• The Lahey Fortran 95 compiler
• CGI script utilities
• DISLIN graphical library
• BLAS Pentium II library
• LAPACK 90 library

Lahey Intel Linux Express Fortran 95

Fortran 90 CGI script module

DISLIN high-level graphics library

I have made my own set of routines for scientific 2D and 3D line, surface and color plotting, based on the familiar MATLAB plotting commands. Take a look at the source file with the Fortran 90 module to see exactly what I did. The module provides several routines:

• InitGraphics(file,file_type,plot_title,x_label,y_label,z_label,my_func)

which must be called to initialize the graphical routines. It takes all optional arguments with the file name, the file type (most often one of "POST" or "PSCL" for PostScript, "TIFF" for tiff images, and "CONS" or "XWIN" for the whole screen or an X window), the plot title and axis labels, and an external function my_func which accepts an integer from -1 to 3 and performs operations of level 0-3 that are not provided by my module. The plot title should be a string of characters (one string for each line that you need), while the other names are simple strings. Note that this is most easly done using array constructors, as in plot_title=(/"Line 1","Line 2"/).
• EndGraphics(my_func)

which closes the graphics routines and accepts the user-defined external function. don't forget to call this routine at the end. NOTE: To close the DISLIN X window with the plot, click the left or middle mouse button.
• AddLegend(legends,pos)

which adds a legend to the plot. It takes the array of strings legends and optionally the position of the legend (3 and 7 are most used--upper right corner of page and plot) as argumens.
• Plot2D(x1,y1,spec1,...,my_func,axis_limits)

which accepts up to 10 sets of x and y data points as vectors, an optional three-character specification string which determines the curve attributes, the external user-defined function, and an optional vector axis_limits with four entries that defines the axis limits. The specification string has the following interpretation:
1. The first character should be one of 'S' (plot data points as symbols), or 'L' (plot data points connected with a line-no symbols).
2. The second character for symbol ('S') plots should be on of 'S' (use squares as symbols), 'C' (circles), 'T' (triangles), 'D' (diamonds), or lower-case letters ('s' 'c' 't' 'd') for the corresponding filled symbols. For line ('L') plots, this character should be one of '-' (solid line), '.' (dotted), ':' (dashed) or '|' (dashed-dotted).
3. The third character determines the color of the curve and should be one of 'R' (red), 'B' (blue), 'G' (green) or 'Y' (yellow).
• Plot3D(x1,y1,z1,spec1,...,my_func,axis_limits)

with the same syntax as Plot2D, but for plotting curves in 3D.
• Plot2DMatrix(x,y,type_spec,line_spec,color_spec,my_func,axis_limits)

Plots several 2D curves contained as columns in the matrices x and y. There are three optional specification strings that specify whether the corresponding column should be plotted as a line or as symbols, the type of the symbol/line, and the color respectively. The length of these strings should be equal to the number of columns to plot and the interpretation of the symbols is the same as in Plot2D. This function is added to overcome the limitation of 10 curves in Plot2D (which is there because Fortran 90 does not support variable argument lists) and to enable faster and more flexible plotting of similar data curves. 
• Plot3DMatrix(x,y,z,type_spec,line_spec,color_spec,my_func,axis_limits,view)

with the same syntax as Plot2DMatrix, but for plotting curves in 3D.
• SurfPlot(x,y,z,spec,my_func,color_range,axis,view)

which accepts a set of points as vectors, an optional three-character string specification, a user-defined external function, and optional 2/3 element arrays specifying the axis ranges / view angle. The specification string has the following interpretation:
1. The first character should be one of '2' (plot data points as a 2D color plot), or '3' (plot data points as a 3D surface).
2. The second character for color ('2') plots should be a digit from 1-9 and specify the increase in the resolution (number of linear-interpolation interior-points). For surface ('3') plots, this character should be one of 'M' (mesh line surface), 'C' (color-shaded surface) or 'S' (both mesh and color shading).
3. The third character determines the color palette and should be one of 'R' or 'r' (rainbow palette in two different directions of hot-cold), 'G' or 'g' (gray palette in two different directions) or 'V' (VGA 16 color palette).

If you want to make readily portable executables, you need to link the static libraries, which is done by simply replacing the shortcut HPF_DISLIN with the lowercase lettered:
    HPF_dislin = "--staticlink -I$HPF_MODULES $HPF_LINK/graphics.o $HPF_LINK/dislin.o -ldislin -L/usr/X11R6/lib -lX11"
NOTE: The executables made this way will be huge, so use this option only if needed.

BLAS Pentium II Optimized Library

For examples on how these are used, take a look at a simple file that times matrix multiplication for several different approaches. The results are as expected. A naive Fortran 77 approach of nested DO loops with most compilers takes about 7 seconds for 500 by 500 double precision matrices, the intrinsic MATMUL takes less (about 3-5 seconds), but the BLAS routine gemm takes only a second or so. Using the BLAS for local computations can often save you orders of magnitude in time!

Physicists often use sparse matrices, and this BLAS supports only banded sparse matrices (the sparse BLAS is not yet finalized even as a proposal). Here is an example program that calculates the lowest energy eigenvector and eigenvalue for a simple harmonic quantum oscillator and plots the eigenvector (it should be a gaussian). The Hamiltonian matrix is banded (tri-diagonal), and the power method that uses BLAS's sbmv is used. The compilation is done via:
    lf95 $RM346 --info -o $HPF_EXE/mmul.exe mmul_timing.f90 $HPF_DISLIN $HPF_BLAS
where
HPF_BLAS = "-I$HPF_MODULES/BLAS $HPF_LINK/blas.so -lBLAS"
There is, of course, a static library lower-case variation:
HPF_blas = "--staticlink -I$HPF_MODULES/BLAS $HPF_LINK/blas.o -lblas"
but this makes huge executables, of the order of 3MB.

LAPACK 90 Library

For an example of how to use the library, here is the same example described in the BLAS section, which finds the lowest few energy eigenstates of an anharmonic QHO. I had some trouble with accuracy in my "hand" implementation which uses the BLAS and a simple power method, but LAPACK does not have such problems and gives very nice results with about the same speed. The text output of the file shows this well, and here is a graphical result showing how the lowest energy of the QHO depends on the anharmonic perturbation.

The compilation is done via the shortcut $HPF_LAPACK, which links shared LAPACK and BLAS with static LAPACK90 libraries (I had lot's of trouble making a shared LAPACK90 library...) and thus makes small executables (the corresponding lower-case static analog should not be used as the executables are more than 10 MB):
    lf95 $RM346 -o $HPF_EXE/b_QHO.exe b_QHO.f90 $HPF_DISLIN $HPF_LAPACK
where
    HPF_LAPACK = "-I$HPF_MODULES -lBLAS -lLAPACK -llapack90"

The distributed-memory implementation ScaLAPACK will be installed too, along with many other similar MPI-based packages.