Squashed 'third_party/blasfeo/' content from commit 2a828ca
Change-Id: If1c3caa4799b2d4eb287ef83fa17043587ef07a3
git-subtree-dir: third_party/blasfeo
git-subtree-split: 2a828ca5442108c4c58e4b42b061a0469043f6ea
diff --git a/examples/tools.c b/examples/tools.c
new file mode 100644
index 0000000..51d9e95
--- /dev/null
+++ b/examples/tools.c
@@ -0,0 +1,724 @@
+/**************************************************************************************************
+* *
+* This file is part of HPMPC. *
+* *
+* HPMPC -- Library for High-Performance implementation of solvers for MPC. *
+* Copyright (C) 2014-2015 by Technical University of Denmark. All rights reserved. *
+* *
+* HPMPC is free software; you can redistribute it and/or *
+* modify it under the terms of the GNU Lesser General Public *
+* License as published by the Free Software Foundation; either *
+* version 2.1 of the License, or (at your option) any later version. *
+* *
+* HPMPC is distributed in the hope that it will be useful, *
+* but WITHOUT ANY WARRANTY; without even the implied warranty of *
+* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
+* See the GNU Lesser General Public License for more details. *
+* *
+* You should have received a copy of the GNU Lesser General Public *
+* License along with HPMPC; if not, write to the Free Software *
+* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
+* *
+* Author: Gianluca Frison, giaf (at) dtu.dk *
+* *
+**************************************************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+//#include "../include/aux_d.h"
+
+//void dgemm_(char *transa, char *transb, int *m, int *n, int *k, double *alpha, double *A, int *lda, double *B, int *ldb, double *beta, double *C, int *ldc);
+//void dgesv_(int *n, int *nrhs, double *A, int *lda, int *ipiv, double *B, int *ldb, int *info);
+//void dcopy_(int *n, double *dx, int *incx, double *dy, int *incy);
+//void daxpy_(int *n, double *da, double *dx, int *incx, double *dy, int *incy);
+//void dscal_(int *n, double *da, double *dx, int *incx);
+
+int posix_memalign(void **memptr, size_t alignment, size_t size);
+
+
+
+/************************************************
+ matrix-matrix multiplication
+************************************************/
+void dgemm_nn_3l(int m, int n, int k, double *A, int lda , double *B, int ldb, double *C, int ldc)
+ {
+
+ int ii, jj, kk;
+
+ for(jj=0; jj<n; jj++)
+ {
+ for(ii=0; ii<m; ii++)
+ {
+ C[ii+ldc*jj] = 0;
+ for(kk=0; kk<k; kk++)
+ {
+ C[ii+ldc*jj] += A[ii+lda*kk] * B[kk+ldb*jj];
+ }
+ }
+ }
+
+ return;
+
+ }
+
+
+void daxpy_3l(int n, double da, double *dx, double *dy)
+ {
+ int i;
+ for(i=0; i<n; i++)
+ {
+ dy[i] += da*dx[i];
+ }
+ }
+
+
+
+void dscal_3l(int n, double da, double *dx)
+ {
+ int i;
+ for(i=0; i<n; i++)
+ {
+ dx[i] *= da;
+ }
+ }
+
+
+
+/************************************************
+ Routine that copies a matrix
+************************************************/
+void dmcopy(int row, int col, double *A, int lda, double *B, int ldb)
+ {
+ int i, j;
+ for(j=0; j<col; j++)
+ {
+ for(i=0; i<row; i++)
+ {
+ B[i+j*ldb] = A[i+j*lda];
+ }
+ }
+ }
+
+
+
+int idamax_3l(int n, double *x)
+ {
+
+ if(n<=0)
+ return 0;
+ if(n==1)
+ return 0;
+
+ double dabs;
+ double dmax = (x[0]>0 ? x[0] : -x[0]);
+ int idmax = 0;
+ int jj;
+ for(jj=1; jj<n; jj++)
+ {
+ dabs = (x[jj]>0 ? x[jj] : -x[jj]);
+ if(dabs>dmax)
+ {
+ dmax = dabs;
+ idmax = jj;
+ }
+ }
+
+ return idmax;
+
+ }
+
+
+
+void dswap_3l(int n, double *x, int incx, double *y, int incy)
+ {
+
+ if(n<=0)
+ return;
+
+ double temp;
+ int jj;
+ for(jj=0; jj<n; jj++)
+ {
+ temp = x[0];
+ x[0] = y[0];
+ y[0] = temp;
+ x += incx;
+ y += incy;
+ }
+
+ }
+
+
+
+void dger_3l(int m, int n, double alpha, double *x, int incx, double *y, int incy, double *A, int lda)
+ {
+
+ if(m==0 || n==0 || alpha==0.0)
+ return;
+
+ int i, j;
+ double *px, *py, temp;
+
+ py = y;
+ for(j=0; j<n; j++)
+ {
+ temp = alpha * py[0];
+ px = x;
+ for(i=0; i<m; i++)
+ {
+ A[i+lda*j] += px[0] * temp;
+ px += incx;
+ }
+ py += incy;
+ }
+
+ return;
+
+ }
+
+
+
+void dgetf2_3l(int m, int n, double *A, int lda, int *ipiv, int *info)
+ {
+
+ if(m<=0 || n<=0)
+ return;
+
+ int i, j, jp;
+
+ double Ajj;
+
+ int size_min = ( m<n ? m : n );
+
+ for(j=0; j<size_min; j++)
+ // find the pivot and test for singularity
+ {
+ jp = j + idamax_3l(m-j, &A[j+lda*j]);
+ ipiv[j] = jp;
+ if( A[jp+lda*j]!=0)
+ {
+ // apply the interchange to columns 0:n-1
+ if(jp!=j)
+ {
+ dswap_3l(n, &A[j], lda, &A[jp], lda);
+ }
+ // compute elements j+1:m-1 of j-th column
+ if(j<m-1)
+ {
+ Ajj = A[j+lda*j];
+ if( ( Ajj>0 ? Ajj : -Ajj ) >= 2.22e-16 )
+ {
+ dscal_3l(m-j-1, 1.0/Ajj, &A[j+1+lda*j]);
+ }
+ else
+ {
+ for(i=j+1; i<m; i++)
+ {
+ A[i+lda*j] /= Ajj;
+ }
+ }
+ }
+ }
+ else if(*info==0)
+ {
+ *info = j+1;
+ }
+
+ if( j < size_min )
+ {
+ // update trailing submatrix
+ dger_3l(m-j-1, n-j-1, -1.0, &A[j+1+lda*j], 1, &A[j+lda*(j+1)], lda, &A[j+1+lda*(j+1)], lda);
+ }
+
+ }
+
+ return;
+
+ }
+
+
+
+void dlaswp_3l(int n, double *A, int lda, int k1, int k2, int *ipiv)
+ {
+
+ int i, j, k, ix, ix0, i1, i2, n32, ip;
+ double temp;
+
+ ix0 = k1;
+ i1 = k1;
+ i2 = k2;
+
+ n32 = (n/32)*32;
+ if(n32!=0)
+ {
+ for(j=0; j<n32; j+=32)
+ {
+ ix = ix0;
+ for(i=i1; i<i2; i++)
+ {
+ ip = ipiv[ix];
+ if(ip!=i)
+ {
+ for(k=j; k<j+32; k++)
+ {
+ temp = A[i+lda*k];
+ A[i+lda*k] = A[ip+lda*k];
+ A[ip+lda*k] = temp;
+ }
+ }
+ ix++;
+ }
+ }
+ }
+ if(n32!=n)
+ {
+ ix = ix0;
+ for(i=i1; i<i2; i++)
+ {
+ ip = ipiv[ix];
+ if(ip!=i)
+ {
+ for(k=n32; k<n; k++)
+ {
+ temp = A[i+lda*k];
+ A[i+lda*k] = A[ip+lda*k];
+ A[ip+lda*k] = temp;
+ }
+ }
+ ix++;
+ }
+ }
+
+ return;
+
+ }
+
+
+
+// left lower no-transp unit
+void dtrsm_l_l_n_u_3l(int m, int n, double *A, int lda, double *B, int ldb)
+ {
+
+ if(m==0 || n==0)
+ return;
+
+ int i, j, k;
+
+ for(j=0; j<n; j++)
+ {
+ for(k=0; k<m; k++)
+ {
+ for(i=k+1; i<m; i++)
+ {
+ B[i+ldb*j] -= B[k+ldb*j] * A[i+lda*k];
+ }
+ }
+ }
+
+ return;
+
+ }
+
+
+
+// left upper no-transp non-unit
+void dtrsm_l_u_n_n_3l(int m, int n, double *A, int lda, double *B, int ldb)
+ {
+
+ if(m==0 || n==0)
+ return;
+
+ int i, j, k;
+
+ for(j=0; j<n; j++)
+ {
+ for(k=m-1; k>=0; k--)
+ {
+ B[k+ldb*j] /= A[k+lda*k];
+ for(i=0; i<k; i++)
+ {
+ B[i+ldb*j] -= B[k+ldb*j] * A[i+lda*k];
+ }
+ }
+ }
+
+ return;
+
+ }
+
+
+
+void dgetrs_3l(int n, int nrhs, double *A, int lda, int *ipiv, double *B, int ldb, int *info)
+ {
+
+ if(n==0 || nrhs==0)
+ return;
+
+ // solve A * X = B
+
+ // apply row interchanges to the rhs
+ dlaswp_3l(nrhs, B, ldb, 0, n, ipiv);
+
+ // solve L*X = B, overwriting B with X
+ dtrsm_l_l_n_u_3l(n, nrhs, A, lda, B, ldb);
+
+ // solve U*X = B, overwriting B with X
+ dtrsm_l_u_n_n_3l(n, nrhs, A, lda, B, ldb);
+
+ return;
+
+ }
+
+
+
+void dgesv_3l(int n, int nrhs, double *A, int lda, int *ipiv, double *B, int ldb, int *info)
+ {
+
+ // compute the LU factorization of A
+ dgetf2_3l(n, n, A, lda, ipiv, info);
+
+ if(*info==0)
+ {
+ // solve the system A*X = B, overwriting B with X
+ dgetrs_3l(n, nrhs, A, lda, ipiv, B, ldb, info);
+ }
+
+ return;
+
+ }
+
+
+
+/* one norm of a matrix */
+double onenorm(int row, int col, double *ptrA)
+ {
+ double max, temp;
+ int i, j;
+ temp = 0;
+ for(j=0; j<col; j++)
+ {
+ temp = abs(*(ptrA+j*row));
+ for(i=1; i<row; i++)
+ {
+ temp += abs(*(ptrA+j*row+i));
+ }
+ if(j==0) max = temp;
+ else if(max>temp) temp = max;
+ }
+ return temp;
+ }
+
+
+
+/* computes the Pade approximation of degree m of the matrix A */
+void padeapprox(int m, int row, double *A)
+ {
+ int ii;
+ int row2 = row*row;
+/* int i1 = 1;*/
+/* double d0 = 0;*/
+/* double d1 = 1;*/
+/* double dm1 = -1;*/
+
+ double *U = (double *) malloc(row*row*sizeof(double)); // d_zeros(&U, row, row);
+ double *V = (double *) malloc(row*row*sizeof(double)); // d_zeros(&V, row, row);
+
+ if(m==3)
+ {
+ double c[] = {120, 60, 12, 1};
+ double *A0 = (double *) malloc(row*row*sizeof(double)); // d_eye(&A0, row);
+ for(ii=0; ii<row*row; ii++)
+ A0[ii] = 0.0;
+ for(ii=0; ii<row; ii++)
+ A0[ii*(row+1)] = 1.0;
+ double *A2 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *temp = malloc(row*row*sizeof(double)); // d_zeros(&temp, row, row);
+// char ta = 'n'; double alpha = 1; double beta = 0;
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A, &row, A, &row, &beta, A2, &row);
+ dgemm_nn_3l(row, row, row, A, row, A, row, A2, row);
+// dscal_(&row2, &d0, temp, &i1);
+ dscal_3l(row2, 0, temp);
+// daxpy_(&row2, &c[3], A2, &i1, temp, &i1);
+ daxpy_3l(row2, c[3], A2, temp);
+// daxpy_(&row2, &c[1], A0, &i1, temp, &i1);
+ daxpy_3l(row2, c[1], A0, temp);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A, &row, temp, &row, &beta, U, &row);
+ dgemm_nn_3l(row, row, row, A, row, temp, row, U, row);
+// dscal_(&row2, &d0, V, &i1);
+ dscal_3l(row2, 0, V);
+// daxpy_(&row2, &c[2], A2, &i1, V, &i1);
+ daxpy_3l(row2, c[2], A2, V);
+// daxpy_(&row2, &c[0], A0, &i1, V, &i1);
+ daxpy_3l(row2, c[0], A0, V);
+ free(A0);
+ free(A2);
+ free(temp);
+ }
+ else if(m==5)
+ {
+ double c[] = {30240, 15120, 3360, 420, 30, 1};
+ double *A0 = (double *) malloc(row*row*sizeof(double)); // d_eye(&A0, row);
+ for(ii=0; ii<row*row; ii++)
+ A0[ii] = 0.0;
+ for(ii=0; ii<row; ii++)
+ A0[ii*(row+1)] = 1.0;
+ double *A2 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *A4 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *temp = malloc(row*row*sizeof(double)); // d_zeros(&temp, row, row);
+// char ta = 'n'; double alpha = 1; double beta = 0;
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A, &row, A, &row, &beta, A2, &row);
+ dgemm_nn_3l(row, row, row, A, row, A, row, A2, row);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A2, &row, A2, &row, &beta, A4, &row);
+ dgemm_nn_3l(row, row, row, A2, row, A2, row, A4, row);
+ dmcopy(row, row, A4, row, V, row);
+ dmcopy(row, row, A4, row, temp, row);
+// daxpy_(&row2, &c[3], A2, &i1, temp, &i1);
+ daxpy_3l(row2, c[3], A2, temp);
+// daxpy_(&row2, &c[1], A0, &i1, temp, &i1);
+ daxpy_3l(row2, c[1], A0, temp);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A, &row, temp, &row, &beta, U, &row);
+ dgemm_nn_3l(row, row, row, A, row, temp, row, U, row);
+// dscal_(&row2, &c[4], V, &i1);
+ dscal_3l(row2, c[4], V);
+// daxpy_(&row2, &c[2], A2, &i1, V, &i1);
+ daxpy_3l(row2, c[2], A2, V);
+// daxpy_(&row2, &c[0], A0, &i1, V, &i1);
+ daxpy_3l(row2, c[0], A0, V);
+ free(A0);
+ free(A2);
+ free(A4);
+ free(temp);
+ }
+ else if(m==7)
+ {
+ double c[] = {17297280, 8648640, 1995840, 277200, 25200, 1512, 56, 1};
+ double *A0 = (double *) malloc(row*row*sizeof(double)); // d_eye(&A0, row);
+ for(ii=0; ii<row*row; ii++)
+ A0[ii] = 0.0;
+ for(ii=0; ii<row; ii++)
+ A0[ii*(row+1)] = 1.0;
+ double *A2 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *A4 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *A6 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *temp = malloc(row*row*sizeof(double)); // d_zeros(&temp, row, row);
+// char ta = 'n'; double alpha = 1; double beta = 1;
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A, &row, A, &row, &beta, A2, &row);
+ dgemm_nn_3l(row, row, row, A, row, A, row, A2, row);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A2, &row, A2, &row, &beta, A4, &row);
+ dgemm_nn_3l(row, row, row, A2, row, A2, row, A4, row);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A4, &row, A2, &row, &beta, A6, &row);
+ dgemm_nn_3l(row, row, row, A4, row, A2, row, A6, row);
+// dscal_(&row2, &d0, temp, &i1);
+ dscal_3l(row2, 0, temp);
+// daxpy_(&row2, &c[3], A2, &i1, temp, &i1);
+ daxpy_3l(row2, c[3], A2, temp);
+// daxpy_(&row2, &c[1], A0, &i1, temp, &i1);
+ daxpy_3l(row2, c[1], A0, temp);
+// daxpy_(&row2, &c[5], A4, &i1, temp, &i1);
+ daxpy_3l(row2, c[5], A4, temp);
+// daxpy_(&row2, &c[7], A6, &i1, temp, &i1);
+ daxpy_3l(row2, c[7], A6, temp);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A, &row, temp, &row, &beta, U, &row);
+ dgemm_nn_3l(row, row, row, A, row, temp, row, U, row);
+// dscal_(&row2, &d0, V, &i1);
+ dscal_3l(row2, 0, V);
+// daxpy_(&row2, &c[2], A2, &i1, V, &i1);
+ daxpy_3l(row2, c[2], A2, V);
+// daxpy_(&row2, &c[0], A0, &i1, V, &i1);
+ daxpy_3l(row2, c[0], A0, V);
+// daxpy_(&row2, &c[4], A4, &i1, V, &i1);
+ daxpy_3l(row2, c[4], A4, V);
+// daxpy_(&row2, &c[6], A6, &i1, V, &i1);
+ daxpy_3l(row2, c[6], A6, V);
+ free(A0);
+ free(A2);
+ free(A4);
+ free(A6);
+ free(temp);
+ }
+ else if(m==9)
+ {
+ double c[] = {17643225600, 8821612800, 2075673600, 302702400, 30270240, 2162160, 110880, 3960, 90, 1};
+ double *A0 = (double *) malloc(row*row*sizeof(double)); // d_eye(&A0, row);
+ for(ii=0; ii<row*row; ii++)
+ A0[ii] = 0.0;
+ for(ii=0; ii<row; ii++)
+ A0[ii*(row+1)] = 1.0;
+ double *A2 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *A4 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *A6 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *A8 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *temp = malloc(row*row*sizeof(double)); // d_zeros(&temp, row, row);
+// char ta = 'n'; double alpha = 1; double beta = 0;
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A, &row, A, &row, &beta, A2, &row);
+ dgemm_nn_3l(row, row, row, A, row, A, row, A2, row);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A2, &row, A2, &row, &beta, A4, &row);
+ dgemm_nn_3l(row, row, row, A2, row, A2, row, A4, row);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A4, &row, A2, &row, &beta, A6, &row);
+ dgemm_nn_3l(row, row, row, A4, row, A2, row, A6, row);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A6, &row, A2, &row, &beta, A8, &row);
+ dgemm_nn_3l(row, row, row, A6, row, A2, row, A8, row);
+ dmcopy(row, row, A8, row, V, row);
+ dmcopy(row, row, A8, row, temp, row);
+// daxpy_(&row2, &c[3], A2, &i1, temp, &i1);
+ daxpy_3l(row2, c[3], A2, temp);
+// daxpy_(&row2, &c[1], A0, &i1, temp, &i1);
+ daxpy_3l(row2, c[1], A0, temp);
+// daxpy_(&row2, &c[5], A4, &i1, temp, &i1);
+ daxpy_3l(row2, c[5], A4, temp);
+// daxpy_(&row2, &c[7], A6, &i1, temp, &i1);
+ daxpy_3l(row2, c[7], A6, temp);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A, &row, temp, &row, &beta, U, &row);
+ dgemm_nn_3l(row, row, row, A, row, temp, row, U, row);
+// dscal_(&row2, &c[8], V, &i1);
+ dscal_3l(row2, c[8], V);
+// daxpy_(&row2, &c[2], A2, &i1, V, &i1);
+ daxpy_3l(row2, c[2], A2, V);
+// daxpy_(&row2, &c[0], A0, &i1, V, &i1);
+ daxpy_3l(row2, c[0], A0, V);
+// daxpy_(&row2, &c[4], A4, &i1, V, &i1);
+ daxpy_3l(row2, c[4], A4, V);
+// daxpy_(&row2, &c[6], A6, &i1, V, &i1);
+ daxpy_3l(row2, c[6], A6, V);
+ free(A0);
+ free(A2);
+ free(A4);
+ free(A6);
+ free(A8);
+ free(temp);
+ }
+ else if(m==13) // tested
+ {
+ double c[] = {64764752532480000, 32382376266240000, 7771770303897600, 1187353796428800, 129060195264000, 10559470521600, 670442572800, 33522128640, 1323241920, 40840800, 960960, 16380, 182, 1};
+ double *A0 = (double *) malloc(row*row*sizeof(double)); // d_eye(&A0, row);
+ for(ii=0; ii<row*row; ii++)
+ A0[ii] = 0.0;
+ for(ii=0; ii<row; ii++)
+ A0[ii*(row+1)] = 1.0;
+ double *A2 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *A4 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *A6 = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+ double *temp = malloc(row*row*sizeof(double)); // d_zeros(&temp, row, row);
+// char ta = 'n'; double alpha = 1; double beta = 0;
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A, &row, A, &row, &beta, A2, &row);
+ dgemm_nn_3l(row, row, row, A, row, A, row, A2, row);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A2, &row, A2, &row, &beta, A4, &row);
+ dgemm_nn_3l(row, row, row, A2, row, A2, row, A4, row);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A4, &row, A2, &row, &beta, A6, &row);
+ dgemm_nn_3l(row, row, row, A4, row, A2, row, A6, row);
+ dmcopy(row, row, A2, row, U, row);
+// dscal_(&row2, &c[9], U, &i1);
+ dscal_3l(row2, c[9], U);
+// daxpy_(&row2, &c[11], A4, &i1, U, &i1);
+ daxpy_3l(row2, c[11], A4, U);
+// daxpy_(&row2, &c[13], A6, &i1, U, &i1);
+ daxpy_3l(row2, c[13], A6, U);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A6, &row, U, &row, &beta, temp, &row);
+ dgemm_nn_3l(row, row, row, A6, row, U, row, temp, row);
+// daxpy_(&row2, &c[7], A6, &i1, temp, &i1);
+ daxpy_3l(row2, c[7], A6, temp);
+// daxpy_(&row2, &c[5], A4, &i1, temp, &i1);
+ daxpy_3l(row2, c[5], A4, temp);
+// daxpy_(&row2, &c[3], A2, &i1, temp, &i1);
+ daxpy_3l(row2, c[3], A2, temp);
+// daxpy_(&row2, &c[1], A0, &i1, temp, &i1);
+ daxpy_3l(row2, c[1], A0, temp);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A, &row, temp, &row, &beta, U, &row);
+ dgemm_nn_3l(row, row, row, A, row, temp, row, U, row);
+ dmcopy(row, row, A2, row, temp, row);
+// dscal_(&row2, &c[8], V, &i1);
+ dscal_3l(row2, c[8], V);
+// daxpy_(&row2, &c[12], A6, &i1, temp, &i1);
+ daxpy_3l(row2, c[12], A6, temp);
+// daxpy_(&row2, &c[10], A4, &i1, temp, &i1);
+ daxpy_3l(row2, c[10], A4, temp);
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A6, &row, temp, &row, &beta, V, &row);
+ dgemm_nn_3l(row, row, row, A6, row, temp, row, V, row);
+// daxpy_(&row2, &c[6], A6, &i1, V, &i1);
+ daxpy_3l(row2, c[6], A6, V);
+// daxpy_(&row2, &c[4], A4, &i1, V, &i1);
+ daxpy_3l(row2, c[4], A4, V);
+// daxpy_(&row2, &c[2], A2, &i1, V, &i1);
+ daxpy_3l(row2, c[2], A2, V);
+// daxpy_(&row2, &c[0], A0, &i1, V, &i1);
+ daxpy_3l(row2, c[0], A0, V);
+ free(A0);
+ free(A2);
+ free(A4);
+ free(A6);
+ free(temp);
+ }
+ else
+ {
+ printf("%s\n", "Wrong Pade approximatin degree");
+ exit(1);
+ }
+ double *D = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+// dcopy_(&row2, V, &i1, A, &i1);
+ dmcopy(row, row, V, row, A, row);
+// daxpy_(&row2, &d1, U, &i1, A, &i1);
+ daxpy_3l(row2, 1.0, U, A);
+// dcopy_(&row2, V, &i1, D, &i1);
+ dmcopy(row, row, V, row, D, row);
+// daxpy_(&row2, &dm1, U, &i1, D, &i1);
+ daxpy_3l(row2, -1.0, U, D);
+ int *ipiv = (int *) malloc(row*sizeof(int));
+ int info = 0;
+// dgesv_(&row, &row, D, &row, ipiv, A, &row, &info);
+ dgesv_3l(row, row, D, row, ipiv, A, row, &info);
+ free(ipiv);
+ free(D);
+ free(U);
+ free(V);
+ }
+
+
+
+void expm(int row, double *A)
+ {
+
+ int i;
+
+ int m_vals[] = {3, 5, 7, 9, 13};
+ double theta[] = {0.01495585217958292, 0.2539398330063230, 0.9504178996162932, 2.097847961257068, 5.371920351148152};
+ int lentheta = 5;
+
+ double normA = onenorm(row, row, A);
+
+ if(normA<=theta[4])
+ {
+ for(i=0; i<lentheta; i++)
+ {
+ if(normA<=theta[i])
+ {
+ padeapprox(m_vals[i], row, A);
+ break;
+ }
+ }
+ }
+ else
+ {
+ int s;
+ double t = frexp(normA/(theta[4]), &s);
+ s = s - (t==0.5);
+ t = pow(2,-s);
+ int row2 = row*row;
+/* int i1 = 1;*/
+// dscal_(&row2, &t, A, &i1);
+ dscal_3l(row2, t, A);
+ padeapprox(m_vals[4], row, A);
+ double *temp = (double *) malloc(row*row*sizeof(double)); // d_zeros(&A2, row, row);
+// char ta = 'n'; double alpha = 1; double beta = 0;
+ for(i=0; i<s; i++)
+ {
+// dgemm_(&ta, &ta, &row, &row, &row, &alpha, A, &row, A, &row, &beta, temp, &row);
+ dgemm_nn_3l(row, row, row, A, row, A, row, temp, row);
+ dmcopy(row, row, temp, row, A, row);
+ }
+ free(temp);
+ }
+ }
+
+