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R8LIB
A Double Precision Real Arithmetic Utility Library {#r8lib-a-double-precision-real-arithmetic-utility-library align="center"}

R8LIB is a C++ library which contains a number of utility routines for "R8" or "double precision real" arithmetic.

Licensing: {#licensing align="center"}

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

Languages: {#languages align="center"}

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

Related Programs: {#related-programs align="center"}

C4LIB, a C++ library which implements certain elementary functions for "C4" or single precision complex variables;

C8LIB, a C++ library which implements certain elementary functions for "C8" or double precision complex variables;

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

I8LIB, a C++ library which contains many utility routines, using "I8" or "double precision integer" arithmetic.

L4LIB, a C++ library which contains many utility routines, using one byte logical (L4) variables.

R4LIB, a C++ library which contains many utility routines, using "R4" or "single precision real" arithmetic.

R8COL, a C++ library which contains utility routines for R8COL's, that is, double precision real 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.

R8ROW, a C++ library which contains utility routines for R8ROW's, that is, double precision real 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: {#source-code align="center"}

Examples and Tests: {#examples-and-tests align="center"}

List of Routines: {#list-of-routines align="center"}

  • GAMMA_VALUES returns some values of the Gamma function.
  • GAMMA_LOG_VALUES returns some values of the Log Gamma function.
  • I4_LOG_10 returns the integer part of the logarithm base 10 of an I4.
  • I4_MAX returns the maximum of two I4's.
  • I4_MIN returns the minimum of two I4's.
  • I4_MODP returns the nonnegative remainder of I4 division.
  • I4_POWER returns the value of I^J.
  • I4_SIGN returns the sign of an I4.
  • I4_UNIFORM_AB returns a scaled pseudorandom I4 between A and B.
  • I4_WRAP forces an I4 to lie between given limits by wrapping.
  • I4INT_TO_R8INT maps an I4 interval to an R8 interval.
  • I4VEC_COPY copies an I4VEC.
  • I4VEC_INDICATOR0_NEW sets an I4VEC to the indicator vector (0,1,2,...).
  • I4VEC_INDICATOR1_NEW sets an I4VEC to the indicator vector (1,2,3,...).
  • I4VEC_PERMUTE permutes an I4VEC in place.
  • I4VEC_PRINT prints an I4VEC.
  • I4VEC_TRANSPOSE_PRINT prints an I4VEC "transposed".
  • I4VEC_ZEROS zeroes an I4VEC.
  • I4VEC_ZEROS_NEW creates and zeroes an I4VEC.
  • LEGENDRE_ZEROS returns the zeros of the Legendre polynomial of degree N.
  • PERM0_CHECK checks a permutation of ( 0, ..., N-1 ).
  • PERM0_UNIFORM_NEW selects a random permutation of 0,...,N-1.
  • PERM1_CHECK checks a permutation of (1, ..., N ).
  • PERM1_UNIFORM_NEW selects a random permutation of 1,...,N.
  • R8_ABS returns the absolute value of an R8.
  • R8_ACOS computes the arc cosine function, with argument truncation.
  • R8_ACOSH returns the inverse hyperbolic cosine of a number.
  • R8_ADD adds two R8's.
  • R8_AGM computes the arithmetic-geometric mean of A and B.
  • R8_AINT truncates an R8 argument to an integer.
  • R8_ASIN computes the arc sine function, with argument truncation.
  • R8_ASINH returns the inverse hyperbolic sine of a number.
  • R8_ATAN computes the inverse tangent of the ratio Y / X.
  • R8_ATANH returns the inverse hyperbolic tangent of a number.
  • R8_BIG returns a "big" R8.
  • R8_CAS returns the "casine" of an R8.
  • R8_CEILING rounds an R8 up to the nearest integral R8.
  • R8_CHOOSE computes the combinatorial coefficient C(N,K).
  • R8_CHOP chops an R8 to a given number of binary places.
  • R8_COSD returns the cosine of an angle given in degrees.
  • R8_COT returns the cotangent of an angle.
  • R8_COTD returns the cotangent of an angle given in degrees.
  • R8_CSC returns the cosecant of X.
  • R8_CSCD returns the cosecant of an angle given in degrees.
  • R8_CUBE_ROOT returns the cube root of an R8.
  • R8_DEGREES converts an angle from radian to degree measure.
  • R8_DIFF computes (X-Y) to a specified accuracy.
  • R8_DIGIT returns a particular decimal digit of an R8.
  • R8_DIVIDE_I4 returns an I4 fraction as an R8.
  • R8_E returns the value of the base of the natural logarithm system.
  • R8_EPSILON returns the R8 roundoff unit.
  • R8_EPSILON_COMPUTE computes the R8 roundoff unit.
  • R8_EXP computes the exponential function, avoiding overflow and underflow.
  • R8_FACTORIAL computes the factorial of N.
  • R8_FACTORIAL_VALUES returns values of the real factorial function.
  • R8_FACTORIAL2 computes the double factorial function.
  • R8_FACTORIAL2_VALUES returns values of the double factorial function.
  • R8_FALL computes the falling factorial function [X]_N.
  • R8_FALL_VALUES returns some values of the falling factorial function.
  • R8_FLOOR rounds an R8 down to the nearest integral R8.
  • R8_FRACTION uses real arithmetic on an integer ratio.
  • R8_FRACTIONAL returns the fractional part of an R8.
  • R8_GAMMA evaluates Gamma(X) for an R8.
  • R8_GAMMA_LOG evaluates the logarithm of the gamma function.
  • R8_HUGE returns a "huge" R8.
  • R8_HYPOT returns the value of sqrt ( X^2 + Y^2 ).
  • R8_IN_01 is TRUE if an R8 is in the range [0,1].
  • R8_INSIGNIFICANT determines if an R8 is insignificant.
  • R8_IS_INT determines if an R8 represents an integer value.
  • R8_LOG_10 returns the logarithm base 10 of the absolute value of an R8.
  • R8_LOG_2 returns the logarithm base 2 of the absolute value of an R8.
  • R8_LOG_B returns the logarithm base B of an R8.
  • R8_MANT computes the "mantissa" or "fraction part" of an R8.
  • R8_MAX returns the maximum of two R8's.
  • R8_MIN returns the minimum of two R8's.
  • R8_MOD returns the remainder of R8 division.
  • R8_MODP returns the nonnegative remainder of R8 division.
  • R8_MOP returns the I-th power of -1 as an R8 value.
  • R8_NINT returns the nearest integer to an R8.
  • R8_NORMAL_01 samples the standard normal probability distribution.
  • R8_NORMAL_AB returns a scaled pseudonormal R8.
  • R8_PI returns the value of PI as an R8.
  • R8_PI_SQRT returns the square root of PI as an R8.
  • R8_POWER computes an integer power of an R8.
  • R8_POWER_FAST computes the P-th power of R, for real R and integer P.
  • R8_PRINT prints an R8.
  • R8_PYTHAG computes sqrt ( A*A + B*B ), avoiding overflow and underflow.
  • R8_RADIANS converts an angle from degree to radian measure.
  • R8_REVERSE_BYTES reverses the bytes in an R8.
  • R8_RISE computes the rising factorial function [X]^N.
  • R8_RISE_VALUES returns some values of the rising factorial function.
  • R8_ROUND rounds an R8 to the nearest integral value.
  • R8_ROUND_I4 rounds an R8, returning an I4.
  • R8_ROUND2 rounds an R8 in base 2.
  • R8_ROUNDB rounds an R8 in a given base.
  • R8_ROUNDX rounds an R8 in base 10.
  • R8_SECD returns the secant of an angle given in degrees.
  • R8_SECH evaluates the hyperbolic secant, while avoiding COSH overflow.
  • R8_SIGN returns the sign of an R8.
  • R8_SIGN3 returns the three-way sign of an R8.
  • R8_SIGN_CHAR returns a character indicating the sign of an R8.
  • R8_SIGN_MATCH is TRUE if two R8's are of the same sign.
  • R8_SIGN_MATCH_STRICT is TRUE if two R8's are of the same strict sign.
  • R8_SIGN_OPPOSITE is TRUE if two R8's are not of the same sign.
  • R8_SIGN_OPPOSITE_STRICT is TRUE if two R8's are strictly of opposite sign.
  • R8_SIGN2 returns the first argument with the sign of the second.
  • R8_SINCOS_SUM simplifies a*sin(cx)+b*cos(cx).
  • R8_SIND returns the sine of an angle given in degrees.
  • R8_SQRT_I4 returns the square root of an I4 as an R8.
  • R8_SUM returns the sum of two R8's.
  • R8_SWAP switches two R8's.
  • R8_SWAP3 swaps three R8's.
  • R8_TAND returns the tangent of an angle given in degrees.
  • R8_TINY returns a "tiny" R8.
  • R8_TO_DHMS converts an R8 day value into days, hours, minutes, seconds.
  • R8_TO_I4 maps real X in [XMIN, XMAX] to integer IX in [IXMIN, IXMAX].
  • R8_TO_R8_DISCRETE maps R to RD in [RMIN, RMAX] with NR possible values.
  • R8_UNIFORM_01 returns a unit pseudorandom R8.
  • R8_UNIFORM_AB returns a scaled pseudorandom R8.
  • R8_UNSWAP3 unswaps three R8's.
  • R8_WALSH_1D evaluates the Walsh function of a real scalar argument.
  • R8_WRAP forces an R8 to lie between given limits by wrapping.
  • R82_DIST_L2 returns the L2 distance between a pair of R82's.
  • R82_PRINT prints an R82.
  • R82_UNIFORM_AB returns a random R82 value in a given range.
  • R82COL_PRINT_PART prints "part" of an R82COL.
  • R82POLY2_PRINT prints a second order polynomial in two variables.
  • R82POLY2_TYPE analyzes a second order polynomial in two variables.
  • R82POLY2_TYPE_PRINT prints the meaning of the output from R82POLY2_TYPE.
  • R82ROW_MAX returns the maximum value in an R82ROW.
  • R82ROW_MIN returns the minimum value in an R82ROW.
  • R82ROW_ORDER_TYPE finds if an R82ROW is (non)strictly ascending/descending.
  • R82ROW_PART_QUICK_A reorders an R82ROW as part of a quick sort.
  • R82ROW_PERMUTE permutes an R82ROW in place.
  • R82ROW_PRINT prints an R82ROW.
  • R82ROW_PRINT_PART prints "part" of an R82ROW.
  • R82ROW_SORT_HEAP_INDEX_A does an indexed heap ascending sort of an R82ROW.
  • R82ROW_SORT_QUICK_A ascending sorts an R82ROW using quick sort.
  • R83_NORM returns the Euclidean norm of an R83.
  • R83COL_PRINT_PART prints "part" of an R83COL.
  • R83ROW_MAX returns the maximum value in an R83ROW.
  • R83ROW_MIN returns the minimum value in an R83ROW.
  • R83ROW_PART_QUICK_A reorders an R83ROW as part of a quick sort.
  • R83ROW_PRINT_PART prints "part" of an R83ROW.
  • R83ROW_SORT_QUICK_A ascending sorts an R83ROW using quick sort.
  • R8BLOCK_DELETE frees memory associated with an R8BLOCK.
  • R8BLOCK_EXPAND_LINEAR linearly interpolates new data into a 3D block.
  • R8BLOCK_NEW allocates a new R8BLOCK.
  • R8BLOCK_PRINT prints an R8BLOCK block (a 3D matrix).
  • R8BLOCK_ZEROS_NEW returns a new zeroed R8BLOCK.
  • R8CMAT_DELETE frees memory associated with an R8CMAT.
  • R8CMAT_NEW allocates a new R8CMAT.
  • R8CMAT_PRINT prints an R8CMAT.
  • R8CMAT_PRINT_SOME prints some of an R8CMAT.
  • R8CMAT_TO_R8MAT_NEW copies data from an R8CMAT to an R8MAT.
  • R8CMAT_ZEROS_NEW allocates and zeros a new R8CMAT.
  • R8INT_TO_R8INT maps one R8 interval to another.
  • R8INT_TO_I4INT maps an R8 interval to an integer interval.
  • R8MAT_ADD computes C = alpha * A + beta * B for R8MAT's.
  • R8MAT_ADD_NEW computes C = alpha * A + beta * B for R8MAT's.
  • R8MAT_AMAX returns the maximum absolute value entry of an R8MAT.
  • R8MAT_BORDER_ADD adds a "border" to an R8MAT.
  • R8MAT_BORDER_CUT cuts the "border" of an R8MAT.
  • R8MAT_CHOLESKY_FACTOR computes the Cholesky factor of a symmetric R8MAT.
  • R8MAT_CHOLESKY_FACTOR_UPPER: upper Cholesky factor of a symmetric R8MAT.
  • R8MAT_CHOLESKY_INVERSE computes the inverse of a symmetric matrix.
  • R8MAT_CHOLESKY_SOLVE solves a Cholesky factored linear system A * x = b.
  • R8MAT_CHOLESKY_SOLVE_UPPER solves Cholesky factored linear system A * x = b.
  • R8MAT_COPY copies one R8MAT to another.
  • R8MAT_COPY_NEW copies one R8MAT to a "new" R8MAT.
  • R8MAT_COVARIANCE computes the sample covariance of a set of vector data.
  • R8MAT_DET computes the determinant of an R8MAT.
  • R8MAT_DET_2D computes the determinant of a 2 by 2 R8MAT.
  • R8MAT_DET_3D computes the determinant of a 3 by 3 R8MAT.
  • R8MAT_DET_4D computes the determinant of a 4 by 4 R8MAT.
  • R8MAT_DET_5D computes the determinant of a 5 by 5 R8MAT.
  • R8MAT_DIAG_ADD_SCALAR adds a scalar to the diagonal of an R8MAT.
  • R8MAT_DIAG_ADD_VECTOR adds a vector to the diagonal of an R8MAT.
  • R8MAT_DIAG_GET_VECTOR gets the value of the diagonal of an R8MAT.
  • R8MAT_DIAG_GET_VECTOR_NEW gets the value of the diagonal of an R8MAT.
  • R8MAT_DIAG_SET_SCALAR sets the diagonal of an R8MAT to a scalar value.
  • R8MAT_DIAG_SET_VECTOR sets the diagonal of an R8MAT to a vector.
  • R8MAT_DIAGONAL_NEW returns a diagonal matrix.
  • R8MAT_DIFF_FROBENIUS returns the Frobenius norm of the difference of R8MAT's.
  • R8MAT_EXPAND_LINEAR linearly interpolates new data into an R8MAT.
  • R8MAT_EXPAND_LINEAR2 expands an R8MAT by linear interpolation.
  • R8MAT_FLIP_COLS_NEW makes a new copy of an R8MAT with reversed column order.
  • R8MAT_FLIP_ROWS_NEW makes a new copy of an R8MAT with reversed row order.
  • R8MAT_FS factors and solves a system with one right hand side.
  • R8MAT_FS_NEW factors and solves a system with one right hand side.
  • R8MAT_FSS factors and solves a system with multiple right hand sides.
  • R8MAT_FSS_NEW factors and solves a system with multiple right hand sides.
  • R8MAT_GIVENS_POST computes the Givens postmultiplier rotation matrix.
  • R8MAT_GIVENS_PRE computes the Givens premultiplier rotation matrix.
  • R8MAT_HESS approximates a Hessian matrix via finite differences.
  • R8MAT_HOUSE_AXH computes A*H where H is a compact Householder matrix.
  • R8MAT_HOUSE_AXH_NEW computes A*H where H is a compact Householder matrix.
  • R8MAT_HOUSE_FORM constructs a Householder matrix from its compact form.
  • R8MAT_HOUSE_HXA computes H*A where H is a compact Householder matrix.
  • R8MAT_HOUSE_POST computes a Householder post-multiplier matrix.
  • R8MAT_HOUSE_PRE computes a Householder pre-multiplier matrix.
  • R8MAT_IDENTITY sets the square matrix A to the identity.
  • R8MAT_IDENTITY_NEW returns an identity matrix.
  • R8MAT_IN_01 is TRUE if the entries of an R8MAT are in the range [0,1].
  • R8MAT_INDICATOR_NEW sets up an "indicator" R8MAT.
  • R8MAT_INSIGNIFICANT determines if an R8MAT is insignificant.
  • R8MAT_INVERSE_2D inverts a 2 by 2 matrix using Cramer's rule.
  • R8MAT_INVERSE_3D inverts a 3 by 3 matrix using Cramer's rule.
  • R8MAT_INVERSE_4D inverts a 4 by 4 matrix using Cramer's rule.
  • R8MAT_IS_IDENTITY determines if an R8MAT is the identity.
  • R8MAT_IS_SYMMETRIC checks an R8MAT for symmetry.
  • R8MAT_JAC estimates a dense jacobian matrix of the function FX.
  • R8MAT_KRONECKER computes the Kronecker product of two R8MAT's.
  • R8MAT_L_INVERSE inverts a lower triangular R8MAT.
  • R8MAT_L_PRINT prints a lower triangular R8MAT.
  • R8MAT_L_SOLVE solves a lower triangular linear system.
  • R8MAT_L1_INVERSE inverts a unit lower triangular R8MAT.
  • R8MAT_LT_SOLVE solves a transposed lower triangular linear system.
  • R8MAT_LU computes the LU factorization of a rectangular R8MAT.
  • R8MAT_MAX returns the maximum entry of an R8MAT.
  • R8MAT_MAX_INDEX returns the location of the maximum entry of an R8MAT.
  • R8MAT_MAXCOL_MINROW gets the maximum column minimum row of an M by N matrix.
  • R8MAT_MAXROW_MINCOL gets the maximum row minimum column of an M by N matrix.
  • R8MAT_MEAN returns the mean of an R8MAT.
  • R8MAT_MIN returns the minimum entry of an R8MAT.
  • R8MAT_MIN_INDEX returns the location of the minimum entry of an R8MAT.
  • R8MAT_MINCOL_MAXROW gets the minimum column maximum row of an M by N matrix.
  • R8MAT_MINROW_MAXCOL gets the minimum row maximum column of an M by N matrix.
  • R8MAT_MINVM computes inverse(A) * B for R8MAT's.
  • R8MAT_MINVM_NEW returns inverse(A) * B for R8MAT's.
  • R8MAT_MM multiplies two matrices.
  • R8MAT_MM_NEW multiplies two matrices.
  • R8MAT_MMT_NEW computes C = A * B'.
  • R8MAT_MTM_NEW computes C = A' * B.
  • R8MAT_MTV multiplies a transposed matrix times a vector.
  • R8MAT_MTV_NEW multiplies a transposed matrix times a vector.
  • R8MAT_MV multiplies a matrix times a vector.
  • R8MAT_MV_NEW multiplies a matrix times a vector.
  • R8MAT_NINT rounds the entries of an R8MAT.
  • R8MAT_NONZEROS returns the number of nonzeros in an R8MAT.
  • R8MAT_NORM_EIS returns the EISPACK norm of an R8MAT.
  • R8MAT_NORM_FRO returns the Frobenius norm of an R8MAT.
  • R8MAT_NORM_FRO_AFFINE returns the Frobenius norm of an R8MAT difference.
  • R8MAT_NORM_L1 returns the matrix L1 norm of an R8MAT.
  • R8MAT_NORM_L2 returns the matrix L2 norm of an R8MAT.
  • R8MAT_NORM_LI returns the matrix L-oo norm of an R8MAT.
  • R8MAT_NORMAL_01_NEW returns a unit pseudonormal R8MAT.
  • R8MAT_NULLSPACE computes the nullspace of a matrix.
  • R8MAT_NULLSPACE_SIZE computes the size of the nullspace of a matrix.
  • R8MAT_ORTH_UNIFORM_NEW returns a random orthogonal matrix.
  • R8MAT_PLOT "plots" an R8MAT.
  • R8MAT_PLOT_SYMBOL returns a symbol for entries of an R8MAT.
  • R8MAT_POLY_CHAR computes the characteristic polynomial of an R8MAT.
  • R8MAT_POWER computes a nonnegative power of an R8MAT.
  • R8MAT_POWER_METHOD applies the power method to a matrix.
  • R8MAT_PRINT prints an R8MAT.
  • R8MAT_PRINT_SOME prints some of an R8MAT.
  • R8MAT_REF computes the row echelon form of a matrix.
  • R8MAT_RMS returns the RMS norm of an R8MAT.
  • R8MAT_ROW_COPY copies a vector into a row of an R8MAT.
  • R8MAT_RREF computes the reduced row echelon form of a matrix.
  • R8MAT_SCALE multiplies an R8MAT by a scalar.
  • R8MAT_SIGNIFICANT determines if an R8MAT is significant compared to another.
  • R8MAT_SOLVE uses Gauss-Jordan elimination to solve an N by N linear system.
  • R8MAT_SOLVE_2D solves a 2 by 2 linear system using Cramer's rule.
  • R8MAT_SOLVE_3D solves a 3 by 3 linear system using Cramer's rule.
  • R8MAT_SOLVE2 computes the solution of an N by N linear system.
  • R8MAT_SUB_NEW computes C = A - B.
  • R8MAT_SUM returns the sum of an R8MAT.
  • R8MAT_SYMM_EIGEN returns a symmetric matrix with given eigensystem.
  • R8MAT_SYMM_JACOBI applies Jacobi eigenvalue iteration to a symmetric matrix.
  • R8MAT_TO_R8CMAT_NEW copies data from an R8MAT to an R8CMAT.
  • R8MAT_TO_R8PLU factors a general matrix.
  • R8MAT_TO_R8RMAT copies data from an R8MAT to an R8RMAT.
  • R8MAT_TRACE computes the trace of an R8MAT.
  • R8MAT_TRANSPOSE_IN_PLACE transposes a square R8MAT in place.
  • R8MAT_TRANSPOSE_NEW returns the transpose of an R8MAT.
  • R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
  • R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
  • R8MAT_U_INVERSE inverts an upper triangular R8MAT.
  • R8MAT_U_SOLVE solves an upper triangular linear system.
  • R8MAT_U1_INVERSE inverts a unit upper triangular R8MAT.
  • R8MAT_UNIFORM_01 returns a unit pseudorandom R8MAT.
  • R8MAT_UNIFORM_01_NEW returns a unit pseudorandom R8MAT.
  • R8MAT_UNIFORM_AB returns a scaled pseudorandom R8MAT.
  • R8MAT_UNIFORM_AB_NEW returns a new scaled pseudorandom R8MAT.
  • R8MAT_UNIFORM_ABVEC returns a scaled pseudorandom R8MAT.
  • R8MAT_UNIFORM_ABVEC_NEW returns a new scaled pseudorandom R8MAT.
  • R8MAT_UT_SOLVE solves a transposed upper triangular linear system.
  • R8MAT_VAND2 returns the N by N row Vandermonde matrix A.
  • R8MAT_VTMV multiplies computes the scalar x' * A * y.
  • R8MAT_ZEROS zeroes an R8MAT.
  • R8MAT_ZEROS_NEW returns a new zeroed R8MAT.
  • R8PLU_DET computes the determinant of a real PLU matrix.
  • R8PLU_INVERSE computes the inverse of a real PLU matrix.
  • R8PLU_MUL computes A * x using the PLU factors of A.
  • R8PLU_SOL solves a linear system A*x=b from the PLU factors.
  • R8PLU_TO_R8MAT recovers the matrix A that was factored by R8MAT_TO_R8PLU.
  • R8POLY_DEGREE returns the degree of a polynomial.
  • R8POLY_DERIV returns the derivative of a polynomial.
  • R8POLY_LAGRANGE_0 evaluates the Lagrange factor at a point.
  • R8POLY_LAGRANGE_1 evaluates the first derivative of the Lagrange factor.
  • R8POLY_LAGRANGE_2 evaluates the second derivative of the Lagrange factor.
  • R8POLY_LAGRANGE_COEF returns the coefficients of a Lagrange polynomial.
  • R8POLY_LAGRANGE_FACTOR evaluates the polynomial Lagrange factor at a point.
  • R8POLY_LAGRANGE_VAL evaluates the IPOL-th Lagrange polynomial.
  • R8POLY_ORDER returns the order of a polynomial.
  • R8POLY_PRINT prints out a polynomial.
  • R8POLY_SHIFT adjusts the coefficients of a polynomial for a new argument.
  • R8POLY_VALUE_HORNER evaluates a polynomial using Horner's method.
  • R8POLY_VALUES_HORNER evaluates a polynomial using Horner's method.
  • R8POLY_VALUE_2D evaluates a polynomial in 2 variables, X and Y.
  • R8POLY2_EX finds the extremal point of a parabola determined by three points.
  • R8POLY2_EX2 finds the extremal point of a parabola determined by three points.
  • R8POLY2_RROOT returns the real parts of the roots of a quadratic polynomial.
  • R8POLY2_VAL evaluates a parabola defined by three data values.
  • R8POLY2_VAL2 evaluates a parabolic function through 3 points in a table.
  • R8PP_DELETE frees the memory set aside by R8PP_NEW.
  • R8PP_NEW allocates a new R8PP.
  • R8R8_COMPARE compares two R8R8's.
  • R8R8_PRINT prints an R8R8.
  • R8R8R8_COMPARE compares two R8R8R8's.
  • R8R8R8VEC_INDEX_INSERT_UNIQUE inserts a unique R8R8R8 value in an indexed sorted list.
  • R8R8R8VEC_INDEX_SEARCH searches for an R8R8R8 value in an indexed sorted list.
  • R8R8VEC_INDEX_INSERT_UNIQUE inserts a unique R8R8 value in an indexed sorted list.
  • R8R8VEC_INDEX_SEARCH searches for an R8R8 value in an indexed sorted list.
  • R8RMAT_COPY_NEW makes a new copy of an R8RMAT .
  • R8RMAT_DELETE frees memory associated with an R8RMAT.
  • R8RMAT_FS_NEW factors and solves an R8RMAT system with one right hand side.
  • R8RMAT_NEW allocates a new R8RMAT.
  • R8RMAT_PRINT prints an R8RMAT.
  • R8RMAT_PRINT_SOME prints some of an R8RMAT.
  • R8RMAT_TO_R8MAT copies data from an R8RMAT to an R8MAT.
  • R8RMAT_ZEROS allocates and zeroes a new R8RMAT.
  • R8ROW_COMPARE compares two rows in an R8ROW.
  • R8ROW_MAX returns the row maximums of an R8ROW.
  • R8ROW_MEAN returns the row means of an R8ROW.
  • R8ROW_MIN returns the row minimums of an R8ROW.
  • R8ROW_PRINT prints an R8ROW.
  • R8ROW_PRINT_SOME prints some of an R8ROW.
  • R8ROW_REVERSE reverses the order of the rows of an R8MAT.
  • R8ROW_RUNNING_AVERAGE computes the running averages of an R8ROW.
  • R8ROW_RUNNING_SUM computes the running sum of an R8ROW.
  • R8ROW_SORT_HEAP_A ascending heapsorts an R8ROW.
  • R8ROW_SUM returns the sums of the rows of an R8ROW.
  • R8ROW_SWAP swaps two rows of an R8ROW.
  • R8ROW_TO_R8VEC converts an R8ROW into an R8VEC.
  • R8ROW_UNIFORM_AB_NEW returns a new scaled pseudorandom R8ROW.
  • R8ROW_VARIANCE returns the variances of an R8ROW.
  • R8SLMAT_PRINT prints a strict lower triangular R8MAT.
  • R8VEC_01_TO_AB shifts and rescales data to lie within given bounds.
  • R8VEC_AB_TO_01 shifts and rescales data to lie within [0,1].
  • R8VEC_AB_TO_CD shifts and rescales data to lie within a given pair of bounds.
  • R8VEC_ADD adds one R8VEC to another.
  • R8VEC_ALL_NONPOSITIVE: ( all ( A <= 0 ) ) for R8VEC's.
  • R8VEC_AMAX returns the maximum absolute value in an R8VEC.
  • R8VEC_AMAX_INDEX returns the index of the maximum absolute value in an R8VEC.
  • R8VEC_AMIN returns the minimum absolute value in an R8VEC.
  • R8VEC_AMIN_INDEX returns the index of the minimum absolute value in an R8VEC.
  • R8VEC_ANY_NEGATIVE: ( any ( A < 0 ) ) for R8VEC's.
  • R8VEC_ANY_NONZERO: ( any A nonzero ) for R8VEC's.
  • R8VEC_ANY_NORMAL returns some normal vector to V1.
  • R8VEC_ASCENDS determines if an R8VEC is (weakly) ascending.
  • R8VEC_ASCENDS_STRICTLY determines if an R8VEC is strictly ascending.
  • R8VEC_ASUM sums the absolute values of the entries of an R8VEC.
  • R8VEC_BIN computes bins based on a given R8VEC.
  • R8VEC_BRACKET searches a sorted array for successive brackets of a value.
  • R8VEC_BRACKET2 searches a sorted array for successive brackets of a value.
  • R8VEC_BRACKET3 finds the interval containing or nearest a given value.
  • R8VEC_BRACKET4 finds the interval containing or nearest a given value.
  • R8VEC_BRACKET5 brackets data between successive entries of a sorted R8VEC.
  • R8VEC_BRACKET6 brackets data between successive entries of a sorted R8VEC.
  • R8VEC_CHEBYSPACE_NEW creates a vector of Chebyshev spaced values in [A,B].
  • R8VEC_CHEBY1SPACE_NEW creates Type 1 Chebyshev spaced values in [A,B].
  • R8VEC_CHEBY2SPACE_NEW creates Type 2 Chebyshev spaced values in [A,B].
  • R8VEC_CIRCULAR_VARIANCE returns the circular variance of an R8VEC.
  • R8VEC_COMPARE compares two R8VEC's.
  • R8VEC_CONCATENATE concatenates two R8VEC's.
  • R8VEC_CONCATENATE_NEW concatenates two R8VEC's.
  • R8VEC_CONVOLUTION returns the convolution of two R8VEC's.
  • R8VEC_CONVOLUTION_CIRC returns the discrete circular convolution of two R8VEC's.
  • R8VEC_COPY copies an R8VEC.
  • R8VEC_COPY_NEW copies an R8VEC to a new R8VEC.
  • R8VEC_CORRELATION returns the correlation of two R8VEC's.
  • R8VEC_COVAR computes the covariance of two vectors.
  • R8VEC_CROSS_PRODUCT_2D finds the cross product of a pair of R8VEC's in 2D.
  • R8VEC_CROSS_PRODUCT_AFFINE_2D finds the affine cross product in 2D.
  • R8VEC_CROSS_PRODUCT_3D computes the cross product of two R8VEC's in 3D.
  • R8VEC_CROSS_PRODUCT_AFFINE_3D computes the affine cross product in 3D.
  • R8VEC_CUM_NEW computes the cumulutive sums of an R8VEC.
  • R8VEC_CUM0_NEW computes the cumulutive sums of an R8VEC.
  • R8VEC_DIF computes coefficients for estimating the N-th derivative.
  • R8VEC_DIFF_NORM returns the L2 norm of the difference of R8VEC's.
  • R8VEC_DIFF_NORM_L1 returns the L1 norm of the difference of R8VEC's.
  • R8VEC_DIFF_NORM_L2 returns the L2 norm of the difference of R8VEC's.
  • R8VEC_DIFF_NORM_LI returns the L-oo norm of the difference of R8VEC's.
  • R8VEC_DIFF_NORM_SQUARED: square of the L2 norm of the difference of R8VEC's.
  • R8VEC_DIRECT_PRODUCT creates a direct product of R8VEC's.
  • R8VEC_DIRECT_PRODUCT2 creates a direct product of R8VEC's.
  • R8VEC_DISTANCE returns the Euclidean distance between two R8VEC's.
  • R8VEC_DISTINCT is true if the entries in an R8VEC are distinct.
  • R8VEC_DIVIDE divides an R8VEC by a nonzero scalar.
  • R8VEC_DOT_PRODUCT computes the dot product of a pair of R8VEC's.
  • R8VEC_DOT_PRODUCT_AFFINE computes the affine dot product.
  • R8VEC_ENTROPY computes the entropy of an R8VEC.
  • R8VEC_EQ is true if every pair of entries in two R8VEC's is equal.
  • R8VEC_EVEN returns an R8VEC of values evenly spaced between ALO and AHI.
  • R8VEC_EVEN_NEW returns an R8VEC of values evenly spaced between ALO and AHI.
  • R8VEC_EVEN_SELECT returns the I-th of N evenly spaced values in [ XLO, XHI ].
  • R8VEC_EVEN2 linearly interpolates new numbers into an R8VECa.
  • R8VEC_EVEN2_SELECT returns the I-th of N evenly spaced midpoint values.
  • R8VEC_EVEN3 evenly interpolates new data into an R8VEC.
  • R8VEC_EXPAND_LINEAR linearly interpolates new data into an R8VEC.
  • R8VEC_EXPAND_LINEAR2 linearly interpolates new data into an R8VEC.
  • R8VEC_FIRST_INDEX indexes the first occurrence of values in an R8VEC.
  • R8VEC_FRAC searches for the K-th smallest entry in an R8VEC.
  • R8VEC_FRACTION returns the fraction parts of an R8VEC.
  • R8VEC_GT == ( A1 > A2 ) for two R8VEC's.
  • R8VEC_HEAP_A reorders an R8VEC into a ascending heap.
  • R8VEC_HEAP_D reorders an R8VEC into a descending heap.
  • R8VEC_HISTOGRAM histograms an R8VEC.
  • R8VEC_HOUSE_COLUMN defines a Householder premultiplier that "packs" a column.
  • R8VEC_I4VEC_DOT_PRODUCT computes the dot product of an R8VEC and an I4VEC.
  • R8VEC_IN_01 is TRUE if the entries of an R8VEC are in the range [0,1].
  • R8VEC_IN_AB is TRUE if the entries of an R8VEC are in the range [A,B].
  • R8VEC_INDEX_DELETE_ALL deletes all occurrences of a value from an indexed sorted list.
  • R8VEC_INDEX_DELETE_DUPES deletes duplicates from an indexed sorted list.
  • R8VEC_INDEX_DELETE_ONE deletes one copy of a value from an indexed sorted list.
  • R8VEC_INDEX_INSERT inserts a value in an indexed sorted list.
  • R8VEC_INDEX_INSERT_UNIQUE inserts a unique value in an indexed sorted list.
  • R8VEC_INDEX_ORDER sorts an R8VEC using an index vector.
  • R8VEC_INDEX_SEARCH searches for a value in an indexed sorted R8VEC.
  • R8VEC_INDEX_SORT_UNIQUE creates a sort index for an R8VEC.
  • R8VEC_INDEX_SORTED_RANGE: search index sorted vector for elements in a range.
  • R8VEC_INDEXED_HEAP_D creates a descending heap from an indexed R8VEC.
  • R8VEC_INDEXED_HEAP_D_EXTRACT: extract from heap descending indexed R8VEC.
  • R8VEC_INDEXED_HEAP_D_INSERT: insert value into heap descending indexed R8VEC.
  • R8VEC_INDEXED_HEAP_D_MAX: maximum value in heap descending indexed R8VEC.
  • R8VEC_INDICATOR0 sets an R8VEC to the indicator vector (0,1,2,...)
  • R8VEC_INDICATOR0_NEW sets an R8VEC to the indicator vector {0,1,2,...}.
  • R8VEC_INDICATOR1 sets an R8VEC to the indicator vector (1,2,3,...)
  • R8VEC_INDICATOR1_NEW sets an R8VEC to the indicator vector {1,2,3,...}.
  • R8VEC_INSERT inserts a value into an R8VEC.
  • R8VEC_INSIGNIFICANT determines if an R8VEC is insignificant.
  • R8VEC_IS_INT is TRUE if an R8VEC is integral.
  • R8VEC_IS_NONNEGATIVE is true if all entries in an R8VEC are nonnegative.
  • R8VEC_IS_ZERO is true if the entries in an R8VEC are all zero.
  • R8VEC_LEGENDRE_NEW creates a vector of Chebyshev spaced values.
  • R8VEC_LINSPACE creates a vector of linearly spaced values.
  • R8VEC_LINSPACE_NEW creates a vector of linearly spaced values.
  • R8VEC_LINSPACE2_NEW creates a vector of linearly spaced values.
  • R8VEC_LT == ( A1 < A2 ) for two R8VEC's.
  • R8VEC_MASK_PRINT prints a masked R8VEC.
  • R8VEC_MAX returns the value of the maximum element in an R8VEC.
  • R8VEC_MAX_ABS_INDEX returns the index of the maximum absolute value in an R8VEC.
  • R8VEC_MAX_INDEX returns the index of the maximum value in an R8VEC.
  • R8VEC_MEAN returns the mean of an R8VEC.
  • R8VEC_MEAN_GEOMETRIC returns the geometric mean of an R8VEC.
  • R8VEC_MEDIAN returns the median of an unsorted R8VEC.
  • R8VEC_MESH_2D creates a 2D mesh from X and Y vectors.
  • R8VEC_MIDSPACE_NEW creates a vector of linearly spaced values.
  • R8VEC_MIN returns the value of the minimum element in an R8VEC.
  • R8VEC_MIN_INDEX returns the index of the minimum value in an R8VEC.
  • R8VEC_MIN_POS returns the minimum positive value of an R8VEC.
  • R8VEC_MIRROR_NEXT steps through all sign variations of an R8VEC.
  • R8VEC_NEGATIVE_STRICT: all entries of R8VEC are strictly negative.
  • R8VEC_NINT rounds the entries of an R8VEC.
  • R8VEC_NINT_NEW rounds the entries of an R8VEC.
  • R8VEC_NORM returns the L2 norm of an R8VEC.
  • R8VEC_NORM_AFFINE returns the affine L2 norm of an R8VEC.
  • R8VEC_NORM_L0 returns the l0 "norm" of an R8VEC.
  • R8VEC_NORM_L1 returns the L1 norm of an R8VEC.
  • R8VEC_NORM_L2 returns the L2 norm of an R8VEC.
  • R8VEC_NORM_LI returns the L-oo norm of an R8VEC.
  • R8VEC_NORM_LP returns the LP norm of an R8VEC.
  • R8VEC_NORMAL_01 returns a unit pseudonormal R8VEC.
  • R8VEC_NORMAL_01_NEW returns a unit pseudonormal R8VEC.
  • R8VEC_NORMAL_AB_NEW returns a scaled pseudonormal R8VEC.
  • R8VEC_NORMALIZE normalizes an R8VEC.
  • R8VEC_NORMALIZE_L1 normalizes an R8VEC to have unit sum.
  • R8VEC_NORMSQ returns the squared L2 norm of an R8VEC.
  • R8VEC_NORMSQ_AFFINE returns the squared affine L2 norm of an R8VEC.
  • R8VEC_ONES_NEW creates a vector of 1's.
  • R8VEC_ORDER_TYPE determines if an R8VEC is (non)strictly ascending/descending.
  • R8VEC_PART_QUICK_A reorders an R8VEC as part of a quick sort.
  • R8VEC_PERMUTE applies a 0-based permutation to an R8VEC.
  • R8VEC_PERMUTE_CYCLIC performs a cyclic permutation of an R8VEC.
  • R8VEC_PERMUTE_UNIFORM randomly permutes an R8VEC.
  • R8VEC_POLARIZE decomposes an R8VEC into normal and parallel components.
  • R8VEC_POSITIVE_STRICT: all entries of R8VEC are strictly positive.
  • R8VEC_PRINT prints an R8VEC.
  • R8VEC_PRINT_16 prints an R8VEC to 16 decimal places.
  • R8VEC_PRINT_PART prints "part" of an R8VEC.
  • R8VEC_PRINT_SOME prints "some" of an R8VEC.
  • R8VEC_PRODUCT returns the product of the entries of an R8VEC.
  • R8VEC_RANGE finds the range of Y's within a restricted X range.
  • R8VEC_RANGE_2 updates a range to include a new R8VEC
  • R8VEC_REVERSE reverses the elements of an R8VEC.
  • R8VEC_RMS returns the RMS norm of an R8VEC.
  • R8VEC_ROTATE "rotates" the entries of an R8VEC in place.
  • R8VEC_RUNNING_AVERAGE computes the running average of an R8VEC.
  • R8VEC_RUNNING_SIGN3 computes the running threeway sign of an R8VEC.
  • R8VEC_RUNNING_SUM computes the running sum of an R8VEC.
  • R8VEC_SCALAR_TRIPLE_PRODUCT computes the scalar triple product.
  • R8VEC_SCALE multiplies an R8VEC by a scale factor.
  • R8VEC_SEARCH_BINARY_A searches an ascending sorted R8VEC.
  • R8VEC_SHIFT performs a shift on an R8VEC.
  • R8VEC_SHIFT_CIRCULAR performs a circular shift on an R8VEC.
  • R8VEC_SORT_BUBBLE_A ascending sorts an R8VEC using bubble sort.
  • R8VEC_SORT_BUBBLE_D descending sorts an R8VEC using bubble sort.
  • R8VEC_SORT_HEAP_A ascending sorts an R8VEC using heap sort.
  • R8VEC_SORT_HEAP_D descending sorts an R8VEC using heap sort.
  • R8VEC_SORT_HEAP_INDEX_A does an indexed heap ascending sort of an R8VEC
  • R8VEC_SORT_HEAP_INDEX_A_NEW: indexed heap ascending sort of an R8VEC
  • R8VEC_SORT_HEAP_INDEX_D_NEW: indexed heap descending sort of an R8VEC.
  • R8VEC_SORT_HEAP_INDEX_D_NEW: indexed heap descending sort of an R8VEC.
  • R8VEC_SORT_HEAP_MASK_A: indexed heap ascending sort of a masked R8VEC.
  • R8VEC_SORT_INSERT_A ascending sorts an R8VEC using an insertion sort.
  • R8VEC_SORT_INSERT_INDEX_A ascending index sorts an R8VEC using insertion.
  • R8VEC_SORT_QUICK_A ascending sorts an R8VEC using quick sort.
  • R8VEC_SORT_SHELL_A ascending sorts an R8VEC using Shell's sort.
  • R8VEC_SORTED_MERGE_A merges two ascending sorted R8VEC's.
  • R8VEC_SORTED_NEAREST returns the nearest element in a sorted R8VEC.
  • R8VEC_SORTED_RANGE searches a sorted vector for elements in a range.
  • R8VEC_SORTED_SPLIT "splits" a sorted R8VEC, given a splitting value.
  • R8VEC_SORTED_UNDEX returns unique sorted indexes for a sorted R8VEC.
  • R8VEC_SORTED_UNIQUE finds the unique elements in a sorted R8VEC.
  • R8VEC_SORTED_UNIQUE_COUNT counts unique elements in a sorted R8VEC.
  • R8VEC_SORTED_UNIQUE_HIST histograms unique elements of a sorted R8VEC.
  • R8VEC_SPLIT "splits" an unsorted R8VEC based on a splitting value.
  • R8VEC_STD returns the standard deviation of an R8VEC.
  • R8VEC_STEP evaluates a unit step function.
  • R8VEC_STUTTER makes a "stuttering" copy of an R8VEC.
  • R8VEC_STUTTER_NEW makes a "stuttering" copy of an R8VEC.
  • R8VEC_SUM returns the sum of an R8VEC.
  • R8VEC_SWAP swaps the entries of two R8VEC's.
  • R8VEC_TRANSPOSE_PRINT prints an R8VEC "transposed".
  • R8VEC_UNDEX returns unique sorted indexes for an R8VEC.
  • R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
  • R8VEC_UNIFORM_01_NEW returns a new unit pseudorandom R8VEC.
  • R8VEC_UNIFORM_AB returns a scaled pseudorandom R8VEC.
  • R8VEC_UNIFORM_AB_NEW returns a scaled pseudorandom R8VEC.
  • R8VEC_UNIFORM_ABVEC returns a scaled pseudorandom R8VEC.
  • R8VEC_UNIFORM_ABVEC_NEW returns a scaled pseudorandom R8VEC.
  • R8VEC_UNIFORM_UNIT_NEW generates a random unit vector.
  • R8VEC_UNIQUE_COUNT counts the unique elements in an unsorted R8VEC.
  • R8VEC_UNIQUE_INDEX indexes the unique occurrence of values in an R8VEC.
  • R8VEC_VARIANCE returns the variance of an R8VEC.
  • R8VEC_VECTOR_TRIPLE_PRODUCT computes the vector triple product.
  • R8VEC_WRITE writes an R8VEC to a file.
  • R8VEC_ZEROS zeroes an R8VEC.
  • R8VEC_ZEROS_NEW creates and zeroes an R8VEC.
  • R8VEC2_COMPARE compares two elements of an R8VEC2.
  • R8VEC2_PRINT prints an R8VEC2.
  • R8VEC2_PRINT_SOME prints "some" of an R8VEC2.
  • R8VEC2_SORT_A ascending sorts an R8VEC2.
  • R8VEC2_SORT_D descending sorts an R8VEC2.
  • R8VEC2_SORT_HEAP_INDEX_A does an indexed heap ascending sort of an R8VEC2.
  • R8VEC2_SORTED_UNIQUE keeps the unique elements in an R8VEC2.
  • R8VEC2_SORTED_UNIQUE_INDEX indexes unique elements in a sorted R8VEC2.
  • R8VEC2_SUM_MAX_INDEX returns the index of the maximum sum of two R8VEC's.
  • R8VEC3_PRINT prints a triple of real vectors.
  • ROOTS_TO_R8POLY converts polynomial roots to polynomial coefficients.
  • S_LEN_TRIM returns the length of a string to the last nonblank.
  • SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
  • TIMESTAMP prints the current YMDHMS date as a time stamp.

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Last revised on 26 February 2016.