HALTON - The Halton Subrandom Sequence

HALTON computes the Halton subrandom sequence. It also includes several subroutines to make it easy to manipulate this computation, to compute the next N entries, to compute a particular entry, to restart the sequence at a particular point, or to compute NDIM-dimensional versions of the sequence.

As an example of the use of Halton sequences, we also use them to compute "random" points on or in the the unit circle in 2D, and on the unit sphere in 3D.

Files you may copy include:

• halton.f90, the source code.
• halton_prb.f90, a sample problem.
• halton_prb.out, sample problem output.

The list of routines includes:

• ATAN4 computes the inverse tangent of the ratio Y / X.
• ARC_COSINE computes the arc cosine function, with argument truncation.
• BALL_UNIT_HALTON_2D returns a Halton point inside the unit ball.
• HALTON_MEMORY sets or returns quantities associated with the Halton sequence.
• HALTON_NUMBER computes the next element in the Halton sequence.
• HALTON_NUMBER_BASE_GET gets the base for a scalar Halton sequence.
• HALTON_NUMBER_BASE_SET sets the base for a scalar Halton sequence.
• HALTON_NUMBER_SEQUENCE computes the next N elements in the Halton sequence.
• HALTON_SEED_GET gets the "seed" for the Halton sequence.
• HALTON_SEED_RANDOMIZE chooses a random Halton seed.
• HALTON_SEED_SET sets the "seed" for the Halton sequence.
• HALTON_VECTOR computes the next element in the Halton N-vector sequence.
• HALTON_VECTOR_BASE_GET gets the base for a vector Halton sequence.
• HALTON_VECTOR_BASE_SET sets the base for a vector Halton sequence.
• HALTON_VECTOR_NDIM_GET gets the dimension for a vector Halton sequence.
• HALTON_VECTOR_NDIM_SET sets the dimension for a vector Halton sequence.
• HALTON_VECTOR_SEQUENCE computes the next N elements in the vector Halton sequence.
• I_TO_HALTON_NUMBER computes an element of a scalar Halton sequence.
• I_TO_HALTON_NUMBER_SEQUENCE computes the next N elements of a scalar Halton sequence.
• I_TO_HALTON_VECTOR computes an element of a vector Halton sequence.
• I_TO_HALTON_VECTOR_SEQUENCE computes N elements of a vector Halton sequence.
• IVEC_IDENTITY sets an integer vector to the identity vector A(I)=I.
• PRIME returns any of the first MAXPRIME prime numbers.
• R_PI returns the value of pi.
• SPHERE_UNIT_HALTON_2D returns a sample Halton point on the unit sphere in 2D.
• SPHERE_UNIT_HALTON_3D picks a Halton point on the unit sphere in 3D.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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