity here 12.1 10122 'Y data without an X is useful for time series data 9.999 'or probability and cumulative distribution 1.23E-6 'scientific notation ok! Example of 1 X and 1 Y variable data file X1 Y1 .99 2222 .999 589 .9999 -98.4 'X values may be user computed probabilities 4 Example of 2 Y variable data file Y1 Y2 3.03333 4343.34 1.0E-38 1.0E+38 'values from +- 10 to the 38th power. 2322 1231 'range limit of 1E+38 Example of 1 X and 2 Y variable data file X1 Y1 Y2 -233 444 3.222 1234567 2.098456-12.34567 'up to 7 significant figures 123456789 44.3 9.982 more are rounded: 1.2345679E+08 Example of 2 X and 2 Y variable data file X1 Y1 X2 Y2 22.222 2342 23422 4343 333.02 23 33 2.1 2232 6454 22 398 Example of 7 X,Y sub variables X1 Y1 1 1 2 2 'a blank or letters in Y1 or Y2 will cause 1 2 a start of a new line to be drawn. This is 2 3 useful for displaying more than 2 lines. Digitized lines can be graphed as was done 1 3 for the map of western U.S states example. 2 4 Confidence limits may be read in as X2,Y2 values with a blank line to separate upper 3 -6 and lower limits. Several confidence levels 22 13 can be added in this manner. Each line for .1 -9 Y2 values will be graphed in a different color or dash style when a blank Y2 value is 5 8 encountered. This allows more than 2 6 9 variables to be graphed with different line styles (see EXAMPLE3.DAT file). # of blank 7 7 blank values before new line can be set 9 4 12 12 15 5 The included utility program PRNWHAT can be used to read your original data file and extract data into columns for EGRAPH if your data file is not in the above form. Lotus worksheet files (.WKS or .WK1) may be read by simply entering the entire worksheet filename with the .WK1 extension and EGRAPH will know to read the file as a Lotus or Symphony worksheet file. You will be prompted to select a X1, Y1, X2, or Y2 variable and the worksheet range to be read into it. For example, to read the first 20 values in column A, you would enter 5 "A1" as the start of the data range and "A20" as the end of data range. Several data ranges in the worksheet can be repeatedly selected for entry into one of EGRAPHS variables in order to graph several data ranges. When you save your Lotus worksheet, you must remember what ranges your data to be graphed is in. The word SHELL may be entered for a filename under the Read Data menu selection for temporary exit to DOS. Type EXIT to return to EGRAPH from DOS. The file COMMAND.COM that comes with DOS must be in your boot drive. File names may use DOS wildcard characters * and ? to help locate files. B:*.dat, Test?.*, \data\project1\cost*.* are legal file names. The files matching the filename mask will be displayed and you may then enter your filename choice for data reading. ENTER, EDIT, & SAVE DATA FROM KEYBOARD: Data can be entered or edited from the keyboard and saved for rereading. A blank cell for Y1 or Y2 values will start the beginning of a new line to be drawn so that 100's of line segments or variables can be graphed. Data entry is terminated by hitting the Escape key. If Y2 values are entered, you may select to either graph them or use them as labels for Y1 values. Editing keys are: Escape....Exit editor Space.....Delete cell contents Insert....Insert cell in data column Ctrl-Y....Remove cell in data column Delete....Delete character Enter.....Enter displayed value and move down 1 cell Arrow.....Move left, right, down, or up 1 cell PageUp....Move up 1 page PageDown..Move down 1 page Home......Move to top of column End.......Move to end of column F1........Swap X1-Y1 with X2-Y2 F2........Copy pointer X-Y to other X-Y F3........Swap pointer X with Y F4........Copy X1 to X2 Graph Titles, Axis Labels, and Scaling: After the data values are edited, the graph titles and axis labels are prompted for. By pressing the ESC key from within one of the label edit lines, the graph will be immediately viewed. Press Alt*H for help in editing graph labels. After entering the graph labels you may select to add grid lines and type of axis, either linear or log, and Y2 line type, solid or dashed. From the grid option you may enter NONE to graph digitized data with out any axis being displayed. 6 A N entered for Auto Scaling will allow manual setting of the X and Y axis scale range. The Y axis may be inverted to graph such things as depth using positive values. Display of the X axis values may be suppressed so that you may add your own labels. A second Y axis for Y2 values may be added. Time series plots with blank rows in the Y2 column may be reset to start of the time scale for graphing several variables using a time series X axis. Once the graph is on the screen, hit any key and you may choose to add text, symbols, straight lines or curved lines. You may also get the cursor coordinates. The cursor is moved using the arrow keys or left Shift*Arrow keys together for small moves. Small moves require the left shift key to be held down while pressing an arrow key on the number pad, not 101 keyboard arrows. After moving to a location begin entering text and terminate with the Enter key. When finished, press the ESC key to redraw the graph. The last line, symbol, or text type added can be deleted with the Delete key. To switch type of editing to delete, enter that type anywhere on the screen and then proceed deleting that type one at a time with the Delete key. Graphic editor keys are: Escape...........End editing and redraw graph Arrow............Move cursor left, right, up, down 8 pixels LeftShift-Arrow..Move cursor 1 pixel (number pad arrows only) Enter or arrow...Enter text string being added F1...............Add a marker F2...............Start or end a dashed line F3...............Start or end a straight line F4...............Mark 3 points on a curved line F5...............Toggle display of cursor x and y coordinates F6...............Increase color, marker & dash type F7...............Decrease color, marker & dash type Delete...........Delete last text, marker, or line type added Graph Printing and Lotus PIC Files: After viewing or editing the graph you are prompted to print the graph. The EPSON option will print your graph as half page size or full page rotated directly on an Epson compatible printer installed on the LPT#1 port. Either Epson FX (9 pin) or LQ (24 pin) type compatible printer may be used. The HP-LaserJet is also supported directly or sent to file. The LaserJet file can be sent to a LaserJet later using Copy filename PRN . The Lotus PIC file option creates a high resolution file that can be graphed or plotted using Lotus' or Symphony's PGRAPH.EXE program. When naming your graph file add the extension .PIC so PGRAPH can locate it. The enclosed graph examples were plotted using Lotus PGRAPH.EXE and an HP lasor printer. Other programs like Freelance, Word Perfect 5, and desktop puplishers can import the PIC file for editing and printing. Although not displayed properly in EGRAPH the Lotus LICS extended character codes can be 7 used as text by holding down the ALT key and entering the code number on the NUMBER PAD only. REPLOT: After viewing a graph on the screen the graph labels and axis types can be changed and the graph reviewed by selecting REPLOT. SPLINE CURVE FITTING: A smooth curve can be fitted to X1,Y1 points by computing X2,Y2 points between the X1,Y1 input data points. Examples of the use of this spline fitting is for interpolating points between rainfall depth-duration data or reservoir elevation-area-capacity data. The X2,Y2 points are interpolated by weighting the tangents of the lines connecting the X1,Y1 data input points to create a smoother curve through the points. The number of interpolated points between input points are user defined. The number of computed points between the input values is limited to 16,000. STATISTICS & OTHER DISTRIBUTIONS: Descriptive statistics for each of the variables can be displayed and include Sample Size, Mean, Median, Min, Max, Variance, Standard Deviation, Skew, and Kurtosis. A frequency histogram will show how many of the Y1 values are in a class (interval or bin) displayed as the X axis. All Y1 plot options should be set to N except Bar Graph. A normal frequency curve will be fit to the Y1 values and can be turned off or on using the Y2 plot settings. A better aid in checking to see if your Y1 data is normally distributed is to use Probability with the Pearson III option with 0 skew. Normally distributed data will plot as a straight line on normal probability paper. The cumulative percent distribution of Y1 and Y2 values may be computed and graphed. The formula used to compute each Y values X plotting percent value is 100*Rank/N for percent of values less than or equal to and 100*(1-(Rank-1)/N) for percent of values greater than or equal to. The X values in the original data will be replaced with the cumulative percentage values. If the Spline or Regression options are used after the cumulative percent then the X values used will be percentages. The cumulative distribution is useful for viewing how your data is distributed. For example, daily streamflow cumulative distribution may be viewed to see what percent of the time flow is below a certain value. Log X axis scaling may be used to 8 expand the lower percentage values. Y1 and Y2 cumulative distributions can be graphed together for comparisons. Mass curves are a cumulative sum of Y1 data usually with time. Changes in slope of the mass curve can show a change in the relation with time. A double mass curve is a cumulative sum of both X1 and Y1 data to show changes in their relation. Sometimes it is helpful using a double mass curve to use the average of several variables as X1 values to limit variability. Regression errors plotted as a residual mass curve can help magnify changes in the variables relationship. REGRESSION: A regression line can be added to either the X1,Y1 or X2,Y2 data. The regression coefficients a and b, R squared, and standard error of regression can be displayed on the graph. Selecting either regression option does not alter the original X,Y values. When using Log10 transforms of the Y values (options 3-5), the R squared value is for untransformed values, not log values and the standard error of regression is given in percent. X,Y data must be greater than zero to compute Log10 transforms. Y=a+b*X will be a straight line with linear axis scaling and Y=aX^b will be a straight line with log axis scaling. An offset value e may also be added for regression of Y=a(X+e)^b. This is useful for data that is not linear on log-log paper. The offset value "e" can be selected if an arbitrary base or datum is known to have been added to the X range values. Otherwise, for curved data sets, the "e" value can be determined by trial and error and noting the R^2 and Standard Error values. The point of zero flow for water discharge ratings with arbitrary datums is an example of regression of data requiring an X offset value. Caution should be used in extending regressions outside the range of data and near zero, especially option 2, Y=a+bX+cX^2. This is a parabolic curve and can reverse direction. The X1-Y1 regression residuals can be plotted as Y'-Y, predicted Y minus data Y. Error plots that show a trend or pattern may indicate the need for a different regression type or transform of the original data. PROBABILITY: A normal probability graph or a log-normal probability graph of the Y1 or Y2 values may be made by selecting either linear or Log Y axis scaling. The non-exceedance probability X axis values (plotting position) are computed by Rank/(N+1) and exceedance values are computed by 1-Rank/(N+1). The X values in the 9 original data set are replaced with the probability values if read. Spline or Regression used after Probability will be based on probability X values. Probabilities for the X axis may also be computed by the user and read in as X values so that other plotting position formulas are possible. Upper and lower confidence limits may be computed by the user and read in as X2,Y2 values and separated with a blank line to start a new line. Probability graphs are similar to Cumulative Distribution graphs and can be used for similar purposes. Probability graphs can be used to view what data lies within a given number of standard deviations. Changes in the slope of the probability curve can show mixed populations in the data. Normally distributed data plots as a straight line on normal probability paper and log- normally distributed data plots as a straight line on log-normal graph paper. The Pearson or Log-Pearson Type III distribution can be fit to the Y data by computing the mean, standard deviation, and skew of the Y data or Log10 transforms. The Pearson Type III deviate K for a given probability is then computed based on the skew and the Y for that probability is computed as Y=mean+std.dev.*K or Log10(Y)=mean+std.dev.*K. The Pearson III distribution with zero skew is the normal distribution. The Log-Pearson III distribution with zero skew is the log-normal distribution. The Pearson III option does not replace any of the original X,Y data. The Log-Pearson Type III distribution is used extensively in low- flow and flood frequency hydrologic analysis. A complete frequency analysis program using the Log-Pearson Type III distribution is available from Great Basin Associates. The Pearson III distribution may fit the Y data better when high negative skew is found by the Log-Pearson III (data more normally distributed). Some annual series such as high 15-day runoff volume may be more normally distributed and fit better with the normal distribution. TIME SERIES: The Y1 and Y2 values may be graphed as an evenly spaced time series. The X1 or X2 values are not needed and are not changed if read. The general time series can be used to graph any evenly spaced data. The X axis starting value and labeling points can be user defined. The other time series options will generate X axis labels based on the starting date for daily, monthly, or annual values. Contour Plots of X,Y,Z data: The included utility program CONTOUR.EXE may be used to create contour plots with EGRAPH. CONTOUR reads randomly spaced X,Y 10 values and an associated Z value to compute Z values on an evenly spaced grid defined by the user. The grid node Z values are computed by weighting the inverse of the distance squared of the nearest number of X,Y points selected by the user. Z value contours are then interpolated between the grid nodes. An output file is created with the X,Y, and a Z label for each contour line. This file can be read by EGRAPH for plotting. The Y2 as labels selection should be made when exiting EGRAPH's editor if the user wants contour line values labeled. The contour value labels (Y2) can be deleted or moved in EGRAPH's data editor for better contour label positioning if needed. The user may also mark the location of the original data points using the F1 symbol marker key and the F5 coordinate key to locate them. Contour plots are useful for displaying variations of Z values such as surface elevations, ground water levels or concentrations, and rainfall depths over an area defined by the X,Y values. 11 P R N W H A T PRNWHAT will extract data form files to be sent to file or printer. It is especially useful for extracting and reformatting data for import into PGRAPH and Lotus 123 (/File Import Numbers) or other programs requiring data to be in columnar ASCII format. ASCII files organized with sequential data in columns is referred to as a TABLE file by PRNWHAT. Files organized with sequential data on rows is referred to as PUNCH file. To select certain columns from a TABLE file, select the TABLE option and enter input and output filenames. Scroll through the data file until data columns are viewable, press F1 and place an X in columns to be extracted and then press Enter. Scroll to where you wish to begin data extraction and press the Spacebar key. The data line will be highlighted. Scoll down through the file pressing the Spacebar to toggle on and off extraction. When finished, press the End key. TABLE Input file... 1978 21 31 41 51 61 71 81 91 101 102 1979 22 32 42 52 62 72 82 92 102 103 1980 23 33 xxxxx 53 xxxxx xxxxx 83 93 103 104 1981 24 34 44 54 64 74 84 94 104 105 TABLE Output file... 41 61 71 42 62 72 43 63 73 44 64 74 45 65 75...ect To convert data on rows to a column, select the PUNCH option and proceed as above. The PUNCH option also allows one data value on the row to be used as a header column as follows. PUNCH Input file... 1978 21 22 23 24 25 26 27 28 29 30 1979 31 32 33 34 35 36 37 38 39 40 ++++ xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 1981 51 52 53 54 55 56 57 58 59 60 PUNCH Output file... 1978 21 1978 22 1978 23 1978 24 1978 25 1978 26 1978 27 1978 28 1978 29 1978 30 1979 31...ect 12 IBM-PC programs for Engineers by Great Basin Associates ENGINEERING GRAPHICS for $29 includes... EGRAPH---Engineering graphics with linear, log, probability, and time series scaling with spline curve fitting, regression, cumulative, Pearson III, and Log-Pearson III distributions. Graphs may be saved as PIC files for high resolution printing and plotting by Lotus 123, Symphony, Freelance, Word Perfect and other PIC file compatible programs. (CGA, EGA, or Hercules graphics) PRNWHAT--Selectively extracts data columns or lines from ASCII files for printing or importing into EGRAPH or Lotus 123. Sequential data on rows may be stacked into a column. HYDRAULIC COMPUTATIONS (Waterboy) for $69 includes... XSEC-----Computes hydraulic cross-sectional properties. SLOPEA---Indirect discharge computation by the slope-area method. PIPESEC--Hydraulic properties of circular x-sections with normal depth discharge. ROADWAY--Discharge computation of roadway overflow at culverts. CULVERTS-Discharge computation through circular and box culverts for the 6 flow types given water surface elevations. FLOOD FREQUENCY ANALYSIS (Waterboy*2) for $69 includes... LP3------Flood frequency computations using the Log-Pearson Type III distribution as outlined in Bulletin #17B. Outliers zero years ok. (CGA, EGA, Hercules) GEOFREQ--Regional flood frequency estimates for ungaged sites based on active channel width for the 17 western states. Great Basin Associates 12990 W. Grand Place Morrison, CO 80465 (303)972-8323