JP3580737B2 - Normal random number generator and recording medium - Google Patents

Description

[0001]
[Industrial applications]
The present invention relates to a normal random number generation device and a recording medium that generate normal random numbers at high speed.
[0002]
[Prior art]
Conventionally, when generating random numbers having a normal distribution (called normal random numbers) required for performing a simulation or the like, normal random numbers have been generated by a method called the Pola method.
[0003]
The Pola method basically generates normal random numbers using uniform random numbers in the following procedure.
Step 1: Generate a uniform random number in the section [-1, 1].
[0004]
Step 2: s ← x ² + y ²
Step 3: If s ≧ 1, goto Otherwise goto 4.
Step 4: r ← {−2ln (s) / s} ^1/2
Step 5: Return the result of step 4 to the request source.
[0005]
Step 6: Steps 1 to 5 are repeated for the requested number of normal random numbers.
[0006]
[Problems to be solved by the invention]
In the above-described method of generating normal random numbers by the Pola method, every time a normal random number is generated, the calculation such as natural logarithm and square root is performed by a computer so that a large amount of calculation time is required because a computer performs an approximate calculation. For example, when millions (10 ⁶ ) of normal random numbers are required, there is a problem that an extremely long time is required.
[0007]
In order to solve these problems, the present invention generates a uniform random number based on information specified by an interface, generates a normal random number based on the random number, stores the generated random number in a pool, and stores the normal random number in the pool. Based on the above, a new normal random number is generated at high speed and stored in another pool and a part of the pool is output.When the pool is switched and repeated a predetermined number of times, the process returns to the beginning and repeats generation of a different uniform random number, The purpose is to automatically generate high-speed reliable normal random numbers corresponding to the interface specification.
[0008]
[Means for Solving the Problems]
Means for solving the problem will be described with reference to FIG.
In FIG. 1, S2 generates a uniform random number, generates a normal random number, and puts the random number into the pool 1.
[0009]
In steps S5 and S6, other normal random numbers are generated from the normal random numbers extracted from the pool.
In step S9, when the number of times of generation of another normal random number exceeds a predetermined value (for example, 1000 times), a normal random number is generated from a uniform random number and stored in a pool.
[0010]
Next, the operation will be described.
A normal random number is generated based on the uniform random number generated by generating the uniform random number in S2, the generated normal random number is stored in the pool 1, and the generated normal random number is stored in the pool 1 in S5. Generates another normal random number, stores the generated other normal random number in the pool 2 and extracts a part from the generated other normal random number. When the number of output normal random numbers does not reach the specified number, By switching between pool 1 and pool 2, generation and storage of another normal random number and output of a part thereof are repeated.
[0011]
At this time, when the generation of another normal random number is repeated a predetermined number of times in S9, a uniform random number is generated, a new normal random number is generated based on the uniform random number, and stored in the pool. To resume.
[0012]
In addition, information required when generating uniform random numbers, information required when generating normal random numbers based on uniform random numbers, information necessary when generating other normal random numbers from normal random numbers, Provide an interface that sets at least one of the information required to output a part of the normal random number and the information required to generate a new normal random number by regenerating a uniform random number. It generates and outputs normal random numbers.
[0013]
Therefore, a uniform random number is generated based on the information specified by the interface, a normal random number is generated based on the random number, stored in the pool, and a new normal random number is rapidly generated based on the pool's normal random number. By storing the data in another pool and outputting a part of the data, when the pool is switched and repeated a predetermined number of times, the process returns to the beginning and repeats the generation of a different uniform random number, etc. Normal random numbers can be automatically generated at high speed.
[0014]
【Example】
Next, an embodiment and operation of the present invention will be sequentially described in detail with reference to FIGS.
[0015]
FIG. 1 shows an operation explanatory diagram of the present invention.
In FIG. 1, S1 determines whether the variable seed is zero. In the case of YES, the variable seed is zero and has been found to be the first, so the process proceeds to S2. In the case of NO, the process proceeds to S3.
[0016]
S2 is
-Generate uniform random numbers and generate normal random numbers. In this method, for example, a normal random number is generated only for the first time by the Pola method described above. Specifically, a uniform random number is generated based on an initial value (positive integer) specified by the interface information, and then a normal random number is generated based on the generated uniform random number.
[0017]
・ Put into pool 1. In this case, the generated normal random numbers are stored in the pool 1 (stored in the pool 1 in FIG. 3A).
The variable ip = 1 is set, and the fact that the normal random number is stored in the pool 1 is stored.
[0018]
-Set the variable seed to zero.
S3 is,
Determine a, b, c, d, and θ. This determines the value of each variable as follows.
[0019]
A and b are uniformly selected from a {3, 5}, b {7, 11}.
C and d are uniformly and randomly selected from {0, 1,... N-1}.
.Theta. Is uniformly and randomly selected within the range of the oblique line in FIG.
[0020]
A step S4 decides whether or not the variable ip = 1. In the case of YES, the process proceeds to S5. In the case of NO, the process proceeds to S6.
S5 is
Generate another normal random number from pool 1 using 2N normal random numbers, and put it into pool 2. This is, as will be described later with reference to FIG. 3A, an orthogonal matrix is operated on 2N normal random numbers extracted from the pool 1 to generate another uniform new normal random number and put into the pool 2. .
[0021]
-Let ip = 2.
Write the first 1 / f (for example, 1/3) of them to the output buffer.
S6 is
Generate another normal random number from the pool 2 with 2N normal random numbers and put it into the pool 1. This is, as will be described later with reference to FIG. 3A, an orthogonal matrix is operated on 2N normal random numbers extracted from the pool 2 to generate another uniform new normal random number and put into the pool 1. .
[0022]
・ Set ip = 1.
Write the first 1 / f (for example, 1/3) of them to the output buffer.
In step S7, the number of times of generation of the normal random number is incremented by one.
[0023]
In S8, it is determined whether or not N (user-specified) normal random numbers have been output. If YES, the process ends. In the case of NO, the process proceeds to S9.
In S9, it is determined whether or not the number of times of generation of the normal random number is 1,000. In the case of YES, normal random numbers are taken out from pool 1 to pool 2 and from pool 2 to pool 1 and orthogonally transformed to generate and store new uniform normal random numbers 1000 times. Determine if any dangers occur. In the case of YES, the process returns to S2, generates a uniform random number based on the new initial value, and uses the new parameters (a, b, c, d, θ, etc.) based on this to generate a normal random number. Is generated and stored in the pool 1, and S4 and subsequent steps are repeated until the number of normal random numbers specified by the user is output.
[0024]
As described above, a uniform random number is generated based on the information specified by the interface information, and the parameters (a, b, c, d, θ, etc.) specified by the interface information are also determined based on the uniform random number. And generates a normal random number in the pool 1 and stores it in the pool 1. Based on the normal random number extracted from the pool 1, a new random number is generated based on parameters (a, b, c, d, θ, etc.) specified in the interface information. By repeatedly generating high-speed normal random numbers and storing them in the pool 2 and outputting the number of normal random numbers specified by the interface information, automatic setting is performed only by setting and inputting interface information (see FIG. 4 described later). It is possible to acquire a specified number of normal random numbers. At this time, by generating a new normal random number based on the normal random number, an operation (such as a natural logarithm or a square root) that requires a lot of time when generating a normal random number from a uniform random number by the conventional Pola method is performed. This eliminates the need for a loop operation using an approximate expression that requires about three times or more the time required for a normal operation), and makes it possible to automatically generate a large number of uniform normal random numbers extremely quickly.
[0025]
FIG. 2 shows an explanatory diagram of the present invention.
FIG. 2A shows a determinant for obtaining a new normal random number from the normal random numbers. This is a modified version of the well-known Wallace method, and calculates A (orthogonal matrix) on a normal random number represented by the determinant on the right side to obtain a new normal random number on the left side. The variables a, b, c, d and the variable θ of A (orthogonal variable) are determined as shown in (b) to (e). By using this determinant, new normal random numbers can be generated based on the normal random numbers extracted from pool 1 / pool 2 and stored in pool 2 / pool 1.
[0026]
FIG. 2B shows the magnitudes of variables a, b, c, d, and N in FIG. 2A. Here, the following is illustrated.
A>b> 1 and a, b, c, and d are positive integers, where a and N and b and N are relatively prime.
[0027]
FIG. 2C shows an example of the orthogonal matrix of FIG. Here, it is an orthogonal matrix as shown, and has a range of θ as shown below.
Π / 6 ≦ θ ≦ π / 3 or 2π / 3 ≦ θ ≦ 5π / 6,
min (| sin θ |, | cos θ |) ≧ 1/2,
t = tan (θ / 2) is generated from uniform random numbers in an appropriate section, and cos θ and sin θ are calculated.
[0028]
FIG. 2D shows a state in which 1 / f (f ≧ 3) of the generated normal random numbers is returned to the user and used for the next spool.
FIG. 2E shows how to select a, b, c, and d. Here, for example, a and b are from a {3,5}, b {7,11} for each pool,
C and d are uniformly and randomly selected from {0, 1... (N-1)}.
[0029]
FIG. 2F shows how to generate a long normal random number. Here, after generating 1000N (1000 sets) normal random numbers, a new normal random number is generated using good uniform random numbers, thereby enabling generation of a longer normal random number.
[0030]
FIG. 3 shows an explanatory diagram of the present invention.
FIG. 3A shows an example of a pool. This is a memory for storing the normal random numbers generated in S2, S5, and S6 of FIG. 1 described above. In S5 and S6 in FIG. 1, new normal random numbers are generated in accordance with the determinant of FIG. 2A based on the normal random numbers extracted from pool 1 / pool 2 and stored in pool 2 / pool 1. Is repeated in a switching manner.
[0031]
FIG. 3B schematically shows normal random numbers. Here, the horizontal axis represents the value of the normal random number, and the vertical axis represents the frequency (number) of the normal random number at that time. The normal random numbers have a normal distribution as shown in the figure, and have a predetermined variance around the average value of all the normal random numbers.
[0032]
FIG. 3C shows an output example. A part of the normal random numbers stored in the generated pools 1 and 2 (a part determined by 1 / f as described above, for example, a 1/3 hatched part from the beginning) is taken out, sequentially stored in an output buffer, and output. When the specified number of normal random numbers are stored in the buffer, they are returned together to the request source.
[0033]
FIG. 3D shows the range of θ. The range of θ used in the above-described orthogonal matrix is determined by a uniform random number within the shaded area shown in the drawing in order to reduce the calculation error (see FIG. 2C described above).
[0034]
FIG. 4 shows an example of an interface according to the present invention. This is an interface for specifying various parameters (such as a, b, c, d, θ, and the number of outputs of the normal random numbers) when generating the normal random numbers according to the flowchart of FIG. By setting necessary information in the following interface and passing (calling and passing) it to the function (routine) that executes the processing of FIG. 1, it is possible to receive the normal random number generated under the automatically specified condition. It becomes possible.
[0035]
CALL DVRANA (DAM, DSD, IX, DA, N, DWORK, NWORK, ICON)
DAM (input): mean of normal distribution m
DSD (input): standard deviation of normal distribution IX (input): input starting value (Seed), a positive integer for the first time, and zero for the second and subsequent times.
[0036]
DA (output): N normal random numbers N (input): number of normal random numbers returned to DA DWORK (work area): one-dimensional array of size NWORK NWORK (input): size ICON of array DWORK (output ): Condition code [0037]
【The invention's effect】
As described above, according to the present invention, a uniform random number is generated based on information specified by an interface, a normal random number is generated based on the random number, and stored in a pool. A configuration in which a new normal random number is generated at high speed, stored in another pool, and a part of the pool is output. Since it is adopted, highly reliable normal random numbers corresponding to interface designation can be automatically generated at high speed. For example, in the present invention, an approximate expression such as a natural logarithm or a square root is compared with a case where it takes a very long time such as a natural logarithm or a square root every time a normal random number is generated in the Pola method described in the section of the related art. , The generation of normal random numbers can be speeded up by eliminating the operation that takes a long time, and the generation of new normal random numbers from the normal random numbers using a determinant allows high-speed generation of large numbers using a vector computer. Can be generated. As a result, it is possible to increase the speed of a simulation or the like performed using a large number of normal random numbers.
[Brief description of the drawings]
FIG. 1 is a diagram illustrating the operation of the present invention.
FIG. 2 is an explanatory view (No. 1) of the present invention.
FIG. 3 is an explanatory diagram (No. 2) of the present invention.
FIG. 4 is an example of an interface according to the present invention.
[Explanation of symbols]
S2: Generating uniform random numbers S3: Generating parameters S5, S6: Generating new normal random numbers from normal random numbers S9: Generating new uniform random numbers / normal random numbers

Claims (4)

In a normal random number generator that generates normal random numbers at high speed,
Means for generating a uniform random number;
First normal random number generation means for generating a normal random number based on the generated uniform random number;
A first pool for storing the generated normal random numbers;
A second normal random number generation means for generating another normal random number based on the normal random number stored in the first pool;
A second pool for storing the other generated normal random numbers,
Means for extracting and outputting a part from the other generated normal random numbers,
When the number of the outputted normal random numbers does not reach the designated number, switching between the first pool and the second pool to generate another normal random number and output a part thereof is repeated. And a means for generating a normal random number. When the generation of the other normal random number is repeated a predetermined number of times, the uniform random number is generated, a new normal random number is generated based on the uniform random number, and stored in the first pool. 2. The normal random number generation device according to claim 1, wherein the generation is restarted. The information required when generating the uniform random number, the information required when generating a normal random number based on the uniform random number, the information required when generating another normal random number from the normal random number, An interface in which at least one of information necessary for outputting a part of another normal random number and information necessary for generating a new normal random number by regenerating the uniform random number is provided. ,
3. The normal random number generation device according to claim 1, wherein the normal random number is generated and output according to the interface. Means for generating a uniform random number;
First normal random number generation means for generating a normal random number based on the generated uniform random number;
Means for storing the generated normal random numbers in a first pool;
A second normal random number generation means for generating another normal random number based on the normal random number stored in the first pool;
Means for storing the other generated normal random numbers in a second pool;
Means for extracting and outputting a part from the other generated normal random numbers,
When the number of the outputted normal random numbers does not reach the designated number, switching between the first pool and the second pool to generate another normal random number and output a part thereof is repeated. A computer-readable recording medium on which a program for functioning as means is recorded.

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