Guide and Reference

Random Number Generation (Message Passing)

This chapter describes the random number generation subroutines.

Overview of the Random Number Generation Subroutines

The random number generation subroutine generates uniformly distributed random numbers.

Table 107. List of Random Number Generation Subroutines (Message Passing)
Descriptive Name Long-Precision Subroutine Page
Uniform Random Number Generator PDURNG PDURNG--Uniform Random Number Generator

Random Number Generation Subroutines

This section contains the random number generation subroutine description.

PDURNG--Uniform Random Number Generator

This subroutine generates a global vector x of n uniform pseudo-random numbers in the ranges (0,1) or (-1,1), depending on the iopt argument. The random numbers are generated using the multiplicative congruential method with a user-specified seed, as follows:

si = (a(si-1)) mod (m) = (ais0) mod (m)
xi = si/m      if iopt = 0
xi = (2si/m)-1    if iopt = 1
   for i = 1, 2, ..., n

where:

s0 is the initial seed provided by the caller.
si for i = 1, n is a random sequence.
xi for i = 1, n are the random numbers.
a = 44485709377909.0
m = 2.048
n is the number of random numbers to be generated.

If n is 0, no computation is performed, and the initial seed is unchanged.

The global output vector x is distributed across the np processes, using block-cyclic distribution with a block size nb. (The processor grid can be one- or two-dimensions. For two dimensions, processes are selected in row-major order.) The length n of vector x must be a multiple of (np)(nb).

Table 108. Data Types
x, seed Subroutine
Long-precision real PDURNG

Syntax

Fortran CALL PDURNG (seed, n, nb, x, iopt, icontxt)
C and C++ pdurng (seed, n, nb, x, iopt, icontxt);

On Entry

seed

is the initial value s0 used to generate the random numbers.

Scope: global

Specified as: a number of the data type indicated in Table 108. You should specify seed to be an odd, whole number; otherwise, PDURNG sets it to an odd, whole number and continues with the computation. The value of seed must be 1.0 <= seed < 2.048.

n

is the global number of random numbers to be generated.

Scope: global

Specified as: a fullword integer; n >= 0 and n must be divisible by (nb)(np).

nb

is the block size for vector x, used in the block-cyclic distribution.

Scope: global

Specified as: a fullword integer; nb > 0.

x

See 'On Return'.

iopt

indicates the range of uniform random numbers to generate, where:

If iopt = 0, the range is (0,1).

If iopt = 1, the range is (-1,1).

Scope: global

Specified as: a fullword integer; iopt = 0 or 1.

icontxt

is the BLACS context parameter.

Scope: global

Specified as: the fullword integer that was returned by a prior call to BLACS_GRIDINIT or BLACS_GRIDMAP.

On Return

seed

is the new seed that is to be used to generate additional random numbers in subsequent invocations of PDURNG, having a value of seed = (ans0) mod (m).

Scope: global

Returned as: a number of the data type indicated in Table 108. It is an odd, whole number, where 1.0 <= seed < 2.048.

x

is the local vector x of size n/np, containing the uniform pseudo-random numbers, where:

If iopt = 0, they are in the range (0,1).

If iopt = 1, they are in the range (-1,1).

Scope: local

Returned as: a one-dimensional array of (at least) length n/np, with a block size of nb, containing numbers of the data type indicated in Table 108.

Notes and Coding Rules

  1. In your C program, argument seed must be passed by reference.

  2. The suggested block size is (data cache size)/2, where, the data cache size can be obtained by entering: 
    lsattr -E -H -l sys0

  3. There is no performance impact for nb = 1.

  4. If you want n/np random numbers generated on each process, just set the block size to nb = n/np.

  5. To generate more than (231-1) random numbers, you should make multiple calls to PDURNG.

  6. The local vector x of length n/np can have sequential correlations. For details, see references [42], [47], [48], [49], and [50].

Error Conditions

Computational Errors

None

Input-Argument and Miscellaneous Errors

Stage 1
  1. icontxt is invalid

Stage 2
  1. PDURNG was called from outside the process grid.

Stage 3
  1. seed < 1.0 or seed >= 2.048
  2. n < 0
  3. n is not divisible by (nb)(np)
  4. nb <= 0
  5. iopt <> 0 or 1

Example

This example generates 30 random numbers in global vector x with a block size of 3, using block-cyclic distribution over a 5 × 1 process grid.

Call Statements and Input
ORDER = 'R'
NPROW = 5
NPCOL = 1
CALL BLACS_GET(0, 0, ICONTXT)
CALL BLACS_GRIDINIT(ICONTXT, ORDER, NPROW, NPCOL)
CALL BLACS_GRIDINFO(ICONTXT, NPROW, NPCOL, MYROW, MYCOL)
 
             SEED   N     NB  X   IOPT  ICONTXT
              |     |     |   |    |        |
CALL PDURNG( SEED , 30 ,  3 , X ,  0 ,  ICONTXT)
 
SEED    = 31415926535897.0
Note: icontxt is the output of the BLACS_GRIDINIT call.

Output

SEED = (a30s0) mod (m) = 6316434292705.0

Global vector x with block size 3: 

B,D             0
     *                      *
     | 0.683821516135299845 |
 0   | 0.058874407800946215 |
     | 0.391855250856924187 |
     | -------------------- |
     | 0.755994653022330709 |
 1   | 0.557764301423606668 |
     | 0.001333801764989317 |
     | -------------------- |
     | 0.056855932753212101 |
 2   | 0.331063036202269956 |
     | 0.347339794409027292 |
     | -------------------- |
     | 0.649429020370863697 |
 3   | 0.386144876217390021 |
     | 0.457224855098420591 |
     | -------------------- |
     | 0.892518134165118937 |
 4   | 0.074548748224632532 |
     | 0.912379366805073033 |
     | -------------------- |
     | 0.112809499110515077 |
 5   | 0.857547605095465570 |
     | 0.756480901897081282 |
     | -------------------- |
     | 0.046993364463578046 |
 6   | 0.889457684002341153 |
     | 0.167775766106718294 |
     | -------------------- |
     | 0.504952722600595649 |
 7   | 0.999725924546471134 |
     | 0.696269487398215148 |
     | -------------------- |
     | 0.671896598019703362 |
 8   | 0.271472156040264423 |
     | 0.566418406688985243 |
     | -------------------- |
     | 0.464684865759100063 |
 9   | 0.982442539763031419 |
     | 0.022440482512937620 |
     *                      *

The following is the 5 × 1 process grid:
B,D 0
0

5

P00
1

6

P10
2

7

P20
3

8

P30
4

9

P40

Local arrays for x: 

p,q  |          0
-----|----------------------
     | 0.683821516135299845
     | 0.058874407800946215
     | 0.391855250856924187
 0   | 0.112809499110515077
     | 0.857547605095465570
     | 0.756480901897081282
-----|----------------------
     | 0.755994653022330709
     | 0.557764301423606668
     | 0.001333801764989317
 1   | 0.046993364463578046
     | 0.889457684002341153
     | 0.167775766106718294
-----|----------------------
     | 0.056855932753212101
     | 0.331063036202269956
     | 0.347339794409027292
 2   | 0.504952722600595649
     | 0.999725924546471134
     | 0.696269487398215148
-----|----------------------
     | 0.649429020370863697
     | 0.386144876217390021
     | 0.457224855098420591
 3   | 0.671896598019703362
     | 0.271472156040264423
     | 0.566418406688985243
-----|----------------------
     | 0.892518134165118937
     | 0.074548748224632532
     | 0.912379366805073033
 4   | 0.464684865759100063
     | 0.982442539763031419
     | 0.022440482512937620

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