R8LIB
A Double Precision Real Arithmetic Utility Library

R8LIB is a MATLAB library which contains a number of utilities for double precision real (R8) arithmetic.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

R8LIB is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Programs:

C8LIB, a MATLAB library which implements certain elementary functions for double precision complex (C8) variables;

I4LIB, a MATLAB library which contains many utility routines, using "I4" or "single precision integer" arithmetic.

SUBPAK, a MATLAB library which contains many utility routines;

References:

1. Thomas Cormen, Charles Leiserson, Ronald Rivest,
   Introduction to Algorithms,
   MIT Press, 2001,
   ISBN: 0262032937,
   LC: QA76.C662.
2. Albert Nijenhuis, Herbert Wilf,
   Combinatorial Algorithms for Computers and Calculators,
   Second Edition,
   Academic Press, 1978,
   ISBN: 0-12-519260-6,
   LC: QA164.N54.

Source Code:

• i4_log_10.m, returns the integer part of the logarithm base 10 of an integer;
• i4_modp.m, returns the nonnegative remainder of integer division;
• i4_sign.m, returns the sign of an I4.
• i4_uniform_ab.m, returns a pseudorandom integer in a given range;
• i4_wrap.m, forces an integer to lie between given limits by wrapping.
• i4int_to_r8int.m, maps an integer interval to a real interval.
• i4vec_indicator.m, sets an I4VEC to the indicator vector.
• i4vec_permute.m, permutes an I4VEC in place;
• i4vec_print.m, prints an I4VEC;
• i4vec_uniform_ab.m, returns a pseudorandom I4VEC in a given range;
• legendre_zeros.m, returns the zeros of the Legendre polynomial of degree N.
• perm_check.m, checks that a vector represents a permutation;
• perm_uniform.m, selects a random permutation of N objects;
• r8_abs.m, returns the absolute value of an R8;
• r8_acos.m, computes the inverse cosine;
• r8_add.m, adds two R8's;
• r8_aint.m, truncates an R8 to an integer value;
• r8_asin.m, computes the inverse sine;
• r8_atan.m, computes the arctangent, with regard to the correct quadrant.
• r8_cas.m, returns the "casine" of an R8;
• r8_ceiling.m, rounds an R8 "up" (towards +oo) to the next integer.
• r8_choose.m, returns a binomial coefficient as an R8.
• r8_chop.m, returns an R8 chopped to a given number of binary digits;
• r8_csc.m, returns the cosecant of an R8;
• r8_cube_root.m, returns the cube root of an R8;
• r8_diff.m, returns the difference of two R8's to a specified accuracy;
• r8_digit.m, returns a decimal digit of an R8;
• r8_divide_i4.m, returns an I4 fraction as an R8;
• r8_epsilon.m, returns the R8 roundoff unit;
• r8_epsilon_compute.m, computes the R8 roundoff unit;
• r8_factorial.m, returns N factorial as an R8;
• r8_factorial2.m, computes the double factorial function;
• r8_floor.m, rounds an R8 "down" (towards -oo) to the next integer.
• r8_fraction.m, computes a ratio of integers as an R8;
• r8_fractional.m, returns the fractional part of an R8;
• r8_gamma.m, evaluates Gamma(X) for an R8.
• r8_huge.m, returns a "huge" R8;
• r8_hypot.m, returns sqrt ( x^2 + y^2 );
• r8_in_01.m, is true if the value is in [0,1];
• r8_insignificant.m, is true if an R8 is insignificant;
• r8_is_int.m, is true if an R8 equals an integer value;
• r8_log_2.m, returns the logarithm base 2 of an R8;
• r8_log_10.m, returns the logarithm base 10 of an R8;
• r8_log_b.m, returns the logarithm base B of an R8;
• r8_mant.m, returns the mantissa of an R8;
• r8_mod.m, returns the remainder of real division;
• r8_modp.m, returns the nonnegative remainder of real division;
• r8_mop.m, returns a power of -1 as an R8;
• r8_normal_01.m, returns a unit pseudonormal R8;
• r8_pi.m, returns the value of Pi as an R8;
• r8_pi_sqrt.m, returns the square root of Pi as an R8;
• r8_power.m, returns the value of an integral power of an R8;
• r8_power_fast.m, quickly returns the value of an integral power of an R8;
• r8_pythag.m, computes sqrt ( A^2 + B^2 ) avoiding unnecessary overflow and underflow;
• r8_round.m, rounds an R8 to the nearest integral value.
• r8_round2.m, rounds an R8 to a specified number of binary digits.
• r8_roundb.m, rounds an R8 to a specified number of digits in a given base.
• r8_roundx.m, rounds an R8 to a specified number of decimal digits.
• r8_sign.m, returns the sign of an R8.
• r8_sign_char.m, returns a character indicating the sign of an R8.
• r8_sign_match.m, is TRUE if two R8's have the same sign.
• r8_sign_match_strict.m, is TRUE if two R8's have the same strict sign.
• r8_sign_opposite.m, is TRUE if two R8's have opposite sign.
• r8_sign_opposite_strict.m, is TRUE if two R8's have strictly opposite signs.
• r8_sqrt_i4.m, returns the square root of an I4 as an R8.
• r8_swap.m, swaps two R8's.
• r8_swap3.m, swaps three R8's.
• r8_tiny.m, returns a "tiny" R8;
• r8_to_r8_discrete.m, maps R to RD in [RMIN,RMAX] with NR discrete values.
• r8_to_dhms.m, converts decimal days into days, hours, minutes, seconds.
• r8_to_i4.m, maps X in [XMIN,XMAX] to I in [IMIN,IMAX];
• r8_uniform_ab.m, returns a scaled pseudorandom R8;
• r8_uniform_01.m, returns a unit pseudorandom R8;
• r8_unswap3.m, unswaps three R8's;
• r8_walsh_1d.m, evaluates the Walsh function;
• r8_wrap.m, forces an R8 to lie between given limits by wrapping.
• r82_dist_l2.m, returns the L2 distance between a pair of R82's.
• r82_print.m, prints an R82;
• r82_to_c8.m, uses two R8's to a C8;
• r82_uniform_ab.m, returns a scaled pseudorandom R82 value;
• r82poly2_print.m, prints a second order polynomial in two variables;
• r82poly2_type.m, analyzes a second order polynomial in two variables.
• r82poly2_type_print.m, prints the meaning of the output from R82POLY2_TYPE.
• r82vec_order_type.m, finds if an R82VEC is (non)strictly ascending/descending.;
• r82vec_part_quick_a.m, reorders an R82VEC as part of a quicksort;
• r82vec_print.m, prints an R82VEC;
• r82vec_print_part.m, prints part of an R82VEC.
• r82vec_sort_quick_a.m, ascending sorts an R82VEC using quicksort;
• r82vec_permute.m, permutes the elements of an R82VEC;
• r82vec_sort_heap_index_a.m, creates an ascending sort index for the elements of an R82VEC;
• r82vec_uniform_ab.m, returns a pseudorandom R82VEC;
• r83_norm.m, returns the Euclidean norm of an R83.
• r83vec_print_part.m, prints part of an R83VEC.
• r8block_print.m, prints an R8BLOCK;
• r8block_expand_linear.m, linearly interpolates new data into an R8BLOCK;
• r8col_compare.m, compares two columns of an R8COL;
• r8col_duplicates.m, generates an R8COL with some duplicate columns;
• r8col_find.m, seeks a column of an R8COL equal to a given vector;
• r8col_first_index.m, indexes the first occurrence of values in an R8COL.
• r8col_insert.m, inserts a column into an R8COL;
• r8col_max.m, computes the column maximums of an R8COL;
• r8col_max_one.m, rescales an R8COL so each column maximum is 1;
• r8col_mean.m, computes the column means of an R8COL;
• r8col_min.m, computes the column minimums of an R8COL;
• r8col_normalize_li.m, normalizes the columns of an R8COL with respect to the infinity norm;
• r8col_part_quick_a.m, partitions the columns of an R8COL;
• r8col_permute_a.m, permutes the columns of an R8COL;
• r8col_sort_heap_a.m, ascending heapsorts the columns of an R8COL;
• r8col_sort_heap_index_a.m, computes an index vector to ascending sort an R8COL;
• r8col_sort_quick_a.m, ascending quicksorts the columns of an R8COL;
• r8col_sorted_tol_undex.m, returns tolerably unique indexes for a sorted R8COL.
• r8col_sorted_tol_unique.m, returns the tolerably unique columns of a sorted R8COL;
• r8col_sorted_tol_unique_count.m, counts the tolerably unique columns of a sorted R8COL;
• r8col_sorted_undex.m, returns unique indexes for a sorted R8COL.
• r8col_sorted_unique.m, returns the unique columns of a sorted R8COL;
• r8col_sorted_unique_count.m, counts the unique columns of a sorted R8COL;
• r8col_sortr_a.m, ascending sorts one column of an R8COL, and adjusts rows;
• r8col_sum.m, computes the column sums of an R8COL;
• r8col_swap.m, swaps two columns of an R8COL;
• r8col_to_r8vec.m, converts an R8COL to an R8VEC;
• r8col_tol_undex.m, indexes tolerably unique entries in an R8COL.
• r8col_tol_unique_count.m, counts tolerably unique entries in an R8COL;
• r8col_tol_unique_index.m, indexes tolerably unique entries in an R8COL.
• r8col_undex.m, indexes unique entries in an R8COL.
• r8col_uniform_abvec.m, fills an R8COL with scaled pseudorandom numbers.
• r8col_unique_count.m, counts unique entries in an R8COL;
• r8col_unique_index.m, indexes unique entries in an R8COL.
• r8col_variance.m, computes the variances of an R8COL;
• r8r8_compare.m, compares two R8R8's;
• r8r8_print.m, prints an R8R8;
• r8r8r8_compare.m, compares two R8R8R8's;
• r8r8r8vec_index_insert_unique.m, inserts unique R8R8R8 values into an index sorted R8R8R8VEC;
• r8r8r8vec_index_search.m, searches for an R8R8R8 value in an index sorted R8R8R8VEC;
• r8r8vec_index_insert_unique.m, inserts unique R8R8 values into an index sorted R8R8VEC;
• r8r8vec_index_search.m, searches for an R8R8 value in an index sorted R8R8VEC;
• r8int_to_r8int.m, maps one double precision interval to another;
• r8int_to_i4int.m, maps an R8 interval to an I4 interval;
• r8mat_add.m, computes C = alpha * A + beta * B for R8MAT's.
• r8mat_amax.m, returns the maximum absolute value element in a rectangular R8MAT;
• r8mat_border_add.m, adds a "border" to an R8MAT.
• r8mat_border_cut.m, cuts the "border" of an R8MAT.
• r8mat_cholesky_factor.m, computes the Cholesky factor L*L' of a symmetric positive definite R8MAT;
• r8mat_cholesky_solve.m, solves a Cholesky factored linear system A * x = b;
• r8mat_choresky_factor.m, computes the "Choresky" factor R*R' of a symmetric positive definite R8MAT;
• r8mat_det_2d.m, computes the determinant of a 2 by 2 R8MAT;
• r8mat_det_3d.m, computes the determinant of a 3 by 3 R8MAT;
• r8mat_det_4d.m, computes the determinant of a 4 by 4 R8MAT;
• r8mat_det_5d.m, computes the determinant of a 5 by 5 R8MAT;
• r8mat_diag_add_scalar.m, adds a scalar to the diagonal of an R8MAT;
• r8mat_diag_add_vector.m, adds a vector to the diagonal of an R8MAT;
• r8mat_diag_get_vector.m, gets the diagonal of an R8MAT;
• r8mat_diag_set_scalar.m, sets the diagonal of an R8MAT to a scalar;
• r8mat_diag_set_vector.m, sets the diagonal of an R8MAT to a vector;
• r8mat_dif_fro.m, returns the Frobenius norm of the difference of two R8MAT's.
• r8mat_expand_linear.m, linearly interpolates new data into an R8MAT;
• r8mat_expand_linear2.m, linearly interpolates new data into an R8MAT;
• r8mat_fss.m, factors and solves a system with multiple right hand sides.
• r8mat_givens_post.m, returns a Givens post-multiplier matrix;
• r8mat_givens_pre.m, returns a Givens pre-multiplier matrix;
• r8mat_hess.m, approximates a Hessian matrix via finite differences.
• r8mat_house_axh.m, computes A*H, where H is a compact Householder matrix;
• r8mat_house_form.m, constructs a Householder matrix from its compact form;
• r8mat_house_hxa.m, computes H*A, where H is a compact Householder matrix;
• r8mat_house_post.m, returns a Householder post-multiplier matrix;
• r8mat_house_pre.m, returns a Householder pre-multiplier matrix;
• r8mat_identity.m, sets an R8MAT to the identity matrix;
• r8mat_in_01.m, is true if every entry of an R8MAT is in [0,1];
• r8mat_insignificant.m, is true if an R8MAT is insignificant;
• r8mat_inverse_2d.m, computes the inverse of a 2 by 2 R8MAT;
• r8mat_inverse_3d.m, computes the inverse of a 3 by 3 R8MAT;
• r8mat_inverse_4d.m, computes the inverse of a 4 by 4 R8MAT;
• r8mat_is_identity.m, determines if a matrix is the identity matrix.
• r8mat_is_symmetric.m, determines if a matrix is symmetric.
• r8mat_jac.m, approximates the Jacobian matrix of a function via finite differences.
• r8mat_l_inverse.m, computes the inverse of a lower triangular matrix;
• r8mat_l_print.m, prints a compact lower triangular matrix;
• r8mat_l_solve.m, solves a lower triangular linear system;
• r8mat_l1_inverse.m, computes the inverse of a unit lower triangular R8MAT;
• r8mat_lt_solve.m, solves a transposed lower triangular linear system;
• r8mat_lu.m, computes the LU factors of a rectangular R8MAT;
• r8mat_max.m, returns the maximum element in a rectangular R8MAT;
• r8mat_max_index.m, returns the index of the maximum element in an R8MAT;
• r8mat_maxcol_minrow.m, returns the maximum column minimum row in a rectangular R8MAT;
• r8mat_maxrow_mincol.m, returns the maximum row minimum column in a rectangular R8MAT;
• r8mat_min.m, returns the minimum element in an R8MAT;
• r8mat_min_index.m, returns the index of the minimum element in an R8MAT;
• r8mat_mincol_maxrow.m, returns the minimum column maximum row in an R8MAT;
• r8mat_minrow_maxcol.m, returns the minimum row maximum column in an R8MAT;
• r8mat_minv.m, computes inverse(A) * B for R8MAT's.
• r8mat_mm.m, computes the product of an R8MAT times a matrix;
• r8mat_mtm.m, computes the product of a transposed R8MAT times a matrix;
• r8mat_mtv.m, computes the product of a transposed R8MAT times a vector;
• r8mat_mv.m, computes the product of an R8MAT times a vector;
• r8mat_nint.m, rounds the entries of an R8MAT to the nearest integer;
• r8mat_norm_eis.m, computes the EISPACK norm of an R8MAT;
• r8mat_norm_fro.m, computes the Frobenius norm of an R8MAT;
• r8mat_norm_fro_affine.m, computes the Frobenius norm of an R8MAT difference;
• r8mat_norm_l1.m, computes the L1 norm of an R8MAT;
• r8mat_norm_l2.m, computes the L2 norm of an R8MAT;
• r8mat_norm_li.m, computes the L-oo norm of an R8MAT;
• r8mat_normal_01.m, returns an R8MAT containing normal random numbers;
• r8mat_nullspace.m, computes the nullspace of an R8MAT;
• r8mat_nullspace_size.m, sizes the nullspace of an R8MAT;
• r8mat_orth_uniform.m, returns a random orthogonal matrix;
• r8mat_plot.m, plots an R8MAT, with an optional title;
• r8mat_plot_symbol.m, returns a symbol for a double precision number;
• r8mat_poly_char.m, computes the characteristic polynomial of an R8MAT;
• r8mat_power.m, computes a positive integer power of a square R8MAT;
• r8mat_power_method.m, applies the power method to seek the dominant eigenvalue and eigenvector;
• r8mat_print.m, prints an R8MAT;
• r8mat_print_some.m, prints some of an R8MAT;
• r8mat_ref.m, returns the row echelon form of an R8MAT.
• r8mat_rms.m, returns the RMS norm of an R8MAT.
• r8mat_rref.m, returns the reduced row echelon form of an R8MAT.
• r8mat_scale.m, multiplies an R8MAT by a scalar.
• r8mat_solve.m, solves an N by N linear system with multiple right hand sides.
• r8mat_solve_2d.m, solves a 2 by 2 linear system using Cramer's rule.
• r8mat_solve_3d.m, solves a 3 by 3 linear system using Cramer's rule.
• r8mat_solve2.m, computes the solution of an N by N linear system.
• r8mat_sum.m, sums an R8MAT.
• r8mat_symm_eigen.m, returns a random symmetric matrix with given eigensystem.
• r8mat_symm_jacobi.m, applies Jacobi eigenvalue iteration to a symmetric matrix.
• r8mat_to_r8plu.m, factors a general R8MAT;
• r8mat_trace.m, returns the trace of an R8MAT;
• r8mat_transpose_print.m, prints the transpose of an R8MAT;
• r8mat_transpose_print_some.m, prints some of the transpose of an R8MAT;
• r8mat_u_inverse.m, returns the inverse of an upper triangular R8MAT;
• r8mat_u1_inverse.m, returns the inverse of a unit upper triangular R8MAT;
• r8mat_uniform_01.m, returns a unit pseudorandom R8MAT;
• r8mat_uniform_ab.m, returns an R8MAT of scaled pseudorandom numbers;
• r8mat_uniform_abvec.m, returns an R8MAT of scaled pseudorandom numbers;
• r8mat_vand2.m, returns the N by N Vandermonde matrix;
• r8plu_det.m, returns the determinant of an R8LPU matrix.
• r8plu_inverse.m, returns the inverse of an R8LPU matrix.
• r8plu_mul.m, computes A * x, after A has been factored by R8MAT_TO_R8PLU.
• r8plu_sol.m, solves A * x = b, after A has been factored by R8MAT_TO_R8PLU.
• r8plu_to_r8mat.m, recovers the matrix A that was factored by R8MAT_TO_R8PLU.
• r8poly_degree.m, returns the degree of a polynomial;
• r8poly_deriv.m, returns the derivative of a polynomial;
• r8poly_lagrange_0.m, evaluates the Lagrange factor at a point;
• r8poly_lagrange_1.m, evaluates the first derivative of the Lagrange factor at a point;
• r8poly_lagrange_2.m, evaluates the second derivative of the Lagrange factor at a point;
• r8poly_lagrange_coef.m, returns the coefficients of a Lagrange polynomial;
• r8poly_lagrange_factor.m, evaluates the polynomial Lagrange factor at a point;
• r8poly_lagrange_val.m, evaluates the IPOL-th Lagrange polynomial;
• r8poly_order.m, returns the order of a polynomial.
• r8poly_print.m, prints a polynomial;
• r8poly_shift.m, adjusts the coefficients of a polynomial for a new argument.
• r8poly_value.m, evaluates a polynomial, using the coefficient ordering that is the opposite of that which Matlab's polyval() assumes.
• r8poly_value_horner.m, evaluates a polynomial in standard form;
• r8poly_value_old.m, evaluates a polynomial in standard form;
• r8poly_value_2d.m, evaluates a polynomial of X and Y of total degree M, using a coefficient ordering that begins with the constant term.
• r8poly2_ex.m, finds the extremal point of a parabola determined by three points.
• r8poly2_ex2.m, finds the extremal point of a parabola determined by three points.
• r8poly2_root.m, returns the two roots of a quadratic polynomial.
• r8poly2_rroot.m, returns the real parts of the two roots of a quadratic polynomial.
• r8poly2_val.m, evaluates a parabola defined by three data values.
• r8poly2_val2.m, evaluates a parabolic interpolant through tabular data.
• r8poly3_root.m, returns the three roots of a cubic polynomial.
• r8poly4_root.m, returns the four roots of a quartic polynomial.
• r8row_compare.m, compares two rows of an R8ROW;
• r8row_max.m, returns the row maximums of an R8ROW.
• r8row_mean.m, returns the row means of an R8ROW.
• r8row_min.m, returns the row minimums of an R8ROW.
• r8row_part_quick_a.m, partitions the rows of an R8ROW;
• r8row_sort_heap_a.m, ascending heapsorts the rows of an R8ROW;
• r8row_sort_heap_index_a.m, computes an index vector to ascending sort an R8ROW;
• r8row_sort_quick_a.m, ascending quicksorts the rows of an R8ROW;
• r8row_sum.m, returns the row sums of an R8ROW.
• r8row_swap.m, swaps two rows of an R8ROW.
• r8row_to_r8vec.m, converts an R8ROW into an R8VEC.
• r8row_variance.m, returns the row variances of an R8ROW.
• r8slmat_print.m, prints a strict lower triangular R8MAT.
• r8vec_01_to_ab.m, shifts and rescales data to lie within given bounds;
• r8vec_amax.m, returns the maximum absolute value in an R8VEC.
• r8vec_amax_index.m, returns the index of the maximum absolute value in an R8VEC.
• r8vec_amin.m, returns the minimum absolute value in an R8VEC.
• r8vec_amin_index.m, returns the index of the minimum absolute value in an R8VEC.
• r8vec_any_negative.m, is true if any entry of an R8VEC is negative;
• r8vec_any_nonzero.m, is true if any entry of an R8VEC is nonzero;
• r8vec_any_normal.m, returns a unit normal vector to a given vector;
• r8vec_ascends.m, is TRUE if the entries of an R8VEC are weakly ascending;
• r8vec_ascends_strictly.m, is TRUE if the entries of an R8VEC are strictly ascending;
• r8vec_bin.m, bins an R8VEC;
• r8vec_blend.m, interpolates an R8VEC given two vectors and weight factors;
• r8vec_bracket.m, searches a sorted R8VEC for successive brackets of a value;
• r8vec_bracket2.m, searches a sorted R8VEC for successive brackets of a value.
• r8vec_bracket3.m, finds the interval containing or nearest a given value;
• r8vec_bracket4.m, finds the interval containing or nearest each of a vector of values;
• r8vec_bracket5.m, searches a sorted R8VEC for successive brackets of a value.
• r8vec_bracket6.m, searches a sorted R8VEC for successive brackets of a vector of values.
• r8vec_chebyspace.m, creates a vector of Chebyshev spaced values in [A,B].
• r8vec_cheby1space.m, creates a vector of Type 1 Chebyshev spaced values in [A,B].
• r8vec_cheby2space.m, creates a vector of Type 2 Chebyshev spaced values in [A,B].
• r8vec_circular_variance.m, returns the circular variance of an R8VEC;
• r8vec_compare.m, compares the order of two R8VEC's;
• r8vec_convolution.m, returns the discrete convolution of two R8VEC's;
• r8vec_convolution_circ.m, returns the discrete circular convolution of two R8VEC's;
• r8vec_copy.m, copies one R8VEC into another;
• r8vec_correlation.m, returns the correlation of two R8VEC's;
• r8vec_cross_product_2d.m, computes the cross product of two R8VEC's in 2D;
• r8vec_cross_product_affine_2d.m, computes the affine cross product of two R8VEC's in 2D;
• r8vec_cross_product_3d.m, computes the cross product of two R8VEC's in 3D;
• r8vec_cross_product_affine_3d.m, computes the affine cross product of two R8VEC's in 3D;
• r8vec_cum.m, returns the cumulative sums of an R8VEC;
• r8vec_cum0.m, returns the cumulative sums of an R8VEC;
• r8vec_dif.m, computes coefficients for estimating the N-th derivative;
• r8vec_diff_norm.m, returns the L2 norm of the difference of two R8VEC's.
• r8vec_diff_norm_l1.m, returns the L1 norm of the difference of two R8VEC's.
• r8vec_diff_norm_l2.m, returns the L2 norm of the difference of two R8VEC's.
• r8vec_diff_norm_li.m, returns the L-oo norm of the difference of two R8VEC's.
• r8vec_direct_product.m, forms the elements of the direct product of R8VEC's.
• r8vec_direct_product2.m, forms the elements of the direct product of R8VEC's.
• r8vec_distance.m, determines the distance between two R8VEC's;
• r8vec_distinct.m, determines if the entries of an R8VEC are distinct;
• r8vec_dot_product.m, computes the dot product of two R8VEC's;
• r8vec_dot_product_affine.m, computes the affine dot product of two R8VEC's;
• r8vec_eq.m, is true if two R8VEC's are equal;
• r8vec_even.m, returns an R8VEC of N values evenly spaced between given limits;
• r8vec_even_select.m, returns the I-th of N evenly spaced values;
• r8vec_even2.m, linearly interpolates new numbers into an R8VEC;
• r8vec_even2_select.m, returns the I-th of N evenly spaced midpoint values;
• r8vec_even3.m, evenly interpolates new data into an R8VEC.
• r8vec_expand_linear.m, linearly interpolates new data into an R8VEC.
• r8vec_expand_linear2.m, linearly interpolates new data into an R8VEC.
• r8vec_first_index.m, indexes the first occurrence of values in an R8VEC.
• r8vec_frac.m, finds the K-th smallest entry of an R8VEC;
• r8vec_fraction.m, returns the fraction part of an R8VEC;
• r8vec_gt.m, is true if one R8VEC is greater than another;
• r8vec_heap_a.m, sets an R8VEC to a ascending heap;
• r8vec_heap_d.m, sets an R8VEC to a descending heap;
• r8vec_histogram.m, returns a histogram of the entries of an R8VEC;
• r8vec_house_column.m, defines a Householder premultiplier that "packs" a column;
• r8vec_i4vec_dot_product.m, the dot product of an R8VEC and an I4VEC;
• r8vec_in_01.m, is true if every entry of an R8VEC is in [0,1];
• r8vec_in_ab.m, is true if every entry of an R8VEC is in [A,B];
• r8vec_index_delete_all.m, deletes all occurrences of a value from an indexed sorted list;
• r8vec_index_delete_dupes.m, deletes duplicates from an indexed sorted list.
• r8vec_index_delete_one.m, deletes one copy of a value from an indexed sorted list.
• r8vec_index_insert.m, inserts a value in an indexed sorted list.
• r8vec_index_insert_unique.m, inserts a unique value in an indexed sorted list.
• r8vec_index_order.m, sorts an integer vector using an index vector.
• r8vec_index_search.m, searches for a value in an indexed sorted list.
• r8vec_index_sort_unique.m, creates a sort index for an R8VEC.
• r8vec_index_sorted_range.m, search index sorted vector for elements in a range.
• r8vec_indexed_heap_d.m, creates a descending heap from an indexed R8VEC.
• r8vec_indexed_heap_d_extract.m, extract from heap descending indexed R8VEC.
• r8vec_indexed_heap_d_insert.m, insert value into heap descending indexed R8VEC.
• r8vec_indexed_heap_d_max.m, maximum value in heap descending indexed R8VEC.
• r8vec_indicator.m, sets an R8VEC to the indicator vector;
• r8vec_insert.m, inserts a new value into an R8VEC;
• r8vec_insignificant.m, is true if an R8VEC is insignificant;
• r8vec_legendre.m, creates a vector of Legendre-spaced values.
• r8vec_linspace.m, returns an R8VEC of values evenly spaced between given limits.
• r8vec_linspace2.m, returns an R8VEC of values evenly spaced between given limits.
• r8vec_lt.m, is true if one R8VEC is less than another;
• r8vec_mask_print.m, prints a masked R8VEC;
• r8vec_max.m, returns the maximum entry in an R8VEC;
• r8vec_max_abs_index.m, returns the index of the maximum absolute value entry in an R8VEC;
• r8vec_max_index.m, returns the index of the maximum entry in an R8VEC;
• r8vec_mean.m, returns the mean of an R8VEC;
• r8vec_median.m, returns the median of an R8VEC;
• r8vec_midspace.m, returns an R8VEC of midpoint values evenly spaced between given limits.
• r8vec_min.m, returns the minimum entry in an R8VEC;
• r8vec_min_index.m, returns the index of the minimum entry in an R8VEC;
• r8vec_min_pos.m, returns the minimum positive entry in an R8VEC;
• r8vec_mirror_next.m, steps through all sign variations of an R8VEC;
• r8vec_nint.m, rounds an R8VEC to the nearest integer.
• r8vec_norm.m, returns the L2 norm of an R8VEC.
• r8vec_norm_affine.m, returns the affine L2 norm of an R8VEC.
• r8vec_norm_l0.m, returns the L0 "norm" of an R8VEC.
• r8vec_norm_l1.m, returns the L1 norm of an R8VEC.
• r8vec_norm_l2.m, returns the L2 norm of an R8VEC.
• r8vec_norm_li.m, returns the L-oo norm of an R8VEC.
• r8vec_norm_lp.m, returns the Lp norm of an R8VEC.
• r8vec_normal_01.m, returns unit pseudonormal R8VEC.
• r8vec_normalize.m, scales an R8VEC to have unit Euclidean norm;
• r8vec_normalize_l1.m, scales an R8VEC to have unit sum;
• r8vec_normsq.m, returns the squared L2 norm of an R8VEC.
• r8vec_normsq_affine.m, returns the squared affine L2 norm of an R8VEC.
• r8vec_order_type.m, finds if an R8VEC is (non)strictly ascending/descending.
• r8vec_part_quick_a.m, reorders an R8VEC as part of a quicksort;
• r8vec_permute.m, permutes an R8VEC;
• r8vec_permute_cyclic.m, cyclically permutes an R8VEC;
• r8vec_permute_uniform.m, randomly permutes an R8VEC;
• r8vec_polarize.m, decomnposes an R8VEC into parts parallel and perpendicular to a given direction;
• r8vec_print.m, prints an R8VEC;
• r8vec_print_part.m, prints "part" of an R8VEC.
• r8vec_print_some.m, prints some of an R8VEC;
• r8vec_product.m, computes the product of the entries of an R8VEC;
• r8vec_range.m, finds the range of Y's within a restricted X range;
• r8vec_range_2.m, updates a range to include values in a new array;
• r8vec_reverse.m, reverses the entries of an R8VEC;
• r8vec_rms.m, returns the RMS norm of an R8VEC.
• r8vec_rotate.m, "rotates" the entries of an R8VEC;
• r8vec_scalar_triple_product.m, computes the scalar triple product;
• r8vec_search_binary_a.m, uses binary search on an R8VEC to find the location of a given value;
• r8vec_shift.m, performs a shift on an R8VEC.
• r8vec_shift_circular.m, performs a circular shift on an R8VEC.
• r8vec_sort_bubble_a.m, ascending sorts an R8VEC using bubble sort;
• r8vec_sort_bubble_d.m, descending sorts an R8VEC using bubble sort;
• r8vec_sort_heap_a.m, ascending sorts an R8VEC using heap sort;
• r8vec_sort_heap_d.m, descending sorts an R8VEC using heap sort;
• r8vec_sort_heap_index_a.m, computes an index vector to ascending sort an R8VEC;
• r8vec_sort_heap_index_d.m, computes an index vector to descending sort an R8VEC;
• r8vec_sort_heap_mask_a.m, indexed heap ascending sort of a masked R8VEC;
• r8vec_sort_insert_a.m, ascending sorts an R8VEC using insertion sort;
• r8vec_sort_insert_index_a.m, ascending index sorts an R8VEC using insertion sort;
• r8vec_sort_insert_index_d.m, descending index sorts an R8VEC using insertion sort;
• r8vec_sort_quick_a.m, ascending quick sorts an R8VEC;
• r8vec_sort_shell_a.m, ascending sorts an R8VEC using Shell's sort;
• r8vec_sorted_merge.m, merges two ascending sorted R8VEC's;
• r8vec_sorted_nearest.m, returns the nearest element in a sorted R8VEC;
• r8vec_sorted_range.m, searches a sorted vector for elements in a range.
• r8vec_sorted_split.m, "splits" a sorted R8VEC, given a splitting value;
• r8vec_sorted_undex.m, returns unique sorted indexes for a sorted R8VEC.
• r8vec_sorted_unique.m, returns the unique elements in a sorted R8VEC;
• r8vec_sorted_unique_count.m, counts the unique elements in a sorted R8VEC;
• r8vec_sorted_unique_hist.m, creates a histogram of the unique elements in a sorted R8VEC;
• r8vec_split.m, splits an unsorted R8VEC based on a splitting value;
• r8vec_std.m, returns the standard deviation of an R8VEC;
• r8vec_stutter.m, makes a "stuttering" copy of an R8VEC;
• r8vec_sum.m, returns the sum of the entries of an R8VEC;
• r8vec_swap.m, swaps the contents of two R8VEC's;
• r8vec_transpose_print.m, prints the "transpose" of an R8VEC.
• r8vec_undex.m, returns unique sorted indexes for an R8VEC.
• r8vec_uniform_01.m, returns a unit pseudorandom R8VEC.
• r8vec_uniform_ab.m, returns a scaled pseudorandom R8VEC;
• r8vec_uniform_abvec.m, returns a scaled pseudorandom R8VEC;
• r8vec_uniform_unit.m, returns a random unit vector.
• r8vec_unique_count.m, counts the number of unique elements in an unsorted R8VEC;
• r8vec_variance.m, returns the variance of an R8VEC;
• r8vec_vector_triple_product.m, computes the vector triple product;
• r8vec_write.m, writes an R8VEC to a file;
• r8vec2_compare.m, compares two entries in an R8VEC2;
• r8vec2_print_some.m, prints some of an R8VEC2;
• r8vec2_print.m, prints an R8VEC2;
• r8vec2_sort_a.m, ascending sorts an R8VEC2;
• r8vec2_sort_d.m, descending sorts an R8VEC2;
• r8vec2_sort_heap_index_a.m, does an indexed heap ascending sort of an R8VEC2;
• r8vec2_sorted_unique.m, keeps unique elements in a sorted R8VEC2;
• r8vec2_sorted_unique_index.m, indexes unique elements in a sorted R8VEC2.
• r8vec2_sum_max_index.m, returns the index of the maximum sum of two R8VEC's.
• r8vec3_print.m, prints an R8VEC3;
• r8vecs_print.m, prints a packed R8VEC.
• roots_to_r8poly.m, converts polynomial roots to polynomial coefficients;
• sort_heap_external.m, external sorts a list of values into ascending order;
• timestamp.m, prints the current YMDHMS date as a timestamp;

Examples and Tests:

• r8lib_test.m, runs all the tests;
• r8lib_test_output.txt, the output file;
• r8lib_test001.m, tests R8_ABS;
• r8lib_test002.m, tests R8_ATAN;
• r8lib_test003.m, tests R8_CAS;
• r8lib_test004.m, tests R8_CEILING;
• r8lib_test005.m, tests R8_DIFF;
• r8lib_test006.m, tests R8_DIGIT;
• r8lib_test007.m, tests R8_EPSILON;
• r8lib_test008.m, tests R8_FRACTIONAL;
• r8lib_test009.m, tests R8_HUGE;
• r8lib_test010.m, tests R8_LOG_2;
• r8lib_test011.m, tests R8_LOG_B;
• r8lib_test012.m, tests R8_MANT;
• r8lib_test013.m, tests R8_MOD;
• r8lib_test014.m, tests R8_MODP;
• r8lib_test015.m, tests R8_NINT;
• r8lib_test016.m, tests R8_NORMAL_01;
• r8lib_test017.m, tests R8_PI;
• r8lib_test018.m, tests R8_POWER;
• r8lib_test019.m, tests R8_POWER_FAST;
• r8lib_test020.m, tests R8_ROUND2;
• r8lib_test021.m, tests R8_ROUNDB;
• r8lib_test022.m, tests R8_ROUNDX;
• r8lib_test023.m, tests R8_SIGN;
• r8lib_test0235.m, tests R8_SWAP;
• r8lib_test024.m, tests R8_TO_R8_DISCRETE;
• r8lib_test025.m, tests R8_TO_I4;
• r8lib_test026.m, tests R8_UNIFORM;
• r8lib_test027.m, tests R8_UNIFORM_01;
• r8lib_test028.m, tests R8_UNIFORM_01;
• r8lib_test029.m, tests R8_WALSH_1D;
• r8lib_test0295.m, tests R8_WRAP;
• r8lib_test031.m, tests R82POLY2_TYPE;
• r8lib_test032.m, tests R82VEC_ORDER_TYPE;
• r8lib_test033.m, tests R82VEC_PART_QUICK_A;
• r8lib_test034.m, tests R82VEC_SORT_HEAP_INDEX_A;
• r8lib_test035.m, tests R82VEC_SORT_QUICK_A;
• r8lib_test036.m, tests R8BLOCK_EXPAND_LINEAR;
• r8lib_test0365.m, tests R8BLOCK_PRINT;
• r8lib_test037.m, tests R8COL_FIND;
• r8lib_test038.m, tests R8COL_INSERT and R8COL_SORT_HEAP_A;
• r8lib_test0385.m, tests R8COL_SORT_HEAP_INDEX_A;
• r8lib_test039.m, tests R8COL_SORT_QUICK_A;
• r8lib_test0393.m, tests R8COL_SORTED_TOL_UNIQUE.
• r8lib_test0395.m, tests R8COL_SORTED_TOL_UNIQUE_COUNT.
• r8lib_test0397.m, tests R8COL_SORTED_UNDEX.
• r8lib_test040.m, tests R8COL_MAX and R8COL_MIN;
• r8lib_test041.m, tests R8COL_MEAN and R8COL_SUM;
• r8lib_test0415.m, tests R8COL_PERMUTE;
• r8lib_test042.m, tests R8COL_SORTR_A;
• r8lib_test043.m, tests R8COL_SWAP;
• r8lib_test044.m, tests R8COL_TO_R8VEC;
• r8lib_test0442.m, tests R8COL_TOL_UNDEX;
• r8lib_test0443.m, tests R8COL_UNDEX;
• r8lib_test0445.m, tests R8COL_UNIQUE_COUNT;
• r8lib_test045.m, tests R8COL_VARIANCE;
• r8lib_test046.m, tests R8R8VEC_INDEX_INSERT_UNIQUE;
• r8lib_test047.m, tests R8R8R8VEC_INDEX_INSERT_UNIQUE;
• r8lib_test048.m, tests R8INT_TO_I4INT and I4INT_TO_R8INT;
• r8lib_test049.m, tests R8MAT_CHOLESKY_FACTOR, R8MAT_CHORESKY_FACTOR and R8MAT_CHOLESKY_SOLVE;
• r8lib_test050.m, tests R8MAT_DET_2D;
• r8lib_test051.m, tests R8MAT_DET_3D;
• r8lib_test052.m, tests R8MAT_DET_4D;
• r8lib_test053.m, tests R8MAT_DET_5D;
• r8lib_test054.m, tests R8MAT_EXPAND_LINEAR;
• r8lib_test055.m, tests R8MAT_EXPAND_LINEAR2;
• r8lib_test0555.m, tests R8MAT_FSS.
• r8lib_test056.m, tests R8MAT_GIVENS_POST;
• r8lib_test057.m, tests R8MAT_GIVENS_PRE;
• r8lib_test058.m, tests R8MAT_HESS;
• r8lib_test058_f.m, is a sample nonlinear function for treatment by R8MAT_HESS;
• r8lib_test058_h.m, is the exact Hessian of TEST058_F;
• r8lib_test059.m, tests R8MAT_HOUSE_FORM and R8VEC_HOUSE_COLUMN;
• r8lib_test060.m, tests R8MAT_HOUSE_FORM;
• r8lib_test061.m, tests R8MAT_HOUSE_POST;
• r8lib_test062.m, tests R8MAT_HOUSE_PRE;
• r8lib_test063.m, tests R8MAT_MAX_INDEX and R8MAT_MIN_INDEX;
• r8lib_test064.m, tests R8MAT_INVERSE_2D;
• r8lib_test065.m, tests R8MAT_INVERSE_3D;
• r8lib_test066.m, tests R8MAT_INVERSE_4D;
• r8lib_test067.m, tests R8MAT_JAC;
• r8lib_test067_f.m, is a sample nonlinear function for treatment by R8MAT_JAC;
• r8lib_test067_jac.m, the exact jacobian of TEST067_F;
• r8lib_test068.m, tests R8MAT_L_INVERSE;
• r8lib_test069.m, tests R8MAT_L_PRINT;
• r8lib_test070.m, tests R8MAT_L1_INVERSE;
• r8lib_test071.m, tests R8MAT_LU;
• r8lib_test072.m, tests R8MAT_MAX and R8MAT_MIN;
• r8lib_test073.m, tests R8MAT_MAXCOL_MINROW, R8MAT_MAXROW_MINCOL, R8MAT_MINCOL_MAXROW and R8MAT_MINROW_MAXCOL;
• r8lib_test0737.m, tests R8MAT_NULLSPACE_SIZE and R8MAT_NULLSPACE;
• r8lib_test074.m, tests R8MAT_ORTH_UNIFORM;
• r8lib_test075.m, tests R8MAT_PLOT;
• r8lib_test076.m, tests R8MAT_POWER_METHOD;
• r8lib_test0764.m, tests R8MAT_REF;
• r8lib_test0766.m, tests R8MAT_RREF;
• r8lib_test077.m, tests R8MAT_SOLVE;
• r8lib_test0775.m, tests R8MAT_SOLVE_2D;
• r8lib_test0776.m, tests R8MAT_SOLVE_3D;
• r8lib_test078.m, tests R8MAT_SOLVE2;
• r8lib_test079.m, tests R8MAT_SYMM_JACOBI;
• r8lib_test080.m, tests R8MAT_TO_R8PLU and R8PLU_TO_R8MAT;
• r8lib_test081.m, tests R8MAT_TRACE;
• r8lib_test082.m, tests R8MAT_TRANSPOSE_PRINT;
• r8lib_test083.m, tests R8MAT_U_INVERSE;
• r8lib_test084.m, tests R8MAT_U1_INVERSE;
• r8lib_test085.m, tests R8MAT_UNIFORM;
• r8lib_test086.m, tests R8PLU_DET;
• r8lib_test087.m, tests R8PLU_INVERSE;
• r8lib_test088.m, tests R8PLU_MUL;
• r8lib_test089.m, tests R8PLU_SOL;
• r8lib_test090.m, tests R8POLY_DERIV;
• r8lib_test091.m, tests R8POLY_LAGRANGE_COEF;
• r8lib_test092.m, tests R8POLY_LAGRANGE_COEF and R8POLY_DERIV;
• r8lib_test093.m, tests R8POLY_LAGRANGE_0, R8POLY_LAGRANGE_1, R8POLY_LAGRANGE_2;
• r8lib_test094.m, tests R8POLY_LAGRANGE_FACTOR;
• r8lib_test095.m, tests R8POLY_LAGRANGE_VAL;
• r8lib_test098.m, tests R8POLY_VALUE_HORNER;
• r8lib_test099.m, tests R8POLY2_EX and R8POLY2_EX2;
• r8lib_test100.m, tests R8POLY2_VAL;
• r8lib_test100_f.m, evaluates a parabola for us.
• r8lib_test101.m, tests R8POLY2_VAL2;
• r8lib_test102.m, tests R8POLY2_ROOT;
• r8lib_test103.m, tests R8POLY3_ROOT;
• r8lib_test104.m, tests R8POLY4_ROOT;
• r8lib_test105.m, tests R8ROW_MAX and R8ROW_MIN;
• r8lib_test106.m, tests R8ROW_MEAN and R8ROW_SUM;
• r8lib_test107.m, tests R8ROW_SWAP;
• r8lib_test108.m, tests R8ROW_TO_R8VEC.
• r8lib_test109.m, tests R8ROW_VARIANCE.
• r8lib_test110.m, tests DSLMAT_PRINT;
• r8lib_test111.m, tests R8VEC_AMAX and R8VEC_AMIN;
• r8lib_test112.m, tests R8VEC_BRACKET;
• r8lib_test113.m, tests R8VEC_BRACKET2;
• r8lib_test114.m, tests R8VEC_BRACKET3;
• r8lib_test1143.m, tests R8VEC_BRACKET5;
• r8lib_test1145.m, tests R8VEC_CHEBYSPACE;
• r8lib_test1147.m, tests R8VEC_CONVOLUTION;
• r8lib_test115.m, tests R8VEC_CONVOLUTION_CIRC;
• r8lib_test116.m, tests R8VEC_DIF;
• r8lib_test1165.m, tests R8VEC_DIRECT_PRODUCT;
• r8lib_test1166.m, tests R8VEC_DIRECT_PRODUCT2;
• r8lib_test116_f.m, evaluates the function used in TEST116;
• r8lib_test117.m, tests R8VEC_EVEN;
• r8lib_test118.m, tests R8VEC_EVEN2.
• r8lib_test119.m, tests R8VEC_EVEN3.
• r8lib_test120.m, tests R8VEC_EXPAND_LINEAR;
• r8lib_test121.m, tests R8VEC_FRAC;
• r8lib_test122.m, tests R8VEC_HISTOGRAM;
• r8lib_test123.m, tests R8VEC_INDEX_INSERT, R8VEC_INDEX_DELETE_ALL, R8VEC_INDEX_DELETE_DUPES;
• r8lib_test124.m, tests R8VEC_INDEX_INSERT_UNIQUE and R8VEC_INDEX_ORDER;
• r8lib_test125.m, tests R8VEC_INDEX_INSERT_UNIQUE and R8VEC_INDEX_SEARCH;
• r8lib_test1251.m, tests R8VEC_INDEX_SORTED_RANGE;
• r8lib_test1252.m, tests R8VEC_INDEXED_HEAP_D;
• r8lib_test1255.m, tests R8VEC_INDEXED_HEAP_D_EXTRACT and others;
• r8lib_test1258.m, tests R8VEC_LINSPACE and R8VEC_MIDSPACE;
• r8lib_test126.m, tests R8VEC_MAX and R8VEC_MIN;
• r8lib_test127.m, tests R8VEC_MAX_INDEX and R8VEC_MIN_INDEX;
• r8lib_test128.m, tests R8VEC_MEAN and R8VEC_MEDIAN.
• r8lib_test129.m, tests R8VEC_NORM_L1, R8VEC_NORM_L2, R8VEC_NORM_LI.
• r8lib_test130.m, tests R8VEC_NORMAL_01;
• r8lib_test152.m, tests R8VEC_NORMALIZE_L1;
• r8lib_test131.m, tests R8VEC_ORDER_TYPE;
• r8lib_test132.m, tests R8VEC_PERMUTE;
• r8lib_test133.m, tests R8VEC_POLARIZE;
• r8lib_test134.m, tests R8VEC_ROTATE;
• r8lib_test135.m, tests R8VEC_REVERSE;
• r8lib_test136.m, tests R8VEC_SEARCH_BINARY_A;
• r8lib_test137.m, tests R8VEC_SORT_BUBBLE_A;
• r8lib_test138.m, tests R8VEC_SORT_HEAP_A.
• r8lib_test139.m, tests R8VEC_SORT_HEAP_D.
• r8lib_test140.m, tests R8VEC_SORT_HEAP_INDEX_A and R8VEC_SORT_HEAP_INDEX_D;
• r8lib_test141.m, tests R8VEC_SORT_HEAP_MASK_A;
• r8lib_test142.m, tests R8VEC_SORT_INSERT_A;
• r8lib_test143.m, tests R8VEC_SORT_INSERT_INDEX_A;
• r8lib_test144.m, tests R8VEC_SORT_QUICK_A;
• r8lib_test145.m, tests R8VEC_SORTED_MERGE_A;
• r8lib_test146.m, tests R8VEC_SORTED_NEAREST;
• r8lib_test1465.m, tests R8VEC_SORTED_RANGE;
• r8lib_test147.m, tests R8VEC_SORTED_SPLIT and R8VEC_SPLIT;
• r8lib_test1475.m, tests R8VEC_SORTED_UNDEX.
• r8lib_test148.m, tests R8VEC_SORTED_UNIQUE.
• r8lib_test149.m, tests R8VEC_SORTED_UNIQUE_COUNT.
• r8lib_test150.m, tests R8VEC_SORTED_UNIQUE_HIST;
• r8lib_test1504.m, tests R8VEC_TRANSPOSE_PRINT;
• r8lib_test1505.m, tests R8VEC_UNDEX;
• r8lib_test151.m, tests R8VEC_UNIFORM;
• r8lib_test153.m, tests R8VEC2_SORT_A and R8VEC2_SORT_D;
• r8lib_test154.m, tests R8VEC2_SORT_HEAP_INDEX_A;
• r8lib_test155.m, tests R8VEC2_SORTED_UNIQUE;
• r8lib_test156.m, tests R8VEC2_SORTED_UNIQUE_INDEX;
• r8lib_test157.m, tests R8VEC2_SUM_MAX_INDEX;
• r8lib_test158.m, tests R8VECS_PRINT;

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