CN102004645A - Method for realizing goal seeking of electronic form - Google Patents
Method for realizing goal seeking of electronic form Download PDFInfo
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- CN102004645A CN102004645A CN2010105932983A CN201010593298A CN102004645A CN 102004645 A CN102004645 A CN 102004645A CN 2010105932983 A CN2010105932983 A CN 2010105932983A CN 201010593298 A CN201010593298 A CN 201010593298A CN 102004645 A CN102004645 A CN 102004645A
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Abstract
The invention discloses a method for realizing goal seeking of an electronic form, which comprises the following steps of: obtaining initial conditions such as an independent variable, an induced variable, an initial value, a target value, the precision and iteration step number limitation and the like through a user interface of the electronic form; and carrying out goal seeking by adopting a continued fraction method as a core to be combined with methods such as the initial searching, a dichotomy method, an advancing and retreating method and the like. The method provided by the invention is applied to the field of the electronic form data analysis, has good calculation performance and precision and reaches the practical application level.
Description
Technical field
The invention belongs to the spread-sheet data analysis field, being specifically related to a kind of is the goal seek method of core with the continued fraction method.
Background technology
Goal seek is a data analysis function in spreadsheet program, and goal seek is by adjusting the value in another cell, thereby can try to achieve the method for the particular value in the designating unit lattice.In the goal seek process, spreadsheet program can constantly be changed the value in the designating unit lattice, returns till the value that meets the demands up to the formula that depends on this cell.The method of existing goal seek mainly contains: dichotomy, Newton method (tangent method), secant method and continued fraction method etc.
When adopting dichotomy to carry out goal seek, require objective function continuously, have and have only a real root between original area, though condition satisfies easily, speed of convergence is slow.Although Newton method speed of convergence very fast (the convergence exponent number is 2) must be used functional derivative, in practical problems, often can not ask or be difficult to obtain the derivative of objective function, so be not suitable for practical application about independent variable.Secant method (the convergence exponent number is about 1.618) and continued fraction method (the convergence exponent number is about 1.83) require function to have conditions such as single order, second derivative between original area, can't guarantee convergence for the function that does not satisfy condition.
By above analysis as can be known, the method that the function conditional request is lower (as dichotomy), speed of convergence is slower; And speed of convergence method faster as Newton method, secant method and continued fraction method etc., all compares harsh to the function condition.The condition of problem is ever-changing in the practical application, and wherein a kind of method of pure use often can't guarantee convergence and speed of convergence.
Summary of the invention
The purpose of this part is to summarize some aspects of embodiments of the invention and briefly introduces some preferred embodiments.In this part and the application's specification digest and denomination of invention, may do a little simplification or omit avoiding the making purpose of this part, specification digest and denomination of invention fuzzy, and this simplification or omit and can not be used to limit the scope of the invention.
Technical matters solved by the invention is to provide a kind of electrical form goal seek method, in order to improve the practicality of goal seek.
In order to address the above problem, according to the invention provides an electrical form goal seek method, it comprises:
A: selected target cell and Changing Cells, the desired value of target setting cell, obtain the iteration initial value of Changing Cells and the initial value as a result of Set cell, the described Changing Cells of formula quoting that contains of this Set cell wherein, the every pair of iterative value and end value can be called as a data point;
B: on the both direction of the primary iteration value left and right sides, carry out initial ranging and obtain new iterative value and end value, wherein for each new end value, judge this new end value whether than the initial results value more near desired value, if then enter step C, otherwise, continue then to judge whether the end value that this is new and the difference of desired value and the difference of initial results value and desired value are contrary sign, if contrary sign then enters step D, otherwise the continuation initial ranging;
C: two initial data point that its end value are defined as the continued fraction iteration near two data points of desired value; Begin the continued fraction iteration based on these two initial data point and obtain new iterative value and end value, wherein for each new end value, whether more last end value is more near desired value to judge this new end value, if then continue the continued fraction iteration, otherwise whether the difference that then continues to judge the difference of end value that this is new and desired value and last end value and desired value contrary sign, if contrary sign then enters step D, otherwise, then enter step e;
D: two initial data point that two data points of the poor contrary sign of its end value and desired value are defined as two fens iteration; Begin two fens iteration based on these two initial data point and obtain new iterative value and end value, wherein for each new end value, judge this new end value whether in more preceding two end values apart from the near end value of desired value more near desired value, if then enter step C, otherwise whether the difference that then continues to judge in the difference of end value that this is new and desired value and preceding two end values and desired value contrary sign, if contrary sign then continues two fens iteration, otherwise, then enter step e;
E: move back search and obtain new iterative value and end value near enterprising the advancing of the iterative value left and right sides both direction of the end value correspondence of desired value current, wherein for each new end value, judge this new end value whether more current near the end value of desired value more near desired value, if then enter step C, otherwise, then continue to judge the difference of end value that this is new and desired value and current near the difference of the end value of desired value and desired value contrary sign whether, if contrary sign then enters step D, otherwise, then continue the advance and retreat search;
All carry out the end condition check after new end value of wherein every acquisition.
Further, also obtain precision and maximum iteration time in steps A, described end condition comprises: | y
k-t|＜ε and k＞MS if one of them condition is true, then finishes to find the solution, and return the iterative value and the end value of trying to achieve, wherein y
kBe k end value, t is described desired value, and ε is a precision, and MS is a maximum iteration time.
Further, in step B, for each new end value, judge this new end value whether than the initial results value more near desired value, if then enter step C, otherwise continue initial ranging.
Further, in step D, for each new end value, judge whether more individual in more preceding two end values of this new end value near desired value, if then enter step C, otherwise, whether the difference that then continues to judge in the difference of end value that this is new and desired value and preceding two end values and desired value contrary sign, if contrary sign then continues two fens iteration, otherwise, step e then entered.
Further, in step e, for each new end value, judge this new end value whether more current near the end value of desired value more near desired value, if then enter step C, otherwise, then continue the advance and retreat search.
Further, in step B, on the both direction of the primary iteration value left and right sides, carry out initial ranging: x in the following sequence
0+ s
I1, x
0-s
I1, x
0+ s
A1, x
0-s
A1, x wherein
0Be primary iteration value, s
I1Be the first microcosmic step-length, s
A1Be first macroscopical step-length, first macroscopical step-length after initial ranging once finishes, is then dwindled the first microcosmic step-length greater than the first microcosmic step-length, enlarges first macroscopical step-length, continues initial ranging afterwards.Further again, first macroscopical step-length is the first microcosmic step-length of twice, when dwindling the first microcosmic step-length it is reduced into original N/one, when enlarging the first macroscopical step-length it is expanded as original N doubly, determine the first microcosmic step-length based on the primary iteration value, N is the natural number greater than 1.
Further, in step C,, be that two initial data point are restarted the continued fraction iteration just with two data points of close desired value if continued fraction reaches predetermined joint number.
Further, in step D, whether the difference of in difference that continues to judge end value that this is new and desired value and preceding two end values and desired value is during contrary sign, if y
K+1-t and y
k-t is a contrary sign, keeps x so
K+1And x
kAnd give up x
K-1, continue two fens iteration afterwards, if y
K+1-t and y
K-1-t is a contrary sign, keeps x so
K+1And x
K-1And give up x
k, continuing two fens iteration afterwards, two fens iteration obtain new iterative value and end value is: x
K+1=(x
k+ x
K-1)/2, y
K+1=f (x
K+1), x wherein
K+1Be new iterative value, y
K+1Be new end value, x
kAnd x
K-1Be two fens iterative value before the iteration, y
kAnd y
K-1Be respectively preceding two end values, t is a desired value.
Further, in step e, the search of on current iterative value left and right sides both direction near the end value correspondence of desired value, advancing and retreat in the following sequence:
x
m+s
i2；x
m+s
i2/2；x
m+s
i2/4；x
m+s
i2/8；
x
m+s
a2；x
m+2s
a2；x
m+4s
a2；x
m+8s
a2；
x＝x
m-s
i2；x＝x
m-s
i2/2；x＝x
m-s
i2/4；x＝x
m-s
i2/8；
x
m-s
a2；x
m-2s
a2；x
m-4s
a2；x
m-8s
a2；
X wherein
mFor current near the iterative value of the end value correspondence of desired value, s
I2Be the second microcosmic step-length, s
A2Be second macroscopical step-length, second macroscopical step-length after the advance and retreat search once finishes, is then dwindled the second microcosmic step-length greater than the second microcosmic step-length, enlarges second macroscopical step-length, continues the advance and retreat search afterwards.
Further again, determine the second microcosmic step-length and second macroscopical step-length near the difference of the iterative value of the iterative value of the end value correspondence of desired value and current end value correspondence according to current, when dwindling the second microcosmic step-length it is reduced into original M/one, when enlarging the first macroscopical step-length it is expanded for original M doubly, M is the natural number greater than 1.
Compared with prior art, adopting with the continued fraction method among the present invention is that core is found the solution in conjunction with methods such as initial ranging, dichotomy and advance and retreat methods, like this for satisfying the local functional equation that can lead continuously, good adaptive faculty is arranged, when performance is found the solution in basic reservation, widen range of application, demonstrated stronger practicality.In addition, it is easily realized by computer software, not only is applicable to the spread-sheet data analytic function, extends to other field easily.
Description of drawings
In conjunction with reaching ensuing detailed description with reference to the accompanying drawings, the present invention will be more readily understood, the structure member that wherein same Reference numeral is corresponding same, wherein:
Fig. 1 is the computing machine structured flowchart in one embodiment of the spreadsheet program among operation the present invention;
Fig. 2 is the electrical form goal seek method method flow diagram in one embodiment among the present invention;
Fig. 3 a is the original state interface of an electrical form goal seek example among the present invention; With
Fig. 3 b is the end-state interface of this electrical form goal seek example among the present invention.
Embodiment
Detailed description of the present invention is mainly come the running of direct or indirect simulation technical solution of the present invention by program, step, logical block, process or other symbolistic descriptions.Be the thorough the present invention that understands, in ensuing description, stated a lot of specific detail.And when not having these specific detail, the present invention then may still can realize.Affiliated those of skill in the art use these descriptions herein and state that the others skilled in the art in affiliated field effectively introduce their work essence.In other words, be the purpose of the present invention of avoiding confusion, owing to method, program and the composition known are readily appreciated that, so they are not described in detail.
Alleged herein " embodiment " or " embodiment " are meant special characteristic, structure or the characteristic that can be contained at least one implementation of the present invention.Different in this manual local " in one embodiment " that occur not are all to refer to same embodiment, neither be independent or optionally mutually exclusive with other embodiment embodiment.In addition, represent the sequence of modules in method, process flow diagram or the functional block diagram of one or more embodiment and revocablely refer to any particular order, also be not construed as limiting the invention.
Since embodiments of the invention usually in conjunction with certain computing environment, computer system in other words hardware realize.So Fig. 1 and corresponding the description aim to provide realizing that the suitable computing environment in the embodiments of the invention carries out description simple and that summarize.Although utilize the computing environment carry out on the personal computer system to describe the present invention as general environment among Fig. 1, those skilled in the art should be appreciated that the present invention's program module of also can unifying in conjunction with the department of computer science of other type realizes.
Please refer to Fig. 1, it shows the illustrative Computer Architecture of the computing machine 100 that uses in one embodiment of the present of invention.Described computing machine 100 is conventional desk-top computer or laptop, described computing machine 100 comprises CPU (central processing unit) (CPU) 101, comprises the system storage 104 of random-access memory (ram) 102 and ROM (read-only memory) (ROM) 103, and the system bus 105 of connected system storer 104 and CPU (central processing unit) 101.Described computing machine 100 also comprises the basic input/output (I/O system) 106 of transmission information between each device that helps in the computing machine and is used for the mass-memory unit 107 of storage operating system, application program and other program modules.
Described basic input/output 106 includes display 108 that is used for display message and the input equipment such as mouse, keyboard 109 that is used for user's input information.Wherein said display 108 and input equipment 109 all are connected to CPU (central processing unit) 101 by the input/output control unit 110 that is connected to system bus 105.Described basic input/output 106 can also comprise that input/output control unit 110 is to be used to receive and handle the input from a plurality of other equipment such as keyboard, mouse or electronic touch pens.
Described mass-memory unit 107 is connected to CPU (central processing unit) 101 by the bulk memory controller (not shown) that is connected to system bus 105.Described mass-memory unit 107 and the computer-readable medium that is associated thereof provide non-volatile memories for computing machine 100.That is to say that described mass-memory unit 107 can comprise the computer-readable medium (not shown) such as hard disk or CD-ROM drive.Described mass-memory unit 107 can store electrons form application program 114, and described spreadsheet applications 114 can be used for generation, visit and modification such as workbook 115.Described spreadsheet applications can be the EXCEL of Microsoft, also can be the spreadsheet program of other companies.Hereinafter, based on computing environment shown in Figure 1 goal seek method in the spreadsheet applications among the present invention is done description further.
In general, function satisfies easily near root continuously and condition such as can lead, thus can be earlier with simple, condition is loose, the slower method of convergence is tried to achieve the approximate solution near root, the method with converges faster makes it precision then.Based on this, the present invention has adopted the combined method of dichotomy, advance and retreat method (slow method) and continued fraction method (fast method) in electrical form goal seek method, has improved the practicality of electrical form goal seek method greatly.
Fig. 2 is the method flow diagram of electrical form goal seek method in an embodiment 200 among the present invention.Described electrical form goal seek method 200 may further comprise the steps.
In one embodiment, the starting condition that obtains goal seek comprises: selected target cell and Changing Cells, the desired value t of target setting cell, the iteration initial value x of acquisition Changing Cells
0The y of initial value as a result with Set cell
0, wherein the formula (y=f (x)) that contains of this Set cell is quoted described Changing Cells, current iteration number of times k=0.
In a preferred embodiment, the starting condition that obtains goal seek also comprises: obtain precision ε and maximum iteration time MS.Described precision ε and maximum iteration time MS can be for default settings, also can be that the user initiatively sets.
Fig. 3 a shows the original state interface of an electrical form goal seek example among the present invention, wherein Set cell is B2, Changing Cells is B1, the iteration initial value of Changing Cells B1 is 3, the initial value as a result of Set cell B2 is 5, and the desired value of Set cell B2 is 10, and the formula that this Set cell contains is=SUM (A1:B1), it quotes described Changing Cells B1, maximum iteration time be 100 and computational accuracy be 0.001.
In the goal seek process, spreadsheet program is the value among the change Changing Cells B1 constantly, up to the Set cell B2 that contains the formula that depends on this Changing Cells B1 return satisfy desired value t till.
In one embodiment, determine that initial step length is 0.01x
0(if x
0=0, initial step length is made as 0.01), set the first microcosmic step-length (s
I1) be initial step length, second macroscopical step-length (s
A1) be the initial step length of twice, the order of initial ranging (i.e. rule) is followed successively by x
0+ s
I1, x
0-s
I1, x
0+ s
A1, x
0-s
A1Specifically, when first time initial ranging, with x
0+ s
I1As new iterative value x
K+1, when second time initial ranging, with x
0-s
I1As new iterative value x
K+1, when initial ranging for the third time, with x
0+ s
A1As new iterative value x
K+1, when the 4th initial ranging, with x
0-s
A1As new iterative value x
K+1After initial ranging finishes for one time, then the first microcosmic step-length is reduced into original N/one (such as 1/2, s
I1=s
I1/ 2), enlarge first macroscopical step-length and be original N doubly (such as 2 times, s
A1=s
A1* 2), N is the natural number greater than 1, continues afterwards with the first microcosmic step-length and first macroscopical step-length respectively at iteration initial value x
0Left and right sides both direction search, search order still is x
0+ s
I1, x
0-s
I1, x
0+ s
A1, x
0-s
A1
In other embodiments, initial step length can be set at other values, such as 0.1x
0, the relative size of the first microcosmic step-length and second macroscopical step-length can be regulated, and the order of search and number also can be adjusted.The primary and foremost purpose of initial ranging is in order to search than initial results value y
0More near the new end value of desired value t, as long as can achieve this end, setting step-length and search rule that the those of ordinary skill in the affiliated field can be random.
In one embodiment, each new end value x that wherein obtains for initial ranging
K+1, judge whether | y
K+1-t|＜| y
0-t|, if then enter step 230, otherwise, then directly continue initial ranging, and do not carry out (y
K+1-t) * (y
0-t)＜0 judgement.
In another embodiment, can also adopt other modes to obtain than initial results value y
0More near the new end value of desired value t.
In one embodiment, if enter step 230 by step 220, then its end value is (x near two data points of desired value
0, y
0) and the data point (x that obtains at last of initial ranging
K+1, y
K+1), if enter step 230 by step 250, its end value is (x near two data points of desired value
m, y
m) and advance and retreat and search for the data point (x that obtains at last
K+1, y
K+1), x wherein
mFor when search advance and retreat near the iterative value of desired value, y
mFor when search advance and retreat near the end value of desired value, if enter step 230 by step 240, its end value is the data point (x that two fens iteration obtain at last near two data points of desired value
K+1, y
K+1) and y
kAnd y
K-1In more near the data point of desired value t.
In one embodiment, if continued fraction reaches predetermined joint number (such as 7,8 or 9 joints), just with the ((x just of two data points of close desired value
k, y
k), (x
K+1, y
K+1)) be that two initial data point are restarted the continued fraction iteration.
Simply introduce the continued fraction method below.
For equation y=f (x), suppose that its inverse function is x=F (y), we represent it with continued fraction, that is:
B wherein
0, b
1..., b
i... can be by each data point (x
i, y
i) (i=0,1,2...) determine.If in following formula, make y=0, then can calculate equation root x
*:.
Claims (11)
1. realize electrical form goal seek method for one kind, it is characterized in that, comprising:
A: selected target cell and Changing Cells, the desired value of target setting cell, obtain the iteration initial value of Changing Cells and the initial value as a result of Set cell, the described Changing Cells of formula quoting that contains of this Set cell wherein, the every pair of iterative value and end value can be called as a data point;
B: on the both direction of the primary iteration value left and right sides, carry out initial ranging and obtain new iterative value and end value, wherein for each new end value, judge this new end value whether than the initial results value more near desired value, if then enter step C, otherwise, continue then to judge whether the end value that this is new and the difference of desired value and the difference of initial results value and desired value are contrary sign, if contrary sign then enters step D, otherwise the continuation initial ranging;
C: two initial data point that its end value are defined as the continued fraction iteration near two data points of desired value; Begin the continued fraction iteration based on these two initial data point and obtain new iterative value and end value, wherein for each new end value, whether more last end value is more near desired value to judge this new end value, if then continue the continued fraction iteration, otherwise whether the difference that then continues to judge the difference of end value that this is new and desired value and last end value and desired value contrary sign, if contrary sign then enters step D, otherwise, then enter step e;
D: two initial data point that two data points of the poor contrary sign of its end value and desired value are defined as two fens iteration; Begin two fens iteration based on these two initial data point and obtain new iterative value and end value, wherein for each new end value, judge this new end value whether in more preceding two end values apart from the near end value of desired value more near desired value, if then enter step C, otherwise whether the difference that then continues to judge in the difference of end value that this is new and desired value and preceding two end values and desired value contrary sign, if contrary sign then continues two fens iteration, otherwise, then enter step e;
E: move back search and obtain new iterative value and end value near enterprising the advancing of the iterative value left and right sides both direction of the end value correspondence of desired value current, wherein for each new end value, judge this new end value whether more current near the end value of desired value more near desired value, if then enter step C, otherwise, then continue to judge the difference of end value that this is new and desired value and current near the difference of the end value of desired value and desired value contrary sign whether, if contrary sign then enters step D, otherwise, then continue the advance and retreat search;
All carry out the end condition check after new end value of wherein every acquisition.
2. goal seek method as claimed in claim 1 is characterized in that, also obtains precision and maximum iteration time in steps A, and described end condition comprises: | y
k-t|＜ε and k＞MS,
If one of them condition is true, then finishes to find the solution, and return the iterative value and the end value of trying to achieve, wherein y
kBe k end value, t is described desired value, and ε is a precision, and MS is a maximum iteration time.
3. goal seek method as claimed in claim 1 is characterized in that, in step B, for each new end value, judge this new end value whether than the initial results value more near desired value, if then enter step C, otherwise continue initial ranging.
4. goal seek method as claimed in claim 1, it is characterized in that, in step D,, judge whether more individual in more preceding two end values of this new end value near desired value for each new end value, if then enter step C, otherwise whether the difference that then continues to judge in the difference of end value that this is new and desired value and preceding two end values and desired value contrary sign, if contrary sign then continues two fens iteration, otherwise, then enter step e.
5. goal seek method as claimed in claim 1 is characterized in that, in step e, for each new end value, judge this new end value whether more current near the end value of desired value more near desired value, if then enter step C, otherwise, then continue the advance and retreat search.
6. as the arbitrary described goal seek method of claim 1-5, it is characterized in that, in step B, on the both direction of the primary iteration value left and right sides, carry out initial ranging in the following sequence:
x
0+s
i1，x
0-s
i1，x
0+s
a1，x
0-s
a1，
X wherein
0Be primary iteration value, s
I1Be the first microcosmic step-length, s
A1Be first macroscopical step-length, first macroscopical step-length is greater than the first microcosmic step-length,
After initial ranging finishes for one time, then dwindle the first microcosmic step-length, enlarge first macroscopical step-length, continue initial ranging afterwards.
7. goal seek method as claimed in claim 6, it is characterized in that, first macroscopical step-length is the first microcosmic step-length of twice, when dwindling the first microcosmic step-length it is reduced into original N/one, when enlarging the first macroscopical step-length it is expanded as original N doubly, determine the first microcosmic step-length based on the primary iteration value, N is the natural number greater than 1.
8. as the arbitrary described goal seek method of claim 1-5, it is characterized in that, in step C, if continued fraction reaches predetermined joint number, is that two initial data point are restarted the continued fraction iteration with two data points of close desired value just.
9. as the arbitrary described goal seek method of claim 1-5, it is characterized in that in step D, the difference of in difference that continues to judge end value that this is new and desired value and preceding two end values and desired value is whether during contrary sign, if y
K+1-t and y
k-t is a contrary sign, keeps x so
K+1And x
kAnd give up x
K-1, continue two fens iteration afterwards, if y
K+1-t and y
K-1-t is a contrary sign, keeps x so
K+1And x
K-1And give up x
k, continue two fens iteration afterwards,
Two fens iteration obtain new iterative value and end value is:
x
k+1＝(x
k+x
k-1)/2，y
k+1＝f(x
k+1)，
X wherein
K+1Be new iterative value, y
K+1Be new end value, x
kAnd x
K-1Be two fens iterative value before the iteration, y
kAnd y
K-1Be respectively preceding two end values, t is a desired value.
10. as the arbitrary described goal seek method of claim 1-5, it is characterized in that, in step e, the search of on current iterative value left and right sides both direction near the end value correspondence of desired value, advancing and retreat in the following sequence:
x
m+s
i2；x
m+s
i2/2；x
m+s
i2/4；x
m+s
i2/8；
x
m+s
a2；x
m+2s
a2；x
m+4s
a2；x
m+8s
a2；
x＝x
m-s
i2；x＝x
m-s
i2/2；x＝x
m-s
i2/4；x＝x
m-s
i2/8；
x
m-s
a2；x
m-2s
a2；x
m-4s
a2；x
m-8s
a2；
X wherein
mFor current near the iterative value of the end value correspondence of desired value, s
I2Be the second microcosmic step-length, s
A2Be second macroscopical step-length, second macroscopical step-length is greater than the second microcosmic step-length,
After the advance and retreat search finishes for one time, then dwindle the second microcosmic step-length, enlarge second macroscopical step-length, continue the advance and retreat search afterwards.
11. goal seek method as claimed in claim 10 is characterized in that,
Determine the second microcosmic step-length and second macroscopical step-length near the difference of the iterative value of the iterative value of the end value correspondence of desired value and current end value correspondence according to current,
When dwindling the second microcosmic step-length it is reduced into original M/one, when enlarging the first macroscopical step-length it is expanded for original M doubly, M is the natural number greater than 1.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104458107A (en) * | 2014-11-25 | 2015-03-25 | 国家电网公司 | Simple detection method of differential pressure device |
| CN111144082A (en) * | 2019-12-23 | 2020-05-12 | 中国建设银行股份有限公司 | Multi-table iterative calculation method and device, electronic equipment and storage medium |
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| CN111144082A (en) * | 2019-12-23 | 2020-05-12 | 中国建设银行股份有限公司 | Multi-table iterative calculation method and device, electronic equipment and storage medium |
| CN111144082B (en) * | 2019-12-23 | 2023-05-12 | 中国建设银行股份有限公司 | Multi-table iterative calculation method, device, electronic equipment and storage medium |
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