使用python实现softmax回归算法，使用已知鸢尾花数据对模型进行训练，并对未知鸢尾花数据进行预测。

首先，我们需要导入必要的库和数据集：

import numpy as np
from sklearn.datasets import load_iris

iris = load_iris()
X = iris.data
y = iris.target

接着，我们将数据集分为训练集和测试集：

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

然后，我们需要对数据进行预处理。首先，我们需要对特征进行归一化处理：

from sklearn.preprocessing import StandardScaler

scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

接下来，我们需要对标签进行one-hot编码：

def one_hot(y):
    n_classes = len(np.unique(y))
    return np.eye(n_classes)[y]

y_train = one_hot(y_train)
y_test = one_hot(y_test)

现在，我们可以实现softmax回归算法。首先，我们需要定义一个softmax函数：

def softmax(z):
    e = np.exp(z - np.max(z, axis=1, keepdims=True))
    return e / np.sum(e, axis=1, keepdims=True)

然后，我们定义一个损失函数：

def cross_entropy_loss(y_true, y_pred):
    return -np.mean(np.sum(y_true * np.log(y_pred), axis=1))

接下来，我们可以开始训练模型了。我们需要定义一个函数来计算梯度：

def grad(X, y_true, y_pred):
    m = X.shape[0]
    return 1/m * np.dot(X.T, (y_pred - y_true))

然后，我们需要定义一个函数来进行模型训练：

def fit(X, y, lr=0.1, n_epochs=1000):
    n_features = X.shape[1]
    n_classes = y.shape[1]
    W = np.random.randn(n_features, n_classes)
    b = np.zeros(n_classes)
    losses = []
    for epoch in range(n_epochs):
        z = np.dot(X, W) + b
        y_pred = softmax(z)
        loss = cross_entropy_loss(y, y_pred)
        losses.append(loss)
        grad_W = grad(X, y, y_pred)
        grad_b = np.mean(y_pred - y, axis=0)
        W -= lr * grad_W
        b -= lr * grad_b
        if (epoch+1) % 100 == 0:
            print(f"Epoch {epoch+1}/{n_epochs}, loss={loss:.4f}")
    return W, b, losses

现在，我们可以对模型进行训练：

W, b, losses = fit(X_train, y_train)

最后，我们可以使用训练好的模型对测试集进行预测，并计算准确率：

def predict(X, W, b):
    z = np.dot(X, W) + b
    y_pred = softmax(z)
    return np.argmax(y_pred, axis=1)

y_pred = predict(X_test, W, b)
accuracy = np.mean(y_pred == np.argmax(y_test, axis=1))
print(f"Accuracy: {accuracy:.2f}")

完整代码如下：

import numpy as np
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

def softmax(z):
    e = np.exp(z - np.max(z, axis=1, keepdims=True))
    return e / np.sum(e, axis=1, keepdims=True)

def cross_entropy_loss(y_true, y_pred):
    return -np.mean(np.sum(y_true * np.log(y_pred), axis=1))

def grad(X, y_true, y_pred):
    m = X.shape[0]
    return 1/m * np.dot(X.T, (y_pred - y_true))

def fit(X, y, lr=0.1, n_epochs=1000):
    n_features = X.shape[1]
    n_classes = y.shape[1]
    W = np.random.randn(n_features, n_classes)
    b = np.zeros(n_classes)
    losses = []
    for epoch in range(n_epochs):
        z = np.dot(X, W) + b
        y_pred = softmax(z)
        loss = cross_entropy_loss(y, y_pred)
        losses.append(loss)
        grad_W = grad(X, y, y_pred)
        grad_b = np.mean(y_pred - y, axis=0)
        W -= lr * grad_W
        b -= lr * grad_b
        if (epoch+1) % 100 == 0:
            print(f"Epoch {epoch+1}/{n_epochs}, loss={loss:.4f}")
    return W, b, losses

def predict(X, W, b):
    z = np.dot(X, W) + b
    y_pred = softmax(z)
    return np.argmax(y_pred, axis=1)

iris = load_iris()
X = iris.data
y = iris.target

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

def one_hot(y):
    n_classes = len(np.unique(y))
    return np.eye(n_classes)[y]

y_train = one_hot(y_train)
y_test = one_hot(y_test)

W, b, losses = fit(X_train, y_train)

y_pred = predict(X_test, W, b)
accuracy = np.mean(y_pred == np.argmax(y_test, axis=1))
print(f"Accuracy: {accuracy:.2f}")