dgemm.c

SuperLU 2.2版本。对大型、稀疏、非对称的线性系统的直接求解

/*  -- translated by f2c (version 19940927).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include "f2c.h"

/* Subroutine */ int dgemm_(char *transa, char *transb, integer *m, integer *
	n, integer *k, doublereal *alpha, doublereal *a, integer *lda, 
	doublereal *b, integer *ldb, doublereal *beta, doublereal *c, integer 
	*ldc)
{


    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, 
	    i__3;

    /* Local variables */
    static integer info;
    static logical nota, notb;
    static doublereal temp;
    static integer i, j, l, ncola;
    extern logical lsame_(char *, char *);
    static integer nrowa, nrowb;
    extern /* Subroutine */ int xerbla_(char *, integer *);


/*  Purpose   
    =======   

    DGEMM  performs one of the matrix-matrix operations   

       C := alpha*op( A )*op( B ) + beta*C,   

    where  op( X ) is one of   

       op( X ) = X   or   op( X ) = X',   

    alpha and beta are scalars, and A, B and C are matrices, with op( A ) 
  
    an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix. 
  

    Parameters   
    ==========   

    TRANSA - CHARACTER*1.   
             On entry, TRANSA specifies the form of op( A ) to be used in 
  
             the matrix multiplication as follows:   

                TRANSA = 'N' or 'n',  op( A ) = A.   

                TRANSA = 'T' or 't',  op( A ) = A'.   

                TRANSA = 'C' or 'c',  op( A ) = A'.   

             Unchanged on exit.   

    TRANSB - CHARACTER*1.   
             On entry, TRANSB specifies the form of op( B ) to be used in 
  
             the matrix multiplication as follows:   

                TRANSB = 'N' or 'n',  op( B ) = B.   

                TRANSB = 'T' or 't',  op( B ) = B'.   

                TRANSB = 'C' or 'c',  op( B ) = B'.   

             Unchanged on exit.   

    M      - INTEGER.   
             On entry,  M  specifies  the number  of rows  of the  matrix 
  
             op( A )  and of the  matrix  C.  M  must  be at least  zero. 
  
             Unchanged on exit.   

    N      - INTEGER.   
             On entry,  N  specifies the number  of columns of the matrix 
  
             op( B ) and the number of columns of the matrix C. N must be 
  
             at least zero.   
             Unchanged on exit.   

    K      - INTEGER.   
             On entry,  K  specifies  the number of columns of the matrix 
  
             op( A ) and the number of rows of the matrix op( B ). K must 
  
             be at least  zero.   
             Unchanged on exit.   

    ALPHA  - DOUBLE PRECISION.   
             On entry, ALPHA specifies the scalar alpha.   
             Unchanged on exit.   

    A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is 
  
             k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.   
             Before entry with  TRANSA = 'N' or 'n',  the leading  m by k 
  
             part of the array  A  must contain the matrix  A,  otherwise 
  
             the leading  k by m  part of the array  A  must contain  the 
  
             matrix A.   
             Unchanged on exit.   

    LDA    - INTEGER.   
             On entry, LDA specifies the first dimension of A as declared 
  
             in the calling (sub) program. When  TRANSA = 'N' or 'n' then 
  
             LDA must be at least  max( 1, m ), otherwise  LDA must be at 
  
             least  max( 1, k ).   
             Unchanged on exit.   

    B      - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is 
  
             n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.   
             Before entry with  TRANSB = 'N' or 'n',  the leading  k by n 
  
             part of the array  B  must contain the matrix  B,  otherwise 
  
             the leading  n by k  part of the array  B  must contain  the 
  
             matrix B.   
             Unchanged on exit.   

    LDB    - INTEGER.   
             On entry, LDB specifies the first dimension of B as declared 
  
             in the calling (sub) program. When  TRANSB = 'N' or 'n' then 
  
             LDB must be at least  max( 1, k ), otherwise  LDB must be at 
  
             least  max( 1, n ).   
             Unchanged on exit.   

    BETA   - DOUBLE PRECISION.   
             On entry,  BETA  specifies the scalar  beta.  When  BETA  is 
  
             supplied as zero then C need not be set on input.   
             Unchanged on exit.   

    C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).   
             Before entry, the leading  m by n  part of the array  C must 
  
             contain the matrix  C,  except when  beta  is zero, in which 
  
             case C need not be set on entry.   
             On exit, the array  C  is overwritten by the  m by n  matrix 
  
             ( alpha*op( A )*op( B ) + beta*C ).   

    LDC    - INTEGER.   
             On entry, LDC specifies the first dimension of C as declared 
  
             in  the  calling  (sub)  program.   LDC  must  be  at  least 
  
             max( 1, m ).   
             Unchanged on exit.   


    Level 3 Blas routine.   

    -- Written on 8-February-1989.   
       Jack Dongarra, Argonne National Laboratory.   
       Iain Duff, AERE Harwell.   
       Jeremy Du Croz, Numerical Algorithms Group Ltd.   
       Sven Hammarling, Numerical Algorithms Group Ltd.   



       Set  NOTA  and  NOTB  as  true if  A  and  B  respectively are not 
  
       transposed and set  NROWA, NCOLA and  NROWB  as the number of rows 
  
       and  columns of  A  and the  number of  rows  of  B  respectively. 
  

    
   Parameter adjustments   
       Function Body */

#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)]
#define C(I,J) c[(I)-1 + ((J)-1)* ( *ldc)]

    nota = lsame_(transa, "N");
    notb = lsame_(transb, "N");
    if (nota) {
	nrowa = *m;
	ncola = *k;
    } else {
	nrowa = *k;
	ncola = *m;
    }
    if (notb) {
	nrowb = *k;
    } else {
	nrowb = *n;
    }

/*     Test the input parameters. */

    info = 0;
    if (! nota && ! lsame_(transa, "C") && ! lsame_(transa, "T")) {
	info = 1;
    } else if (! notb && ! lsame_(transb, "C") && ! lsame_(transb, 
	    "T")) {
	info = 2;
    } else if (*m < 0) {
	info = 3;
    } else if (*n < 0) {
	info = 4;
    } else if (*k < 0) {
	info = 5;
    } else if (*lda < max(1,nrowa)) {
	info = 8;
    } else if (*ldb < max(1,nrowb)) {
	info = 10;
    } else if (*ldc < max(1,*m)) {
	info = 13;
    }
    if (info != 0) {
	xerbla_("DGEMM ", &info);
	return 0;
    }

/*     Quick return if possible. */

    if (*m == 0 || *n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
	return 0;
    }

/*     And if  alpha.eq.zero. */

    if (*alpha == 0.) {
	if (*beta == 0.) {
	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		i__2 = *m;
		for (i = 1; i <= *m; ++i) {
		    C(i,j) = 0.;
/* L10: */
		}
/* L20: */
	    }
	} else {
	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		i__2 = *m;
		for (i = 1; i <= *m; ++i) {
		    C(i,j) = *beta * C(i,j);
/* L30: */
		}
/* L40: */
	    }
	}
	return 0;
    }

/*     Start the operations. */

    if (notb) {
	if (nota) {

/*           Form  C := alpha*A*B + beta*C. */

	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		if (*beta == 0.) {
		    i__2 = *m;
		    for (i = 1; i <= *m; ++i) {
			C(i,j) = 0.;
/* L50: */
		    }
		} else if (*beta != 1.) {
		    i__2 = *m;
		    for (i = 1; i <= *m; ++i) {
			C(i,j) = *beta * C(i,j);
/* L60: */
		    }
		}
		i__2 = *k;
		for (l = 1; l <= *k; ++l) {
		    if (B(l,j) != 0.) {
			temp = *alpha * B(l,j);
			i__3 = *m;
			for (i = 1; i <= *m; ++i) {
			    C(i,j) += temp * A(i,l);
/* L70: */
			}
		    }
/* L80: */
		}
/* L90: */
	    }
	} else {

/*           Form  C := alpha*A'*B + beta*C */

	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		i__2 = *m;
		for (i = 1; i <= *m; ++i) {
		    temp = 0.;
		    i__3 = *k;
		    for (l = 1; l <= *k; ++l) {
			temp += A(l,i) * B(l,j);
/* L100: */
		    }
		    if (*beta == 0.) {
			C(i,j) = *alpha * temp;
		    } else {
			C(i,j) = *alpha * temp + *beta * C(i,j);
		    }
/* L110: */
		}
/* L120: */
	    }
	}
    } else {
	if (nota) {

/*           Form  C := alpha*A*B' + beta*C */

	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		if (*beta == 0.) {
		    i__2 = *m;
		    for (i = 1; i <= *m; ++i) {
			C(i,j) = 0.;
/* L130: */
		    }
		} else if (*beta != 1.) {
		    i__2 = *m;
		    for (i = 1; i <= *m; ++i) {
			C(i,j) = *beta * C(i,j);
/* L140: */
		    }
		}
		i__2 = *k;
		for (l = 1; l <= *k; ++l) {
		    if (B(j,l) != 0.) {
			temp = *alpha * B(j,l);
			i__3 = *m;
			for (i = 1; i <= *m; ++i) {
			    C(i,j) += temp * A(i,l);
/* L150: */
			}
		    }
/* L160: */
		}
/* L170: */
	    }
	} else {

/*           Form  C := alpha*A'*B' + beta*C */

	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		i__2 = *m;
		for (i = 1; i <= *m; ++i) {
		    temp = 0.;
		    i__3 = *k;
		    for (l = 1; l <= *k; ++l) {
			temp += A(l,i) * B(j,l);
/* L180: */
		    }
		    if (*beta == 0.) {
			C(i,j) = *alpha * temp;
		    } else {
			C(i,j) = *alpha * temp + *beta * C(i,j);
		    }
/* L190: */
		}
/* L200: */
	    }
	}
    }

    return 0;

/*     End of DGEMM . */

} /* dgemm_ */