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<html>
<head>
<title>
R8LIB - A Double Precision Real Arithmetic Utility Library
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
R8LIB <br> A Double Precision Real Arithmetic Utility Library
</h1>
<hr>
<p>
<b>R8LIB</b>
is a FORTRAN90 library which
contains a number of utility routines for "R8" or "double precision real"
arithmetic.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>R8LIB</b> is available in
<a href = "../../c_src/r8lib/r8lib.html">a C version</a> and
<a href = "../../cpp_src/r8lib/r8lib.html">a C++ version</a> and
<a href = "../../f77_src/r8lib/r8lib.html">a FORTRAN77 version</a> and
<a href = "../../f_src/r8lib/r8lib.html">a FORTRAN90 version</a> and
<a href = "../../m_src/r8lib/r8lib.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/c4lib/c4lib.html">
C4LIB</a>,
a FORTRAN90 library which
implements certain elementary functions for "C4" or
single precision complex variables;
</p>
<p>
<a href = "../../f_src/c8lib/c8lib.html">
C8LIB</a>,
a FORTRAN90 library which
implements certain elementary functions for "C8" or
double precision complex variables;
</p>
<p>
<a href = "../../f_src/i4lib/i4lib.html">
I4LIB</a>,
a FORTRAN90 library which
contains many utility routines, using "I4" or "single precision integer"
arithmetic.
</p>
<p>
<a href = "../../f_src/i8lib/i8lib.html">
I8LIB</a>,
a FORTRAN90 library which
contains many utility routines, using "I8" or "double precision integer"
arithmetic.
</p>
<p>
<a href = "../../f_src/r16lib/r16lib.html">
R16LIB</a>,
a FORTRAN90 library which
contains many utility routines, using "R16" or
"quadruple precision real" arithmetic.
</p>
<p>
<a href = "../../f_src/r4lib/r4lib.html">
R4LIB</a>,
a FORTRAN90 library which
contains many utility routines, using "R4" or
"single precision real" arithmetic.
</p>
<p>
<a href = "../../f_src/subpak/subpak.html">
SUBPAK</a>,
a FORTRAN90 library which
contains many utility routines;
</p>
<h3 align = "center">
References:
</h3>
<p>
<ol>
<li>
Thomas Cormen, Charles Leiserson, Ronald Rivest,<br>
Introduction to Algorithms,<br>
MIT Press, 2001,<br>
ISBN: 0262032937,<br>
LC: QA76.C662.
</li>
<li>
Albert Nijenhuis, Herbert Wilf,<br>
Combinatorial Algorithms for Computers and Calculators,<br>
Second Edition,<br>
Academic Press, 1978,<br>
ISBN: 0-12-519260-6,<br>
LC: QA164.N54.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "r8lib.f90">r8lib.f90</a>, the source code;
</li>
<li>
<a href = "r8lib.sh">r8lib.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "r8lib_prb.f90">r8lib_prb.f90</a>, a sample calling
program;
</li>
<li>
<a href = "r8lib_prb.sh">r8lib_prb.sh</a>, commands to
compile, link and run the sample calling program;
</li>
<li>
<a href = "r8lib_prb_output.txt">r8lib_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4_LOG_10</b> returns the integer part of the logarithm base 10 of an I4.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of I4 division.
</li>
<li>
<b>I4_UNIFORM</b> returns a scaled pseudorandom I4.
</li>
<li>
<b>I4_WRAP</b> forces an I4 to lie between given limits by wrapping.
</li>
<li>
<b>I4INT_TO_R8INT</b> maps an I4INT to an R8INT.
</li>
<li>
<b>I4VEC_INDICATOR</b> sets an I4VEC to the indicator vector.
</li>
<li>
<b>I4VEC_PERMUTE</b> permutes an I4VEC in place.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>LEGENDRE_ZEROS</b> computes the zeros of the Legendre polynomial of degree N.
</li>
<li>
<b>PERM_CHECK</b> checks that a vector represents a permutation.
</li>
<li>
<b>PERM_UNIFORM</b> selects a random permutation of N objects.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8_ADD</b> returns the sum of two R8's.
</li>
<li>
<b>R8_AINT</b> truncates an R8 argument to an integer.
</li>
<li>
<b>R8_ATAN</b> computes the inverse tangent of the ratio Y / X.
</li>
<li>
<b>R8_CAS</b> returns the "casine" of an R8.
</li>
<li>
<b>R8_CEILING</b> rounds an R8 "up" (towards +oo) to an integral R8.
</li>
<li>
<b>R8_CHOOSE</b> computes the binomial coefficient C(N,K) as an R8.
</li>
<li>
<b>R8_CHOP</b> chops an R8 to a given number of binary places.
</li>
<li>
<b>R8_CSC</b> returns the cosecant of X.
</li>
<li>
<b>R8_CSQRT</b> returns the complex square root of an R8.
</li>
<li>
<b>R8_CUBE_ROOT</b> returns the cube root of an R8.
</li>
<li>
<b>R8_DIFF</b> computes the difference of two R8's to a specified accuracy.
</li>
<li>
<b>R8_DIGIT</b> returns a particular decimal digit of an R8.
</li>
<li>
<b>R8_DIVIDE_I4</b> returns an I4 fraction as an R8.
</li>
<li>
<b>R8_EPSILON</b> returns the R8 roundoff unit.
</li>
<li>
<b>R8_EXP</b> computes the exponential of an R16, avoiding overflow and underflow.
</li>
<li>
<b>R8_FACTORIAL</b> computes the factorial of N.
</li>
<li>
<b>R8_FACTORIAL2</b> computes the double factorial function.
</li>
<li>
<b>R8_FLOOR</b> rounds an R8 "down" (towards -oo) to the nearest integral R8.
</li>
<li>
<b>R8_FRACTION</b> uses real arithmetic on an integer ratio.
</li>
<li>
<b>R8_FRACTIONAL</b> returns the fractional part of an R8.
</li>
<li>
<b>R8_GAMMA</b> evaluates Gamma(X) for a real argument.
</li>
<li>
<b>R8_HUGE</b> returns a very large R8.
</li>
<li>
<b>R8_HYPOT</b> returns the value of sqrt ( X^2 + Y^2 ).
</li>
<li>
<b>R8_IN_01</b> is TRUE if an R8 is in the range [0,1].
</li>
<li>
<b>R8_INSIGNIFICANT</b> determines if an R8 is insignificant.
</li>
<li>
<b>R8_IS_INT</b> determines if an R8 represents an integer value.
</li>
<li>
<b>R8_LOG_2</b> returns the logarithm base 2 of an R8.
</li>
<li>
<b>R8_LOG_10</b> returns the logarithm base 10 of an R8.
</li>
<li>
<b>R8_LOG_B</b> returns the logarithm base B of an R8.
</li>
<li>
<b>R8_MANT</b> computes the "mantissa" or "fraction part" of an R8.
</li>
<li>
<b>R8_MOD</b> returns the remainder of R8 division.
</li>
<li>
<b>R8_MODP</b> returns the nonnegative remainder of R8 division.
</li>
<li>
<b>R8_MOP</b> returns the I-th power of -1 as an R8.
</li>
<li>
<b>R8_NINT</b> returns the nearest integer to an R8.
</li>
<li>
<b>R8_NORMAL</b> returns a scaled pseudonormal R8.
</li>
<li>
<b>R8_NORMAL_01</b> returns a unit pseudonormal R8.
</li>
<li>
<b>R8_PI</b> returns the value of pi as an R8.
</li>
<li>
<b>R8_POWER</b> computes the P-th power of an R8.
</li>
<li>
<b>R8_POWER_FAST</b> computes an integer power of an R8.
</li>
<li>
<b>R8_PYTHAG</b> computes sqrt ( A * A + B * B ), avoiding overflow and underflow.
</li>
<li>
<b>R8_ROUND2</b> rounds an R8 in base 2.
</li>
<li>
<b>R8_ROUNDB</b> rounds an R8 in a given base.
</li>
<li>
<b>R8_ROUNDX</b> rounds an R8 in base 10.
</li>
<li>
<b>R8_SIGN</b> returns the sign of an R8.
</li>
<li>
<b>R8_SIGN_CHAR</b> returns a character indicating the sign of an R8.
</li>
<li>
<b>R8_SIGN_MATCH</b> is TRUE if two R8's are of the same sign.
</li>
<li>
<b>R8_SIGN_MATCH_STRICT</b> is TRUE if two R8's are of the same strict sign.
</li>
<li>
<b>R8_SIGN_OPPOSITE</b> is TRUE if two R8's are not of the same sign.
</li>
<li>
<b>R8_SIGN_OPPOSITE_STRICT</b> is TRUE if two R8's are strictly of opposite sign.
</li>
<li>
<b>R8_SQRT_I4</b> returns the square root of an I4 as an R8.
</li>
<li>
<b>R8_SWAP</b> swaps two R8's.
</li>
<li>
<b>R8_SWAP3</b> swaps three R8's.
</li>
<li>
<b>R8_TINY</b> returns a very small but positive R8.
</li>
<li>
<b>R8_TO_R8_DISCRETE</b> maps R to RD in [RMIN, RMAX] with NR possible values.
</li>
<li>
<b>R8_TO_DHMS</b> converts decimal days into days, hours, minutes, seconds.
</li>
<li>
<b>R8_TO_I4</b> maps X in [XMIN, XMAX] to integer IX in [IXMIN, IXMAX].
</li>
<li>
<b>R8_UNIFORM</b> returns a scaled pseudorandom R8.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8_UNSWAP3</b> unswaps three R8's.
</li>
<li>
<b>R8_WALSH_1D</b> evaluates the Walsh function.
</li>
<li>
<b>R8_WRAP</b> forces an R8 to lie between given limits by wrapping.
</li>
<li>
<b>R82_CHEBY</b> sets up the Chebyshev abscissas in an R8 interval.
</li>
<li>
<b>R82_DIST_L2</b> returns the L2 distance between a pair of R82's.
</li>
<li>
<b>R82_EQ</b> == ( A1 == A2 ) for two R82's.
</li>
<li>
<b>R82_GE</b> == ( A1 >= A2 ) for two R82's.
</li>
<li>
<b>R82_GT</b> == ( A1 > A2 ) for two R82's.
</li>
<li>
<b>R82_LE</b> == ( A1 <= A2 ) for two R82's.
</li>
<li>
<b>R82_LT</b> == ( A1 < A2 ) for two R82's.
</li>
<li>
<b>R82_NE</b> == ( A1 /= A2 ) for two R82's.
</li>
<li>
<b>R82_NORM</b> returns the Euclidean norm of an R82.
</li>
<li>
<b>R82_NORMALIZE</b> Euclidean normalizes an R82.
</li>
<li>
<b>R82_PRINT</b> prints an R82.
</li>
<li>
<b>R82_SWAP</b> swaps two R82 values.
</li>
<li>
<b>R82_UNIFORM</b> returns a random R82 value in a given range.
</li>
<li>
<b>R82POLY2_PRINT</b> prints a second order polynomial in two variables.
</li>
<li>
<b>R82POLY2_TYPE</b> analyzes a second order polynomial in two variables.
</li>
<li>
<b>R82POLY2_TYPE_PRINT</b> prints the meaning of the output from R82POLY2_TYPE.
</li>
<li>
<b>R82VEC_MAX</b> returns the maximum value in an R82VEC.
</li>
<li>
<b>R82VEC_MIN</b> returns the minimum value in an R82VEC.
</li>
<li>
<b>R82VEC_ORDER_TYPE</b> finds the order type of an R82VEC.
</li>
<li>
<b>R82VEC_PART_QUICK_A</b> reorders an R82VEC as part of a quick sort.
</li>
<li>
<b>R82VEC_PERMUTE</b> permutes an R82VEC in place.
</li>
<li>
<b>R82VEC_PRINT</b> prints an R82VEC.
</li>
<li>
<b>R82VEC_PRINT_PART</b> prints "part" of an R82VEC.
</li>
<li>
<b>R82VEC_SORT_HEAP_INDEX_A</b> ascending index heaps an R82VEC.
</li>
<li>
<b>R82VEC_SORT_QUICK_A</b> ascending sorts an R82VEC using quick sort.
</li>
<li>
<b>R83_NORM</b> returns the Euclidean norm of an R83.
</li>
<li>
<b>R83_NORMALIZE</b> normalizes an R83.
</li>
<li>
<b>R83_PRINT</b> prints an R83.
</li>
<li>
<b>R83_SWAP</b> swaps two R83's.
</li>
<li>
<b>R83VEC_MAX</b> returns the maximum value in an R83VEC.
</li>
<li>
<b>R83VEC_MIN</b> returns the minimum value in an R83VEC.
</li>
<li>
<b>R83VEC_NORMALIZE</b> normalizes each R83 in an R83VEC.
</li>
<li>
<b>R83VEC_PRINT_PART</b> prints "part" of an R83VEC.
</li>
<li>
<b>R84_NORMALIZE</b> normalizes an R84.
</li>
<li>
<b>R8BLOCK_EXPAND_LINEAR</b> linearly interpolates new data into an R8BLOCK.
</li>
<li>
<b>R8BLOCK_PRINT</b> prints an R8BLOCK.
</li>
<li>
<b>R8COL_COMPARE</b> compares columns in an R8COL.
</li>
<li>
<b>R8COL_DUPLICATES</b> generates an R8COL with some duplicate columns.
</li>
<li>
<b>R8COL_FIND</b> seeks a column value in an R8COL.
</li>
<li>
<b>R8COL_FIRST_INDEX</b> indexes the first occurrence of values in an R8COL.
</li>
<li>
<b>R8COL_INSERT</b> inserts a column into an R8COL.
</li>
<li>
<b>R8COL_MAX</b> returns the maximums in an R8COL.
</li>
<li>
<b>R8COL_MAX_INDEX</b> returns the indices of column maximums in an R8COL.
</li>
<li>
<b>R8COL_MAX_ONE</b> rescales an R8COL so each column maximum is 1.
</li>
<li>
<b>R8COL_MEAN</b> returns the column means of an R8COL.
</li>
<li>
<b>R8COL_MIN</b> returns the column minimums of an R8COL.
</li>
<li>
<b>R8COL_MIN_INDEX</b> returns the indices of column minimums in an R8COL.
</li>
<li>
<b>R8COL_NORMALIZE_LI</b> normalizes an R8COL with the column infinity norm.
</li>
<li>
<b>R8COL_PART_QUICK_A</b> reorders the columns of an R8COL.
</li>
<li>
<b>R8COL_PERMUTE</b> permutes an R8COL in place.
</li>
<li>
<b>R8COL_SORT_HEAP_A</b> ascending heapsorts an R8COL.
</li>
<li>
<b>R8COL_SORT_HEAP_INDEX_A</b> does an indexed heap ascending sort of an R8COL.
</li>
<li>
<b>R8COL_SORT_QUICK_A</b> ascending quick sorts an R8COL.
</li>
<li>
<b>R8COL_SORTED_TOL_UNDEX</b> indexes tolerably unique entries in a sorted R8COL.
</li>
<li>
<b>R8COL_SORTED_TOL_UNIQUE</b> keeps tolerably unique elements in a sorted R8COL.
</li>
<li>
<b>R8COL_SORTED_TOL_UNIQUE_COUNT:</b> tolerably unique elements in a sorted R8COL.
</li>
<li>
<b>R8COL_SORTED_UNDEX</b> returns unique sorted indexes for a sorted R8COL.
</li>
<li>
<b>R8COL_SORTED_UNIQUE</b> keeps unique elements in a sorted R8COL.
</li>
<li>
<b>R8COL_SORTED_UNIQUE_COUNT</b> counts unique elements in a sorted R8COL.
</li>
<li>
<b>R8COL_SORTR_A</b> ascending sorts one column of an R8COL, adjusting all columns.
</li>
<li>
<b>R8COL_SUM</b> sums the columns of an R8COL.
</li>
<li>
<b>R8COL_SWAP</b> swaps columns I and J of an R8COL.
</li>
<li>
<b>R8COL_TO_R8VEC</b> converts an R8COL to an R8VEC.
</li>
<li>
<b>R8COL_TOL_UNDEX</b> indexes tolerably unique entries of an R8COL.
</li>
<li>
<b>R8COL_TOL_UNIQUE_COUNT</b> counts tolerably unique entries in an R8COL.
</li>
<li>
<b>R8COL_TOL_UNIQUE_INDEX</b> indexes tolerably unique entries in an R8COL.
</li>
<li>
<b>R8COL_UNDEX</b> returns unique sorted indexes for an R8COL.
</li>
<li>
<b>R8COL_UNIFORM</b> fills an R8COL with scaled pseudorandom numbers.
</li>
<li>
<b>R8COL_UNIQUE_COUNT</b> counts the unique columns in an unsorted R8COL.
</li>
<li>
<b>R8COL_UNIQUE_INDEX</b> indexes the unique occurrence of values in an R8COL.
</li>
<li>
<b>R8COL_VARIANCE</b> returns the variances of an R8COL.
</li>
<li>
<b>R8R8_COMPARE</b> compares two R8R8's.
</li>
<li>
<b>R8R8_PRINT</b> prints an R8R8.
</li>
<li>
<b>R8R8R8_COMPARE</b> compares two R8R8R8's.
</li>
<li>
<b>R8R8R8VEC_INDEX_INSERT_UNIQUE</b> inserts unique R8R8R in an indexed sorted list.
</li>
<li>
<b>R8R8R8VEC_INDEX_SEARCH</b> searches for R8R8R8 value in an indexed sorted list.
</li>
<li>
<b>R8R8VEC_INDEX_INSERT_UNIQUE</b> inserts a unique R8R8 in an indexed sorted list.
</li>
<li>
<b>R8R8VEC_INDEX_SEARCH</b> searches for an R8R8 in an indexed sorted list.
</li>
<li>
<b>R8INT_TO_R8INT</b> maps one R8INT to another.
</li>
<li>
<b>R8INT_TO_I4INT</b> maps an R8INT to an integer interval.
</li>
<li>
<b>R8MAT_ADD</b> computes C = alpha * A + beta * B for R8MAT's.
</li>
<li>
<b>R8MAT_AMAX</b> returns the maximum absolute value entry of an R8MAT.
</li>
<li>
<b>R8MAT_BORDER_ADD</b> adds a "border" to an R8MAT.
</li>
<li>
<b>R8MAT_BORDER_CUT</b> cuts the "border" of an R8MAT.
</li>
<li>
<b>R8MAT_CHOLESKY_FACTOR</b> computes the Cholesky factor of a symmetric matrix.
</li>
<li>
<b>R8MAT_CHOLESKY_SOLVE</b> solves a Cholesky factored linear system A * x = b.
</li>
<li>
<b>R8MAT_CHORESKY_FACTOR</b> computes the "Choresky" factor of a symmetric matrix.
</li>
<li>
<b>R8MAT_COPY</b> copies an R8MAT.
</li>
<li>
<b>R8MAT_DET</b> computes the determinant of an R8MAT.
</li>
<li>
<b>R8MAT_DET_2D</b> computes the determinant of a 2 by 2 R8MAT.
</li>
<li>
<b>R8MAT_DET_3D</b> computes the determinant of a 3 by 3 R8MAT.
</li>
<li>
<b>R8MAT_DET_4D</b> computes the determinant of a 4 by 4 R8MAT.
</li>
<li>
<b>R8MAT_DET_5D</b> computes the determinant of a 5 by 5 R8MAT.
</li>
<li>
<b>R8MAT_DIAG_ADD_SCALAR</b> adds a scalar to the diagonal of an R8MAT.
</li>
<li>
<b>R8MAT_DIAG_ADD_VECTOR</b> adds a vector to the diagonal of an R8MAT.
</li>
<li>
<b>R8MAT_DIAG_GET_VECTOR</b> gets the value of the diagonal of an R8MAT.
</li>
<li>
<b>R8MAT_DIAG_SET_SCALAR</b> sets the diagonal of an R8MAT to a scalar value.
</li>
<li>
<b>R8MAT_DIAG_SET_VECTOR</b> sets the diagonal of an R8MAT to a vector.
</li>
<li>
<b>R8MAT_EXPAND_LINEAR</b> linearly interpolates new data into an R8MAT.
</li>
<li>
<b>R8MAT_EXPAND_LINEAR2</b> expands an R8MAT by linear interpolation.
</li>
<li>
<b>R8MAT_FLIP_COLS</b> swaps the columns of an R8MAT.
</li>
<li>
<b>R8MAT_FLIP_ROWS</b> swaps the rows of an R8MAT.
</li>
<li>
<b>R8MAT_FSS</b> factors and solves a system with multiple right hand sides.
</li>
<li>
<b>R8MAT_GIVENS_POST</b> computes the Givens postmultiplier rotation matrix.
</li>
<li>
<b>R8MAT_GIVENS_PRE</b> computes the Givens premultiplier rotation matrix.
</li>
<li>
<b>R8MAT_HESS</b> approximates a Hessian matrix via finite differences.
</li>
<li>
<b>R8MAT_HOUSE_AXH</b> computes A*H where H is a compact Householder matrix.
</li>
<li>
<b>R8MAT_HOUSE_FORM</b> constructs a Householder matrix from its compact form.
</li>
<li>
<b>R8MAT_HOUSE_HXA</b> computes H*A where H is a compact Householder matrix.
</li>
<li>
<b>R8MAT_HOUSE_POST</b> computes a Householder post-multiplier matrix.
</li>
<li>
<b>R8MAT_HOUSE_PRE</b> computes a Householder pre-multiplier matrix.
</li>
<li>
<b>R8MAT_IDENTITY</b> stores the identity matrix in an R8MAT.
</li>
<li>
<b>R8MAT_IN_01</b> is TRUE if the entries of an R8MAT are in the range [0,1].
</li>
<li>
<b>R8MAT_INDICATOR</b> sets up an "indicator" R8MAT.
</li>
<li>
<b>R8MAT_INSIGNIFICANT</b> determines if an R8MAT is insignificant.
</li>
<li>
<b>R8MAT_INVERSE_2D</b> inverts a 2 by 2 R8MAT using Cramer's rule.
</li>
<li>
<b>R8MAT_INVERSE_3D</b> inverts a 3 by 3 R8MAT using Cramer's rule.
</li>
<li>
<b>R8MAT_INVERSE_4D</b> inverts a 4 by 4 R8MAT using Cramer's rule.
</li>
<li>
<b>R8MAT_IS_IDENTITY</b> determines if an R8MAT is the identity.
</li>
<li>
<b>R8MAT_IS_NONNEGATIVE</b> checks whether an R8MAT is nonnegative.
</li>
<li>
<b>R8MAT_JAC</b> estimates a dense jacobian matrix of the function FX.
</li>
<li>
<b>R8MAT_L_INVERSE</b> inverts a lower triangular R8MAT.
</li>
<li>
<b>R8MAT_L_PRINT</b> prints a lower triangular R8MAT.
</li>
<li>
<b>R8MAT_L_SOLVE</b> solves a lower triangular linear system.
</li>
<li>
<b>R8MAT_L1_INVERSE</b> inverts a unit lower triangular R8MAT.
</li>
<li>
<b>R8MAT_LT_SOLVE</b> solves a transposed lower triangular linear system.
</li>
<li>
<b>R8MAT_LU</b> computes the LU factorization of a rectangular R8MAT.
</li>
<li>
<b>R8MAT_MAX</b> returns the maximum entry of an R8MAT.
</li>
<li>
<b>R8MAT_MAX_INDEX</b> returns the location of the maximum entry of an R8MAT.
</li>
<li>
<b>R8MAT_MAXCOL_MINROW</b> gets the maximum column minimum row of an M by N R8MAT.
</li>
<li>
<b>R8MAT_MAXROW_MINCOL</b> gets the maximum row minimum column of an M by N R8MAT.
</li>
<li>
<b>R8MAT_MIN</b> returns the minimum entry of an M by N R8MAT.
</li>
<li>
<b>R8MAT_MIN_INDEX</b> returns the location of the minimum entry of an R8MAT.
</li>
<li>
<b>R8MAT_MINCOL_MAXROW</b> gets the minimum column maximum row of an M by N R8MAT.
</li>
<li>
<b>R8MAT_MINROW_MAXCOL</b> gets the minimum row maximum column of an M by N R8MAT.
</li>
<li>
<b>R8MAT_MINVM</b> computes inverse(A) * B for R8MAT's.
</li>
<li>
<b>R8MAT_MM</b> multiplies two R8MAT's.
</li>
<li>
<b>R8MAT_MTV</b> multiplies a transposed matrix times a vector
</li>
<li>
<b>R8MAT_MV</b> multiplies a matrix times a vector.
</li>
<li>
<b>R8MAT_NINT</b> rounds the entries of an R8MAT.
</li>
<li>
<b>R8MAT_NORM_EIS</b> returns the EISPACK norm of an R8MAT.
</li>
<li>
<b>R8MAT_NORM_FRO</b> returns the Frobenius norm of an R8MAT.
</li>
<li>
<b>R8MAT_NORM_L1</b> returns the matrix L1 norm of an R8MAT.
</li>
<li>
<b>R8MAT_NORM_L2</b> returns the matrix L2 norm of an R8MAT.
</li>
<li>
<b>R8MAT_NORM_LI</b> returns the matrix L-oo norm of an R8MAT.
</li>
<li>
<b>R8MAT_NULLSPACE</b> computes the nullspace of a matrix.
</li>
<li>
<b>R8MAT_NULLSPACE_SIZE</b> computes the size of the nullspace of a matrix.
</li>
<li>
<b>R8MAT_ORTH_UNIFORM</b> returns a random orthogonal R8MAT.
</li>
<li>
<b>R8MAT_PLOT</b> "plots" an R8MAT, with an optional title.
</li>
<li>
<b>R8MAT_PLOT_SYMBOL</b> returns a symbol for an element of an R8MAT.
</li>
<li>
<b>R8MAT_POLY_CHAR</b> computes the characteristic polynomial of an R8MAT.
</li>
<li>
<b>R8MAT_POWER</b> computes a nonnegative power of an R8MAT.
</li>
<li>
<b>R8MAT_POWER_METHOD</b> applies the power method to an R8MAT.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8MAT_PRINT2</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_REF</b> computes the row echelon form of a matrix.
</li>
<li>
<b>R8MAT_RMS</b> returns the RMS norm of an R8MAT.
</li>
<li>
<b>R8MAT_RREF</b> computes the reduced row echelon form of a matrix.
</li>
<li>
<b>R8MAT_SCALE</b> multiplies an R8MAT by a scalar.
</li>
<li>
<b>R8MAT_SOLVE</b> uses Gauss-Jordan elimination to solve an N by N linear system.
</li>
<li>
<b>R8MAT_SOLVE_2D</b> solves a 2 by 2 linear system using Cramer's rule.
</li>
<li>
<b>R8MAT_SOLVE_3D</b> solves a 3 by 3 linear system using Cramer's rule.
</li>
<li>
<b>R8MAT_SOLVE2</b> computes the solution of an N by N linear system.
</li>
<li>
<b>R8MAT_SUM</b> returns the sum of the entries of an R8MAT.
</li>
<li>
<b>R8MAT_SYMM_EIGEN</b> returns a symmetric matrix with given eigensystem.
</li>
<li>
<b>R8MAT_SYMM_JACOBI</b> applies Jacobi eigenvalue iteration to a symmetric matrix.
</li>
<li>
<b>R8MAT_TO_R8PLU</b> factors a general R8MAT.
</li>
<li>
<b>R8MAT_TRACE</b> computes the trace of an R8MAT.
</li>
<li>
<b>R8MAT_TRANSPOSE</b> makes a transposed copy of a matrix.
</li>
<li>
<b>R8MAT_TRANSPOSE_IN_PLACE</b> transposes a square matrix in place.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8MAT_U_INVERSE</b> inverts an upper triangular R8MAT.
</li>
<li>
<b>R8MAT_U1_INVERSE</b> inverts a unit upper triangular R8MAT.
</li>
<li>
<b>R8MAT_UNIFORM</b> fills an R8MAT with scaled pseudorandom numbers.
</li>
<li>
<b>R8MAT_UNIFORM_01</b> fills an R8MAT with unit pseudorandom numbers.
</li>
<li>
<b>R8MAT_VAND2</b> returns the N by N row Vandermonde matrix A.
</li>
<li>
<b>R8MAT_ZERO</b> zeroes an R8MAT.
</li>
<li>
<b>R8PLU_DET</b> computes the determinant of an R8PLU matrix.
</li>
<li>
<b>R8PLU_INVERSE</b> computes the inverse of an R8PLU matrix.
</li>
<li>
<b>R8PLU_MUL</b> computes A * x using the PLU factors of A.
</li>
<li>
<b>R8PLU_SOL</b> solves a linear system A*x=b from the PLU factors.
</li>
<li>
<b>R8PLU_TO_R8MAT</b> recovers the matrix A that was factored by R8MAT_TO_R8PLU.
</li>
<li>
<b>R8POLY_DEGREE</b> returns the degree of a polynomial.
</li>
<li>
<b>R8POLY_DERIV</b> returns the derivative of a polynomial.
</li>
<li>
<b>R8POLY_LAGRANGE_0</b> evaluates the Lagrange factor at a point.
</li>
<li>
<b>R8POLY_LAGRANGE_1</b> evaluates the first derivative of the Lagrange factor.
</li>
<li>
<b>R8POLY_LAGRANGE_2</b> evaluates the second derivative of the Lagrange factor.
</li>
<li>
<b>R8POLY_LAGRANGE_COEF</b> returns the coefficients of a Lagrange polynomial.
</li>
<li>
<b>R8POLY_LAGRANGE_FACTOR</b> evaluates the polynomial Lagrange factor at a point.
</li>
<li>
<b>R8POLY_LAGRANGE_VAL</b> evaluates the IPOL-th Lagrange polynomial.
</li>
<li>
<b>R8POLY_ORDER</b> returns the order of a polynomial.
</li>
<li>
<b>R8POLY_PRINT</b> prints out a polynomial.
</li>
<li>
<b>R8POLY_SHIFT</b> adjusts the coefficients of a polynomial for a new argument.
</li>
<li>
<b>R8POLY_VALUE</b> evaluates an R8POLY.
</li>
<li>
<b>R8POLY_VALUE_HORNER</b> evaluates a polynomial using Horner's method.
</li>
<li>
<b>R8POLY2_EX</b> finds the extremal point of a parabola determined by three points.
</li>
<li>
<b>R8POLY2_EX2</b> finds extremal point of a parabola determined by three points.
</li>
<li>
<b>R8POLY2_ROOT</b> returns the two roots of a quadratic polynomial.
</li>
<li>
<b>R8POLY2_RROOT</b> returns the real parts of the roots of a quadratic polynomial.
</li>
<li>
<b>R8POLY2_VAL</b> evaluates a parabola defined by three data values.
</li>