C8LIB
A Double Precision Complex Arithmetic Utility Library

C8LIB is a FORTRAN90 library which implements certain elementary functions for double precision complex (C8) variables.

The symbol "C8" is used to suggest a double precision complex variable. Here the 8 indicates that the underlying pair of real numbers each use 8 bytes of storage.

C8LIB contains routines that operate on scalars, vectors or doubly dimensioned arrays of C8's. A vector of C8's is denoted a C8VEC, and a doubly dimensioned array is a C8MAT.

Licensing:

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

Languages:

C8LIB is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version..

Related Data and Programs:

BLAS1_Z, a FORTRAN90 library which contains basic linear algebra routines for vector-vector operations, using double precision complex arithmetic.

C4LIB, a FORTRAN90 library which implements certain elementary functions for "C4" or single precision complex variables.

COMPLEX_NUMBERS, a FORTRAN90 program which demonstrates some simple features involved in the use of complex numbers in FORTRAN90 programming.

I4LIB, a FORTRAN90 library which contains many utility routines, using "I4" or "single precision integer" arithmetic.

I8LIB, a FORTRAN90 library which contains many utility routines, using "I8" or "double precision integer" arithmetic.

L4LIB, a FORTRAN90 library which contains many utility routines, using one byte logical (L4) variables.

LINPACK_Z, a FORTRAN90 library which solves linear systems using double precision complex arithmetic;

R16LIB, a FORTRAN90 library which contains many utility routines, using "R16" or "quadruple precision real" arithmetic.

R4LIB, a FORTRAN90 library which contains many utility routines, using "R4" or "single precision real" arithmetic.

R8LIB, a FORTRAN90 library which contains many utility routines, using "R8" or "double precision real" arithmetic.

Source Code:

• c8lib.f90, the source code.

Examples and Tests:

• c8lib_test.f90, a sample calling program.
• c8lib_test.txt, the output file.

List of Routines:

• C8_ABS evaluates the absolute value of a C8.
• C8_ACOS evaluates the inverse cosine of a C8.
• C8_ACOSH evaluates the inverse hyperbolic cosine of a C8.
• C8_ADD adds two C8's.
• C8_ARG returns the argument of a C8.
• C8_ASIN evaluates the inverse sine of a C8.
• C8_ASINH evaluates the inverse hyperbolic sine of a C8.
• C8_ATAN evaluates the inverse tangent of a C8.
• C8_ATANH evaluates the inverse hyperbolic tangent of a C8.
• C8_CONJ evaluates the conjugate of a C8.
• C8_COPY copies a C8.
• C8_COS evaluates the cosine of a C8.
• C8_COSH evaluates the hyperbolic cosine of a C8.
• C8_CUBE_ROOT returns the principal cube root of a C8.
• C8_DIV divides two C8's.
• C8_DIV_R8 divides a C8 by an R8.
• C8_EXP evaluates the exponential of a C8.
• C8_I returns the imaginary unit, i as a C8.
• C8_IMAG evaluates the imaginary part of a C8.
• C8_INV evaluates the inverse of a C8.
• C8_LE_L1 := X <= Y for C8 values, and the L1 norm.
• C8_LE_L2 := X <= Y for C8 values, and the L2 norm.
• C8_LE_LI := X <= Y for C8 values, and the L Infinity norm.
• C8_LOG evaluates the logarithm of a C8.
• C8_MAG returns the magnitude of a C8.
• C8_MUL multiplies two C8's.
• C8_NEG returns the negative of a C8.
• C8_NINT returns the nearest complex integer of a C8.
• C8_NORM_L1 evaluates the L1 norm of a C8.
• C8_NORM_L2 evaluates the L2 norm of a C8.
• C8_NORM_LI evaluates the L-infinity norm of a C8.
• C8_NORMAL_01 returns a unit pseudonormal C8.
• C8_ONE returns the value of 1 as a C8.
• C8_PRINT prints a C8.
• C8_REAL evaluates the real part of a C8.
• C8_SIN evaluates the sine of a C8.
• C8_SINH evaluates the hyperbolic sine of a C8.
• C8_SQRT returns the principal square root of a C8.
• C8_SUB subtracts two C8's.
• C8_SWAP swaps two C8's.
• C8_TAN evaluates the tangent of a C8.
• C8_TANH evaluates the hyperbolic tangent of a C8.
• C8_TO_CARTESIAN converts a C8 to Cartesian form.
• C8_TO_POLAR converts a C8 to polar form.
• C8_UNIFORM_01 returns a unit pseudorandom C8.
• C8_ZERO returns the value of 0 as a C8.
• C8MAT_ADD combines two C8MAT's with complex scalar factors.
• C8MAT_ADD_R8 combines two C8MAT's with real scalar factors.
• C8MAT_COPY copies a C8MAT.
• C8MAT_FSS factors and solves a system with multiple right hand sides.
• C8MAT_IDENTITY sets a C8MAT to the identity.
• C8MAT_INDICATOR returns the C8MAT indicator matrix.
• C8MAT_MINVM computes inverse(A) * B for C8MAT's.
• C8MAT_MM multiplies two C8MAT's.
• C8MAT_NINT rounds the entries of a C8MAT.
• C8MAT_NORM_FRO returns the Frobenius norm of a C8MAT.
• C8MAT_NORM_L1 returns the matrix L1 norm of a C8MAT.
• C8MAT_NORM_LI returns the matrix L-oo norm of a C8MAT.
• C8MAT_PRINT prints a C8MAT.
• C8MAT_PRINT_SOME prints some of a C8MAT.
• C8MAT_SCALE scales a C8MAT by a complex scalar factor.
• C8MAT_SCALE_R8 scales a C8MAT by a real scalar factor.
• C8MAT_UNIFORM_01 returns a unit pseudorandom C8MAT.
• C8MAT_ZERO zeroes a C8MAT.
• C8VEC_COPY copies a C8VEC.
• C8VEC_INDICATOR sets a C8VEC to the indicator vector.
• C8VEC_NINT rounds the entries of a C8VEC.
• C8VEC_NORM_L1 returns the L1 norm of a C8VEC.
• C8VEC_NORM_L2 returns the L2 norm of a C8VEC.
• C8VEC_NORM_LI returns the Loo norm of a C8VEC.
• C8VEC_NORM_SQUARED returns the square of the L2 norm of a C8VEC.
• C8VEC_PRINT prints a C8VEC, with an optional title.
• C8VEC_PRINT_PART prints "part" of a C8VEC.
• C8VEC_PRINT_SOME prints some of a C8VEC.
• C8VEC_SORT_A_L1 ascending sorts a C8VEC by L1 norm.
• C8VEC_SORT_A_L2 ascending sorts a C8VEC by L2 norm.
• C8VEC_SORT_A_LI ascending sorts a C8VEC by L-infinity norm.
• C8VEC_SPIRAL returns N points on a spiral between C1 and C2.
• C8VEC_UNIFORM_01 returns a unit pseudorandom C8VEC.
• C8VEC_UNITY returns the N roots of unity.
• CARTESIAN_TO_C8 converts a Cartesian form to a C8.
• POLAR_TO_C8 converts a polar form to a C8.
• R8_ATAN computes the inverse tangent of the ratio Y / X.
• R8_CSQRT returns the complex square root of an R8.
• R8_FLOOR rounds an R8 "down" (towards -oo) to the nearest integral R8.
• R8_LOG_2 returns the logarithm base 2 of an R8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8POLY2_ROOT returns the two roots of a quadratic polynomial.
• R8POLY3_ROOT returns the three roots of a cubic polynomial.
• R8POLY4_ROOT returns the four roots of a quartic polynomial.
• 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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