使用C中的dgesv确定有和没有截距的线性回归

Question

以下代码在C中使用dgesv库来计算线性回归。它有X个观测值和Y个预测值，X和Y保存为双数组。我想知道

1）此代码是否通过截距计算线性回归？ 2）在使用或不使用拦截方面，如何更改代码以使其与1相反？

以下是代码：

#include <stdio.h>
#define N 16  /* number of observations */
#define P 2   /* number of predictors */

void dgesv_(int *n, int *nrhs, double *a, int *lda, int *ipiv, double *b, int *ldb, int *info);

int main(){
  /* longley dataset from R: Employed (Y) GNP.deflator and Population (X) */
  double Y[N] = {60.323,61.122,60.171,61.187,63.221,63.639,64.989,63.761,66.019,67.857,68.169,66.513,68.655,69.564,69.331,70.551};
  double X[N][P] =
  {{83,107.608},
  {88.5,108.632},
  {88.2,109.773},
  {89.5,110.929},
  {96.2,112.075},
  {98.1,113.27},
  {99,115.094},
  {100,116.219},
  {101.2,117.388},
  {104.6,118.734},
  {108.4,120.445},
  {110.8,121.95},
  {112.6,123.366},
  {114.2,125.368},
  {115.7,127.852},
  {116.9,130.081}};

  int i, j, k, n1=P+1, n2=1, ipiv[P+1], info;
  double X1[N][P+1], XtX[(P+1) * (P+1)], XtY[P+1];

其余代码如下：

  /* design matrix */
  for (i=0; i<N; i++){
    X1[i][0] = 1;
    for (j=1; j<n1; j++)
      X1[i][j] = X[i][j-1];
  }

  /* t(X1) %*% X1 */
  for (i=0; i<n1; i++){
    for (j=0; j<n1; j++){
      XtX[i*n1+j] = 0;
      for (k=0; k<N; k++)
        XtX[i*n1+j] += X1[k][i] * X1[k][j];
    }
  }

  /* t(X1) %*% Y */
  for (i=0; i<n1; i++){
    XtY[i] = 0;
    for (j=0; j<N; j++){
      XtY[i] += X1[j][i] * Y[j];
    }
  }

其余代码如下......

  /* XtX is symmetric, no transpose needed before passing to Fortran subrountine */
  dgesv_(&n1, &n2, XtX, &n1, ipiv, XtY, &n1, &info);
  if (info!=0)  printf("failure with error %d\n", info);

  /* print beta */
  printf("The regression coefficients: ");
  for (i=0; i<n1; i++){
    printf("%f ", XtY[i]);
  }
  printf("\n");

  return 0;
}