r8lib

r8lib, a MATLAB code which contains utilities for real 64 bit (R8) arithmetic.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

r8lib is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and an Octave version and a Python version and an R version.

Related Programs:

c8lib, a MATLAB code which implements certain elementary functions for complex 64 bit (C8) variables;

i4lib, a MATLAB code which contains many utility routines, integer 32 bit arithmetic.

quaternions, a MATLAB code which carries out some simple arithmetic operations for quaternions.

r8col, a MATLAB code which contains utility routines for R8COL's, that is, real 64 bit MxN arrays, considered as N column vectors, each of length M. The data may be thought of as a matrix of multiple columns, and many operations will be carried out columnwise.

r8lib_test

r8poly, a MATLAB code which contains a number of utilities for polynomials with R8 coefficients, that is, using real 64 bit arithmetic.

r8row, a MATLAB code which contains utility routines for R8ROW's, that is, real 64 bit MxN arrays, considered as M row vectors, each of length N. The data may be thought of as a matrix of multiple rows, and many operations will be carried out rowwise.

Source Code:

• boolean_to_string.m, returns "True" or "False", given a boolean value.
• c8_sqrt_r8.m, returns the complex square root of an R8;
• gamma_log_values.m returns some values of the logarithm of the Gamma function.
• gamma_values.m, returns selected values of the Gamma function.
• 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.
• i4mat_print.m, prints an I4MAT;
• i4mat_print_some.m, prints some of an I4MAT;
• i4vec_indicator0.m, sets an I4VEC to the indicator vector.
• i4vec_indicator1.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;
• ksub_next4.m, compute K-subsets of an N-set, one at a time.
• legendre_zeros.m, returns the zeros of the Legendre polynomial of degree N.
• perm0_check.m, checks that a vector represents a 0-based permutation;
• perm0_uniform.m, selects a random permutation of 0,...,N-1;
• perm1_check.m, checks that a vector represents a 1-based permutation;
• perm1_uniform.m, selects a random permutation of 1,...,N;
• r8_abs.m, returns the absolute value of an R8;
• r8_acos.m, computes the inverse cosine;
• r8_acosh.m, computes the inverse hyperbolic cosine;
• r8_add.m, adds two R8's;
• r8_agm.m, computes the arithmetic-geometric mean of two R8's;
• r8_aint.m, truncates an R8 to an integer value by rounding towards zero;
• r8_asin.m, computes the inverse sine;
• r8_asinh.m, computes the inverse hyperbolic sine of a value;
• r8_atan.m, computes the arctangent, with regard to the correct quadrant.
• r8_atanh.m, computes the inverse hyperbolic tangent of a value;
• r8_big.m, returns a "big" R8;
• 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_cosd.m, returns the cosine of an angle given in degrees.
• r8_cot.m, computes the cotangent of an angle;
• r8_cotd.m, returns the cotangent of an angle given in degrees.
• r8_csc.m, returns the cosecant of an R8;
• r8_cscd.m, returns the cosecant of an angle given in degrees.
• r8_cube_root.m, returns the cube root of an R8;
• r8_days_to_dhms.m, converts decimal days into days, hours, minutes, seconds.
• r8_degrees.m, converts an angle from radians to degrees.
• r8_dhms_to_days.m, converts days, hours, minutes, seconds into decimal days.
• 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_e.m, returns the value of the base of the natural logarithm system;
• r8_epsilon.m, returns the R8 roundoff unit;
• r8_epsilon_compute.m, computes the R8 roundoff unit;
• r8_exp.m, computes the exponential function, avoiding overflow and underflow.
• r8_factorial.m, returns N factorial as an R8;
• r8_factorial_sterling.m computes Stirling's approximation to the factorial function.
• r8_factorial_values.m, returns selected values of the factorial function.
• r8_factorial2.m, computes the double factorial function;
• r8_factorial2_values.m, returns selected values of the double factorial function.
• r8_fall.m, computes a falling factorial as an R8;
• r8_fall_values.m, returns selected values of the falling factorial function.
• r8_floor.m, rounds an R8 "down" (towards -oo) to the next integer.
• r8_fractional.m, returns the fractional part of an R8;
• r8_gamma.m, evaluates Gamma(X) for an R8.
• r8_gamma_log.m, evaluates Log(Gamma(X)) for an R8.
• r8_haversine.m, returns the haversine of an angle;
• r8_heaviside.m, evaluates the Heaviside step function;
• r8_huge.m, returns a "huge" R8;
• r8_hypot.m, returns sqrt ( x^2 + y^2 ) as an R8;
• r8_is_in_01.m, is true if an R8 is in [0,1];
• r8_is_inf.m, is true if an R8 if plus or minus infinity;
• r8_is_insignificant.m, is true if an R8 is insignificant;
• r8_is_integer.m, is true if an R8 equals an integer value;
• r8_is_nan.m, is true if an R8 is a NaN;
• 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_max.m, returns the maximum of two R8's;
• r8_min.m, returns the minimum of two R8's;
• r8_mod.m, returns the remainder of R8 division;
• r8_modp.m, returns the nonnegative remainder of R8 division;
• r8_mop.m, returns a power of -1 as an R8;
• r8_nint.m, returns, for a given R8, the nearest integer value;
• r8_normal_01.m, returns a unit pseudonormal R8;
• r8_normal_ab.m, returns a pseudonormal R8 with mean A and variance B.
• r8_nth_root.m, returns the Nth root of an R8.
• r8_pi.m, returns the value 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_print.m, prints an R8.
• r8_radians.m, converts an angle from degrees to radians.
• r8_relu.m, computes max(x,0);
• r8_rise.m, computes a rising factorial;
• r8_rise_values.m, returns selected values of the rising factorial function.
• 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_secd.m, returns the secant of an angle given in degrees.
• r8_sech.m, evaluates the hyperbolic secant of an R8.
• r8_sigmoid.m, evaluates the sigmoid function for an R8.
• 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_sign3.m, returns the three-way sign of an R8.
• r8_sincos_sum.m, simplifies a*sin(cx)+b*cos(cx).
• r8_sind.m, returns the sine of an angle given in degrees.
• r8_softplus.m, evaluates a smoothed version of the max(x,0) function.
• r8_sqrt_i4.m, returns the square root of an I4 as an R8.
• r8_sqrt_pi.m, returns the square root of Pi as an R8;
• r8_swap.m, swaps two R8's.
• r8_swap3.m, swaps three R8's.
• r8_tand.m, returns the tangent of an angle given in degrees.
• r8_tiny.m, returns a "tiny" R8;
• r8_to_i4.m, maps X in [XMIN,XMAX] to I in [IMIN,IMAX];
• r8_to_r8_discrete.m, maps R to RD in [RMIN,RMAX] with NR discrete values.
• r8_uniform_01.m, returns a unit pseudorandom R8;
• r8_uniform_ab.m, returns a scaled 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.
• r8_zeta.m, returns an estimate of the zeta function.
• 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 create a C8;
• r82_uniform_ab.m, returns a scaled pseudorandom R82 value;
• r82col_print_part.m, prints part of an R82ROW.
• r82row_order_type.m, finds if an R82ROW is (non)strictly ascending/descending.;
• r82row_part_quick_a.m, reorders an R82ROW as part of a quicksort;
• r82row_permute.m, permutes the elements of an R82ROW;
• r82row_print.m, prints an R82ROW;
• r82row_print_part.m, prints part of an R82ROW.
• r82row_sort_heap_index_a.m, creates an ascending sort index for the elements of an R82ROW;
• r82row_sort_quick_a.m, ascending sorts an R82ROW using quicksort;
• r82row_uniform_ab.m, returns a pseudorandom R82ROW;
• r82vec_order_type.m, returns the order type of an R82VEC.
• r82vec_part_quick_a.m, reorders an R82VEC as part of a quicksort operation.
• r82vec_permute.m, permutes an R82VEC.
• r82vec_print.m, prints an R82VEC.
• r82vec_print_part.m, prints part of an R82VEC.
• r82vec_sort_heap_index_a.m, ascending sort index for an R82VEC.
• r82vec_sort_quick_a.m, applies ascending quicksort to an R82VEC.
• r82vec_uniform_01.m, randomly sets an R82VEC by selecting from the interval [0,1].
• r82vec_uniform_ab.m, randomly sets an R82VEC by selecting from the interval [A,B].
• r83_norm.m, returns the Euclidean norm of an R83.
• r8int_to_i4int.m maps an R8 interval to an I4 interval.
• r8int_to_r8int.m maps one R8 interval to another.
• r8r8_compare.m, compares two R8R8's;
• r8r8_print.m, prints an R8R8, that is, a pair of R8's.
• r8r8vec_index_insert_unique.m, inserts unique R8R8 values into an index sorted R8R8VEC;
• r8r8r8_compare.m, compares two R8R8R8's;
• r8r8vec_index_search.m, searches for an R8R8 value in an index sorted R8R8VEC;
• 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;
• 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" of zeros 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_factor_upper.m, computes the upper Cholesky factor R'*R of a symmetric positive definite R8MAT;
• r8mat_cholesky_inverse.m, computes the inverse of a symmetric positive definite matrix using the Cholesky factor;
• r8mat_cholesky_solve.m, solves a Cholesky factored linear system A * x = b;
r8
• r8mat_cholesky_solve_upper.m, solves an upper-Cholesky factored linear system A * x = b;
• r8mat_covariance.m, computes the sample covariance of a set of vector data.
• 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_diagonal.m, returns a diagonal matrix as an R8MAT.
• r8mat_diff_frobenius.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_flip_cols.m, reverses the order of the columns of an R8MAT.
• r8mat_flip_rows.m, reverses the order of the rows of an R8MAT.
• r8mat_fs.m, factors and solves a system with one hand side.
• 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_post.m
• r8mat_givens_pre.m, returns a Givens pre-multiplier matrix;
• r8mat_givens_pre.m
• 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 MxN identity matrix;
• r8mat_indicator.m, returns the indicator matrix as an R8MAT.
• 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 an R8MAT is the identity matrix.
• r8mat_is_in_01.m, is true if every entry of an R8MAT is in [0,1];
• r8mat_is_insignificant.m, is true if an R8MAT is insignificant relative to another;
• r8mat_is_integer.m, is true if all entries of an R8MAT are integers;
• r8mat_is_significant.m, is true if an R8MAT is significant relative to another;
• r8mat_is_symmetric.m, determines if an R8MAT is symmetric.
• r8mat_jac.m, approximates the Jacobian matrix of a function via finite differences.
• r8mat_kronecker.m, computes the Kronecker product of two R8MAT's.
• 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_l1_solve.m, solves a unit lower triangular linear system;
• r8mat_l1t_solve.m, solves a transposed unit lower triangular linear system;
• r8mat_ldlt_factor.m, computes the LDLT factors (unit lower triangular L and diagonal D) for a symmetric matrix.
• r8mat_ldlt_solve.m, solves a linear system involving a symmetric matrix that has been LDLT factored.
• 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_mean.m, returns the mean of an R8MAT;
• r8mat_min.m, returns the minimum element of 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_minvm.m, computes inverse(A) * B for R8MAT's.
• r8mat_mm.m, computes the product of a matrix times a matrix;
• r8mat_mmt.m, computes the product of a matrix times a transposed matrix;
• r8mat_mtm.m, computes the product of a transposed matrix times a matrix;
• r8mat_mtv.m, computes the product of a transposed matrix 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_nonzeros.m, counts the nonzeros in an R8MAT.
• 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_norm_rms.m, returns the RMS 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_plu.m, computes the PLU factors of a rectangular R8MAT;
• 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_product_elementwise.m, computes the elementwise product of two R8MAT's;
• r8mat_ref.m, returns the row echelon form of an R8MAT.
• r8mat_row_copy.m, copies a vector into a row of an R8MAT.
• r8mat_rref.m, returns the reduced row echelon form of an R8MAT.
• r8mat_rref_solve_binary.m, seeks binary solutions (if any) of a row reduced echelon form linear system.
• r8mat_rref_solve_binary_nz.m, seeks binary solutions (if any) of a row reduced echelon form linear system, but only consider solutions with exactly NZ nonzeros.
• r8mat_scale_01.m, shifts and scales an R8MAT to have min 0 and max 1;
• r8mat_scale_ab.m, shifts and scales an R8MAT to have min A and max B;
• 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_standardize.m, shifts and scales an R8MAT to have zero mean and unit variance.
• 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_plu.m, factors a general R8MAT to separate P, L, U factors;
• r8mat_to_r8cmat.m, copies data from an R8MAT to an R8CMAT.
• r8mat_to_r8plu.m, factors a general R8MAT to a condensed PLU factor;
• r8mat_trace.m, returns the trace of an R8MAT;
• r8mat_transpose.m, transposes 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_u_solve.m, solves an upper triangular linear system;
• 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_ut_solve.m, solves a transposed upper triangular linear system;
• r8mat_vand2.m, returns the M by N row 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.
• r8rows_to_r8mat.m, copies rowwise data from a vector to a doubly dimensioned array.
• r8slmat_print.m, prints a strict lower triangular R8MAT.
• r8vec_01_to_ab.m, shifts and rescales data from [0,1] to [A,B];
• 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_normal.m, returns a unit normal vector to a given vector;
• r8vec_asum.m, returns the sum of the absolute values of the entries of an R8VEC;
• r8vec_bin.m, bins an R8VEC;
• r8vec_binary_next.m, returns the next binary 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_cheby_extreme.m, creates a vector of Chebyshev Extreme values in [A,B].
• r8vec_cheby_zero.m, creates a vector of Chebyshev Zero 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_compare.m, compares the order of two R8VEC's;
• r8vec_concatenate.m, concatenates 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_covariance.m, computes the sample covariance 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 zero-based 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_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_entropy.m, returns the entropy of an R8VEC.
• r8vec_eq.m, is true if two R8VEC's are equal;
• 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_fill.m, sets all entries of an R8VEC to a given value.
• 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_ge.m, is true if one R8VEC is greater than or equal to another;
• 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_identity_row.m, returns a row of the identity matrix as an R8VEC.
• r8vec_i4vec_dot_product.m, the dot product of an R8VEC and an I4VEC;
• 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_indicator0.m, sets an R8VEC to the indicator vector;
• r8vec_indicator1.m, sets an R8VEC to the indicator vector;
• r8vec_insert.m, inserts a new value into an R8VEC;
• r8vec_is_ascending.m, is true if all entries of an R8VEC are weakly ascending;
• r8vec_is_ascending_strictly.m, is true if all entries of an R8VEC are strictly ascending;
• r8vec_is_binary.m, is true if all entries of an R8VEC are 0 or 1.
• r8vec_is_distinct.m, is true if all entries of an R8VEC are distinct;
• r8vec_is_in_01.m, is true if all enries of an R8VEC are in [0,1];
• r8vec_is_in_ab.m, is true if all entries of an R8VEC are in [A,B];
• r8vec_is_integer.m, is true if all entries of an R8VEC are integers;
• r8vec_is_insignificant.m, is true if an R8VEC is insignificant;
• r8vec_is_negative.m, is true if all entries of an R8VEC are strictly negative;
• r8vec_is_negative_any.m, is true if any entry of an R8VEC is negative;
• r8vec_is_nonnegative.m, is true if all entries of an R8VEC are nonnegative;
• r8vec_is_nonpositive.m, is true if all entries of an R8VEC are nonpositive;
• r8vec_is_nonzero_any.m, is true if any entry of an R8VEC is nonzero;
• r8vec_is_one.m, is true if all entries of an R8VEC are one;
• r8vec_is_positive.m, is true if all entries of an R8VEC are strictly positive;
• r8vec_is_zero.m, is true if all entries of an R8VEC are zero;
• r8vec_le.m, is true if one R8VEC is less than or equal to another;
• r8vec_legendre.m, creates a vector of Legendre-spaced values.
• 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_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_mean_geometric.m, returns the geometric mean of an R8VEC;
• r8vec_mean_running.m, computes the running averages of an R8VEC;
• r8vec_mean_update.m, updates the mean of an R8VEC with one new entry.
• r8vec_median.m, returns the median of an R8VEC;
• r8vec_mesh_2d.m, creates a 2D mesh from 2 R8VEC's.
• 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_mirror_ab_next.m, steps through all 3^M mirror variations of an R8VEC X in a box defined by A and B;
• r8vec_multispace.m, returns a scaled list of values;
• r8vec_ne.m, is true if one R8VEC is not equal to another;
• 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_norm_rms.m, returns the RMS norm of an R8VEC.
• r8vec_normal_01.m, returns unit pseudonormal R8VEC.
• r8vec_normal_ab.m, returns an R8VEC of random normal values with mean A and variance B.
• r8vec_normalize.m, scales an R8VEC to have unit Euclidean norm;
• r8vec_normalize_l1.m, scales an R8VEC to have unit l1 norm;
• 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_pair_sums.m, finds all sums formed by a pair of vectors.;
• 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_16.m, prints an R8VEC to 16 decimal places;
• r8vec_print_mask.m, prints a masked 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_rotate.m, "rotates" the entries of an R8VEC;
• r8vec_rsquared.m, returns the R^2 "goodness of fit" statistic;
• r8vec_rsquared_adjusted.m, returns the adjusted R^2 "goodness of fit" statistic;
• r8vec_scalar_triple_product.m, computes the scalar triple product;
• r8vec_scale.m, scales an R8VEC by a factor.
• r8vec_scale_01.m, shifts and scales an R8VEC to have min 0 and max 1;
• r8vec_scale_ab.m, shifts and scales an R8VEC to have min A and max B;
• r8vec_search_binary_a.m, uses binary search on an R8VEC to find the location of a given value;
• r8vec_shift.m, performs a right shift on an R8VEC.
• r8vec_shift_circular.m, performs a circular shift on an R8VEC.
• r8vec_sign3_running.m, computes the running sign3 of an R8VEC;
• r8vec_smooth.m, smooths an R8VEC using averaging;
• r8vec_softmax.m, evaluates the softmax function of 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_a.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_standardize.m, shifts and scales an R8VEC to have zero mean and unit variance.
• r8vec_std.m, returns the standard deviation of an R8VEC;
• r8vec_std_sample.m, returns the sample standard deviation of an R8VEC;
• r8vec_std_sample_update.m, updates the sample standard deviation of an R8VEC when one more element has been added.
• r8vec_std_update.m, updates the standard deviation of an R8VEC when one more element has been added.
• r8vec_step.m, evaluates a unit step function.
• r8vec_stutter.m, makes a "stuttering" copy of an R8VEC;
• r8vec_sum.m, returns the sum of the entries of an R8VEC;
• r8vec_sum_running.m, computes the running averages 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 R8VEC.
• r8vec_unique_count.m, counts the number of unique elements in an unsorted R8VEC;
• r8vec_unique_index.m, indexes the unique elements in an unsorted R8VEC;
• r8vec_variance.m, returns the variance of an R8VEC;
• r8vec_variance_circular.m, returns the circular variance of an R8VEC;
• r8vec_variance_sample.m, returns the sample variance of an R8VEC;
• r8vec_variance_sample_update.m, updates the sample variance of an R8VEC for the addition of one new entry;
• r8vec_variance_update.m, updates the variance of an R8VEC for the addition of one new entry;
• r8vec_vector_triple_product.m, computes the vector triple product of three R8VEC's;
• r8vec_wrap.m, wraps the entries of an R8VEC to lie between given bounds.
• r8vec_write.m, writes an R8VEC to a file.
• r8vec2_compare.m, compares two entries in an R8VEC2;
• r8vec2_print.m, prints an R8VEC2;
• r8vec2_print_some.m, prints some of 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;
• rms.m, returns the RMS norm of a vector or matrix;
• sort_heap_external.m, externally sorts a list of values into ascending order;