org.math.array.IntegerArray Maven / Gradle / Ivy
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package org.math.array;
/**
* A collection of static methods for generating, modifying, and reading
* arrays and matrices of integers.
* BSD License
*
* @author Yann RICHET
*/
public class IntegerArray {
// creation of integer arrays
/**
* Returns an m x m matrix. result has constants along the diagonal
* and zeros everywhere else.
* @param m an integer > 0.
* @param c Constant that lies along diagonal. Set c=1 for identity matrix.
* @return m x m two dimensional array of integers.
*/
public static int[][] diagonal(int m, int c) {
int[][] I = new int[m][m];
for (int i = 0; i < I.length; i++)
I[i][i] = c;
return I;
}
/**
* Returns an mxn matrix of constants
* @param m number of rows in matrix
* @param n number of columns in matrix
* @param c constant matrix is filled with.
* @return mxn two dimensional array of constants
*/
public static int[][] fill(int m, int n, int c) {
int[][] o = new int[m][n];
for (int i = 0; i < o.length; i++)
for (int j = 0; j < o[i].length; j++)
o[i][j] = c;
return o;
}
/**
* Generates an m point array of constants
* @param m Size of array
* @param c constant array is to be filled with
* @return array of constants.
*/
public static int[] fill(int m, int c) {
int[] o = new int[m];
for (int i = 0; i < m; i++)
o[i] = c;
return o;
}
// conversion from/to double methods
/**
* Truncates each double value in a matrix to an integer that is less than or equal to the double.
* @param v The input matrix of doubles
* @return The truncated version of the input matrix.
*/
public static int[][] floor(double[][] v) {
int[][] ia = new int[v.length][];
for (int i = 0; i < v.length; i++) {
ia[i] = new int[v[i].length];
for (int j = 0; j < ia[i].length; j++) {
ia[i][j] = (int) Math.floor(v[i][j]);
}
}
return ia;
}
/**
* Truncates each double value in an array to an integer that is less than or equal to the double.
* @param v The input array of doubles
* @return The truncated version of the input matrix.
*/
public static int[] floor(double[] v) {
int[] ia = new int[v.length];
for (int i = 0; i < v.length; i++) {
ia[i] = (int) Math.floor(v[i]);
}
return ia;
}
/**
* Converts each element in an integer matrix to a double
* @param v matrix of integers
* @return matrix of doubles
*/
public static double[][] int2double(int[][] v) {
double[][] ia = new double[v.length][];
for (int i = 0; i < v.length; i++) {
ia[i] = new double[v[i].length];
for (int j = 0; j < ia[i].length; j++) {
ia[i][j] = v[i][j];
}
}
return ia;
}
/**
* Converts each element in an integer array to a double
* @param v array of integers
* @return array of doubles
*/
public static double[] int2double(int[] v) {
double[] ia = new double[v.length];
for (int i = 0; i < v.length; i++) {
ia[i] = v[i];
}
return ia;
}
// Modify rows & colmumns methods
/**
* Generate a copy of an array
* @param M Input array.
* @return A copy of the input array.
*/
public static int[] copy(int[] M) {
int[] array = new int[M.length];
System.arraycopy(M, 0, array, 0, M.length);
return array;
}
/**
* Generate a copy of a matrix
* @param M Input matrix.
* @return A copy of the input matrix
*/
public static int[][] copy(int[][] M) {
int[][] array = new int[M.length][M[0].length];
for (int i = 0; i < array.length; i++)
System.arraycopy(M[i], 0, array[i], 0, M[i].length);
return array;
}
/**
* Carve out a submatrix from the input matrix and return a copy.
* Result is the intersection of rows i1 through i2
* and columns j1 through j2 inclusive.
* Example:
*
* int[][] a =
* {{0,1,2,3,4},
* {1,7,8,9,10},
* {2,13,14,15,16},
* {3,19,20,21,22},
* {4,25,26,27,28}};
* int[][] b = getSubMatrixRangeCopy(a, 2, 3, 1, 3);
* Result is:
* 13 14 15
* 19 20 21
*
* @param M Input matrix
* @param i1 first row in cut
* @param i2 last row in cut
* @param j1 first column in cut
* @param j2 last column in cut
* @return submatrix. Input matrix is left unharmed.
*/
public static int[][] getSubMatrixRangeCopy(int[][] M, int i1, int i2, int j1, int j2) {
int[][] array = new int[i2 - i1 + 1][j2 - j1 + 1];
for (int i = 0; i < i2 - i1 + 1; i++)
System.arraycopy(M[i + i1], j1, array[i], 0, j2 - j1 + 1);
return array;
}
/**
* Extract a range of columns from a matrix.
* Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,25,26,27,28}};
* int[][] z = getColumnsRangeCopy(a, 2, 4);
* input is:
* 0 1 2 3 4
* 1 7 8 9 10
* 2 13 14 15 16
* 3 19 20 21 22
* 4 25 26 27 28
* result is:
* 2 3 4
* 8 9 10
* 14 15 16
* 20 21 22
* 26 27 28
*
* @param M Input matrix
* @param j1 Index of first column to be extracted.
* @param j2 Index of last column to be extracted.
* @return An mxn matrix where m=number of rows in M and n=j2-j1+1
*/
public static int[][] getColumnsRangeCopy(int[][] M, int j1, int j2) {
int[][] array = new int[M.length][j2 - j1 + 1];
for (int i = 0; i < M.length; i++)
System.arraycopy(M[i], j1, array[i], 0, j2 - j1 + 1);
return array;
}
/**
* Extract specific columns from a matrix.
* Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,25,26,27,28}};
* int[][] z = getColumnsCopy(a, 2, 4);
* input is:
* 0 1 2 3 4
* 1 7 8 9 10
* 2 13 14 15 16
* 3 19 20 21 22
* 4 25 26 27 28
* result is:
* 0 2 4
* 1 8 10
* 2 14 16
* 3 20 22
* 4 26 28
*
* @param M Input matrix
* @param J Each is the index of a column. There can be as many indices listed as there are columns in M.
* @return An mxn matrix where m=number of rows in M and n=number of indices listed
*/
public static int[][] getColumnsCopy(int[][] M, int... J) {
int[][] array = new int[M.length][J.length];
for (int i = 0; i < M.length; i++)
for (int j = 0; j < J.length; j++)
array[i][j] = M[i][J[j]];
return array;
}
/**
* Extract one column from a matrix.
*
Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,25,26,27,28}};
* int[][] z = getColumnCopy(a, 2);
* input is:
* 0 1 2 3 4
* 1 7 8 9 10
* 2 13 14 15 16
* 3 19 20 21 22
* 4 25 26 27 28
* Result is:
* 2 8 14 20 26
*
* @param M Input matrix
* @param j Index of desired column
* @return Array of values from extracted column.
*/
public static int[] getColumnCopy(int[][] M, int j) {
int[] array = new int[M.length];
for (int i = 0; i < M.length; i++)
array[i] = M[i][j];
return array;
}
/**
* Extract one column from a three dimensional array. The result is an array of the
* values in the first dimension.
* @param M Input 3D array
* @param j The index of the second dimension.
* @param k The index of the third dimension
* @return An array
*/
public static int[] getColumnCopy(int[][][] M, int j, int k) {
int[] array = new int[M.length];
for (int i = 0; i < M.length; i++)
array[i] = M[i][j][k];
return array;
}
/**
* Extract specific rows from a matrix.
* Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,25,26,27,28}};
* int[][] z = getRowsCopy(a, 2, 4);
* input is:
* 0 1 2 3 4
* 1 7 8 9 10
* 2 13 14 15 16
* 3 19 20 21 22
* 4 25 26 27 28
* result is:
* 2 13 14 15 16
* 4 25 26 27 28
*
* @param M Input matrix
* @param I Each is the index of a column. There can be as many indices listed as there are rows in M.
* @return An mxn matrix where m=number of indices listed and n=number of columns in m
*/
public static int[][] getRowsCopy(int[][] M, int... I) {
int[][] array = new int[I.length][M[0].length];
for (int i = 0; i < I.length; i++)
System.arraycopy(M[I[i]], 0, array[i], 0, M[I[i]].length);
return array;
}
/**
* Extract a row from a matrix.
* Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,25,26,27,28}};
* int[] z = getRowCopy(a, 2);
* input is:
* 0 1 2 3 4
* 1 7 8 9 10
* 2 13 14 15 16
* 3 19 20 21 22
* 4 25 26 27 28
* result is:
* 2 13 14 15 16
*
* @param M Input matrix
* @param i index of row to copy
* @return An array of n values where n = number of columns in M
*/
public static int[] getRowCopy(int[][] M, int i) {
int[] array = new int[M[0].length];
System.arraycopy(M[i], 0, array, 0, M[i].length);
return array;
}
/**
* Extract a range of rows from a matrix.
* Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,25,26,27,28}};
* int[][] z = getRowsRangeCopy(a, 2, 4);
* input is:
* 0 1 2 3 4
* 1 7 8 9 10
* 2 13 14 15 16
* 3 19 20 21 22
* 4 25 26 27 28
* result is:
* 2 13 14 15 16
* 3 19 20 21 22
* 4 25 26 27 28
*
* @param M Input matrix
* @param i1 Index of first row to be extracted.
* @param i2 Index of last row to be extracted.
* @return An mxn matrix where m=j2-j1+1 and n=number of columns in M
*/
public static int[][] getRowsRangeCopy(int[][] M, int i1, int i2) {
int[][] array = new int[i2 - i1 + 1][M[0].length];
for (int i = 0; i < i2 - i1 + 1; i++)
System.arraycopy(M[i + i1], 0, array[i], 0, M[i + i1].length);
return array;
}
/**
* Extract a section of an array.
* Example:
*
* int[] a = {00,11,22,33,44,55,66,77,88,99};
* int[] z = getRangeCopy(a, 2, 5);
* result is:
* 22 33 44 55
*
* @param M Input array
* @param j1 Index of first term to get
* @param j2 Index of last term to get
* @return An array with j2-j1+1 elements
*/
public static int[] getRangeCopy(int[] M, int j1, int j2) {
int[] array = new int[j2 - j1 + 1];
System.arraycopy(M, j1, array, 0, j2 - j1 + 1);
return array;
}
/**
* Extract specific elements from an array.
* Example:
*
*
* int[] a = {00,11,22,33,44,55,66,77,88,99};
* int[] z = getCopy(a, 2, 5);
* result is:
* 22 55
*
* @param M The input array.
* @param I the indices of the elements to extract
* @return The output array of n elements where n=number of indices listed.
*/
public static int[] getCopy(int[] M, int... I) {
int[] array = new int[I.length];
for (int i = 0; i < I.length; i++)
array[i] = M[I[i]];
return array;
}
/**
* Get the number of columns in a specified row of a matrix. Used for oddly sized matrices.
* @param M Input matrix
* @param i Index of row whose column length will be returned
* @return The number of columns in row i
*/
public static int getColumnDimension(int[][] M, int i) {
return M[i].length;
}
/**
* Extract diagonal from a matrix.
* Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,25,26,27,28}};
* int[] z = getDiagonal(a, 1);
* input is:
* 0 1 2 3 4
* 1 7 8 9 10
* 2 13 14 15 16
* 3 19 20 21 22
* 4 25 26 27 28
* result is:
* 1 8 15 22
*
* @param M Input matrix
* @param I index of diagonal to copy
* @return An array
*/
public static int[] getDiagonal(int[][] M, int I) {
int nr = M.length, nc = M.length;
int nd = 0;
if (nc < nr) {
if (I >= 0) {
nd = nc - I;
} else if (I < (nc - nr)) {
nd = nr + I;
} else {
nd = nc;
}
} else {
if (I <= 0) {
nd = nr + I;
} else if (I > (nc - nr)) {
nd = nc - I;
} else {
nd = nr;
}
}
int[] d = new int[nd];
for (int i = 0; i < d.length; i++)
d[i] = M[i + I][i + I];
return d;
}
/**
* Combine a set of arrays into a matrix. Each array becomes a row.
* Example:
*
* int[] a = {0,11,22,33,44}, b = {55,66,77,88};
* int[][] z = mergeRows(a, b);
* result is:
* 0 11 22 33 44
* 55 66 77 88
*
* @param x Input arrays
* @return A matrix. May non-rectangular if arrays are not all the same length.
*/
public static int[][] mergeRows(int[]... x) {
int[][] array = new int[x.length][];
for (int i = 0; i < array.length; i++) {
array[i] = new int[x[i].length];
System.arraycopy(x[i], 0, array[i], 0, array[i].length);
}
return array;
}
/**
* Combine a set of arrays into a matrix. Each array becomes a column. Arrays must all be of same length.
* Example:
*
* int[] a = {00,11,22,33,44}, b = {55,66,77,88,99};
* int[][] z = mergeColumns(a, b);
* result is:
* 0 55
* 11 66
* 22 77
* 33 88
* 44 99
*
* @param x Input arrays
* @return An mxn matrix where m=size of any input array and n is the number of arrays.
*/
public static int[][] mergeColumns(int[]... x) {
int[][] array = new int[x[0].length][x.length];
for (int i = 0; i < array.length; i++)
for (int j = 0; j < array[i].length; j++)
array[i][j] = x[j][i];
return array;
}
/**
* Concatenates arrays.
*
Example:
*
* int[] a = {00,11,22,33,44}, b = {55,66,77,88,99};
* int[] z = merge(a, b, a);
* result is:
* 0 11 22 33 44 55 66 77 88 99 0 11 22 33 44
*
* @param x Input arrays
* @return Output array.
*/
public static int[] merge(int[]... x) {
int[] xlength_array = new int[x.length];
xlength_array[0] = x[0].length;
for (int i = 1; i < x.length; i++)
xlength_array[i] = x[i].length + xlength_array[i - 1];
int[] array = new int[xlength_array[x.length - 1]];
System.arraycopy(x[0], 0, array, 0, x[0].length);
for (int i = 1; i < x.length; i++)
System.arraycopy(x[i], 0, array, xlength_array[i - 1], x[i].length);
return array;
}
// I didn't favor this insertColumns method because it was so different from insertRows()
// and it just seemed more likely that someone would want to insert arrays rather than
// whole matrices. See the new version below.
/* public static int[][] insertColumns(int[][] x, int J, int[]... y) {
int[][] array = new int[x.length][x[0].length + y[0].length];
for (int i = 0; i < array.length; i++) {
System.arraycopy(x[i], 0, array[i], 0, J);
System.arraycopy(y[i], 0, array[i], J, y[i].length);
System.arraycopy(x[i], J, array[i], J + y[i].length, x[i].length - J);
}
return array;
}
*/
/*public static int[][] insertColumn(int[][] x, int[] y, int J) {
int[][] array = new int[x.length][x[0].length + 1];
for (int i = 0; i < array.length; i++) {
System.arraycopy(x[i], 0, array[i], 0, J);
array[i][J] = y[i];
System.arraycopy(x[i], J, array[i], J + 1, x[i].length - J);
}
return array;
}*/
/**
* Insert any number of arrays between 2 columns of a matrix. Size of the arrays must
* equal number of rows in the matrix.
* Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,23,24,25,26}};
* int[] b = {00,11,22,33,44}, c = {55,66,77,88,99};
* int[][] z = insertColumns(a, 2, b, c);
* input matrix is:
* 0 1 2 3 4
* 1 7 8 9 10
* 2 13 14 15 16
* 3 19 20 21 22
* 4 23 24 25 26
* result is:
* 0 1 0 55 2 3 4
* 1 7 11 66 8 9 10
* 2 13 22 77 14 15 16
* 3 19 33 88 20 21 22
* 4 23 44 99 24 25 26
*
* @param x Input m x n matrix.
* @param J Index of column before which the new columns will be inserted.
* @param y The arrays to be inserted
* @return New matrix with added columns.
*/
public static int[][] insertColumns(int[][] x, int J, int[]... y) {
return transpose(insertRows(transpose(x), J, y));
}
/**
* Insert any number of arrays between 2 rows of a matrix. Size of the arrays must
* equal number of columns in the matrix.
* Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22}};
* int[] b = {0,11,22,33,44}, c = {55,66,77,88,99};
* int[][] z = insertRows(a, 1, b, c);
* result is:
* 0 1 2 3 4
* 0 11 22 33 44
* 55 66 77 88 99
* 1 7 8 9 10
* 2 13 14 15 16
* 3 19 20 21 22
*
* @param x Input m x n matrix.
* @param I Index of row before which the new rows will be inserted.
* @param y The arrays to be inserted
* @return New matrix with added rows.
*/
public static int[][] insertRows(int[][] x, int I, int[]... y) {
int[][] array = new int[x.length + y.length][x[0].length];
for (int i = 0; i < I; i++)
System.arraycopy(x[i], 0, array[i], 0, x[i].length);
for (int i = 0; i < y.length; i++)
System.arraycopy(y[i], 0, array[i + I], 0, y[i].length);
for (int i = 0; i < x.length - I; i++)
System.arraycopy(x[i + I], 0, array[i + I + y.length], 0, x[i].length);
return array;
}
/*public static int[][] insertRow(int[][] x, int[] y, int I) {
int[][] array = new int[x.length + 1][x[0].length];
for (int i = 0; i < I; i++)
System.arraycopy(x[i], 0, array[i], 0, x[i].length);
System.arraycopy(y, 0, array[I], 0, y.length);
for (int i = 0; i < x.length - I; i++)
System.arraycopy(x[i + I], 0, array[i + I + 1], 0, x[i].length);
return array;
}*/
/**
* Insert any number of values, or a single array, between 2 elements of an array.
* Example:
*
* int[] b = {00,11,22,33,44}, c = {55,66,77,88,99};
* int[] z = insert(b, 2, 333, 444);
* result is:
* 0 11 333 444 22 33 44
* int[] z = insert(b, 2, c);
* result is:
* 0 11 55 66 77 88 99 22 33 44
*
* @param x Input array.
* @param I Index of element before which the values will be inserted.
* @param y Values to be inserted. Can also be a single array.
* @return Expanded array.
*/
public static int[] insert(int[] x, int I, int... y) {
int[] array = new int[x.length + y.length];
System.arraycopy(x, 0, array, 0, I);
System.arraycopy(y, 0, array, I, y.length);
System.arraycopy(x, I, array, I + y.length, x.length - I);
return array;
}
/**
* Deletes a range of columns from a matrix.
* Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,23,24,25,26}};
* int[][] z = deleteColumnsRange(a, 1, 3);
* result is:
* 0 4
* 1 10
* 2 16
* 3 22
* 4 26
*
* @param x The input matrix
* @param J1 The Index of the first column to delete.
* @param J2 The index of the last column to delete.
* @return The reduced matrix.
*/
public static int[][] deleteColumnsRange(int[][] x, int J1, int J2) {
int[][] array = new int[x.length][x[0].length - (J2 - J1 + 1)];
for (int i = 0; i < array.length; i++) {
System.arraycopy(x[i], 0, array[i], 0, J1);
//if (J2
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,23,24,25,26}};
* int[][] z = deleteColumns(a, 1, 3);
* result is:
* 0 2 4
* 1 8 10
* 2 14 16
* 3 20 22
* 4 24 26
*
* @param x The input matrix
* @param J The indices of the columns to be deleted. There must be no more indices listed
* than there are columns in the input matrix.
* @return The reduced matrix.
*/
public static int[][] deleteColumns(int[][] x, int... J) {
/*int[][] array = new int[x.length][x[0].length - J.length];
for (int i = 0; i < array.length; i++) {
System.arraycopy(x[i], 0, array[i], 0, J[0]);
for (int j = 0; j < J.length - 1; j++)
System.arraycopy(x[i], J[j] + 1, array[i], J[j] - j, J[j + 1] - J[j] - 1);
System.arraycopy(x[i], J[J.length - 1] + 1, array[i], J[J.length - 1] - J.length + 1, x[i].length - J[J.length - 1] - 1);
}
return array;*/
// TODO improve efficiency here
return transpose(deleteRows(transpose(x), J));
}
/**
* Deletes a range of rows from a matrix.
* Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,23,24,25,26}};
* int[][] z = deleteRowsRange(a, 1, 3);
* result is:
* 0 1 2 3 4
* 4 23 24 25 26
*
* @param x The input matrix
* @param I1 The Index of the first row to delete.
* @param I2 The index of the last row to delete.
* @return The reduced matrix.
*/
public static int[][] deleteRowsRange(int[][] x, int I1, int I2) {
int[][] array = new int[x.length - (I2 - I1 + 1)][x[0].length];
for (int i = 0; i < I1; i++)
System.arraycopy(x[i], 0, array[i], 0, x[i].length);
for (int i = 0; i < x.length - I2 - 1; i++)
System.arraycopy(x[i + I2 + 1], 0, array[i + I1], 0, x[i].length);
return array;
}
/**
* Deletes a list of rows from a matrix.
* Example:
*
* int[][] a = {{0,1,2,3,4},{1,7,8,9,10},{2,13,14,15,16},{3,19,20,21,22},{4,23,24,25,26}};
* int[][] z = deleteRows(a, 1, 3);
* result is:
* 0 1 2 3 4
* 2 13 14 15 16
* 4 23 24 25 26
*
* @param x The input matrix
* @param I The indices of the rows to delete.
* @return The reduced matrix.
*/
public static int[][] deleteRows(int[][] x, int... I) {
int[][] array = new int[x.length - I.length][x[0].length];
int i2 = 0;
for (int i = 0; i < x.length; i++) {
if (!into(i, I)) {
System.arraycopy(x[i], 0, array[i2], 0, x[i].length);
i2++;
}
}
/*for (int i = 0; i < I[0]; i++)
System.arraycopy(x[i], 0, array[i], 0, x[i].length);
for (int j = 0; j < I.length - 1; j++)
for (int i = I[j] + 1; i < I[j + 1]; i++)
System.arraycopy(x[i], 0, array[i - j], 0, x[i].length);
for (int i = I[I.length - 1] + 1; i < x.length; i++)
System.arraycopy(x[i], 0, array[i - I.length], 0, x[i].length);*/
return array;
}
/**
* Delete a range of elements from an array.
* Example:
*
* int[] b = {00,11,22,33,44};
* int[] z = deleteRange(b, 1, 3);
* Result is:
* 0 44
*
* @param x Input array
* @param J1 Index of first element to delete. Must be > = 0 and < = x.length
* @param J2 Index of last element to delete. Must be >= J1 and < = x.length
* @return Reduced array.
*/
public static int[] deleteRange(int[] x, int J1, int J2) {
int[] array = new int[x.length - (J2 - J1 + 1)];
System.arraycopy(x, 0, array, 0, J1);
//if (J2
*
* int[] b = {00,11,22,33,44};
* int[] z = deleteRange(b, 1, 3);
* Result is:
* 0 22 44
*
* @param x Input array
* @param J Index of elements to delete. Each must be > = 0 and < x.length
* @return Reduced array.
*/
public static int[] delete(int[] x, int... J) {
int[] array = new int[x.length - J.length];
int j2 = 0;
for (int j = 0; j < x.length; j++) {
if (!into(j, J)) {
array[j2] = x[j];
j2++;
}
}
/*System.arraycopy(x, 0, array, 0, J[0]);
for (int j = 0; j < J.length - 1; j++)
System.arraycopy(x, J[j] + 1, array, J[j] - j, J[j + 1] - J[j] - 1);
System.arraycopy(x, J[J.length - 1] + 1, array, J[J.length - 1] - J.length + 1, x.length - J[J.length - 1] - 1);*/
return array;
}
/**
* Determines if a value is within an array
* @param i Value to be searched for.
* @param I array to be searched
* @return true if found. fales if not.
*/
private static boolean into(int i, int[] I) {
boolean in = false;
for (int j = 0; j < I.length; j++) {
in = in || (i == I[j]);
}
return in;
}
// min/max methods
/**
* Finds the minimum value in each column of a matrix.
* Example:
*
* int[][] a = {{0, 13, 22, 3, 44},
* {1, 7, 28, 9, 10},
* {2, 1, 14, 15, 6},
* {3, 19, 20, 21, 2},
* {4, 23, 24, 25, 6}};
* int[] z = min(a);
* Result is:
* 0 1 14 3 2
*
* @param M The input matrix
* @return Array of minimums from each column of M.
*/
public static int[] min(int[][] M) {
int[] min = new int[M[0].length];
for (int j = 0; j < min.length; j++) {
min[j] = M[0][j];
for (int i = 1; i < M.length; i++)
min[j] = Math.min(min[j], M[i][j]);
}
return min;
}
/**
* Finds minimum value in either a list of numbers or a single array.
* @param M Can be a list of values e.g. min(1,22,333,.4) or an array.
* @return The minimum value.
*/
public static int min(int... M) {
int min = M[0];
for (int i = 1; i < M.length; i++)
min = Math.min(min, M[i]);
return min;
}
/**
* Finds the maximum value in each column of a matrix.
* Example:
*
* int[][] a = {{0, 1, 2, 3, 4},
* {1, 7, 88, 9, 10},
* {2, 13, 14, 15, 16},
* {3, 19, 20, 201, 22},
* {4, 23, 24, 25, 26}};
* int[] z = max(a);
* Result is:
* 4 23 88 201 26
*
* @param M The input matrix
* @return Array of maximums from each column of M.
*/
public static int[] max(int[][] M) {
int[] max = new int[M[0].length];
for (int j = 0; j < max.length; j++) {
max[j] = M[0][j];
for (int i = 1; i < M.length; i++)
max[j] = Math.max(max[j], M[i][j]);
}
return max;
}
/**
* Finds maximum value in either a list of numbers or a single array.
* @param M Can be a list of values e.g. min(1,22,333,.4) or an array.
* @return The maximum value.
*/
public static int max(int... M) {
int max = M[0];
for (int i = 1; i < M.length; i++)
max = Math.max(max, M[i]);
return max;
}
/**
* Finds the indices of the minimum values in each column of a matrix.
* Example:
*
* int[][] a = {{0, 13, 22, 3, 44},
* {1, 7, 28, 9, 10},
* {2, 1, 14, 15, 6},
* {3, 19, 20, 21, 2},
* {4, 23, 24, 25, 6}};
* int[] z = minIndex(a);
* Result is:
* 0 2 2 0 3
*
* @param M Input matrix.
* @return Array of indices of the minimums from each column of M.
*/
public static int[] minIndex(int[][] M) {
int[] minI = new int[M[0].length];
for (int j = 0; j < minI.length; j++) {
minI[j] = 0;
for (int i = 1; i < M.length; i++)
if (M[i][j] < M[minI[j]][j])
minI[j] = i;
}
return minI;
}
/**
* Finds the index of the minumum value in a list of values or an array.
* @param M Can be a list of values e.g. minIndex(11,22,44,2) or an array
* @return index of minimum value in M
*/
public static int minIndex(int... M) {
int minI = 0;
for (int i = 1; i < M.length; i++)
if (M[i] < M[minI])
minI = i;
return minI;
}
/**
* Finds the indices of the maximum values in each column of a matrix.
* Example:
*
* int[][] a = {{0, 1, 2, 3, 4},
* {1, 7, 88, 9, 10},
* {2, 13, 14, 15, 16},
* {3, 19, 20, 201, 22},
* {4, 23, 24, 25, 26}};
* int[] z = maxIndex(a);
* Result is:
* 4 4 1 3 4
*
* @param M Input matrix.
* @return Array of indices of the maximums from each column of M.
*/
public static int[] maxIndex(int[][] M) {
int[] maxI = new int[M[0].length];
for (int j = 0; j < maxI.length; j++) {
maxI[j] = 0;
for (int i = 1; i < M.length; i++)
if (M[i][j] > M[maxI[j]][j])
maxI[j] = i;
}
return maxI;
}
/**
* Finds the index of the maximum value in a list of values or an array.
* @param M Can be a list of values e.g. maxIndex(11,22,44,2) or an array
* @return index of maximum value in M
*/
public static int maxIndex(int... M) {
int maxI = 0;
for (int i = 1; i < M.length; i++)
if (M[i] > M[maxI])
maxI = i;
return maxI;
}
// cumulative methods
/**
* Calculate the sum of the values in an array
* @param v input array
* @return sum of values in v
*/
public static int sum(int[] v) {
int m = v.length;
int s = 0;
for (int i = 0; i < m; i++)
s += v[i];
return s;
}
/**
* Calculates the sum of each column in a matrix.
* @param v
* @return Array. value of i'th element is sum of values in column(i)
*/
public static int[] sum(int[][] v) {
int m = v.length;
int n = v[0].length;
int[] X = new int[n];
int s;
for (int j = 0; j < n; j++) {
s = 0;
for (int i = 0; i < m; i++)
s += v[i][j];
X[j] = s;
}
return X;
}
/**
* Calculates the cumulative sum of an array. Think of it as an integral.
* Example:
*
* int[] b = {0,1,2,3,4};
* int[] z = cumSum(b);
* result is:
* 0 1 3 6 10
*
* @param v Input array.
* @return Output array of same length as v.
*/
public static int[] cumSum(int[] v) {
int m = v.length;
int[] X = new int[m];
int s = 0;
for (int i = 0; i < m; i++) {
s += v[i];
X[i] = s;
}
return X;
}
/**
* Calculates the cumulative sum of each column in a matrix.
* Example:
*
* int[][] a = {{0, 1, 2, 3, 4},
* {1, 7, 8, 9, 10},
* {2, 13, 14, 15, 16},
* {3, 19, 20, 21, 22},
* {4, 23, 24, 25, 26}};
* int[][] z = cumSum(a);
* result is:
* 0 1 2 3 4
* 1 8 10 12 14
* 3 21 24 27 30
* 6 40 44 48 52
* 10 63 68 73 78
*
* @param v
* @return Output matrix. Each column is the cumulative sum of each column in v.
*/
public static int[][] cumSum(int[][] v) {
int m = v.length;
int n = v[0].length;
int[][] X = new int[m][n];
int s;
for (int j = 0; j < n; j++) {
s = 0;
for (int i = 0; i < m; i++) {
s += v[i][j];
X[i][j] = s;
}
}
return X;
}
/**
* Calculates the product of the values in an array.
* @param v Input array.
* @return The product of the values in v.
*/
public static int product(int[] v) {
int m = v.length;
int p = 1;
for (int i = 0; i < m; i++)
p *= v[i];
return p;
}
/**
* Calculates the product of the values in each column of a matrix.
* @param v Input matrix.
* @return An array of n values where n=number of columns in v. The i'th element is product
* of the values in the i'th column of v.
*/
public static int[] product(int[][] v) {
int m = v.length;
int n = v[0].length;
int[] X = new int[n];
for (int j = 0; j < n; j++) {
int p = 1;
for (int i = 0; i < m; i++)
p *= v[i][j];
X[j] = p;
}
return X;
}
/**
* Calculates cumulative product of the values in an array.
* Example:
*
* int[] b = {1,2,3,4};
* int[] z = cumProduct(b);
* Result is:
* 1 2 6 24
*
* @param v Input array
* @return Out put array of same size as v.
*/
public static int[] cumProduct(int[] v) {
int m = v.length;
int[] X = new int[m];
int s = 1;
for (int i = 0; i < m; i++) {
s *= v[i];
X[i] = s;
}
return X;
}
/**
* Calculates the cumulative product of each column in a matrix.
* Example:
*
* int[][] a = {{0, 1, 2, 3, 4},
* {1, 7, 8, 9, 10},
* {2, 13, 14, 15, 16},
* {3, 19, 20, 21, 22},
* {4, 23, 24, 25, 26}};
* Result is:
* 0 1 2 3 4
* 0 7 16 27 40
* 0 91 224 405 640
* 0 1729 4480 8505 14080
* 0 39767 107520 212625 366080
*
* @param v
* @return Output matrix. Each column is the cumulative product of each column in v.
*/
public static int[][] cumProduct(int[][] v) {
int m = v.length;
int n = v[0].length;
int[][] X = new int[m][n];
int s;
for (int j = 0; j < n; j++) {
s = 1;
for (int i = 0; i < m; i++) {
s *= v[i][j];
X[i][j] = s;
}
}
return X;
}
// print methods
/**
* Generates a string that holds a nicely organized version of a matrix or array.
* Note the lower case S. It's tostring() not toString().
* Example:
*
* int[][] a = {{1,22,333},{4444,555,7}};
* System.out.println(tostring(a));
* result is:
* 1 22 333
* 4444 555 7
*
* @param v Matrix or array
* @return A string of a nicely organized version of the matrix or array.
*/
public static String toString(int[]... v) {
StringBuffer str = new StringBuffer();
for (int i = 0; i < v.length; i++) {
for (int j = 0; j < v[i].length - 1; j++)
str.append(v[i][j] + " ");
str.append(v[i][v[i].length - 1]);
if (i < v.length - 1)
str.append("\n");
}
return str.toString();
}
/**
* Generates a string that holds a nicely organized version of a matrix or array.
* Uses format specifier, e.g. "%5d"
* An extra space is automatically included.
* Note the lower case S. It's tostring() not toString().
* Example:
*
* int[][] a = fill(2, 3, 555);
* System.out.println(tostring("%11d", a));
* result is:
* 555 555 555
* 555 555 555
*
* @param format A standard format specifier for one value
* @param v Matrix or array
* @return A string of a nicely organized version of the matrix or array.
*/
public static String toString(String format, int[]... v) {
StringBuffer str = new StringBuffer();
for (int i = 0; i < v.length; i++) {
for (int j = 0; j < v[i].length - 1; j++)
str.append(String.format(format + " ", v[i][j]));
str.append(String.format(format, v[i][v[i].length - 1]));
if (i < v.length - 1)
str.append("\n");
}
return str.toString();
}
// transpose
/**
* Transposes an mxn matrix into an nxm matrix. Each row of the input matrix becomes a column in the
* output matrix.
* @param M Input matrix.
* @return Transposed version of M.
*/
public static int[][] transpose(int[][] M) {
int[][] tM = new int[M[0].length][M.length];
for (int i = 0; i < tM.length; i++)
for (int j = 0; j < tM[0].length; j++)
tM[i][j] = M[j][i];
return tM;
}
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