Symbolic calculation system, symbolic calculation method and parallel circuit simulation system

A parallel circuit simulation system comprising a plurality of nodes each having an element processor and local memory including a program area which stores a predetermined program to be executed by the corresponding element processor and a work area used by said element processor, and an interconnection network which interconnects said plurality of nodes, wherein said element processors of said plurality of nodes are capable of cooperating with each other,

• said parallel circuit simulation system comprising a first computer which is connected to said interconnection network, said first computer dividing a circuit to be simulated into a plurality of circuit pieces, preparing circuit piece matrix representing circuit equations corresponding to divided circuit pieces respectively, and transmitting the prepared circuit piece matrix to said plurality of nodes,
• wherein each of said element processor executes the predetermined program stored in said program area thereby said plurality of nodes:
• executes symbolic calculation on the circuit piece matrix transmitted by said first computer, executes numeric calculation on the result of the symbolic calculation executed by each node, and resolves the circuit equation represented by the received circuit piece matrix,
• said parallel circuit simulation system comprises:
• a second computer which is connected to said interconnection network and which prepares a circuit matrix of connected circuits including connected circuit pieces, based on the obtained resolution of the circuit equation for the circuit pieces;
• and
• a third computer which is connected to said interconnection network, and which divides the prepared circuit matrix of the connected circuits into a plurality of row sets each comprising at least one of rows of said matrix, and which transmits the plurality of row sets to said plurality of nodes respectively,
• wherein each element processor executes the predetermined program stored in the program area, thereby each of said plurality of nodes further:
• adds entries specifying nonzero elements contained in the row sets associated with said plurality of nodes to a plurality of entry sets which are in one-to-one correspondence with said plurality of row sets;
• sequentially attains a first variable which specifies an unknown that can be eliminated with a minimum number of calculations, among a plurality of unknowns which are designated by a second variable whose value sequentially changes from 1 up to a value equal to the number of rows included in said matrix, by cooperating with other nodes;
• replaces one row specified by said first variable and another row specified by said second variable with each other, among the rows of said matrix, by cooperating with other nodes;
• replaces one column specified by said first variable and another column specified by said second variable with each other, among columns of said matrix, by cooperating with other nodes;
• obtains fill-ins belonging to the associated row sets from a plurality of fill-ins which occur in eliminating the unknown in regard to said matrix including the rows and/or columns replaced with each other, and further adds entries specifying the obtained fill-ins to said plurality of entry sets to said entry sets.

A symbolic calculation system for performing a symbolic calculation to solve simultaneous linear equations, comprising:

• a matrix divider which divides a matrix, representing the simultaneous linear equations to be solved, into a plurality of row sets each comprising at least one of rows of said matrix;
• a plurality of first entry adders, each of which is associated with one of said plurality of row sets divided by said matrix divider, and which add entries specifying nonzero elements contained in the row sets associated with said plurality of first entry adders to a plurality of entry sets which are in one-to-one correspondence with said plurality of row sets;
• a pivot selector which sequentially attains a first variable specifying an unknown that can be eliminated with a minimum number of calculations, among a plurality of unknowns which are designated by a second variable whose value sequentially changes from 1 up to a value equal to the number of rows included in said matrix;
• a pivot replacer which replaces one row specified by said first variable and another row specified by said second variable with each other, among the rows of said matrix, and replaces one column specified by said first variable and another column specified by said second variable with each other, among columns of said matrix;
• and
• a plurality of second entry adders, provided in one-to-one correspondence with said plurality of first entry adders, and which obtain fill-ins belonging to the associated row sets from a plurality of fill-ins that occur in eliminating the unknown in regard to said matrix including the rows and columns replaced with each other by said pivot replacer, and which add entries specifying the obtained fill-ins to said plurality of entry sets to which the entries have been added by said plurality of first entry adders that are in one-to-one correspondence with said plurality of second entry adders.

A symbolic calculation system for performing a symbolic calculation to solve simultaneous linear equations, comprising:

• a plurality of first entry adders, each of which is associated with one of a plurality of row sets each comprising at least one of different rows of a matrix representing the simultaneous linear equations to be solved, and which add entries specifying nonzero elements contained in the row sets associated with said plurality of first entry adders to a plurality of entry sets that are in one-to-one correspondence with said plurality of row sets;
• a pivot selector which sequentially attains a first variable specifying an unknown that can be eliminated with a minimum number of calculations, among a plurality of unknowns which are designated by a second variable whose value sequentially changes from 1 up to a value equal to the number of rows included in said matrix;
• a pivot replacer which replaces one row specified by said first variable and another row specified by said second variable with each other, among the rows of said matrix, and which replaces one column specified by said first variable and another column specified by said second variable, among columns of said matrix;
• and
• a plurality of second entry adders, provided in one-to-one correspondence with said plurality of first entry adders, and which obtain fill-ins belonging to the associated row sets from a plurality of fill-ins that occur in eliminating the unknown in regard to said matrix including the rows and columns replaced with each other by said pivot replacer, and which add entries specifying the obtained fill-ins to said plurality of entry sets to which the entries have been added by said plurality of first entry adders that are in one-to-one correspondence with said plurality of second entry adders.

A symbolic calculation method for performing a symbolic calculation to solve simultaneous linear equations, comprising:

• dividing a matrix, which represents the simultaneous linear equations to be solved, into a plurality of row sets each comprising at least one of rows of said matrix;
• adding, in parallel, entries specifying nonzero elements contained in said plurality of row sets divided by said dividing to a plurality of entry sets which are in one-to-one correspondence with said plurality of row sets;
• sequentially attaining a first variable which specifies an unknown that can be eliminated with a minimum number of calculations, among a plurality of unknowns which are designated by a second variable whose value sequentially changes from 1 up to a value equal to the number of rows included in said matrix;
• replacing one row specified by said first variable and another row specified by said second variable with each other, among the rows of said matrix, and replacing one column specified by said first variable and another column specified by said second variable with each other, among columns of said matrix;
• and
• obtaining, in parallel, fill-ins belonging to said plurality of row sets from a plurality of fill-ins which occur in eliminating the unknown in regard to said matrix including the rows and columns replaced with each other by said replacing, and adding, in parallel, entries specifying the obtained fill-ins to said plurality of entry sets to which the entries specifying the nonzero elements contained in said plurality of row sets have been added in parallel.

A parallel circuit simulation system comprising:

• a circuit divider which divides a circuit to be simulated into partial circuits;
• a plurality of partial circuit matrix calculators, each of which is associated with one of said partial circuits divided by said circuit divider, and which create partial circuit matrices representing circuit equations of the partial circuits associated with said plurality of partial circuit matrix calculators;
• a plurality of partial circuit symbolic calculators, each of which is associated with one of said partial circuits, and which perform symbolic calculations based on the partial circuit matrices representing the circuit equations of the associated partial circuits and created by said plurality of partial circuit matrix calculators;
• a plurality of partial circuit numerical calculators, each of which is associated with one of said partial circuits, and which solve the circuit equations of the associated partial circuits by performing numerical calculations using calculation results obtained as a result of the symbolic calculations which said plurality of partial circuit symbolic calculators have performed based on the partial circuit matrices representing the circuit equations of the associated circuit sections;
• a combination circuit matrix calculator which creates a combination circuit matrix representing circuit equations of a combination circuit that is a combination of said partial circuits, based on solutions of the circuit equations of said partial circuits which have been solved by said plurality of partial circuit numerical calculators;
• a combination circuit symbolic calculator which performs symbolic calculations based on the combination circuit matrix created by said combination circuit matrix calculator;
• and
• a combination circuit numerical calculator which solves the circuit equations of said combination circuit by performing numerical calculations using calculation results obtained as a result of the symbolic calculations performed by said combination circuit symbolic calculator;
• wherein said combination circuit symbolic calculator comprises:
• a matrix divider which divides said combination circuit matrix into a plurality of row sets each comprising at least one of rows of said combination circuit matrix;
• a plurality of first entry adders, each of which is associated with one of said plurality of row sets divided by said matrix divider, and which add entries specifying nonzero elements contained in the row sets associated with said plurality of first entry adders to a plurality of entry sets that are in one-to-one correspondence with said plurality of row sets;
• a pivot selector which sequentially attains a first variable specifying an unknown that can be eliminated with a minimum number of calculations, among a plurality of unknowns which are designated by a second variable whose value sequentially changes from 1 up to a value equal to the number of rows included in said combination circuit matrix;
• a pivot replacer which replaces one row specified by said first variable and another row specified by said second variable with each other, among the rows of said combination circuit matrix, and which replaces one column specified by said first variable and another column specified by said second variable with each other, among columns of said combination circuit matrix;
• and
• a plurality of second entry adders, provided in one-to-one correspondence with said plurality of first entry adders, and which obtain fill-ins belonging to the associated row sets from a plurality of fill-ins that occur in eliminating the unknown in regard to said combination circuit matrix including the rows and columns replaced with each other by said pivot replacer, and which add entries specifying the obtained fill-ins to said plurality of entry sets to which the entries have been added by said plurality of first entry adders that are in one-to-one correspondence with said plurality of second entry adders.

A computer usable storage medium containing a computer readable program stored therein for causing a computer to serve as:

• a matrix divider which divides a matrix, representing simultaneous linear equations to be solved, into a plurality of row sets each comprising at least one of rows of said matrix;
• a plurality of first entry adders, each of which is associated with one of said plurality of row sets divided by said matrix divider, and which add entries specifying nonzero elements contained in the row sets associated with said plurality of first entry adders to a plurality of entry sets that are in one-to-one correspondence with said plurality of row sets;
• a pivot selector which sequentially attains a first variable specifying an unknown that can be eliminated with a minimum number of calculations, among a plurality of unknowns which are designated by a second variable whose value sequentially changes from 1 up to a value equal to the number of rows included in said matrix;
• a pivot replacer which replaces one row specified by said first variable and another row specified by said second variable with each other, among the rows of said matrix, and which replaces one column specified by said first variable and another column specified by said second variable with each other, among columns of said matrix;
• and
• a plurality of second entry adders, provided in one-to-one correspondence with said plurality of first entry adders, and which obtain fill-ins belonging to the associated row sets from a plurality of fill-ins which occur in eliminating the unknown in regard to said matrix including the rows and columns replaced with each other by said pivot replacer, and which add entries specifying the obtained fill-ins to said plurality of entry sets to which the entries have been added by said plurality of first entry adders that are in one-to-one correspondence with said plurality of second entry adders.

A program signal embedded in a carrier wave, for causing a computer to serve as:

• a matrix divider which divides a matrix, representing simultaneous linear equations to be solved, into a plurality of row sets each comprising at least one of rows of said matrix;
• a plurality of first entry adders, each of which is associated with one of said plurality of row sets divided by said matrix dividers, and which add entries specifying nonzero elements contained in the row sets associated with said plurality of first entry adders to a plurality of entry sets that are in one-to-one correspondence with said plurality of row sets;
• a pivot selector which sequentially attains a first variable specifying an unknown that can be eliminated with a minimum number of calculations, among a plurality of unknowns which are designated by a second variable whose value sequentially changes from 1 up to a value equal to the number of rows included in said matrix;
• a pivot replacer which replaces one row specified by said first variable and another row specified by said second variable with each other, among the rows of said matrix, and which replaces one column specified by said first variable and another column specified by said second variable with each other, among columns of said matrix;
• and
• a plurality of second entry adders, provided in one-to-one correspondence with said plurality of first entry adders, and which obtain fill-ins belonging to the associated row sets from a plurality of fill-ins that occur in eliminating the unknown in regard to said matrix including the rows and columns replaced with each other by said pivot replacer, and which add entries specifying the obtained fill-ins to said plurality of entry sets to which the entries have been added by said plurality of first entry adders that are in one-to-one correspondence with said plurality of second entry adders.