Problem: Gaussian-Weighted Binary Image Band Analysis

The problem involves locating binary file AA in three paths, reading flipped 600x600 bands, using Gaussian spatial weighting to compute metrics like FFT magnitudes, energies, mean/variance, pixel counts, and their differences, and returning results for band data analysis or testing.


Input/Output: The problem takes function-specific input parameters (e.g., integer band_num, double radius_threshold/magnitude_threshold, integers band1/band2) and requires a binary file "AA" stored in paths test_data/AA, ../test_data/AA, or ../../test_data/AA. The file contains consecutive 600x600 unsigned char bands. It first locates "AA"; if not found, it outputs an error and returns -1. For valid files, it reads the specified band(s), flips rows vertically, then computes metrics (weighted center FFT magnitude, weighted energy within radius, weighted variance, weighted total energy, weighted pixel count over threshold, sum of energy differences, absolute FFT difference) using Gaussian spatial weights (centered at the image midpoint, sigma = max(rows, cols)/4). It returns the computed double (or integer for pixel count) result for each subproblem.

Required dependencies:
#include <vector>
#include <string>
#include <fstream>
#include <iostream>
#include <cmath>
#include <complex>
#include <iomanip>
#include <cstdlib>
using namespace std;

Sub-steps:
step_number: 1
step_description_prompt: Please write a C++ function named problem_19_1 that takes an int parameter band_num and returns a double, which implements the function of reading the specified band data from the binary file "AA" and calculating the weighted FFT center magnitude with Gaussian spatial weighting.

Function definition: double problem_19_1(int band_num);

Algorithm flow:
1. Search for the file "AA" in the paths "test_data/AA", "../test_data/AA", "../../test_data/AA" in order, and use the first existing path as the file path. If no file is found, output an error message and return -1.0.
2. Read the binary file: the data has 600 rows and 600 columns. Skip (band_num - 1) * 600 * 600 bytes from the start of the file, then read each row of data, and store the i-th row of the file as the (600 - 1 - i)-th row of the 2D vector band (rows are flipped).
3. Calculate the weighted FFT center magnitude: use PI_FFT = 3.14159265358979323846, center at (300, 300) (since rows = cols = 600), sigma = max(600, 600) / 4.0. For each (i, j) in 0~599, compute the weight as exp(-((i - 300.0)² + (j - 300.0)²) / (2 * sigma²)), compute the phase as -2.0 * PI_FFT * ((i - 300) * 300 + (j - 300) * 300) / (600 * 600), calculate the weighted complex sum of band[i][j] * complex(cos(phase), sin(phase)) * weight, and sum the weights.
4. Return the absolute value of the complex sum divided by the weight sum (if weight sum > 1e-10, otherwise return the absolute value of the complex sum).

Note: Include necessary headers such as <bits/stdc++.h>, <cmath>, <iomanip>, <numeric>, <random>, <fstream>, <complex>, <algorithm>, and use namespace std. When reading the file, open it in binary mode, use ifstream to check if the file exists, and read data using seekg and read functions. Standard library functions are assumed to be available.
function_header: double problem_19_1(int band_num)
test_cases: // ==================== Main function: Testing ====================

int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 19.1" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-3;
    
    // Test 1
    int band1 = 1;

    double result1 = problem_19_1(band1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 49.596764;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;

    double result2 = problem_19_1(band2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 22.584103;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;

    double result3 = problem_19_1(band3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 25.597810;  // Expected value (updated from actual result)
        if (abs(result3 - correct3) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 2
step_description_prompt: Please write a C++ function named problem_19_2 that takes an integer band_num and a double radius_threshold as parameters, and returns a double value representing the weighted energy of the specified band image within the given radius threshold. The function signature is double problem_19_2(int band_num, double radius_threshold). First, search for the data file "AA" in three paths: "test_data/AA", "../test_data/AA", "../../test_data/AA". If none exist, output "Error: Cannot find data file AA" to cerr and return -1.0. Then, read the 600x600 binary image data of the specified band: skip (band_num - 1) * 600 * 600 bytes from the file start. When reading rows, store the i-th file row as the (599 - i)-th row in the band matrix (rows are flipped). Next, calculate the weighted energy: For each pixel (i,j), compute the distance to the center (300,300). If distance ≤ radius_threshold, compute Gaussian weight with sigma = 150.0 (max(600,600)/4), where weight = exp(-((i-300.0)^2 + (j-300.0)^2)/(2*sigma*sigma)). Accumulate band[i][j] * band[i][j] * weight to total_energy. Return total_energy. Ensure file reading uses binary mode, and the band matrix is a 2D vector of unsigned char with size 600x600 initialized to 0.
function_header: double problem_19_2(int band_num, double radius_threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 19.2" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-3;
    
    // Test 1
    int band1 = 1;
    double radius1 = 50.0;

    double result1 = problem_19_2(band1, radius1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 54638606.674529;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;
    double radius2 = 100.0;

    double result2 = problem_19_2(band2, radius2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 40600339.587099;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;
    double radius3 = 150.0;

    double result3 = problem_19_2(band3, radius3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 98671830.682563;  // Expected value (updated from actual result)
        if (abs(result3 - correct3) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 3
step_description_prompt: Please write a C++ function named problem_19_3 with parameter int band_num that returns a double, which calculates the weighted variance of the specified band's image data using Gaussian spatial weighting.
The function is defined as double problem_19_3(int band_num);
Algorithm flow: 1. Check three paths ("test_data/AA", "../test_data/AA", "../../test_data/AA") to find the existing file. If no file is found, output "Error: Cannot find data file AA" to cerr and return -1.0. 2. Read the specified band's data: skip (band_num - 1) * 600 * 600 bytes from the file start, read 600x600 data into a vector<vector<unsigned char>> original with rows reversed (rows - 1 - i). 3. Compute Gaussian weights for each pixel based on distance to center (center_i = 600/2.0, center_j = 600/2.0, sigma = max(600,600)/4.0). 4. Calculate weighted mean using the weights. 5. Calculate weighted variance using the same weights and return variance divided by weight sum (handle weight_sum < 1e-10).
When reading the file, use ios::binary mode. Functions like ifstream::open, seekg, read are available.
function_header: double problem_19_3(int band_num)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 19.3" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    int band1 = 1;

    double result1 = problem_19_3(band1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 44.370669;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;

    double result2 = problem_19_3(band2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 26.573545;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;

    double result3 = problem_19_3(band3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 94.112739;  // Expected value (updated from actual result)
        if (abs(result3 - correct3) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 4
step_description_prompt: Please write a C++ function named problem_19_4 that calculates the weighted energy of a specific band from a binary data file using Gaussian spatial weighting based on the distance from the center of the band.

Function definition: double problem_19_4(int band_num);

Algorithm flow:
1. Try opening the binary file from paths "test_data/AA", "../test_data/AA", "../../test_data/AA". If no path is valid, output "Error: Cannot find data file AA" to cerr and return -1.0.
2. Initialize a 600x600 vector<vector<unsigned char>> band with zeros.
3. Read the specified band from the binary file: Skip (band_num - 1) * 600 * 600 bytes from the start. Read each row (600 columns) and store rows in reverse order (band[599 - i][j] = buf[j] for row index i).
4. Calculate weighted energy: For each pixel in the 600x600 band, compute the Gaussian weight using the squared Euclidean distance from the pixel to the center (center_i = 300.0, center_j = 300.0, sigma = 150.0). The weight is exp(-dist_sq / (2.0 * sigma * sigma)). Sum (static_cast<double>(v) * v * weight) for all pixels, where v is the pixel value (unsigned char). Return the sum as the energy.

Note: Assume all used functions (like ifstream, vector operations) are already defined. Read the file in binary mode and handle file operations correctly.
function_header: double problem_19_4(int band_num)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 19.4" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-3;
    
    // Test 1
    int band1 = 1;

    double result1 = problem_19_4(band1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 863338566.166085;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;

    double result2 = problem_19_4(band2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 183480875.393759;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;

    double result3 = problem_19_4(band3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 247329869.948873;  // Expected value (updated from actual result)
        if (abs(result3 - correct3) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 5
step_description_prompt: Please write a C++ function named problem_19_5 that takes an integer band_num (the band index to read) and a double magnitude_threshold (pixel value threshold), and returns an integer representing the rounded Gaussian-weighted count of pixels above the threshold. 

The function definition is: int problem_19_5(int band_num, double magnitude_threshold); 

Algorithm steps: 1. Check three paths ("test_data/AA", "../test_data/AA", "../../test_data/AA") to find an existing binary file. If no file exists, output "Error: Cannot find data file AA" to cerr and return -1. 2. Read 600x600 band data from the file: skip (band_num-1)*600*600 bytes using seekg, read each row into a unsigned char buffer, then store rows in reverse order (rows-1-i) into a 2D vector band. 3. Compute center (300.0, 300.0) and sigma=150.0 (max(600,600)/4). For each pixel (i,j), if band[i][j] > magnitude_threshold, calculate squared distance to center, weight=exp(-dist_sq/(2*sigma*sigma)), add weight to weighted_count. 4. Return (int)(weighted_count + 0.5). 

Notes: Open files in ios::binary mode. Use ifstream to check file existence and read data. Assume necessary headers (e.g., <vector>, <fstream>, <cmath>, <iostream>) and pre-defined functions are available.
function_header: int problem_19_5(int band_num, double magnitude_threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 19.5" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1 = 1;
    double magnitude1 = 100.0;

    int result1 = problem_19_5(band1, magnitude1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 921;  // Expected value (updated from actual result)
        if (result1 == correct1) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;
    double magnitude2 = 150.0;

    int result2 = problem_19_5(band2, magnitude2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 0;  // Expected value (updated from actual result)
        if (result2 == correct2) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;
    double magnitude3 = 200.0;

    int result3 = problem_19_5(band3, magnitude3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 0;  // Expected value (updated from actual result)
        if (result3 == correct3) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 6
step_description_prompt: Please use C++ code to create a function named problem_19_6 that takes an integer parameter band_num and returns a double, which computes a feature by analyzing weighted energy differences from a specific band of a binary image file.
Function definition: double problem_19_6(int band_num);
Algorithm flow:1. Check three paths ("test_data/AA", "../test_data/AA", "../../test_data/AA") to find the existing binary file; if not found, output "Error: Cannot find data file AA" to cerr and return -1.0.2. Read the 600x600 target band data by skipping (band_num-1)*600*600 bytes from the file start, and flip the row order (store row i as rows-1 -i in the output band vector of unsigned char).3. Compute three weighted energies (radius1=50.0, radius2=100.0, radius3=150.0): for each pixel within the radius from the center (rows/2, cols/2), calculate Gaussian weight (sigma = max(rows,cols)/4.0) based on distance to the center (rows/2.0, cols/2.0), then sum (pixel value squared * weight) for each radius.4. Return the sum of absolute differences between consecutive energies (abs(energy1-energy2) + abs(energy2-energy3)).
Handle binary file reading correctly, and assume other called functions are pre-defined.
function_header: double problem_19_6(int band_num)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 19.6" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-3;
    
    // Test 1
    int band1 = 1;

    double result1 = problem_19_6(band1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 314044736.825382;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;

    double result2 = problem_19_6(band2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 64203951.662157;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;

    double result3 = problem_19_6(band3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 83090250.961952;  // Expected value (updated from actual result)
        if (abs(result3 - correct3) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 7
step_description_prompt: Please write a C++ function named problem_19_7 that takes two integers band1 and band2 as parameters, returns a double, and computes the absolute difference between weighted FFT results of two specified bands from a binary file. Function definition: double problem_19_7(int band1, int band2); Algorithm flow: 1. Check paths "test_data/AA", "../test_data/AA", "../../test_data/AA" to find the binary file; output error and return -1.0 if not found. 2. Read 600x600 unsigned char data for band1 and band2: open in binary mode, skip (band-1)*600*600 bytes, read each row, and store in rows-1-i index (vertical flip). 3. For each band, compute weighted FFT using Gaussian weight (sigma = max(600,600)/4, based on squared distance to center (300.0, 300.0)), phase as -2*3.14159265358979323846*((i-300)*300 + (j-300)*300)/(600*600); accumulate weighted complex values and weight sum, normalize the absolute value by weight sum if sum>1e-10. 4. Return the absolute difference between the two FFT results. Ensure file reading follows the described steps and use existing pre-defined functions.
function_header: double problem_19_7(int band1, int band2)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 19.7" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-3;
    
    // Test 1
    int band1_1 = 1, band2_1 = 2;

    double result1 = problem_19_7(band1_1, band2_1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 27.012661;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band1_2 = 2, band2_2 = 3;

    double result2 = problem_19_7(band1_2, band2_2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 3.013707;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band1_3 = 3, band2_3 = 4;

    double result3 = problem_19_7(band1_3, band2_3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 2.372783;  // Expected value (updated from actual result)
        if (abs(result3 - correct3) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 8
step_description_prompt: Please write a C++ function named problem_19_8 that takes an int parameter band_num and returns a double. This function computes a result based on spatial and frequency energy of a specified band from a binary image file. Function definition: double problem_19_8(int band_num); Algorithm steps: 1. Check paths in {"test_data/AA", "substep/test_data/AA", "../test_data/AA", "../../test_data/AA", "AA"} to find the existing binary file "AA". If not found, output "Error: Cannot find data file AA" to cerr and return -1.0. 2. Read band data with rows=600 and cols=600: skip (band_num-1)*rows*cols bytes from the file start, read each row into a buffer, then store in a 2D vector<vector<unsigned char>> band with row index reversed as rows-1-i. 3. Calculate spatial_energy: use sigma = max(rows,cols)/4.5, center_i=rows/2.0, center_j=cols/2.0. For each pixel (i,j), compute dist_sq=(i-center_i)^2+(j-center_j)^2, weight=1.0+0.25*exp(-dist_sq/(2*sigma*sigma)), sum band[i][j]*band[i][j]*weight. 4. Compute mean_band as the average of all elements in band. 5. Calculate freq_energy: for each pixel (i,j), compute gradient_x (abs(band[i][j+1]-band[i][j-1]) if j is not on the edge) and gradient_y (abs(band[i+1][j]-band[i-1][j]) if i is not on the edge). Compute dist_sq same as step3, weight=1.0+0.2*exp(-dist_sq/(2*sigma*sigma)), sum (gradient_x²+gradient_y²)*weight*(1.0+0.1*band_num/10.0). 6. Compute total_energy=spatial_energy+freq_energy. If total_energy<1e-10, return 0.0. Compute ratio=freq_energy/(spatial_energy+1e-6). Result=log(1.0+ratio*10.0)*15.0 + band_num*0.5. Return the result. Note: Ensure correct binary file reading, path checking, and row reversal. Pre-defined functions (e.g., ifstream) are available.
function_header: double problem_19_8(int band_num)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 19.8" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    double correct1 = 1.370275;
    int band1 = 1;
    double result1 = problem_19_8(band1);
    if (abs(result1 - correct1) < tolerance) {
        cout << "Correct" << endl;
        correct_count++;
    } else {
        cout << "Wrong" << endl;
    }

    // Test 2
    double correct2 = 3.123006;
    int band2 = 2;
    double result2 = problem_19_8(band2);
    if (abs(result2 - correct2) < tolerance) {
        cout << "Correct" << endl;
        correct_count++;
    } else {
        cout << "Wrong" << endl;
        cout << "Expected: " << correct2 << ", Got: " << result2 << endl;
    }

    // Test 3
    double correct3 = 6.332952;
    int band3 = 3;
    double result3 = problem_19_8(band3);
    if (abs(result3 - correct3) < tolerance) {
        cout << "Correct" << endl;
        correct_count++;
    } else {
        cout << "Wrong" << endl;
        cout << "Expected: " << correct3 << ", Got: " << result3 << endl;
    }
    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 9
step_description_prompt: Please write a C++ function named problem_19_9 that calculates the ratio of filtered weighted energy to total weighted energy for a specified band of image data.
The function definition is double problem_19_9(int band_num, double radius_threshold).
Algorithm flow: 1. Search for the binary file "AA" in paths {"test_data/AA", "../test_data/AA", "../../test_data/AA"}; if not found, output "Error: Cannot find data file AA" to cerr and return -1.0. 2. Read the band_num-th band from the binary file into a 600x600 vector<vector<unsigned char>> band, reversing rows by storing buf[j] in band[rows-1 -i][j] (rows=cols=600). 3. Compute center_i=600/2.0, center_j=600/2.0, sigma=max(600,600)/4.0, center_r=600/2, center_c=600/2. 4. Calculate filtered_energy: sum (band[i][j]*band[i][j]*weight) for pixels where distance from (center_r,center_c) ≤ radius_threshold; weight is exp(-((i-center_i)^2 + (j-center_j)^2)/(2*sigma*sigma)). 5. Calculate total_energy: sum (static_cast<double>(band[i][j])*band[i][j]*weight) for all pixels. 6. If total_energy < 1e-10 return 0.0; else return filtered_energy/total_energy.
The function reads the binary file as described, handles row reversal for the band data, and applies Gaussian weighting. Ensure correct file reading: skip (band_num-1)*rows*cols bytes to reach the specified band, use a buffer to read each row. Assume necessary headers and pre-defined functions are available.
function_header: double problem_19_9(int band_num, double radius_threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 19.9" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    int band1 = 1;
    double radius1 = 50.0;

    double result1 = problem_19_9(band1, radius1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 0.063288;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;
    double radius2 = 100.0;

    double result2 = problem_19_9(band2, radius2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 0.221278;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;
    double radius3 = 150.0;

    double result3 = problem_19_9(band3, radius3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 0.398948;  // Expected value (updated from actual result)
        if (abs(result3 - correct3) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

General solution:

General tests: