hadamard               package:survey               R Documentation

_H_a_d_a_m_a_r_d _m_a_t_r_i_c_e_s

_D_e_s_c_r_i_p_t_i_o_n:

     Returns a Hadamard matrix of dimension larger than the argument.
     Matrices of dimension every multiple of 4 are thought to exist,
     but this function doesn't know about all of them, so it will
     sometimes return matrices that are larger than necessary.

_U_s_a_g_e:

     hadamard(n)

_A_r_g_u_m_e_n_t_s:

       n: lower bound for size 

_V_a_l_u_e:

     A Hadamard matrix

_N_o_t_e:

     Strictly speaking, a Hadamard matrix has entries +1 and -1 rather
     than 1 and 0, so '2*hadamard(n)-1' is a Hadamard matrix

_R_e_f_e_r_e_n_c_e_s:

     Sloane NJA. A Library of Hadamard Matrices <URL:
     http://www.research.att.com/~njas/hadamard/>

_S_e_e _A_l_s_o:

     'brrweights'

_E_x_a_m_p_l_e_s:

     par(mfrow=c(2,2))
     ## Sylvester-type
     image(hadamard(63),main="Sylvester: 64")
     ## Paley-type
     image(hadamard(57),main="Paley: 60")
     ## hybrid
     image(hadamard(23),main="Stored: 24")
     image(hadamard(90),main="Constructed: 96=4x24")

     par(mfrow=c(1,1))
     plot(2:150,sapply(2:150,function(i) ncol(hadamard(i))),type="S",
          ylab="Matrix size",xlab="n",xlim=c(1,150),ylim=c(1,150))
     abline(0,1,lty=3)
     lines(2:150, 2:150-(2:150 %% 4)+4,col="purple",type="S",lty=2)
     legend(c(x=10,y=140),legend=c("Actual size","Minimum possible size"),
          col=c("black","purple"),bty="n",lty=c(1,2))

