vector.cpp

矩阵运算

    j=j-1;
    k=0;
    while ((k<=j)&&(a[k*n+k]!=0.0))
{
  k=k+1;
}
    k=k-1;
    for (i=0; i<=n-1; i++)
{
  for (j=0; j<=m-1; j++)
  {
   t=i*m+j;
   aa[t]=0.0;
   for (l=0; l<=k; l++)
   {
    f=l*n+i;
    p=j*m+l;
    q=l*n+l;
    aa[t]=aa[t]+v[f]*u[p]/a[q];
   }
  }
}
    return(1);
} //实数矩阵的奇异值分解
//利用Householder变换及变形QR算法
//a-长度为m*n的数组，返回时其对角线依次给出奇异值，其余元素为0
//m-矩阵的行数
//n-矩阵的列数
//u-长度为m*m的数组，返回时存放奇异值分解的左奇异量U
//v-长度为n*n的数组，返回时存放奇异值分解的左奇异量V
//eps-精度要求
//ka-整型变量，其值为max(n,m)+1
//调用函数：dluav(),ppp(),sss()
static void ppp(double a[],double e[],double s[],double v[],int m,int n);
static void sss(double fg[2],double cs[2]);
int dluav(double a[],int m,int n,double u[],double v[],double eps,int ka)
{
int i,j,k,l,it,ll,kk,ix,iy,mm,nn,iz,m1,ks;
double d,dd,t,sm,sm1,em1,sk,ek,b,c,shh,fg[2],cs[2];
double *s,*e,*w;
s=malloc(ka*sizeof(double));
e=malloc(ka*sizeof(double));
w=malloc(ka*sizeof(double));
it=60;
k=n;
if (m-1<n)
{
  k=m-1;
}
l=m;
if (n-2<m)
{
  l=n-2;
}
if (l<0)
{
  l=0;
}
ll=k;
if (l>k)
{
  ll=l;
}
if (ll>=1)
{
  for (kk=1; kk<=ll; kk++)
  {
   if (kk<=k)
   {
    d=0.0;
    for (i=kk; i<=m; i++)
    {
     ix=(i-1)*n+kk-1;
     d=d+a[ix]*a[ix];
    }
    s[kk-1]=sqrt(d);
    if (s[kk-1]!=0.0)
{
     ix=(kk-1)*n+kk-1;
     if (a[ix]!=0.0)
     {
      s[kk-1]=fabs(s[kk-1]);
      if (a[ix]<0.0)
      {
       s[kk-1]=-s[kk-1];
      }
     }
     for (i=kk; i<=m; i++)
     {
      iy=(i-1)*n+kk-1;
      a[iy]=a[iy]/s[kk-1];
     }
     a[ix]=1.0+a[ix];
    }
    s[kk-1]=-s[kk-1];
   }
   if (n>=kk+1)
   {
    for (j=kk+1; j<=n; j++)
    {
     if ((kk<=k)&&(s[kk-1]!=0.0))
     {
      d=0.0;
      for (i=kk; i<=m; i++)
      {
       ix=(i-1)*n+kk-1;
       iy=(i-1)*n+j-1;
       d=d+a[ix]*a[iy];
      }
      d=-d/a[(kk-1)*n+kk-1];
      for (i=kk; i<=m; i++)
      {
       ix=(i-1)*n+j-1;
       iy=(i-1)*n+kk-1;
       a[ix]=a[ix]+d*a[iy];
      }
     }
  e[j-1]=a[(kk-1)*n+j-1];
    }
   }
   if (kk<=k)
   {
    for (i=kk; i<=m; i++)
    {
     ix=(i-1)*m+kk-1;
     iy=(i-1)*n+kk-1;
     u[ix]=a[iy];
    }
   }
   if (kk<=l)
   {
    d=0.0;
    for (i=kk+1; i<=n; i++)
    {
     d=d+e[i-1]*e[i-1];
    }
    e[kk-1]=sqrt(d);
    if (e[kk-1]!=0.0)
    {
     if (e[kk]!=0.0)
     {
      e[kk-1]=fabs(e[kk-1]);
      if (e[kk]<0.0)
      {
       e[kk-1]=-e[kk-1];
      }
     }
     for (i=kk+1; i<=n; i++)
     {
      e[i-1]=e[i-1]/e[kk-1];
     }
     e[kk]=1.0+e[kk];
    }
    e[kk-1]=-e[kk-1];
    if ((kk+1<=m)&&(e[kk-1]!=0.0))
    {
     for (i=kk+1; i<=m; i++)
     {
      w[i-1]=0.0;
     }
     for (j=kk+1; j<=n; j++)
     {
      for (i=kk+1; i<=m; i++)
{
       w[i-1]=w[i-1]+e[j-1]*a[(i-1)*n+j-1];
      }
     }
     for (j=kk+1; j<=n; j++)
     {
      for (i=kk+1; i<=m; i++)
      {
       ix=(i-1)*n+j-1;
       a[ix]=a[ix]-w[i-1]*e[j-1]/e[kk];
      }
     }
    }
    for (i=kk+1; i<=n; i++)
    {
     v[(i-1)*n+kk-1]=e[i-1];
    }
   }
  }
}
mm=n;
if (m+1<n)
{
  mm=m+1;
}
if (k<n)
{
  s[k]=a[k*n+k];
}
if (m<mm)
{
  s[mm-1]=0.0;
}
if (l+1<mm)
{
  e[l]=a[l*n+mm-1];
}
e[mm-1]=0.0;
nn=m;
if (m>n)
{
  nn=n;
}
if (nn>=k+1)
{
  for (j=k+1; j<=nn; j++)
  {
   for (i=1; i<=m; i++)
   {
    u[(i-1)*m+j-1]=0.0;
   }
   u[(j-1)*m+j-1]=1.0;
  }
}
if (k>=1)
{
  for (ll=1; ll<=k; ll++)
  {
   kk=k-ll+1; iz=(kk-1)*m+kk-1;
   if (s[kk-1]!=0.0)
   {
    if (nn>=kk+1)
    {
     for (j=kk+1; j<=nn; j++)
     {
      d=0.0;
      for (i=kk; i<=m; i++)
{
       ix=(i-1)*m+kk-1;
       iy=(i-1)*m+j-1;
       d=d+u[ix]*u[iy]/u[iz];
      }
      d=-d;
      for (i=kk; i<=m; i++)
      {
       ix=(i-1)*m+j-1;
       iy=(i-1)*m+kk-1;
       u[ix]=u[ix]+d*u[iy];
      }
     }
    }
    for (i=kk; i<=m; i++)
    {
     ix=(i-1)*m+kk-1;
     u[ix]=-u[ix];
    }
    u[iz]=1.0+u[iz];
    if (kk-1>=1)
    {
     for (i=1; i<=kk-1; i++)
     {
      u[(i-1)*m+kk-1]=0.0;
     }
    }
   }
   else
   {
    for (i=1; i<=m; i++)
    {
     u[(i-1)*m+kk-1]=0.0;
    }
    u[(kk-1)*m+kk-1]=1.0;
   }
  }
}
for (ll=1; ll<=n; ll++)
{
  kk=n-ll+1;
  iz=kk*n+kk-1;
  if ((kk<=l)&&(e[kk-1]!=0.0))
  {
   for (j=kk+1; j<=n; j++)
   {
    d=0.0;
    for (i=kk+1; i<=n; i++)
 {
     ix=(i-1)*n+kk-1;
     iy=(i-1)*n+j-1;
     d=d+v[ix]*v[iy]/v[iz];
    }
    d=-d;
    for (i=kk+1; i<=n; i++)
    {
     ix=(i-1)*n+j-1;
     iy=(i-1)*n+kk-1;
     v[ix]=v[ix]+d*v[iy];
    }
   }
  }
  for (i=1; i<=n; i++)
  {
   v[(i-1)*n+kk-1]=0.0;
  }
  v[iz-n]=1.0;
}
for (i=1; i<=m; i++)
{
  for (j=1; j<=n; j++)
  {
   a[(i-1)*n+j-1]=0.0;
  }
}
m1=mm;
it=60;
while (1==1)
{
  if (mm==0)
  {
   ppp(a,e,s,v,m,n);
   free(s);
   free(e);
   free(w);
   return(1);
  }
  if (it==0)
  {
   ppp(a,e,s,v,m,n);
   free(s);
   free(e);
   free(w);
   return(-1);
  }
  kk=mm-1;
  while ((kk!=0)&&(fabs(e[kk-1])!=0.0))
  {
   d=fabs(s[kk-1])+fabs(s[kk]);
   dd=fabs(e[kk-1]);
   if (dd>eps*d)
   {
    kk=kk-1;
   }
   else
   {
    e[kk-1]=0.0;
   }
  }
  if (kk==mm-1)
  {
   kk=kk+1;
   if (s[kk-1]<0.0)
   {
    s[kk-1]=-s[kk-1];
#  for (i=1; i<=n; i++)
    {
     ix=(i-1)*n+kk-1;
     v[ix]=-v[ix];
    }
   }
   while ((kk!=m1)&&(s[kk-1]<s[kk]))
   {
    d=s[kk-1];
    s[kk-1]=s[kk];
    s[kk]=d;
    if (kk<n)
    {
     for (i=1; i<=n; i++)
     {
      ix=(i-1)*n+kk-1;
      iy=(i-1)*n+kk;
      d=v[ix];
      v[ix]=v[iy];
      v[iy]=d;
     }
    }
    if (kk<m)
    {
     for (i=1; i<=m; i++)
     {
      ix=(i-1)*m+kk-1; iy=(i-1)*m+kk;
      d=u[ix]; u[ix]=u[iy]; u[iy]=d;
     }
    }
    kk=kk+1;
   }
   it=60;
   mm=mm-1;
  }
  else
  {
   ks=mm;
   while ((ks>kk)&&(fabs(s[ks-1])!=0.0))
   {
    d=0.0;
    if (ks!=mm)
    {
     d=d+fabs(e[ks-1]);
    }
    if (ks!=kk+1)
    {
     d=d+fabs(e[ks-2]);
    }
 dd=fabs(s[ks-1]);
    if (dd>eps*d)
    {
     ks=ks-1;
    }
    else
    {
     s[ks-1]=0.0;
    }
   }
   if (ks==kk)
   {
    kk=kk+1;
    d=fabs(s[mm-1]);
    t=fabs(s[mm-2]);
    if (t>d)
    {
     d=t;
    }
    t=fabs(e[mm-2]);
    if (t>d)
    {
     d=t;
    }
    t=fabs(s[kk-1]);
    if (t>d)
    {
     d=t;
    }
    t=fabs(e[kk-1]);
    if (t>d)
    {
     d=t;
    }
    sm=s[mm-1]/d;
    sm1=s[mm-2]/d;
    em1=e[mm-2]/d;
    sk=s[kk-1]/d;
    ek=e[kk-1]/d;
    b=((sm1+sm)*(sm1-sm)+em1*em1)/2.0;
    c=sm*em1;
    c=c*c;
    shh=0.0;
    if ((b!=0.0)(c!=0.0))
    {
     shh=sqrt(b*b+c);
     if (b<0.0)
     {
      shh=-shh;
     }
     shh=c/(b+shh);
    }
    fg[0]=(sk+sm)*(sk-sm)-shh;
    fg[1]=sk*ek;
    for (i=kk; i<=mm-1; i++)
    {
     sss(fg,cs);
     if (i!=kk)
     {
      e[i-2]=fg[0];
     }
     fg[0]=cs[0]*s[i-1]+cs[1]*e[i-1];
     e[i-1]=cs[0]*e[i-1]-cs[1]*s[i-1];
     fg[1]=cs[1]*s[i];
     s[i]=cs[0]*s[i];
     if ((cs[0]!=1.0)(cs[1]!=0.0))
     {
      for (j=1; j<=n; j++)
      {
       ix=(j-1)*n+i-1;
       iy=(j-1)*n+i;
       d=cs[0]*v[ix]+cs[1]*v[iy];
       v[iy]=-cs[1]*v[ix]+cs[0]*v[iy];
       v[ix]=d;
      }
     }
     sss(fg,cs);
     s[i-1]=fg[0];
     fg[0]=cs[0]*e[i-1]+cs[1]*s[i];
     s[i]=-cs[1]*e[i-1]+cs[0]*s[i];
     fg[1]=cs[1]*e[i];
     e[i]=cs[0]*e[i];
     if (i<m)
     {
      if ((cs[0]!=1.0)(cs[1]!=0.0))
      {
       for (j=1; j<=m; j++)
       {
        ix=(j-1)*m+i-1;
      iy=(j-1)*m+i;
        d=cs[0]*u[ix]+cs[1]*u[iy];
        u[iy]=-cs[1]*u[ix]+cs[0]*u[iy];
        u[ix]=d;
       }
      }
     }
    }
    e[mm-2]=fg[0];
    it=it-1;
   }
   else
   {
    if (ks==mm)
    {
     kk=kk+1;
     fg[1]=e[mm-2];
     e[mm-2]=0.0;
     for (ll=kk; ll<=mm-1; ll++)
     {
      i=mm+kk-ll-1;
      fg[0]=s[i-1];
      sss(fg,cs);
      s[i-1]=fg[0];
      if (i!=kk)
      {
       fg[1]=-cs[1]*e[i-2];
       e[i-2]=cs[0]*e[i-2];
      }
      if ((cs[0]!=1.0)(cs[1]!=0.0))
      {
       for (j=1; j<=n; j++)
       {
        ix=(j-1)*n+i-1;
        iy=(j-1)*n+mm-1;
        d=cs[0]*v[ix]+cs[1]*v[iy];
        v[iy]=-cs[1]*v[ix]+cs[0]*v[iy];
       v[ix]=d;
       }
      }
     }
    }
    else
    {
     kk=ks+1;
     fg[1]=e[kk-2];
     e[kk-2]=0.0;
     for (i=kk; i<=mm; i++)
     {
      fg[0]=s[i-1];
      sss(fg,cs);
      s[i-1]=fg[0];
      fg[1]=-cs[1]*e[i-1];
      e[i-1]=cs[0]*e[i-1];
      if ((cs[0]!=1.0)(cs[1]!=0.0))
      {
       for (j=1; j<=m; j++)
       {
        ix=(j-1)*m+i-1;
        iy=(j-1)*m+kk-2;
        d=cs[0]*u[ix]+cs[1]*u[iy];
        u[iy]=-cs[1]*u[ix]+cs[0]*u[iy];
        u[ix]=d;
       }
      }
     }
    }
   }
  }
}
return(1);
}


static void ppp(double a[],double e[],double s[],double v[],int m,int n)
{ int i,j,p,q;
double d;
if (m>=n)
{
  i=n;
}
else
{
  i=m;
}
for (j=1; j<=i-1; j++)
{
  a[(j-1)*n+j-1]=s[j-1];
  a[(j-1)*n+j]=e[j-1];
}
a[(i-1)*n+i-1]=s[i-1];
if (m<n)
{
  a[(i-1)*n+i]=e[i-1];
}
for (i=1; i<=n-1; i++)
{
  for (j=i+1; j<=n; j++)
  {
   p=(i-1)*n+j-1;
   q=(j-1)*n+i-1;
   d=v[p];
   v[p]=v[q];
   v[q]=d;
  }
}
return;
}

static void sss(double fg[2],double cs[2])
{
double r,d;
if ((fabs(fg[0])+fabs(fg[1]))==0.0)
{
  cs[0]=1.0;
  cs[1]=0.0;
  d=0.0;
}
else
{
  d=sqrt(fg[0]*fg[0]+fg[1]*fg[1]);
  if (fabs(fg[0])>fabs(fg[1]))
  {
   d=fabs(d);
   if (fg[0]<0.0)
   {
    d=-d;
   }
  }
  if (fabs(fg[1])>=fabs(fg[0]))
  {
   d=fabs(d);
   if (fg[1]<0.0)
   {
    d=-d;
   }
  }
  cs[0]=fg[0]/d;
  cs[1]=fg[1]/d;
}
r=1.0;
if (fabs(fg[0])>fabs(fg[1]))
{
  r=cs[1];
}
else
{
  if(cs[0]!=0.0)
  {
   r=1.0/cs[0];
  }
  fg[0]=d;
  fg[1]=r;
  return;
}
}

//复数矩阵相乘
//计算矩阵A（m*n）和B（n*k）的乘积，结果保存在C（m*k）中
//ar-长度为m*n的数组,存放A的实部
//ai-长度为m*n的数组,存放A的虚部
//br-长度为n*k的数组,存放B的实部
//bi-长度为n*k的数组,存放B的虚部
//cr-长度为m*k的数组，存放结果C的实部
//ci-长度为m*k的数组，存放结果C的虚部
void dbcmul(double ar[],double ai[],double br[],double bi[],int m,int n,int k,double cr[],double ci[])
{ int i,j,l,u,v,w;
double p,q,s;
for (i=0; i<=m-1; i++)
{
  for (j=0; j<=k-1; j++)
 {
   u=i*k+j;
   cr[u]=0.0;
   ci[u]=0.0;
   for (l=0; l<=n-1; l++)
   {
    v=i*n+l; w=l*k+j;
    p=ar[v]*br[w];
    q=ai[v]*bi[w];
    s=(ar[v]+ai[v])*(br[w]+bi[w]);
    cr[u]=cr[u]+p-q;
    ci[u]=ci[u]+s-p-q;
   }
  }
}
  return;
} //复数矩阵求逆
//ar-长度为n*n的数组, n*n矩阵的实部
//ai-长度为n*n的数组, n*n矩阵的虚部
//n 矩阵的维数
int ddcinv(double ar[],double ai[],int n)
{
int *is,*js,i,j,k,l,u,v,w;
    double p,q,s,t,d,b;
    is=malloc(n*sizeof(int));
    js=malloc(n*sizeof(int));
    for (k=0; k<=n-1; k++)
{
  d=0.0;
        for (i=k; i<=n-1; i++)
  {
   for (j=k; j<=n-1; j++)
   {
    u=i*n+j;
    p=ar[u]*ar[u]+ai[u]*ai[u];
    if (p>d)
    {
     d=p;
     is[k]=i;
     js[k]=j;
    }
   }
  }
  if (d+1.0==1.0)
  {
   free(is);
   free(js);
   printf("err**not inv\n");
   return(0);
  }
  if (is[k]!=k)
  {
   for (j=0; j<=n-1; j++)
   {
    u=k*n+j;
    v=is[k]*n+j;
    t=ar[u]; ar[u]=ar[v]; ar[v]=t;
    t=ai[u]; ai[u]=ai[v]; ai[v]=t;
   }
  }
  if (js[k]!=k)
  {
   for (i=0; i<=n-1; i++)
   {
    u=i*n+k;
    v=i*n+js[k];
    t=ar[u]; ar[u]=ar[v]; ar[v]=t;
    t=ai[u]; ai[u]=ai[v]; ai[v]=t;
   }
  }
  l=k*n+k;
  ar[l]=ar[l]/d;
  ai[l]=-ai[l]/d;
  for (j=0; j<=n-1; j++)
  {
   if (j!=k)
   {
    u=k*n+j;
    p=ar[u]*ar[l];
    q=ai[u]*ai[l];
    s=(ar[u]+ai[u])*(ar[l]+ai[l]);
    ar[u]=p-q;
    ai[u]=s-p-q;
   }
  }
  for (i=0; i<=n-1; i++)
  {
   if (i!=k)
   {
    v=i*n+k;
    for (j=0; j<=n-1; j++)
    {
     if (j!=k)
     {
      u=k*n+j;  
      w=i*n+j;
      p=ar[u]*ar[v];
      q=ai[u]*ai[v];
      s=(ar[u]+ai[u])*(ar[v]+ai[v]);
      t=p-q;
      b=s-p-q;
      ar[w]=ar[w]-t;
      ai[w]=ai[w]-b;
     }
    }
   }
  }
  for (i=0; i<=n-1; i++)
  {
   if (i!=k)
   {
    u=i*n+k;
    p=ar[u]*ar[l];
    q=ai[u]*ai[l];
    s=(ar[u]+ai[u])*(ar[l]+ai[l]);
    ar[u]=q-p;
    ai[u]=p+q-s;
   }
  }
}
    for (k=n-1; k>=0; k--)
{
  if (js[k]!=k)
  {
   for (j=0; j<=n-1; j++)
            {
    u=k*n+j;
    v=js[k]*n+j;
    t=ar[u]; ar[u]=ar[v]; ar[v]=t;
    t=ai[u]; ai[u]=ai[v]; ai[v]=t;
            }
  }
  if (is[k]!=k)
  {
   for (i=0; i<=n-1; i++)
   {
    u=i*n+k;
    v=i*n+is[k];
    t=ar[u]; ar[u]=ar[v]; ar[v]=t;
    t=ai[u]; ai[u]=ai[v]; ai[v]=t;
   }
  }
}
    free(is);
free(js);
    return(1);
}