用好blas和lapack库，dtrsm举例

最近要使用 dtrsm 进行解方程，试用了一两个例子，但总是有误，归根结底还是对fortran的一些性质不熟悉，这里做一下记录

1、 XTRSM(SIDE, UPLD, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)

主要用来解方程，而且花样很多

op( A )*X = alpha*B, or X*op( A ) = alpha*B,

op( A ) = A or op( A ) = A**T.

我使用了别人x学习BLAS库 -- DTRSM_cocoonyang的专栏-CSDN博客

写的一个例子，错误颇多，这里做一些订正

2、fortran中数组是按列排列的，二维在内存也是按列排列的，所以它经常用的 LDA or LDB 就是说的行数，或者说一段内存按列走排列，碰到 LDX个就立刻卡断弯折

所以数组的大小是 A(LDA,列数)，B(LDB,列数)

给数组赋值的时候:

a = (double *) malloc(lda * m * sizeof(double));// a size lda *m
b = (double *) malloc(ldb * n * sizeof(double));// b size ldb *n

    for (i = 0; i < lda; i++)//lda =4
   {
       for (j = 0; j <m ; j++)//m =4
       {
           a[i + j * lda] = xxx; // 列优先，如果是行优先，这个地方变成 a[i*lda + j]

}

3 、具体的里一个例子：

void dtrsm_test()
{
   double *a;
   double alpha;
   double *b;
   char diag;
   int i;
   int j;
   int lda;
   int ldb;
   int m;
   int n;
   char side;
   char transa;
   char transb;
   char uplo;

   char functionName[] = "DTRSM";
   printf("================================================ \n");
   printf("Testing BLAS library function -- %s \n", functionName);

   printf("\n");
   //printf ( "TEST DTRSM\n" );
   printf(" DTRSM solves a linear system involving a triangular\n");
   printf(" matrix A and a rectangular matrix B.\n");
   printf("\n");
   printf(" 1: Solve A * X = alpha * B;\n");
   printf(" 2: Solve A' * X = alpha * B;\n");
   printf(" 3: Solve X * A = alpha * B;\n");
   printf(" 4: Solve X * A' = alpha * B;\n");

   /*
   Solve A * X = alpha * B.
   */
   side = 'L';
   uplo = 'U';
   transa = 'N';
   diag = 'N';
   m = 4;
   n = 5;
   alpha = 2.0;
   lda = m;
   ldb = m;

   //全部按列排列！
   // a(lda,m) = 4 *4 or a(m,m)
   // b(ldb,n) =4 *5 or b(m,n)

a = (double *) malloc(lda * m * sizeof(double));
b = (double *) malloc(ldb * n * sizeof(double));

   for (i = 0; i < lda; i++)//lda =4
   {
       for (j = 0; j <= i; j++)//m =4
       {

           a[i + j * lda] = 0.0;
       }
       for (j = i ; j < m; j++)
       {
           a[i + j * lda] = (double) (i + j + 2);
       }
   }

   transb = 'N';

   for ( i = 0; i < ldb; i++ )//ldb=4
   {
         for ( j = 0; j <n; j++ )//n=5
         {
           b[i+j*ldb] = 10 * (i+1) + (j+1);
         }
   }

   printf("Test matrix \n");
   r8mat_print(m, m, a, " A = ");
   r8mat_print(m, n, b, "   B:");

   dtrsm_(&side, &uplo, &transa, &diag, &m, &n, &alpha, a, &lda, b, &ldb);

   r8mat_print(m, n, b, " X = inv ( A ) * alpha * B:");

   free(a);
   free(b);
}

4、DTRSM 中单元三角阵的研究

XTRSM(SIDE, UPLD, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)

其他参数其实说的都很明白，只有这个

DIAG
DIAG is CHARACTER*1
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.

试验了一下，如果 DIAG 为U，就是单元三角阵，那么A的主对角线都将设为1

你比如A 原本是

但如果你设定 DIAG 为 u，那么A会自动变成下面，不管你A的主对角线初值是什么

用好blas和lapack库，dtrsm举例

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