SU1056192A1 - Stochastic device for multiplying matrices - Google Patents

Abstract

PROBABILITY DEVICE FOR MULTIPLICATION OF G4ATRITS, containing the first and second key blocks, whose input groups are device inputs, number to probability transducer block, the first input group of which is connected to the first output group of the first key block, multiplier block, first and second input gaps which are connected respectively with the first group of outputs of the second key block and the group of outputs of the converter block number-probability, block of adders, the group of inputs of which is connected to the group of outputs of the block multipliers, integrator block whose input group is connected to the group of outputs of the adder block, third key block whose group of inputs is connected to the group of outputs of the integrator block, and the output group is device outputs, random sequence generator whose output is connected to the input of adder block, generator random numbers, the output of which is connected to the input of a random sequence generator and the control input of the converter unit number-probability, clock generator, output which is connected to the input of the random number generator, the control unit, consisting of successively connected trigger, element U and counter, and you (L trigger stroke is connected to the first input of the element and the control inputs of the first, second and third blocks of keys, the second the input element and connected to the output of the generator of pulses, and the output of the counter is connected to the reset input of the trigger, the installation input of which is with the starting input of the device, so that accuracy, second 3 grams Upps of the outputs of the first and second key blocks are connected respectively to the third group of inputs of the block, about ka multipliers and the second group of N5 inputs of the number of transducers - BepoHTHocTis.

Description

The invention relates to computing and can be used to calculate the elements of a matrix obtained by multiplying two square matrices of the nth order.

A probabilistic device for multiplying matrices is known, containing number-probability converters, multiplication and addition blocks, a random number generator, integrators of elements of the output matrix l.

A disadvantage of this device is the low accuracy associated with the use of single-mode probability coding of 2n the number of elements of the two source matrices.

The closest technical solution to the invention is a probabilistic device for multiplying matrices, comprising a first key block, the second group of outputs of which is connected to the second group of inputs of a multiplier block through the second group of inputs of the converter block, the first group of inputs of which is connected to the first group of outputs of the third key block, and the outputs through the series-connected addendum block, the integration block are connected respectively to the inputs of the second key block, the outputs of which are outputs to the device controlling

the input of the second key block is connected to the control inputs of the first and third key blocks and the output of the control block, the input of which is connected to the output of the clock generator and the input of the random number generator whose output is connected to the control input of the number-probability converter unit and to the input of the generator stochastic constants, the output of which is connected to the input of the addition block.

The process of calculating the elements of the output matrix (i, j 1, 2 ... n)

where is the probability of the occurrence of symbol 1 in a random binary sequence produced by the TopdM generator of stochastic constants, associated with the conversion of n numbers of the original matrix b into random binary sequences 2.

A disadvantage of the known device is the low statistical accuracy of calculations of the elements of the matrix c;

The purpose of the invention is to improve accuracy.

The goal is achieved by the fact that in a probabilistic device for multiplying matrices containing the first and second key blocks, whose input groups are device inputs, the number-to-probability transducer block, the first input group of which is connected to the first output block of the first key block , block of multipliers, the first and second groups of inputs of which are connected respectively to the first groups. Understanding the outputs of the second key block and the group of outputs of the converter block number-probability, block adders, a group of inputs of which is connected to the group of outputs of the block of intelligent residents, block of integrators, group

the inputs of which are connected to the group of outputs of the block of adders, the third block of keys, the group of inputs of which is connected to the group of outputs of the block of integrators, and the group of outputs is the outputs of the device, the random sequence generator, the output of which is connected to the input of the block of adders, the random number generator, the output of which connected

5 with the input of the random sequence generator and the control input of the converter unit number - probability, clock generator, the output of which is connected to the input,

0 house of a random number generator, a control unit consisting of a series-connected trigger, an element and a counter, the trigger output connected to the first 1.1m input of the U element and the control inputs of the first, second and third key blocks, the second input of the U element is connected to the output of the clock generator, and the output of the counter is connected to the trigger reset input, the setup input of which is the starting input of the device, the second groups of the first and second key blocks are connected respectively

5 with the third group of block inputs

multipliers and the second group of inputs of the converter unit number probability.

FIG. 1 shows a block diagram of the proposed device; pas figs. 2 is a block diagram of a control unit.

The device (Fig. 1) contains the first block 1 of keys, block 2 of the number-probability transducers, block 3 of multipliers, block 4 of sumat 1mators, block 5 of integrators, third block b of keys, second block 7 of keys, generator 8 of random sequence, generator 9 clock pulses, random number generator 10, control block 11 (FIG. 2), which in turn contains a trigger 12, an element U 13, and a counter 14.

The second group of outputs of the first key unit 1 is connected to the third group of inputs of the block 3 multipliers, the first group of inputs of which is connected, to the first group of outputs of the second key block 7. The second group of outputs of block 7 is connected to the second group of inputs of block 2 of transducers number-probability, the first group of inputs of which is connected to the first group of outputs of the first block 1 of keys, and the outputs to the second group of inputs of block 3 of multipliers, the outputs of block 3 of multipliers are connected to group inputs of block 4 adders, a group of outputs of which is connected to a group of inputs of block 5 of integrators, a group of outputs of block 5 is connected to a group of inputs of the third block b of keys, the outputs of which are the outputs of the device. The control input of the third block b-keys is connected to the control inputs of the first 1 and second 7 key blocks and the output of the trigger 12 of the control block 11, the second input of the element 13 of which is connected to the output of the clock generator 9 and the input of the 10 random numbers generator. The output of the generator 10 is connected to the control input of the converter unit 2, the probability number, and to the input of the generator 8 of a random sequence, the output of which is connected to the input of the unit 4 of adders. In control block 11, the first input of the element 13 is connected to the output of the trigger 12, the output to the input of the counter 14, and the output of the counter 1 to the input of the trigger 12.

 The device works as follows.

According to the Start signal, which is external to the device, trigger 12 is set to 1. This trigger state is an information transmission enable signal through blocks 1 and 7 of the keys. At the same time, the element opens and 13 and pulses from the generator 9 of clock pulses begin to flow to the input of the counter 14. The counter size is determined by the resolution time and depends on the specified level of calculation error. Impulse overflow of the counter 14 sets the trigger to the zero state,

0 which is a signal to allow the transfer of the results of the calculations through the third key block 6. As in the known device, the elements of the matrices Sz, -l. i before

S put double books “1 I-bit codes with a fixation of a comma before a high bit. According to the signal from block 11 of control, the most significant bits of the numbers a, -, and b, j through blocks 1 and 7 of the keys

Q is transmitted to block 3 multipliers. At the same time, all the remaining 1-g low-order bits of numbers through blocks 1 and 7 of the keys arrive at block 2 of the number-probability converters.

where they are converted to random sequences of binary symbols x ;: and with probabilities, respectively, p (x, i 1)

 /, Р (УМ) 5m -И 5

SM binary values of 1-g-bit numbers, respectively, a ;; and b ;; .

19 17 For example, if a-; -jj, b- yy,

1 TT

then with OL-w, S,

Formed random sequences x; j and). represent the low order of the numbers and b, j, respectively. In block 3 of the multipliers, the multiplication of the indicated probability rounded numbers is carried out according to the known rules of matrix multiplication. For example, to obtain an element with-45

) In block 4, adders are performed in accordance with the expression (1), the summation of the obtained works

with a weight of -. Weight coefficient y-,

generated by the random sequence generator 8, is represented by a binary random sequence of symbols f with a probability P (f) f.

The use of incompatible random sequences fg (5 1 2 ..., p) ensures that the outputs of the block 4 of adders of random binary sequences

numbers whose mathematical expectations for each machine cycle correspond to the expression (1). In block 5 of the integrators, the corresponding stochastic quantities are decoded, i.e. obtaining estimates of matrix elements sc. According to the signal from the control unit 11, the contents of the adders of the unit 5 are transmitted via the third block 6 of the keys to the output of the device. I Thus, the calculations in from; in the natural and proposed devices; are made in accordance with

tJS, 7 (1J, i.e., the arithmetic capabilities of the devices are the same, however, the accuracy characteristics are significantly different. In the proposed device, an increase in accuracy in operation is achieved by reducing the dispersion of the flow of numbers at the outputs of the multiplier block. Thus, the technical and economic effect The proposed device as compared with the known one consists in a significant decrease in the static error when performing matrix multiplication.

Claims (1)

A PROBABILITY DEVICE FOR MATRIX MULTIPLICATION, containing the first and second key blocks, the input groups of which are the device inputs, the number converter is the probability, the first group of inputs of which is connected to the first group of outputs of the first key block, the multiplier block, the first and second groups of inputs of which are connected respectively, with the first group of outputs of the second block of keys and the group of outputs of the number-probability converter, the adder block, the group of inputs of which is connected to the group of outputs of the block will multiply oil, integrator block, the input group of which is connected to the output group of the adder block, the third key block, the input group of which is connected to the output group of the integrator block, and the output group is the device outputs, a random sequence generator, the output of which is connected to the input of the adder block, random number generator, the output of which is connected to the input of the random sequence generator and the control input of the number-probability converter, a clock pulse generator, the output of which is connected nen with the input of the random number generator, a control unit consisting of a trigger connected in series, <g of the U element and a counter, the trigger output being connected to the first input of the U element and the control inputs of the first, second and third key blocks, the second input of the U element is connected to the output a clock pulse generator, and the output of the counter is connected to the trigger reset input, the installation input of which is the starting input of the device, which requires that, in order to increase accuracy, the second groups of outputs of the first and second blocks of keys are connected respectively with the third group of inputs of the block of multipliers and the second group; inputs of the block of converters number - probability. SU, „1056192 1056192 '