SU648987A1 - Device for expansion and computation of matrix determinants - Google Patents

Description

The first inputs and outputs are connected in a ring, the second inputs of the last cells of each row of the matrix are connected to the first inputs of the corresponding DICH first input elements OR each row of the matrix of the second, third, fourth and fifth outputs of the control unit Lenin are respectively connected to the first inputs of the second input elements OR the third, fourth, fifth, and sixth rows of matrixes, the secondary inputs of which are connected respectively to the output of the first element AND, and the outputs of the second input elements OR to the third, fourth, fifth and third lines of the m Attributes are connected respectively to the second inputs of the first, cells of these, rows of the matrix; the outputs of the first environmental elements OR of each row are connected to the third inputs of the first cells of each row of the matrix} the output signal distributor KOS group is connected to the Perz group of memory block inputs, each output from this output group is connected to the first Input of the corresponding AND element in the matrix J-OM ; the outputs of the corresponding ETU elements and the i-th row of the matrix are combined and connected to the corresponding inputs of the memory block and the zero-term-definition block whose output is connected to the second input of the third element AND, the cells of the matrices are interconnected by the second and third inputs, and the outputs are consecutive in rows and fourth and fourth inputs - outputs parallel to the HQ.tjo columns; The second code of the corresponding AND element is connected to the sixth output of the k j-ofl cell, the fifth output of the first cell of the first line, the second cell of the second line, "., the n-th cell of the n-th line are connected to one input of the output element AND of each line , another input of which is connected to the output of the output element AND of each line located in the adjacent bottom line; the outputs of the output element And the first row and the output of the arithmetic unit are the outputs of the device; the third input of the generator, the second inputs of the first and second elements And, the second inputs of the first. the OR input elements of each line are the control inputs of the device, as well as the fact that in each k. | in the cell, the first input of the cell is connected to the first inputs of the trigger and the first element I, the output of which is connected to the first:. the input of the first element And the output of the first IDN element is connected to the first, the output of the cell, the second inlet of the cell is connected to the second input of three heras, the third input of the cell is connected to the third and fourth inputs of a trigger and the third output of the cell, a fourth and fifth vym and second inputs of the second OR element, the output of which is connected to the fifth trigger input, to the second move of the first AND element and to the fourth output of the cell; the zero output of the rigger is connected to the second output of the cell, the single output of the trigger is connected to the second input of the first element OR, the fifth and sixth output of the cell. FIG. Figure 1 shows the structural heme of the device for PB, where n is according to the determinant; in fig. 2 - structural diagram of the cell. The device contains a generator 1, block 2 of the sign definition, block 3 of control, block 4 of the definition of zero len, distributor 5 signals, block b of memory, arithmetic block 7, matrix of n identical cells 8, elements AND 9, 10, 11, elements OR 12, 13, the first input elements AND 14, the second input elements OR 15, the elements AND 16., the output elements AND 17 of each line, the delay element 18. Each of the cells consists of a trigger 19, the element AND 20, the elements OR 21, 22, key 23. Before the device starts operation, the matrix scheme is set up. To do this, close the keys 23 of all the cells 8 that correspond to the non-zero elements of the determinant matrix. ElementMBFiTy of the determinant matrix, located in the i-th row and j-th column of the matrix, corresponds to cell 8, located in the i-th row and J-OM column. To the control inputs from the generator 1 and from the block 3, the sequences im- ported relative to each other are fed by time. pulses. The input associated with the first row of the matrix is supplied with a sequence of pulses having the following period T, the input associated with the second row is delayed relative to the previous sequence with period T, the input of the third row with a period 2T, and the input of the fourth row with period 6T, at the input of the fifth line - with a period of 24T, etc. In the general case, the pulse follow-up period is T (i-I). Unit 3 acts as a frequency divider of the pulses arriving at its input from generator 1 with a period T. In the first cycle of operation of the device, a signal with a duration T (n-1) t + T is output at the device input clock, where Su is the control sequence pulse. This signal goes through the elements OR 14 to the inputs of the first cells in the row of cells 8, through the elements AND 10 and OR 13 to the input of the recording unit 5 of the signal distributor and to the input of the generator 1. The generator 1 generates a control signal of the first cycle, which goes to the inputs of the cells the first column, as well as to the input of block 3 and through the delay element 18 to the synchronous input of the distributor 5. At the same time, the unit is recorded in the first digit of the distributor 5. In addition, in the first cycle, during the input signal, units of 8 rows are written Next in order of p; in the first cell of the first line below, in the second cell of the next line, in the third cell of the third line below, etc. and finally the last cell of the top row. A basic permutation is implemented (1,2,3 ... n, i.e., In accordance with a predetermined rearrangement, the signals from the outputs of the distributor 5 through the elements 16 pass to the inputs of blocks 5 and b. Each state of the matrix circuit corresponds to It belongs to one member of the open definition of the nth order, since if we arrange the first indices of the elements of the determinant of the matrix ... and .JKotoy is equal to the sum of the products of the form "n," n, ,, „1Ы.-1 2Л2 ОЛПП“. In the order of their increase, the set of second indices forms a certain permutation (оС, d, ..-, п) of the set of numbers from 1 to n. each cycle of the device i runs / Bce bits of the distributor 5, and then along the feedback circuit through the element OR 13 is recorded in the first bit of the distributor 5. After the output of each sync pulse, one determinant element is sampled. the distributor 5 is fed simultaneously to the first horizontal input of the cell sample of block b and to the input of the ei and vertical sample, while sampling and reading out of the cell in which element a is stored, since The unit cells in block B are designed in such a way that these cells form a matrix similar to the determinant matrix. After reading the next element of the determinant in block 6, a signal is generated,; the defining end of the readout. Which is supplied as a sync pulse, the synchronous input of the distributor 5. The signal from the second output of the distributor 5 is fed to the second horizontal input of block B and to O, vertical, the input of block 6 At that, sampling and reading from the cell in which the element 02 is stored (2-Similarly, the remaining elements that are included in this product of the form ° -io4 "z L2" 3 ta-- tv in are calculated. This calculation is produced by c in the arithmetic unit 7, the input of which receives the determinant elements read from block 6. The signal from the last output of the distributor 5 determines the start of a new cycle of the device operation. This signal goes to the input of the generator 1, which generates a control signal of the new. operation of the device after the basic permutation (1,2,3,4,5,6) was installed on it in the first cycle for the case when, in the second cycle, the unit recorded in the trigger 19 is the second cell on the right of the second 8 on the top of the matrix line under action pack The equalizing signal arriving at the input of this cell is shifted to the last cell 8 of this line. The unit recorded in the trigger 19 of the last cell of the first row from the top, under the action of the control signal shifted relative to the signal acting on the cells of the row below, passes through the elements 21 of the last cell OR 14 of the first line and further through the AND 20 element of the first cells of the second line opened by the signal from the output of the element OR 22. At the output of the element OR 22 there is a single signal, since the trigger 19 of the first cell of the bottom line contains one. The unit coming from the output of the element OR 22 does not record the 3 trigger 19 of the first cell 8 of the first line, since its single input is closed by the signal from the output of the element OR 22 input to the second single input of the trigger 19. During the n clock ticks, the device generates all n permutations, ok . In order not to sample the determinant elements equal to zero, block 4 is used, which is an OR scheme. After a complete enumeration of all possible permutations at the inputs of each element And 17, there appears a signal-, FLY passing to the output of the upper element AND 17 as a signal defining the end of the inferior detectors. In this device, compared with the prototype HciMHoro, hardware costs are reduced, and it is also possible to calculate the value of the determinant and its individual members. The device can be used autonomously as a specialized machine, as well as additional equipment for a universal digital computer. Formula 1. A device for disclosing and calculating matrix determinants, comprising a generator, a control unit, a sign determining unit, a zero member determination unit, and a matrix of n identical cells, that is, with, simplify the device, the elements AND, OR, spreading, the sienal divider, the memory block and the arithmetic unit are entered, the generator output is connected to the first inputs of the control unit, the first and second elements AND, the first cells of the first and second rows of the matrix and input block definition The second input of which is connected to the first output of the control unit, and the second output of the sign determining unit to the first input of the arithmetic unit, the second input of which is connected to the first output of the memory block, the second output of the memory block is connected to the first inputs of the first OR element and the third element And, the output of which is connected to the first inputs of the generator and the second element OR, the outputs of the first and second elements OR are connected respectively to the first and second inputs of the signal distributor, the output of which is connected to the second inputs s second OR and the generator; the output of the second element And is connected through, the delay element with the second input of the first element OR and directly with the third input of the second element OR; the cells of each row of the matrix are connected to the first inputs and outputs by a ring B, the second outputs of the last cells of each row of the matrix are connected to the first inputs of the corresponding first input elements IL of each row of the matrix; the second, third, fourth and fifth outputs of the control unit are connected respectively to the first inputs of the second input elements OR of the third, fourth, fifth and sixth rows of the matrix, the second inputs of which are connected respectively to the output of the first element AND, and the outputs of the second input elements OR the third fourth , the fifth and sixth rows of the matrix are connected respectively with the second inputs of the first cells of the same rows of the matrix; the outputs of the first input elements OR of each row are connected to the third inputs of the first cells of each row of the matrix; the group of outputs of the signal distributor is connected to the first group of inputs of the memory block, each output from this group of outputs being connected to the first input of the corresponding element AND in the j-th column of the matrix; the outputs of the corresponding elements AND of the i-th row of the matrix are combined and connected to the corresponding inputs of the memory block and the block for determining the zero term, the output of which is connected to the second input of the third element I; cells of the matrix are interconnected by the second and third inputs and outputs sequentially in rows and fourth and fifth inputs - outputs in parallel in columns; the second input of the corresponding element I is connected to the sixth output K -: - oh cell, the fifth outputs of the first cell of the first row, the second cell of the second row, ..., the n-th cell of the p-th row are connected to one input of the output element AND of each row , the other input of which is connected to the output of the output element AND of each line located in the adjacent lower line; the outputs of the output element And the first row and the output of the arithmetic unit are the outputs of the device; the third input of the generator, the second inputs of the first and second elements AND, the second inputs of the first input elements OR of each row are the control inputs of the device.

2. The device according to claim .1, which is based on the fact that in each 1c „;; - first cell the first input of the cell is connected to the first inputs of the trigger and the first element AND, the output of which is connected to the first input of the first element OR, the output of the first element OR is connected to the first output of the cell, the second input. the cells are connected to the second trigger input, the third inlet cell is connected to the third and fourth fourth trigger inputs and, to the third output of the cell, the fourth and fifth inputs of the cell are connected to the first and second inputs of the second element OR-, the output of which is connected to the fifth to the trigger input, to the second input of the first element I and to the fourth output of the cell; the zero output of the trigger is connected to the second output of the cell, a single output of the trigger is connected to the second input of the first OR element to the fifth sixth output of the cell.

Sources of information taken into account in the examination.

1, USSR Author's Certificate 255647, MLSL.2 G 06 F 15/32, 1967.

2, USSR Copyright Certificate No. 294144, M. KlG G O F 15/32, 1968.

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