Question

（与此问题有点相关Linear fit including all errors with NumPy/SciPy，并从此Linear fitting in python with uncertainty in both x and y coordinates 借用代码）

我使用y=a*x+b使用scipy.odr（代码如下）使用x,y中的固定错误拟合线性模型（Parameters (a, b): [ 5.21806759 -4.08019995] Standard errors: [ 0.83897588 2.33472161] Squared diagonal covariance: [ 1.06304228 2.9582588 ]），我得到：

a, b

拟合Squared diagonal covariance参数的正确标准偏差值是多少？我假设必须从Standard errors值获取这些值，但这些值与ali_m如何相关？

添加

正如np.sqrt(np.diag(out.cov_beta * out.res_var))对How to compute standard error from ODR results?的回答所述，这显然与a bug in scipy.odr有关。如果使用

np.sqrt(np.diag(out.cov_beta))

（即：将协方差乘以残差方差）而不仅仅是

out.sd_beta

结果现在与(a, b)重合。

所以现在我的问题是：哪个是拟合参数out.sd_beta的正确标准偏差？是np.sqrt(np.diag(out.cov_beta * out.res_var))（相当于：np.sqrt(np.diag(out.cov_beta))）还是import numpy as np from scipy.odr import Model, RealData, ODR import random random.seed(9001) np.random.seed(117) def getData(c): """Initiate random data.""" x = np.array([0, 1, 2, 3, 4, 5]) y = np.array([i**2 + random.random() for i in x]) xerr = c * np.array([random.random() for i in x]) yerr = c * np.array([random.random() for i in x]) return x, y, xerr, yerr def linear_func(p, x): """Linear model.""" a, b = p return a * x + b def fitModel(x, y, xerr, yerr): # Create a model for fitting. linear_model = Model(linear_func) # Create a RealData object using our initiated data from above. data = RealData(x, y, sx=xerr, sy=yerr) # Set up ODR with the model and data. odr = ODR(data, linear_model, beta0=[0., 1.]) # Run the regression. out = odr.run() # Estimated parameter values beta = out.beta print("Parameters (a, b): {}".format(beta)) # Standard errors of the estimated parameters std = out.sd_beta print("Standard errors: {}".format(std)) # Covariance matrix of the estimated parameters cov = out.cov_beta stddev = np.sqrt(np.diag(cov)) print("Squared diagonal covariance: {}".format(stddev)) # Generate data and fit the model. x, y, xerr, yerr = getData(1.) fitModel(x, y, xerr, yerr)？

#ifndef ADD_PARAMETERS_GROUPBOX
#define ADD_PARAMETERS_GROUPBOX

#include <QGroupBox>
#include <QAbstractTableModel>

namespace Ui {
class AdditionalParameters;
}

class AdditionalParameters : public QGroupBox
{
    Q_OBJECT

public:

    explicit AdditionalParameters(QWidget *parent = 0);
    ~AdditionalParameters();

private:
    Ui::AdditionalParameters *ui;

signals:
    void stateChanged(int state);

private slots:
    void PARAMTER_SEL(QModelIndex box);
};

#endif // ADD_PARAMETERS_GROUPBOX

#ifndef ADD_PARAMETERS_SELECTION_TABLE
#define ADD_PARAMETERS_SELECTION_TABLE

#include <QAbstractTableModel>
#include <QString>
class MainWindow;

const int ROWS = 63;
const int COLS = 5;
class ParametersTable : public QAbstractTableModel
{
    Q_OBJECT
public:
    ParametersTable(QObject *parent);
    int rowCount(const QModelIndex &parent = QModelIndex()) const ;
    int columnCount(const QModelIndex &parent = QModelIndex()) const;
    QVariant data(const QModelIndex &index, int role = Qt::DisplayRole) const;
    QVariant headerData(int section, Qt::Orientation orientation, int role) const;
    //bool setData(const QModelIndex & index, const QVariant & value, int role = Qt::CheckStateRole);
    Qt::ItemFlags flags(const QModelIndex & index) const;

private:
     //QString m_gridData[ROWS][COLS];  //holds text entered into QTableView
     //bool m_gridData[ROWS][COLS];  //holds state entered into QTableView

signals:
    void editCompleted(const QString &);
    void stateChanged(int state);

private slots:
    //void updateTable();
    //void PARAMTER_SEL(QModelIndex box);
};




#include "add_parameters_groupbox.h"
#include "ui_add_parameters_groupbox.h"
#include "add_parameters_selection_table.h"


#include <QTableView>
#include <QAbstractTableModel>
#include <QList>
#include <QTimer>
#include <QDebug>
#include <qcheckbox.h>

QStringList paraHold;
QStringList paraSymbols;
QString Parameters[500][5];
QAbstractTableModel *paraTable;
QItemSelectionModel *selectionModel;

bool m_gridData[ROWS][COLS];

AdditionalParameters::AdditionalParameters(QWidget *parent) :
QGroupBox(parent),
ui(new Ui::AdditionalParameters)
{
    ui->setupUi(this);

    paraTable = new ParametersTable(this);
    ui->AddPara_tableView->setModel(paraTable);

    connect(ui->AddPara_tableView,SIGNAL(clicked(QModelIndex)),
            this, SLOT(PARAMTER_SEL(QModelIndex)));

    paraHold 
             << "60 xxxx"
             << "lines"
             << "of strings";
    paraSymbols
             << "60+/-"
             << "lines"
             << "of strings";

    for(int i = 0; i<(paraHold.size()); i++)
    {
        Parameters[i][0] = paraHold.at(i);
        m_gridData[i][0] = false;
//        qDebug() << "m_gridData[i][0]:" << m_gridData[i][0];
        if((!Parameters[i][0].contains("T",Qt::CaseInsensitive))
                || (Parameters[i][0].contains("FET",Qt::CaseInsensitive))
                || (Parameters[i][0].contains("NT",Qt::CaseInsensitive))
                || (Parameters[i][0].contains("LT",Qt::CaseInsensitive))
                || (Parameters[i][0].contains("TAT",Qt::CaseInsensitive))){
        Parameters[i][1] = "Current/Voltage";
        m_gridData[i][1] = true;
//        qDebug() << "m_gridData[i][1]:" << m_gridData[i][1];
        }
        if(!((Parameters[i][0].contains("V",Qt::CaseInsensitive))
             || (Parameters[i][0].contains("I_",Qt::CaseInsensitive))
             || (Parameters[i][0].contains("cell",Qt::CaseInsensitive))
             || (Parameters[i][0].contains("FET",Qt::CaseInsensitive))
             || (Parameters[i][0].contains("NT",Qt::CaseInsensitive))
             || (Parameters[i][0].contains("LT",Qt::CaseInsensitive))
             || (Parameters[i][0].contains("_SCD",Qt::CaseInsensitive))
             || (Parameters[i][0].contains("_CFA",Qt::CaseInsensitive))
             || (Parameters[i][0].contains("_OWD",Qt::CaseInsensitive))
             || (Parameters[i][0].contains("_CHG",Qt::CaseInsensitive))
             || (Parameters[i][0].contains("_DSG",Qt::CaseInsensitive))
             || (Parameters[i][0].contains("OC",Qt::CaseInsensitive)))){
        Parameters[i][2] = "Tempurature";
        m_gridData[i][2] = true;
//        qDebug() << "m_gridData[i][2]:" << m_gridData[i][2];
        }
        Parameters[i][3] = paraSymbols.at(i);
    }
    QTimer *timer = new QTimer(this);
    connect(timer, SIGNAL(timeout()), ui->AddPara_tableView, SLOT(doItemsLayout()));
//    connect(timer, SIGNAL(timeout()), ui->AddPara_tableView, SLOT(resizeColumnsToContents()));
//    QTimer::singleShot(20000, ui->AddPara_tableView, SLOT(doItemsLayout()));
    QTimer::singleShot(1000, ui->AddPara_tableView, SLOT(resizeColumnsToContents()));
    timer->start(1000);
}

AdditionalParameters::~AdditionalParameters()
{
    delete ui;
}

ParametersTable::ParametersTable(QObject *parent)
    :QAbstractTableModel(parent)
{

}

int ParametersTable::rowCount(const QModelIndex & /*parent*/) const
{
    //int pararow = Parameters.size();
    //return pararow;
    return 62;
}

int ParametersTable::columnCount(const QModelIndex & /*parent*/) const
{
    //int paracol;
    return 5;
}

QVariant ParametersTable::headerData(int section, Qt::Orientation orientation, int role) const
{
    if (role == Qt::DisplayRole)
    {
        if (orientation == Qt::Horizontal) {
            switch (section)
            {
            case 0:
                return QString("Parameter");
            case 1:
                return QString("Current/Voltage Chart");
            case 2:
                return QString("Tempurature Chart");
            case 3:
                return QString("Symbol");
            case 4:
                return QString("Color");
            }
        }
    }

    return QVariant();
}

QVariant ParametersTable::data(const QModelIndex &index, int role) const
{
    int row = index.row();
    int col = index.column();

    switch(role){
    case Qt::DisplayRole:

        return QString("%1")
                .arg(Parameters[row][col]);

        break;
    case Qt::FontRole:
        if (Parameters[row][col] != "_")
        {
            QFont boldFont;
            boldFont.setBold(true);
            return boldFont;
        }

        break;
    case Qt::BackgroundRole:

        if(col == 4)
        {
            if (Parameters[row][0].contains("cell1",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::blue);
                return redBackground;
            }
            if (Parameters[row][0].contains("cell2",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::cyan);
                return redBackground;
            }
            if (Parameters[row][0].contains("cell3",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::magenta);
                return redBackground;
            }
            if (Parameters[row][0].contains("cell4",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::yellow);
                return redBackground;
            }
            if (Parameters[row][0].contains("cell5",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::darkGray);
                return redBackground;
            }
            if (Parameters[row][0].contains("cell6",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::red);
                return redBackground;
            }
            if (Parameters[row][0].contains("cell7",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::darkGreen);
                return redBackground;
            }

            if (Parameters[row][0].contains("I_",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::green);
                return redBackground;
            }
            if ((Parameters[row][0].contains("CH",Qt::CaseInsensitive))
                 || (Parameters[row][3].contains("+",Qt::CaseInsensitive)))
            {
                QBrush redBackground(Qt::green);
                return redBackground;
            }
            if ((Parameters[row][0].contains("DS",Qt::CaseInsensitive))
                    || (Parameters[row][3].contains("-",Qt::CaseInsensitive)))
            {
                QBrush redBackground(Qt::red);
                return redBackground;
            }
            if (Parameters[row][0].contains("V_Pack",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::darkRed);
                return redBackground;
            }

            if (Parameters[row][0].contains("T_ISL",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::darkMagenta);
                return redBackground;
            }
            if (Parameters[row][0].contains("T_HS",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::darkYellow);
                return redBackground;
            }
            if (Parameters[row][0].contains("T_LS",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::darkCyan);
                return redBackground;
            }
            if (Parameters[row][0].contains("T_B",Qt::CaseInsensitive))
            {
                QBrush redBackground(Qt::darkBlue);
                return redBackground;
            }

        }
        break;
    case Qt::TextAlignmentRole:

        if (col == 3) //change text alignment only for colum 3
        {
             return Qt::AlignCenter;//+ Qt::AlignVCenter;
        }
        break;
    case Qt::CheckStateRole:

        if((col == 0) && (m_gridData[row][0] == false)){  //add a checkbox to all rows in colum 0
//            qDebug() << "m_gridData[" << row << "][0]:" << m_gridData[row][0];
            return Qt::Unchecked;
        }
        else if((col == 0) && (m_gridData[row][0] == true)){
//            qDebug() << "m_gridData[" << row << "][0]:" << m_gridData[row][0];
            return Qt::Checked;
        }

        if((Parameters[row][1].contains("Current/Voltage",Qt::CaseSensitive)
            && (col == 1)) && (m_gridData[row][1] == true)){
//            qDebug() << "m_gridData[" << row << "][1]:" << m_gridData[row][1];
            return Qt::Checked;
        }
        else if((Parameters[row][1].contains("Current/Voltage",Qt::CaseSensitive) && (col == 1))
                && (m_gridData[row][1] == false)){
//            qDebug() << "m_gridData[" << row << "][1]:" << m_gridData[row][1];
            return Qt::Unchecked;
        }

        if(Parameters[row][2].contains("Tempurature",Qt::CaseSensitive)
                && (col == 2) && (m_gridData[row][2] == true)){
//            qDebug() << "m_gridData[" << row << "][2]:" << m_gridData[row][2];
            return Qt::Checked;
        }
        else if((Parameters[row][2].contains("Tempurature",Qt::CaseSensitive)
                 && (col == 2)) && (m_gridData[row][2] == false)){
//            qDebug() << "m_gridData[" << row << "][2]:" << m_gridData[row][2];
            return Qt::Unchecked;
        }
    }
    return QVariant();
}


Qt::ItemFlags ParametersTable::flags(const QModelIndex & /*index*/) const
{
    return Qt::ItemIsSelectable |  Qt::ItemIsUserCheckable | Qt::ItemIsEnabled;
}

void AdditionalParameters::PARAMTER_SEL(QModelIndex Box)
{
    int row = Box.row();
    int col = Box.column();

    if(!Parameters[row][col].isEmpty()){
        m_gridData[row][col] = (!(m_gridData[row][col]));
        qDebug() << "PARA_SEL @ m_gridData[row][col]:(" << row << "," << col << "):" << m_gridData[row][col];
    }
    emit stateChanged(m_gridData[row][col]);

}

Answer 1

是的，out.sd_beta包含估计参数的标准偏差，它们等于参数协方差矩阵中对角线项的平方根。

如上所述，scipy.odr中存在一个错误，即您必须将out.cov_beta乘以剩余方差out.res_var才能得出实际的协方差矩阵。参数。

估计scipy.odr中拟合参数的标准偏差？

1 个答案: