CN111260782B - Interpolation data calculation and reading method, system and storage medium of discrete data set - Google Patents
Interpolation data calculation and reading method, system and storage medium of discrete data set Download PDFInfo
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Abstract
The invention discloses a method, a system and a storage medium for calculating and reading interpolation data of a discrete data set, wherein the method comprises the following steps: inputting a discrete data set, wherein the discrete data set comprises a plurality of elements, and each element is represented by a key value pair consisting of a position and a numerical value; constructing a numerical accumulation array and a drop point statistics array, wherein the size of the numerical accumulation array and the size of the drop point statistics array are preset values; sequentially and linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array in sequence in an accumulated projection mode; low-pass filtering is carried out on the counted value accumulation array and the counted falling point counting array; dividing elements in the low-pass filtered numerical value accumulation array by elements in the low-pass filtered drop point statistics array to obtain an interpolation result array; and reading the interpolation result from the interpolation result array. The memory space occupied by the invention is a fixed value, and can be widely applied to the field of computer application.
Description
Technical Field
The invention relates to the field of computer application, in particular to a method, a system and a storage medium for calculating and reading interpolation data of a discrete data set.
Background
In the fields of engineering measurement, scientific experiments, signal processing, image processing, computer simulation, etc., the obtained data are generally discrete, and interpolation from known data is required to obtain values at points other than these discrete points. For example, it is currently necessary to map a rainfall area of a certain region at a certain time, and the raw data of the rainfall is measured by an automatic ground weather observation station. Each ground automatic weather observation station can only measure the rainfall of the place, but the distribution diagram needs to display continuous rainfall areas, so that the rainfall of other unmeasured places needs to be obtained through interpolation. The number of ground automatic weather observation stations is limited, and in practical application, real-time rainfall distribution is often required to be displayed, which puts a high requirement on the calculation efficiency of an interpolation algorithm. To this end, computer programs are commonly employed in the industry to perform interpolation calculations of discrete data points instead of manually. However, when the number of discrete data points input is increased, the memory occupied by the discrete data point interpolation method adopting the computer program is increased, which will definitely increase the cost of interpolation calculation and reduce the performance of the computer.
Disclosure of Invention
In order to solve the above technical problems, an embodiment of the present invention is to: provided are a method, a system and a storage medium for calculating and reading interpolation data of a discrete data set.
The technical scheme adopted by one aspect of the embodiment of the invention is as follows:
a method for calculating and reading interpolation data of a discrete data set comprises the following steps:
inputting a discrete data set, wherein the discrete data set comprises a plurality of elements, and each element is represented by a key value pair consisting of a position and a numerical value;
constructing a numerical accumulation array and a drop point statistics array, wherein the size of the numerical accumulation array and the size of the drop point statistics array are preset values;
sequentially and linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array in sequence in an accumulated projection mode to obtain a counted numerical value accumulation array and a counted falling point statistics array;
low-pass filtering is carried out on the counted value accumulation array and the counted falling point counting array;
dividing elements in the low-pass filtered numerical value accumulation array by elements in the low-pass filtered drop point statistics array to obtain an interpolation result array;
And reading the interpolation result from the interpolation result array.
Further, the step of sequentially linearly mapping the positions of each dimension of each element in the discrete dataset to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array in order by means of accumulated projection to obtain the counted numerical value accumulation array and the counted falling point statistics array specifically comprises the following steps:
determining a numerical range of position coordinates of each dimension of each element in the discrete dataset;
according to the determined numerical range, sequentially and linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array to obtain a coordinate result after linear mapping;
according to the coordinate result after linear mapping, determining the weights of sub-pixel levels of each element in the discrete data set on the numerical accumulation array element and the drop point statistics array element respectively;
and according to the determined weight, respectively carrying out sub-pixel level value accumulation projection and drop point counting accumulation projection on each element of the discrete data set to the value accumulation array and the drop point counting array to obtain a counted value accumulation array and a counted drop point counting array.
Further, the step of performing low-pass filtering on the counted value accumulation array and the counted falling point counting array specifically includes:
respectively carrying out Fourier transform on the counted numerical value accumulation array and the counted falling point counting array to obtain a Fourier transform result of the numerical value accumulation array and a Fourier transform result of the falling point counting array;
clearing high-frequency components in the Fourier transform result of the numerical accumulation array and the Fourier transform result of the falling point statistics array to 0 respectively to obtain a Fourier transform result after the numerical accumulation array is filtered and a Fourier transform result after the falling point statistics array is filtered;
and respectively carrying out inverse Fourier transform on the Fourier transform result after the numerical value accumulation array is filtered and the Fourier transform result after the falling point statistics array is filtered, so as to obtain a numerical value accumulation array after the low-pass filtering and a falling point statistics array after the low-pass filtering.
Further, the step of reading the interpolation result from the interpolation result array specifically includes:
taking the coordinate to be read as a first coordinate, and calculating the subscript reference position of the first coordinate in the interpolation result array;
the corresponding elements are taken out from the interpolation result array according to the calculated subscript reference position;
And calculating an interpolation result under the first coordinate according to the extracted element.
Further, according to the determined numerical range, the step of linearly mapping the positions of each dimension of each element in the discrete dataset to the subscript of the numerical accumulation array and the subscript of the falling point statistics array in sequence to obtain a coordinate result after linear mapping specifically includes:
linearly mapping the N-dimensional positions of the ith element in the discrete data set to subscripts of the numerical accumulation array and the drop point statistics array respectively to obtain a coordinate result of the ith element in the discrete data set after linear mapping, wherein the ith element x in the discrete data set (i) Linearly mapped coordinate result pos (i) The expression of (2) is:
wherein ,is the element x (i) Coordinates of j-th dimension of (a)>Is->The coordinate result after linear mapping, LB (j) is +.>Is the minimum value of UB (j) is +.>E is a numerical valueCumulative array or drop point statistics array, dim (E, j) is the size of array E in the j-th dimension, j=0, 1,2, … … N-1, i=0, 1,2, … … k-1, k is the total number of elements of the discrete dataset, and N and k are both positive integers.
Further, the step of determining weights of sub-pixel levels of each element in the discrete dataset on the numerical accumulation array element and the drop point statistics array element according to the coordinate result after the linear mapping specifically includes:
Determining weights of sub-pixel levels of an ith element in a discrete data set on a numerical accumulation array element and a drop point statistics array element respectively, wherein the determined weights of the sub-pixel levels are expressed as follows:
where n is a continuous multiplication symbol and w (I, I) is the ith element x of the discrete dataset (i) Weights at sub-pixel levels on array E, I is the subscript of array E, E is the number accumulation array or drop point statistics array,is->Linearly mapped coordinate results, +.>Is the element x (i) I=0, 1,2, … … k-1, j=0, 1,2, … … N-1; k is the total number of elements of the discrete dataset, N and k are positive integers, +.> To round down the symbol,% is the remainder operation symbol, u is the implicit variable of I, and there are:
further, according to the determined weight, each element of the discrete dataset is respectively projected to a numerical accumulation array and a drop point statistics array at a sub-pixel level to obtain a counted numerical accumulation array and a counted drop point statistics array, which specifically includes:
according to the determined weight, carrying out sub-pixel level value accumulation projection on each element of the discrete data set to a value accumulation array to obtain a counted value accumulation array, wherein the expression of the element in the counted value accumulation array is as follows:
wherein ,for the full-scale word, element a in the numerical value accumulation array is I I W (I, I) is the element x (i) Weights at sub-pixel level on a value accumulation array, v i For the i-th element x in the discrete dataset (i) Is the value of (t)/(t) is the sum of pos (i) Set of all subscripts with Manhattan distance less than 1, pos (i) Is the element x (i) As a result of the coordinates after linear mapping, i=0, 1,2, … … k-1, k is the total number of elements of the discrete dataset, and k is a positive integer;
according to the determined weight, each element of the discrete data set is subjected to drop point counting accumulation projection to a drop point statistics array, so that a statistical drop point statistics array is obtained, and the expression of the element in the statistical drop point statistics array is as follows:
wherein ,for the full-scale word, I is element b in the falling point statistics array I W (I, I) is the element x (i) Weights at sub-pixel level on the drop point statistics array, ψ is the sum pos (i) Set of all subscripts with Manhattan distance less than 1, pos (i) Is the element x (i) As a result of the linear mapping, i=0, 1,2, … … k-1, k is the total number of elements of the discrete dataset and k is a positive integer.
The technical scheme adopted by the embodiment of the invention is as follows:
an interpolation data calculation and reading system for discrete data sets, comprising:
The input module is used for inputting a discrete data set, the discrete data set comprises a plurality of elements, and each element is represented by a key value pair consisting of a position and a numerical value;
the construction module is used for constructing a numerical accumulation array and a drop point statistics array, wherein the size of the numerical accumulation array and the size of the drop point statistics array are both preset values;
the mapping module is used for sequentially linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array in sequence in an accumulated projection mode to obtain a counted numerical value accumulation array and a counted falling point statistics array;
the low-pass filtering module is used for carrying out low-pass filtering on the counted value accumulation array and the counted falling point counting array;
the division module is used for dividing elements in the low-pass filtered numerical value accumulation array by elements in the low-pass filtered drop point statistics array to obtain an interpolation result array;
and the reading module is used for reading the interpolation result from the interpolation result array.
The technical scheme adopted by the embodiment of the invention is as follows:
an interpolation data calculation and reading system for discrete data sets, comprising:
At least one processor;
at least one memory for storing at least one program;
the at least one program, when executed by the at least one processor, causes the at least one processor to implement the method of computing and reading interpolated data for a discrete data set.
The technical scheme adopted by the embodiment of the invention is as follows:
a storage medium having stored therein processor-executable instructions which, when executed by a processor, are for implementing the method of interpolation data calculation and reading for discrete data sets.
One or more of the above technical solutions in the embodiments of the present invention have the following advantages: according to the embodiment of the invention, the numerical value accumulation array and the drop point statistics array with the preset values are built, and then the drop point distribution and the numerical information of the data points in the input discrete data set are recorded in the numerical value accumulation array and the drop point statistics array with the fixed values in an accumulated projection mode, so that the memory space occupied by interpolation calculation is a fixed value and cannot be increased along with the increase of the input discrete data points, the cost of interpolation calculation is reduced, and the performance of a computer is improved.
Drawings
FIG. 1 is a flowchart of a method for calculating and reading interpolation data of a discrete data set according to an embodiment of the present invention;
FIG. 2a is a schematic diagram of a set of drop point statistics obtained after projection of a first discrete data point according to an embodiment of the present invention;
FIG. 2b is a diagram of a cumulative array of values obtained after projection of a first discrete data point according to an embodiment of the present invention;
FIG. 2c is a schematic diagram of a set of drop point statistics obtained after projection of a second discrete data point according to an embodiment of the present invention;
FIG. 2d is a diagram of a cumulative array of values obtained after projection of a second discrete data point according to an embodiment of the present invention;
FIG. 2e is a schematic diagram of a set of drop point statistics obtained after projection of a third discrete data point according to an embodiment of the present invention;
FIG. 2f is a diagram of a cumulative array of values obtained after projection of a third discrete data point according to an embodiment of the present invention;
FIG. 2g is a schematic diagram of a set of drop point statistics obtained after projection of a fourth discrete data point according to an embodiment of the present invention;
FIG. 2h is a diagram of a cumulative array of values obtained after projection of a fourth discrete data point according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a set of drop point statistics obtained by low-pass filtering the signal coverage intensity sample data of an outdoor wireless base station using the method of the present invention;
FIG. 4 is a schematic diagram of a numerical accumulation array obtained by low-pass filtering the signal coverage intensity sample data of an outdoor wireless base station by adopting the method of the invention;
fig. 5 is a schematic diagram of an interpolation result array obtained by interpolating signal coverage intensity sample data of an outdoor wireless base station by adopting the method of the invention.
Detailed Description
The invention is further explained and illustrated below with reference to the drawing and the specific embodiments of the present specification. The step numbers in the embodiments of the present invention are set for convenience of illustration, and the order of steps is not limited in any way, and the execution order of the steps in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.
Referring to fig. 1, an embodiment of the present invention provides a method for calculating and reading interpolation data of a discrete data set, which specifically includes the following steps:
s101, inputting a discrete data set, wherein the discrete data set comprises a plurality of elements, and each element is represented by a key value pair consisting of a position and a numerical value;
in particular, assuming that the discrete dataset X consists of k discrete data points (i.e., elements), the ith element of X is noted as bracketed superscript X (i) Then x= { X (0) ,x (1) ,x (2) ,…,x (k-1) }. To be able to interpolate, the data set X needs to be non-empty, i.e. k is a positive integer greater than 1,i＝0,1,2,……k-1。
the discrete data points (i.e. source data) aimed at by the present invention are represented in a position-value format, and each element X of the present embodiment X is used for accelerating the subsequent interpolation (i) Are all expressed in the form of "key value pairs", i.e., x (i) ＝{key (i) ,v i }. Wherein each key is (i) For a real number whose N dimension represents the position, the dimensions N of all keys are the same, N>=1, and each value takes the value (i.e. value) v i Is a real number, the ith data point (i.e. element) X of X (i) The format of (2) isWherein the bond is->
For example, when a rainfall area distribution map of a certain region at a certain time is drawn, the { longitude, latitude } coordinates of each ground automatic weather observation station may be used as a "key", the rainfall amount of each ground station may be used as a "value", and then the rainfall amount may be interpolated, where n=2.
S102, constructing a numerical accumulation array and a drop point statistics array, wherein the size of the numerical accumulation array and the size of the drop point statistics array are both preset values;
specifically, to facilitate the subsequent statistics of the N-dimensional data set X in step S101, the present embodiment creates an N-dimensional numerical accumulation array a and a drop point statistics array B, and initializes the values of all of their elements to 0. The individual elements in A are denoted as a I Wherein subscript i= { p 0 ,p 1 ,…,p N-1 The range of values of the index in dimension i of A is denoted as p i E [0, dim (A, i)), where brackets [ … ] represent left-hand closed intervals, right-hand open intervals, and(/>representing non-negativeInteger sets). Similarly, a single element in B is denoted B J Wherein subscript j= { q 0 ,q 1 ,…,q N-1 The range of values of the i-th dimension index in B is denoted as q i E [0, dim (B, i)), and +.>dim (a, i), dim (B, i) being the subscript size of a and B in each dimension, determines the statistical resolution, and for all i, dim (a, i) =dim (B, i), dim (a, i) is satisfied>0; dim is used to describe the dimension of the data. All elements in the numerical accumulation array A and the falling point statistics array B are real numbers mathematically, and floating point values can be used for approximate substitution in actual recording. The numerical accumulation array A and the falling point statistics array B are used for recording the distribution of all data points and numerical information, and the size of the numerical accumulation array A and the falling point statistics array B can be fixed values which are preset, so that the memory occupied space of the numerical accumulation array A and the falling point statistics array B is fixed and does not change along with the increase of input data points, which is difficult to achieve by a traditional interpolation system.
S103, sequentially and linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array in sequence in an accumulated projection mode to obtain a counted numerical value accumulation array and a counted falling point statistics array;
If the data information of the discrete data set is recorded directly by an array or matrix, then as the input data points increase, the size of the array or matrix also increases, meaning that the memory space occupied by it also increases. In order to record all data point information input through the numerical accumulation array A and the falling point statistics array B with fixed memory occupied space, the embodiment introduces the concepts of 'falling point' and 'projection accumulation'.
Taking n=2 as an example, at this time, array a, array B, and keys are two-dimensional, and at the beginning, all elements of array a and array B are 0. At this time, if the first discrete data point in the input discrete data set is (4,5,2), where the first two numbers 4 and 5 represent positions and 2 represent values, the drop point statistics and the value accumulation obtained after the discrete data point is projected are shown in fig. 2a and 2b, respectively. FIG. 2a fills in the array element at column 4, row 5 position with 1 to record the drop point of the discrete data point; FIG. 2b writes a corresponding value of 2 to record the value of the discrete data point in the array element at the column 4, row 5 position; the unfilled elements in fig. 2a and 2b remain unchanged at 0. If the second discrete data point in the input discrete data set is (7, 8, 9), the drop point statistics and numerical accumulation arrays of fig. 2c and 2d are continuously accumulated on the basis of fig. 2a and 2 b. Fig. 2c fills in the array element at the 8 th column and 9 th row position as 1 on the basis of fig. 2a, while fig. 2d writes the corresponding value 9 on the array element at the 8 th column and 9 th row position on the basis of fig. 2 b. If the third discrete data point in the input discrete data set is (4, 5, 1), the positions of the third discrete data point and the first discrete data point are the same and only different in value, adding 1 to the array element at the position of the 4 th column and the 5 th row of the figure 2c to be 2 of the figure 2e on the basis of being 1 when the third discrete data point falls; and simultaneously changing the original value 2 of the array element at the 4 th column and 5 th row positions of the figure 2d plus the value 1 of the third discrete data point into 3 of the figure 2 f. Similarly, other new data points can be recorded in the numerical accumulation array A and the drop point statistics array B in a similar accumulation manner. The way of recording the drop point and the value thereof is to change the values of the arrays A and B no matter how many data points are input, and the requirement on the storage space is not increased.
In addition, considering that the corresponding element can be found out through the subscript of the array, the position of each dimension is sequentially mapped onto the subscripts of the arrays A and B in a linear manner, and the association between the key and the subscript of the array in the key value pair is established, so that further calculation and data information reading operation are facilitated.
S104, performing low-pass filtering on the counted value accumulation array and the counted falling point counting array;
specifically, the logarithmic accumulation array a and the falling point statistics array B are respectively subjected to N-dimensional low-pass filtering by using filters, and filtering results can be recorded as a 'and B'. Wherein the dimensions of A 'and B' and the subscript sizes of the dimensions should be consistent with A and B. Each element of a 'and B' may be a floating point value.
While alternative methods of low pass filtering include fourier transforms, FIR filters, IIR filters, etc.
Taking an FIR filter as an example of N-dimensional low-pass filtering, the N-dimensional filtering can be completed at one time by directly using the N-dimensional IIR filter, and filtering can be respectively carried out on different dimension directions, different coordinate planes or different coordinate combinations by a synthesis method, so that an N-dimensional low-pass filtering result is finally synthesized.
When a uses an N-dimensional FIR filter, B should also use the same N-dimensional FIR filter, and when a uses a synthesis method for filtering, B should use the same synthesis method for filtering as a. However, if it is ensured that both modes of synthesis or some mode of synthesis are equivalent to the N-dimensional filter, the above limitation may be canceled, and a and B may be filtered using both equivalent methods.
The filter processing passband bandwidths for each dimension a and B may be different: when the bandwidth is wider, the interpolation result is sharper, and when the bandwidth is narrower, the interpolation result is smoother, and for different dimension directions, the bandwidth can be set to be different according to the characteristics of the numerical values, so that the interpolation smoothness of each dimension can be finely controlled. But all corresponding dimensions of a and B, such as the bandwidths of the a and B dimensions, should be consistent.
S105, dividing elements in the low-pass filtered numerical accumulation array by elements in the low-pass filtered drop point statistics array to obtain an interpolation result array;
specifically, dividing each element in the low-pass filtered value accumulation array by a corresponding element in the low-pass filtered drop point statistics array to obtain a corresponding element in the interpolation result array, and finally obtaining an interpolation result array C, namely:
wherein ,c is the full scale word I As a single element in C, subscript i= { p 0 ,p 1 ,…,p N }，p i E [0, dim (A, i)). The value range of each dimension of C should be consistent with a, and each element of C may be a floating point value.
S106, reading an interpolation result from the interpolation result array.
As can be seen from steps S105 and S106, in this embodiment, only one filtering is performed on the arrays a and B after all data are input, and then the elements in the two filtered arrays a 'and B' are divided correspondingly to obtain the interpolation result array C, and only the array C is needed to be used in any subsequent number taking process without re-filtering, so that the value taking efficiency is higher.
According to the method, the drop point distribution and the numerical information of the data points in the input discrete data set are recorded in the numerical accumulation array and the drop point statistics array with fixed sizes in an accumulated projection mode, so that the input data point number is limited and can be processed, the input data point number is not limited, the memory space requirement is unchanged under any data point number, the recording precision can be adjusted to adapt to the storage capacity of different equipment, the interpolation result can be extracted quickly, the interpolation result is smooth, and any dimension data is supported mathematically.
Further as a preferred embodiment, the step S103 of sequentially linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array in order by means of accumulated projection to obtain a statistical numerical value accumulation array and a statistical falling point statistics array specifically includes:
s1031, determining a numerical range of position coordinates of each dimension of each element in the discrete data set;
specifically, for the ith element X in the discrete dataset X (i) Its coordinates in any dimension jThe numerical range of (2) is a defined value, if LB (j) is +. >Is the minimum value (lower limit of the value) of UB (j) of +.>Maximum value (upper limit of value) of (a) is +.>
The numerical range of (a) can be set by a user according to actual needs before interpolation, or can be calculated according to a complete data set (for example, the numerical range is obtained from all data points through a maximum value function and a minimum value function). Taking the case of dead reckoning from a complete dataset, there are:
where function min represents the smallest number from the plurality of real numbers and function max represents the largest number from the plurality of real numbers. Whether user set or inferred from the dataset, LB (j) < UB (j) must be satisfied for all j, otherwise the interpolation method is not effective.
S1032, according to the determined numerical range, sequentially and linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical accumulation array and the subscript of the falling point statistics array to obtain a coordinate result after linear mapping;
from the foregoing description, the present embodiment can establish a relationship between the "key" (i.e. position) of each element in the discrete data set and the subscript of the numerical accumulation array a and the subscript of the falling point statistics array B through linear mapping, so as to facilitate further calculation and data information reading operations.
Specifically, the ith element in the discrete data setElement x (i) Coordinate result pos linearly mapped to numerical accumulation array a (i) The expression of (2) is:
while the i-th element x in the discrete dataset (i) Coordinate result pos linearly mapped to drop point statistics array B (i) The expression of (2) is:
wherein ,as a real number, floating point number records and representations may be used in the calculation process. pos (i) Is used as corresponding to x (i) The reference positions of the subscripts on arrays a and B correspond to, but are not directly used as subscript values.
S1033, determining weights of sub-pixel levels of each element in the discrete data set on the numerical accumulation array element and the drop point statistics array element respectively according to the coordinate result after linear mapping;
this step can be further subdivided into the following implementation steps:
s10331, constructorWherein the symbol->For rounding down, the symbol "%" is the remainder operation and defines +.>z∈[0,N),/>u∈[0,2 N )。
S10332, determining all the preferable values of the numerical accumulation array element or the falling point statistics array subscript I, and if the values are represented by a set:
s10333, calculating the ith element x (i) The weights w (I, I) of the sub-pixel levels on the numerical accumulation array element and the drop point statistics array element are specifically:
where u is an implicit variable of I, u∈[0,2 N ) I is determined when u takes a particular value, affecting the value of w (I, I).
S10334, according to the determined weight, performing sub-pixel level value accumulation projection and drop point counting accumulation projection on each element of the discrete data set respectively to the value accumulation array and the drop point counting array to obtain a counted value accumulation array and a counted drop point counting array.
After determining the weights w (I, I) at the sub-pixel level, the data points X of the discrete data set X may be determined (0) ,x (1) ,x (2) ,…,x (k-1) (i.e. element x (i) ) Sequentially and respectively carrying out sub-pixel level value accumulation projection on the falling point statistical array B to obtain a statistical value accumulation array, x (i) The projection mode of (a) is as follows:
the meaning of the above formula is: array B at x (i) The element value after projection is equal to the value of the array B at x (i) The pre-projection element value is added with a weight w (I, I). By continually accumulating new values in array BAnd finally obtaining a statistical falling point statistical array by a data point projection (namely weight) mode.
After determining the weights w (I, I) at the sub-pixel level, the data points X of the discrete data set X may be determined (0) ,x (1) ,x (2) ,…,x (k-1) (i.e. element x (i) ) Sequentially and respectively carrying out sub-pixel level value accumulation projection on the value accumulation array A to obtain a counted value accumulation array, x (i) The projection mode of (a) is as follows:
the meaning of the above formula is: array A is at x (i) The value of the projected element is equal to x (i) The product of the value multiplied by the weight w (I, I) plus the array A at x (i) Numerical values of the elements before projection. The counted value accumulation array can be finally obtained by continuously accumulating new data point projections (namely the product of the new data point and the weight value) in the array A.
Element b I And element a I The subscript I of (a) is the same because the locations of the discrete data set X that it maps to arrays a and B are the same for one data point of the discrete data set X, except that the specific stored content (i.e., element values) is different.
Taking fig. 2d as the array B before projection and fig. 2e as the array a before projection as an example, if the fourth discrete data point in the input discrete data set is (1.2,1.3,1.5), since the positions 1.2 and 1.3 are non-integers, the weights need to be distributed to four points (i.e. the elements of the 1 st column and the 2 nd column of the 1 st row and the 1 st column and the 2 nd column of the 2 nd row) which are adjacent to each other for recording. The fractional parts of positions 1.2 and 1.3 are 0.2 and 0.3 for the substituted weights w (I, I) the calculation formula calculates the corresponding w (I, I), specifically:
w (I, I) of column 1 element of row 1 is: (1-0.2) × (1-0.3) =0.56
W (I, I) of the 2 nd column element of row 1 is: 0.2× (1-0.3) =0.14
W (I, I) of column 1 element of row 2 is: (1-0.2) ×0.3=0.24
W (I, I) of the 2 nd column element of row 2 is: 0.2×0.3=0.06
And b of the four points before projection I If the value is 0, the element values of the four points after projection are equal to the weights w (I, I) of the sub-pixel level, so the array B after projection is shown in fig. 2 g.
Similarly, a of the four points before projection I If 0, the element values of the four points after projection are equal to the product of the weight w (I, I) of the sub-pixel level and the value 1.5, specifically:
the projected values of column 1 elements of column 1 are: 0.56×1.5=0.84
The projected values of column 2 elements of column 1 are: 0.14×1.5=0.21
The projected values of column 1 elements of row 2 are: 0.24×1.5=0.36
The projected values of the 2 nd column elements of row 2 are: 0.06×1.5=0.09
Therefore, the projected array A shown in FIG. 2h can be obtained according to the above calculation result.
In order to cope with the situation that the positions and values of data points in the discrete data set may be non-integer, the embodiment introduces the weights of the sub-pixel level to represent the decimal through the values of a plurality of integer position elements of the neighbor in a mode of combining accumulated projection, so that the interpolation requirement of more types of data is met, and the applicability is wider.
Further as a preferred embodiment, the step S106 of low-pass filtering the statistical value accumulation array and the statistical drop point statistical array specifically includes:
S1061, performing Fourier transform on the counted value accumulation array and the counted falling point counting array respectively to obtain a Fourier transform result of the value accumulation array and a Fourier transform result of the falling point counting array;
s1062, clearing high-frequency components in the Fourier transform result of the numerical accumulation array and the Fourier transform result of the falling point statistics array to 0 to obtain the Fourier transform result after the numerical accumulation array is filtered and the Fourier transform result after the falling point statistics array is filtered;
s1063, performing inverse Fourier transform on the Fourier transform result after the numerical value accumulation array is filtered and the Fourier transform result after the falling point statistics array is filtered respectively to obtain a numerical value accumulation array after the low-pass filtering and a falling point statistics array after the low-pass filtering.
The embodiment carries out low-pass filtering on the counted numerical value accumulation array and the counted falling point counting array through Fourier transformation, and has the advantages of easy calculation of inverse transformation, easy realization through a computer, high speed and the like.
Further, as a preferred embodiment, the step S106 of reading the interpolation result from the interpolation result array specifically includes:
s1061, taking the coordinate to be read as a first coordinate, and calculating the subscript reference position of the first coordinate in an interpolation result array;
From the foregoing discussion, dim (a, i) =dim (C, i). Substituting the coordinate G of the required value into pos (i) The subscript reference position posg thereof in the interpolation result array C can be calculated:
s1062, extracting corresponding elements from the interpolation result array according to the calculated subscript reference position;
specifically, the corresponding element { C } can be extracted from the interpolation result array C according to the subscript reference position pos H And to further calculate the interpolation result at the coordinates G. Wherein the method comprises the steps of
S1063, calculating an interpolation result under the first coordinate according to the extracted element.
Specifically, H may be substituted into the expression of the weight w (I, I) of the sub-pixel level to obtain the corresponding weight w (H, I), and then the interpolation result G under the coordinate G is calculated in the following specific calculation manner:
in summary, the interpolation data calculating and reading method of the present embodiment has the following advantages:
(1) Fixed occupied memory space
In this embodiment, the distribution of all data points and the numerical information are recorded in the arrays a and B with fixed space sizes, so that the memory occupation space of the array is not changed with the increase of the input data points, which is difficult to achieve by the conventional interpolation system.
(2) Saving memory space
Different from the traditional interpolation mode, in the interpolation calculation process described in the embodiment, each data point can be input in series, and the data points do not need to be stored in a memory at one time in operation, so that the occupation of space is saved.
(3) Memory space occupation can be adjusted according to equipment capacity
The memory occupation space required in the design of the embodiment is relatively loose, and when the available memory of the device is less, the device can be adapted by reducing the scale of the subscript of each dimension of the arrays a and B. As long as the fitting fineness requirement is met, the present embodiment can use a smaller scale of the subscripts to achieve interpolation results that are substantially consistent with the use of a larger scale of the subscripts.
(4) Interpolation smoothness can be fine tuned
In the interpolation data calculation process described in this embodiment, the bandwidth during low-pass filtering may be set according to actual needs, when the bandwidth is wider, the interpolation result is sharper, and when the bandwidth is narrower, the interpolation result is smoother, and for different dimension directions, the bandwidth may be set to be different according to the characteristics of the values, so that the embodiment may finely control the interpolation smoothness of each dimension.
(5) The quick value taking can be carried out for any time only by one-time pre-calculation
In the interpolation data calculation process of the invention, the interpolation result array C can be obtained by only filtering the arrays A and B once respectively after all data are input and then dividing the filtered data, and the array C is only needed to be used and the filtering is not needed again in the random number taking process, so the value taking efficiency of the embodiment is higher.
(6) After interpolation is carried out by adopting the method of the embodiment, the gap areas of all original discrete data points can be reasonably filled according to nearby data points, and the actual situation can be well restored in actual engineering.
(7) The interpolation data calculation and reading method of the embodiment has popularization, can be used for processing two-dimensional and three-dimensional data, and can also be used for processing data of any dimension on the premise of allowing the memory capacity of a computer.
(8) The low-pass filtering can adopt modes of an FIR filter, fourier transform and the like, all the filtering modes have ready parallelization methods, and when the interpolation result array C is obtained, the interpolation result array C is read only, the problem of synchronous atomicity is not needed to be considered, and a plurality of points can be obtained together without collision. Therefore, the method of the embodiment is easy to parallelize during implementation, and efficiency is improved.
The method of the embodiment is applicable to drawing rainfall area distribution map, and can be applied to any discrete data interpolation application occasion with a position-value source data format. For example, it is impossible to measure the altitude of each position of a mountain in practice, only some places can be selected for measurement, after measurement, the places are restored to the original mountain terrain by the interpolation data calculation method of this embodiment, then the numerical accumulation matrix records the altitude measured by each point, and the falling point statistical matrix records the longitude and latitude (i.e. position) of each measurement point.
For another example, in the application of estimating the signal coverage intensity of an outdoor wireless base station, it is assumed that a coordinate (x, y) is used to represent a position of a land with a size of 10km x 10km, and a coordinate z is used to represent the signal intensity at the (x, y) position, that is, a combination of { { { x, y }, z } is used to represent a set of position and signal intensity information. The amount of work is too great for intensive grid measurement, but the labor is limited, so that sampling measurement can be performed only in a small number of places. Assume that the measured data samples are:
X＝{{{8,2},0.25},{{0,8},1.5},{{6,3},2.25},{{0,9},.5},{{3,2},.5},{{2,6},.75}}
the numerical cumulative array a ', the falling point statistical array B', and the interpolation result array C obtained by processing the samples by the interpolation data calculation method of the present embodiment are shown in fig. 3, fig. 4, and fig. 5, respectively. In this example, a two-dimensional normal distribution function is employed as the convolution kernel of the FIR filter to low-pass filter the primitive arrays a and B. In fig. 3, 4 and 5, the contour lines are used to intuitively and conveniently show the values of the elements of the arrays a ', B' and C, the X, y and z coordinates are the coordinates of the source data X, the array subscript coordinates of the arrays a ', B' and C are not overlapped and are directly marked on the number axis, but the array subscript of each position can be seen by multiplying the values of the X and y coordinates by 10; while the z value is unchanged, common to all A, A ', B, B' and C. The solid origin in fig. 4 is recorded for the falling points of the samples, and the falling points of the samples are not repeated, so the z-axis coordinates of all the falling points are 1.
Corresponding to the method of fig. 1, the embodiment of the invention further provides a system for calculating and reading interpolation data of a discrete data set, which comprises:
the input module is used for inputting a discrete data set, the discrete data set comprises a plurality of elements, and each element is represented by a key value pair consisting of a position and a numerical value;
the construction module is used for constructing a numerical accumulation array and a drop point statistics array, wherein the size of the numerical accumulation array and the size of the drop point statistics array are both preset values;
the mapping module is used for sequentially linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array in sequence in an accumulated projection mode to obtain a counted numerical value accumulation array and a counted falling point statistics array;
the low-pass filtering module is used for carrying out low-pass filtering on the counted value accumulation array and the counted falling point counting array;
the division module is used for dividing elements in the low-pass filtered numerical value accumulation array by elements in the low-pass filtered drop point statistics array to obtain an interpolation result array;
and the reading module is used for reading the interpolation result from the interpolation result array.
Corresponding to the method of fig. 1, the embodiment of the application further provides a system for calculating and reading interpolation data of a discrete data set, which comprises:
at least one processor;
at least one memory for storing at least one program;
the at least one program, when executed by the at least one processor, causes the at least one processor to implement the method of computing and reading interpolated data for a discrete data set.
Embodiments of the present application also provide a storage medium having stored therein processor-executable instructions which, when executed by a processor, are for implementing the method of interpolation data calculation and reading of discrete data sets.
The content in the method embodiment is applicable to the system and the storage medium embodiment, and the functions specifically realized by the system and the storage medium embodiment are the same as those of the method embodiment, and the achieved beneficial effects are the same as those of the method embodiment.
While the preferred embodiment of the present application has been described in detail, the present application is not limited to the embodiments described above, and various equivalent modifications and substitutions can be made by those skilled in the art without departing from the spirit of the present application, and these equivalent modifications and substitutions are intended to be included in the scope of the present application as defined in the appended claims.
Claims (10)
1. A method for calculating and reading interpolation data of a discrete data set is characterized in that: the method comprises the following steps:
inputting a discrete data set, wherein the discrete data set comprises a plurality of elements, and each element is represented by a key value pair consisting of a position and a numerical value; the position is the position of the ground automatic weather observation station, the numerical value is the rainfall of each ground, and the position of the ground automatic weather observation station and the rainfall of each ground are interpolated to construct the key value pair;
constructing a numerical accumulation array and a drop point statistics array, wherein the size of the numerical accumulation array and the size of the drop point statistics array are preset values;
sequentially and linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array in sequence in an accumulated projection mode to obtain a counted numerical value accumulation array and a counted falling point statistics array;
low-pass filtering is carried out on the counted value accumulation array and the counted falling point counting array;
dividing elements in the low-pass filtered numerical value accumulation array by elements in the low-pass filtered drop point statistics array to obtain an interpolation result array;
And reading the interpolation result from the interpolation result array.
2. The method for computing and reading interpolation data of discrete data sets according to claim 1, wherein: the step of sequentially and linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array in an accumulated projection mode to obtain the counted numerical value accumulation array and the counted falling point statistics array specifically comprises the following steps:
determining a numerical range of position coordinates of each dimension of each element in the discrete dataset;
according to the determined numerical range, sequentially and linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array to obtain a coordinate result after linear mapping;
according to the coordinate result after linear mapping, determining the weights of sub-pixel levels of each element in the discrete data set on the numerical accumulation array element and the drop point statistics array element respectively;
and according to the determined weight, respectively carrying out sub-pixel level value accumulation projection and drop point counting accumulation projection on each element of the discrete data set to the value accumulation array and the drop point counting array to obtain a counted value accumulation array and a counted drop point counting array.
3. The method for computing and reading interpolation data of discrete data sets according to claim 1, wherein: the step of low-pass filtering the counted value accumulation array and the counted falling point counting array specifically comprises the following steps:
respectively carrying out Fourier transform on the counted numerical value accumulation array and the counted falling point counting array to obtain a Fourier transform result of the numerical value accumulation array and a Fourier transform result of the falling point counting array;
clearing high-frequency components in the Fourier transform result of the numerical accumulation array and the Fourier transform result of the falling point statistics array to 0 respectively to obtain a Fourier transform result after the numerical accumulation array is filtered and a Fourier transform result after the falling point statistics array is filtered;
and respectively carrying out inverse Fourier transform on the Fourier transform result after the numerical value accumulation array is filtered and the Fourier transform result after the falling point statistics array is filtered, so as to obtain a numerical value accumulation array after the low-pass filtering and a falling point statistics array after the low-pass filtering.
4. The method for computing and reading interpolation data of discrete data sets according to claim 1, wherein: the step of reading the interpolation result from the interpolation result array specifically includes:
Taking the coordinate to be read as a first coordinate, and calculating the subscript reference position of the first coordinate in the interpolation result array;
the corresponding elements are taken out from the interpolation result array according to the calculated subscript reference position;
and calculating an interpolation result under the first coordinate according to the extracted element.
5. The method for computing and reading interpolation data of discrete data sets according to claim 2, wherein: according to the determined numerical range, the step of sequentially and linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical accumulation array and the subscript of the falling point statistics array to obtain a coordinate result after linear mapping specifically comprises the following steps:
linearly mapping the N-dimensional positions of the ith element in the discrete data set to subscripts of the numerical accumulation array and the drop point statistics array respectively to obtain a coordinate result of the ith element in the discrete data set after linear mapping, wherein the ith element x in the discrete data set (i) Linearly mapped coordinate result pos (i) The expression of (2) is:
wherein ,is the element x (i) Coordinates of j-th dimension of (a)>Is->The coordinate result after linear mapping, LB (j) is +.>Is the minimum value of UB (j) is +.>E is a cumulative array of values or a statistical array of drop points, dim (E, j) is the size of array E in the j-th dimension, j=0, 1,2, … … N-1, i=0, 1,2, … … k-1, k is the total number of elements of the discrete dataset, and N and k are both positive integers.
6. The method for computing and reading interpolation data of discrete data sets according to claim 2, wherein: the step of determining the weights of sub-pixel levels of each element in the discrete data set on the numerical accumulation array element and the drop point statistics array element respectively according to the coordinate result after the linear mapping specifically comprises the following steps:
determining weights of sub-pixel levels of an ith element in a discrete data set on a numerical accumulation array element and a drop point statistics array element respectively, wherein the determined weights of the sub-pixel levels are expressed as follows:
where n is a continuous multiplication symbol and w (I, I) is the ith element x of the discrete dataset (i) Weights at sub-pixel levels on array E, I is the subscript of array E, E is the number accumulation array or drop point statistics array,is->Linearly mapped coordinate results, +.>Is the element x (i) I=0, 1,2, … … k-1, j=0, 1,2, … … N-1; k is the total number of elements of the discrete dataset, N and k are positive integers, +.>To round down the symbol,% is the remainder operation symbol, u is the implicit variable of I, and there are:
7. the method for computing and reading interpolation data of discrete data sets according to claim 2, wherein: according to the determined weight, each element of the discrete data set is respectively subjected to sub-pixel level value accumulation projection and drop point counting accumulation projection to obtain a counted value accumulation array and a counted drop point counting array, and the method specifically comprises the following steps:
According to the determined weight, carrying out sub-pixel level value accumulation projection on each element of the discrete data set to a value accumulation array to obtain a counted value accumulation array, wherein the expression of the element in the counted value accumulation array is as follows:
wherein ,for the full-scale word, element a in the numerical value accumulation array is I I W (I, I) is the element x (i) Weights at sub-pixel level on a value accumulation array, v i For the i-th element x in the discrete dataset (i) Is the value of (t)/(t) is the sum of pos () Set of all subscripts with Manhattan distance less than 1, pos (i) Is the element x (i) Linear mapped coordinates result, i=0, 1,2, … … k-1; k is the total number of elements of the discrete dataset, k is a positive integer;
according to the determined weight, each element of the discrete data set is subjected to drop point counting accumulation projection to a drop point statistics array, so that a statistical drop point statistics array is obtained, and the expression of the element in the statistical drop point statistics array is as follows:
wherein ,for the full-scale word, I is element b in the falling point statistics array I W (I, I) is the element x (i) Weights at sub-pixel level on the drop point statistics array, ψ is the sum pos () Set of all subscripts with Manhattan distance less than 1, pos (i) Is the element x (i) As a result of the linear mapping, i=0, 1,2, … … k-1, k is the total number of elements of the discrete dataset and k is a positive integer.
8. An interpolation data calculation and reading system for discrete data sets, characterized in that: comprising the following steps:
the input module is used for inputting a discrete data set, the discrete data set comprises a plurality of elements, and each element is represented by a key value pair consisting of a position and a numerical value; the position is the position of the ground automatic weather observation station, the numerical value is the rainfall of each ground, and the position of the ground automatic weather observation station and the rainfall of each ground are interpolated to construct the key value pair;
the construction module is used for constructing a numerical accumulation array and a drop point statistics array, wherein the size of the numerical accumulation array and the size of the drop point statistics array are both preset values;
the mapping module is used for sequentially linearly mapping the positions of each dimension of each element in the discrete data set to the subscript of the numerical value accumulation array and the subscript of the falling point statistics array in sequence in an accumulated projection mode to obtain a counted numerical value accumulation array and a counted falling point statistics array;
the low-pass filtering module is used for carrying out low-pass filtering on the counted value accumulation array and the counted falling point counting array;
The division module is used for dividing elements in the low-pass filtered numerical value accumulation array by elements in the low-pass filtered drop point statistics array to obtain an interpolation result array;
and the reading module is used for reading the interpolation result from the interpolation result array.
9. An interpolation data calculation and reading system for discrete data sets, characterized in that: comprising the following steps:
at least one processor;
at least one memory for storing at least one program;
the at least one program, when executed by the at least one processor, causes the at least one processor to implement the method of interpolation data calculation and reading of discrete data sets as claimed in any one of claims 1-7.
10. A storage medium having stored therein instructions executable by a processor, characterized by: the processor-executable instructions, when executed by a processor, are for implementing the method of interpolation data calculation and reading of discrete data sets according to any one of claims 1-7.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| IL121013A0 (en) * | 1996-06-06 | 1997-11-20 | Yeda Res & Dev | Computerized tomography scanner and method of performing computerized tomography |
| CN105677617A (en) * | 2016-01-06 | 2016-06-15 | 广东工业大学 | Method for discrete point interpolation based on dual low-pass filtering |
| CN110333504A (en) * | 2019-07-16 | 2019-10-15 | 哈尔滨工程大学 | A fast broadband beamforming method for space-time two-dimensional filtering |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| IL121013A0 (en) * | 1996-06-06 | 1997-11-20 | Yeda Res & Dev | Computerized tomography scanner and method of performing computerized tomography |
| CN105677617A (en) * | 2016-01-06 | 2016-06-15 | 广东工业大学 | Method for discrete point interpolation based on dual low-pass filtering |
| CN110333504A (en) * | 2019-07-16 | 2019-10-15 | 哈尔滨工程大学 | A fast broadband beamforming method for space-time two-dimensional filtering |
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