c15ecc30-5c90-401f-909a-ca1d74d5b84f 22 4 5 decimal
&[DATE] &[TIME] - &[FILENAME]
&[PAGENUM] / &[COUNT]
 <p> HadCRU [767 months] </p>

1950 -0.638 1950.0833 -0.389 1950.1667 -0.248 1950.25 -0.311 1950.3333 -0.164 1950.4167 -0.093 1950.5 -0.239 1950.5833 -0.299 1950.6667 -0.157 1950.75 -0.203 1950.8333 -0.701 1950.9167 -0.332 1951 -0.555 1951.0833 -0.834 1951.1667 -0.442 1951.25 -0.081 1951.3333 -0.023 1951.4167 -0.101 1951.5 -0.048 1951.5833 0.125 1951.6667 0.206 1951.75 0.156 1951.8333 -0.02 1951.9167 0.417 1952 0.294 1952.0833 0.072 1952.1667 -0.406 1952.25 -0.03 1952.3333 -0.045 1952.4167 -0.013 1952.5 0.117 1952.5833 0.089 1952.6667 0.127 1952.75 -0.139 1952.8333 -0.549 1952.9167 -0.208 1953 0.16 1953.0833 0.186 1953.1667 0.221 1953.25 0.22 1953.3333 0.053 1953.4167 0.179 1953.5 -0.009 1953.5833 0.146 1953.6667 0.112 1953.75 0.199 1953.8333 -0.136 1953.9167 0.257 1954 -0.506 1954.0833 -0.229 1954.1667 -0.365 1954.25 -0.206 1954.3333 -0.301 1954.4167 -0.105 1954.5 -0.187 1954.5833 -0.061 1954.6667 -0.004 1954.75 0.079 1954.8333 0.248 1954.9167 -0.198 1955 0.411 1955.0833 -0.131 1955.1667 -0.797 1955.25 -0.361 1955.3333 -0.204 1955.4167 -0.104 1955.5 -0.211 1955.5833 0.036 1955.6667 -0.032 1955.75 0.006 1955.8333 -0.383 1955.9167 -0.497 1956 -0.341 1956.0833 -0.7 1956.1667 -0.578 1956.25 -0.536 1956.3333 -0.434 1956.4167 -0.263 1956.5 -0.292 1956.5833 -0.39 1956.6667 -0.419 1956.75 -0.321 1956.8333 -0.478 1956.9167 -0.377 1957 -0.27 1957.0833 -0.23 1957.1667 -0.46 1957.25 -0.165 1957.3333 -0.115 1957.4167 0.062 1957.5 -0.181 1957.5833 0.036 1957.6667 0.061 1957.75 -0.06 1957.8333 0.151 1957.9167 0.36 1958 0.505 1958.0833 0.244 1958.1667 -0.065 1958.25 0.027 1958.3333 0.042 1958.4167 -0.081 1958.5 0.019 1958.5833 -0.04 1958.6667 -0.125 1958.75 0.011 1958.8333 0.08 1958.9167 -0.009 1959 0.127 1959.0833 0.064 1959.1667 0.198 1959.25 0.069 1959.3333 -0.127 1959.4167 0.127 1959.5 0.047 1959.5833 0.025 1959.6667 0.054 1959.75 -0.162 1959.8333 -0.172 1959.9167 -0.02 1960 0.034 1960.0833 0.348 1960.1667 -0.717 1960.25 -0.316 1960.3333 -0.343 1960.4167 0.052 1960.5 -0.102 1960.5833 -0.019 1960.6667 0.04 1960.75 0.017 1960.8333 -0.223 1960.9167 0.317 1961 0.09 1961.0833 0.278 1961.1667 0.096 1961.25 0.103 1961.3333 0.09 1961.4167 0.087 1961.5 -0.034 1961.5833 -0.013 1961.6667 0.051 1961.75 -0.053 1961.8333 0.006 1961.9167 -0.186 1962 0.186 1962.0833 0.273 1962.1667 -0.012 1962.25 0.047 1962.3333 -0.089 1962.4167 -0.147 1962.5 -0.067 1962.5833 -0.07 1962.6667 -0.016 1962.75 0.124 1962.8333 0.083 1962.9167 0.048 1963 -0.074 1963.0833 0.415 1963.1667 -0.316 1963.25 -0.234 1963.3333 -0.181 1963.4167 -0.139 1963.5 0.069 1963.5833 0.049 1963.6667 0.141 1963.75 0.4 1963.8333 0.276 1963.9167 -0.122 1964 -0.038 1964.0833 -0.287 1964.1667 -0.522 1964.25 -0.379 1964.3333 -0.191 1964.4167 -0.247 1964.5 -0.202 1964.5833 -0.282 1964.6667 -0.294 1964.75 -0.41 1964.8333 -0.297 1964.9167 -0.449 1965 -0.067 1965.0833 -0.453 1965.1667 -0.284 1965.25 -0.472 1965.3333 -0.233 1965.4167 -0.11 1965.5 -0.289 1965.5833 -0.224 1965.6667 -0.205 1965.75 -0.063 1965.8333 -0.252 1965.9167 -0.16 1966 -0.231 1966.0833 -0.169 1966.1667 -0.132 1966.25 -0.297 1966.3333 -0.194 1966.4167 0.047 1966.5 -0.007 1966.5833 -0.014 1966.6667 -0.026 1966.75 -0.181 1966.8333 -0.161 1966.9167 -0.395 1967 -0.286 1967.0833 -0.447 1967.1667 -0.103 1967.25 -0.08 1967.3333 0.115 1967.4167 -0.245 1967.5 -0.118 1967.5833 -0.089 1967.6667 -0.132 1967.75 0.348 1967.8333 0.015 1967.9167 -0.124 1968 -0.369 1968.0833 -0.257 1968.1667 0.36 1968.25 -0.216 1968.3333 -0.325 1968.4167 -0.307 1968.5 -0.221 1968.5833 -0.204 1968.6667 -0.209 1968.75 -0.135 1968.8333 -0.26 1968.9167 -0.449 1969 -0.651 1969.0833 -0.745 1969.1667 -0.321 1969.25 -0.016 1969.3333 -0.023 1969.4167 -0.099 1969.5 0.038 1969.5833 -0.026 1969.6667 -0.086 1969.75 -0.057 1969.8333 0.189 1969.9167 0.259 1970 -0.055 1970.0833 0.298 1970.1667 -0.263 1970.25 0.007 1970.3333 -0.111 1970.4167 0.089 1970.5 -0.008 1970.5833 -0.075 1970.6667 0.009 1970.75 -0.185 1970.8333 -0.117 1970.9167 -0.329 1971 -0.072 1971.0833 -0.436 1971.1667 -0.484 1971.25 -0.379 1971.3333 -0.298 1971.4167 -0.314 1971.5 -0.168 1971.5833 -0.111 1971.6667 0.001 1971.75 -0.067 1971.8333 -0.003 1971.9167 -0.089 1972 -0.805 1972.0833 -0.654 1972.1667 -0.294 1972.25 -0.177 1972.3333 -0.193 1972.4167 -0.039 1972.5 -0.08 1972.5833 -0.084 1972.6667 -0.234 1972.75 -0.104 1972.8333 -0.285 1972.9167 0.073 1973 0.167 1973.0833 0.53 1973.1667 0.386 1973.25 0.274 1973.3333 0.163 1973.4167 0.264 1973.5 0.086 1973.5833 0.033 1973.6667 -0.035 1973.75 0.001 1973.8333 -0.132 1973.9167 -0.064 1974 -0.474 1974.0833 -0.634 1974.1667 -0.203 1974.25 -0.157 1974.3333 -0.236 1974.4167 -0.189 1974.5 -0.072 1974.5833 -0.118 1974.6667 -0.253 1974.75 -0.357 1974.8333 -0.326 1974.9167 -0.351 1975 0.122 1975.0833 -0.029 1975.1667 0.031 1975.25 0.037 1975.3333 0.019 1975.4167 -0.001 1975.5 -0.016 1975.5833 -0.143 1975.6667 0.051 1975.75 -0.18 1975.8333 -0.288 1975.9167 -0.283 1976 -0.071 1976.0833 -0.362 1976.1667 -0.747 1976.25 -0.182 1976.3333 -0.319 1976.4167 -0.29 1976.5 -0.312 1976.5833 -0.287 1976.6667 -0.228 1976.75 -0.705 1976.8333 -0.453 1976.9167 -0.297 1977 -0.433 1977.0833 0.11 1977.1667 0.269 1977.25 0.271 1977.3333 0.111 1977.4167 0.218 1977.5 0.071 1977.5833 0 1977.6667 0.023 1977.75 -0.052 1977.8333 0.397 1977.9167 0.03 1978 0.048 1978.0833 -0.037 1978.1667 0.141 1978.25 0.009 1978.3333 -0.075 1978.4167 -0.176 1978.5 -0.082 1978.5833 -0.274 1978.6667 -0.077 1978.75 -0.071 1978.8333 0.148 1978.9167 -0.168 1979 -0.15 1979.0833 -0.317 1979.1667 0.014 1979.25 -0.266 1979.3333 -0.092 1979.4167 0.098 1979.5 0.025 1979.5833 0.052 1979.6667 0.084 1979.75 0.197 1979.8333 0.132 1979.9167 0.646 1980 0.114 1980.0833 0.27 1980.1667 -0.103 1980.25 0.177 1980.3333 0.258 1980.4167 0.142 1980.5 0.059 1980.5833 0.078 1980.6667 0.099 1980.75 0.124 1980.8333 0.271 1980.9167 0.133 1981 0.782 1981.0833 0.627 1981.1667 0.524 1981.25 0.429 1981.3333 0.116 1981.4167 0.151 1981.5 0.096 1981.5833 0.26 1981.6667 0.111 1981.75 0.029 1981.8333 0.157 1981.9167 0.526 1982 -0.204 1982.0833 0.106 1982.1667 -0.256 1982.25 0.065 1982.3333 0.021 1982.4167 -0.125 1982.5 0.035 1982.5833 0.016 1982.6667 0.097 1982.75 -0.129 1982.8333 -0.113 1982.9167 0.459 1983 0.755 1983.0833 0.5 1983.1667 0.373 1983.25 0.143 1983.3333 0.148 1983.4167 0.113 1983.5 0.253 1983.5833 0.342 1983.6667 0.398 1983.75 0.215 1983.8333 0.579 1983.9167 0.148 1984 0.17 1984.0833 -0.093 1984.1667 0.024 1984.25 -0.136 1984.3333 0.227 1984.4167 0.03 1984.5 -0.004 1984.5833 0.038 1984.6667 -0.138 1984.75 0.083 1984.8333 -0.214 1984.9167 -0.528 1985 0.011 1985.0833 -0.308 1985.1667 -0.094 1985.25 -0.001 1985.3333 0.067 1985.4167 -0.061 1985.5 -0.135 1985.5833 0.118 1985.6667 -0.028 1985.75 0.037 1985.8333 -0.046 1985.9167 0.041 1986 0.452 1986.0833 0.207 1986.1667 0.233 1986.25 0.298 1986.3333 0.201 1986.4167 0.153 1986.5 -0.044 1986.5833 0.022 1986.6667 -0.066 1986.75 -0.003 1986.8333 -0.036 1986.9167 0.028 1987 0.179 1987.0833 0.676 1987.1667 -0.122 1987.25 0.185 1987.3333 0.167 1987.4167 0.207 1987.5 0.368 1987.5833 0.188 1987.6667 0.305 1987.75 0.237 1987.8333 0.106 1987.9167 0.531 1988 0.641 1988.0833 0.261 1988.1667 0.414 1988.25 0.331 1988.3333 0.369 1988.4167 0.429 1988.5 0.345 1988.5833 0.325 1988.6667 0.389 1988.75 0.378 1988.8333 0.109 1988.9167 0.509 1989 0.15 1989.0833 0.459 1989.1667 0.415 1989.25 0.244 1989.3333 0.178 1989.4167 0.155 1989.5 0.216 1989.5833 0.219 1989.6667 0.218 1989.75 0.308 1989.8333 0.062 1989.9167 0.32 1990 0.39 1990.0833 0.527 1990.1667 1.186 1990.25 0.619 1990.3333 0.413 1990.4167 0.436 1990.5 0.286 1990.5833 0.356 1990.6667 0.195 1990.75 0.491 1990.8333 0.589 1990.9167 0.419 1991 0.522 1991.0833 0.533 1991.1667 0.255 1991.25 0.599 1991.3333 0.33 1991.4167 0.583 1991.5 0.455 1991.5833 0.368 1991.6667 0.388 1991.75 0.363 1991.8333 0.259 1991.9167 0.106 1992 0.73 1992.0833 0.561 1992.1667 0.432 1992.25 0.071 1992.3333 0.155 1992.4167 0.047 1992.5 -0.258 1992.5833 -0.086 1992.6667 -0.241 1992.75 -0.222 1992.8333 -0.247 1992.9167 0.179 1993 0.485 1993.0833 0.459 1993.1667 0.361 1993.25 0.208 1993.3333 0.25 1993.4167 0.198 1993.5 0.17 1993.5833 0.114 1993.6667 -0.125 1993.75 0.105 1993.8333 -0.366 1993.9167 0.241 1994 0.349 1994.0833 -0.184 1994.1667 0.333 1994.25 0.428 1994.3333 0.397 1994.4167 0.444 1994.5 0.274 1994.5833 0.279 1994.6667 0.342 1994.75 0.514 1994.8333 0.515 1994.9167 0.419 1995 0.89 1995.0833 1.252 1995.1667 0.511 1995.25 0.528 1995.3333 0.364 1995.4167 0.536 1995.5 0.427 1995.5833 0.616 1995.6667 0.486 1995.75 0.691 1995.8333 0.587 1995.9167 0.211 1996 0.195 1996.0833 0.458 1996.1667 0.136 1996.25 -0.013 1996.3333 0.295 1996.4167 0.267 1996.5 0.289 1996.5833 0.217 1996.6667 0.078 1996.75 0.166 1996.8333 0.234 1996.9167 0.408 1997 0.423 1997.0833 0.651 1997.1667 0.55 1997.25 0.41 1997.3333 0.345 1997.4167 0.525 1997.5 0.397 1997.5833 0.497 1997.6667 0.574 1997.75 0.664 1997.8333 0.546 1997.9167 0.635 1998 0.725 1998.0833 1.355 1998.1667 0.785 1998.25 0.965 1998.3333 0.831 1998.4167 0.889 1998.5 0.984 1998.5833 0.919 1998.6667 0.701 1998.75 0.7 1998.8333 0.285 1998.9167 0.874 1999 0.773 1999.0833 1.18 1999.1667 0.211 1999.25 0.488 1999.3333 0.393 1999.4167 0.466 1999.5 0.501 1999.5833 0.43 1999.6667 0.571 1999.75 0.546 1999.8333 0.372 1999.9167 0.808 2000 0.321 2000.0833 0.985 2000.1667 0.771 2000.25 0.953 2000.3333 0.505 2000.4167 0.427 2000.5 0.394 2000.5833 0.547 2000.6667 0.395 2000.75 0.263 2000.8333 0.05 2000.9167 0.194 2001 0.718 2001.0833 0.523 2001.1667 0.798 2001.25 0.667 2001.3333 0.702 2001.4167 0.565 2001.5 0.646 2001.5833 0.808 2001.6667 0.55 2001.75 0.615 2001.8333 1.032 2001.9167 0.546 2002 1.212 2002.0833 1.368 2002.1667 1.174 2002.25 0.697 2002.3333 0.598 2002.4167 0.659 2002.5 0.788 2002.5833 0.622 2002.6667 0.7 2002.75 0.501 2002.8333 0.744 2002.9167 0.272 2003 1.002 2003.0833 0.576 2003.1667 0.572 2003.25 0.612 2003.3333 0.853 2003.4167 0.71 2003.5 0.628 2003.5833 0.796 2003.6667 0.757 2003.75 0.933 2003.8333 0.676 2003.9167 1.12 2004 0.81 2004.0833 1.073 2004.1667 0.916 2004.25 0.705 2004.3333 0.345 2004.4167 0.527 2004.5 0.388 2004.5833 0.465 2004.6667 0.549 2004.75 0.772 2004.8333 1.076 2004.9167 0.459 2005 0.96 2005.0833 0.566 2005.1667 0.872 2005.25 1.022 2005.3333 0.762 2005.4167 0.869 2005.5 0.828 2005.5833 0.709 2005.6667 0.91 2005.75 1.093 2005.8333 1.205 2005.9167 0.787 2006 0.608 2006.0833 0.93 2006.1667 0.775 2006.25 0.574 2006.3333 0.506 2006.4167 0.867 2006.5 0.792 2006.5833 0.732 2006.6667 0.77 2006.75 0.974 2006.8333 0.884 2006.9167 1.313 2007 1.697 2007.0833 0.904 2007.1667 1.01 2007.25 1.126 2007.3333 0.786 2007.4167 0.582 2007.5 0.622 2007.5833 0.784 2007.6667 0.827 2007.75 0.989 2007.8333 0.778 2007.9167 0.798 2008 0.385 2008.0833 0.499 2008.1667 1.204 2008.25 0.557 2008.3333 0.479 2008.4167 0.605 2008.5 0.73 2008.5833 0.569 2008.6667 0.563 2008.75 1.011 2008.8333 1.065 2008.9167 0.67 2009 0.779 2009.0833 0.792 2009.1667 0.633 2009.25 0.829 2009.3333 0.581 2009.4167 0.659 2009.5 0.587 2009.5833 0.876 2009.6667 0.976 2009.75 0.724 2009.8333 0.845 2009.9167 0.492 2010 0.778 2010.0833 0.826 2010.1667 1.111 2010.25 1.062 2010.3333 0.936 2010.4167 0.996 2010.5 0.974 2010.5833 0.863 2010.6667 0.732 2010.75 0.888 2010.8333 1.195 2010.9167 0.448 2011 0.467 2011.0833 0.382 2011.1667 0.585 2011.25 0.83 2011.3333 0.523 2011.4167 0.778 2011.5 0.775 2011.5833 0.766 2011.6667 0.852 2011.75 0.941 2011.8333 0.609 2011.9167 0.827 2012 0.557 2012.0833 0.323 2012.1667 0.645 2012.25 1.03 2012.3333 0.963 2012.4167 0.947 2012.5 0.792 2012.5833 0.891 2012.6667 0.9 2012.75 0.847 2012.8333 0.849 2012.9167 0.261 2013 0.935 2013.0833 0.949 2013.1667 0.669 2013.25 0.581 2013.3333 0.773 2013.4167 0.827 2013.5 0.671 2013.5833 0.706 2013.6667 0.776 2013.75 0.83 2013.8333 0.964

<p> linfit modules </p>

Applicable parts are: Optimiz "numeric"

XY f φ β βlinfit X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky Gradient Matrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for Cholesky solver [LS] Φ M transpose M * : d M transpose Y vx - ( * : Δβ Φ 1 - ^ eval d * : b β Δβ + : 13 1 line :

Vector gradient ... Optimiz Symbolic

x β f n φ ct 1 : i 1 n range PD ct el x β f ( β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 2 1 line ct ct 1 + : 4 1 line for V 3 1 line :

The linfitCheby Procedure

0. reserve for backscale in original domain

xy XY : minXd xy 1 1 el : maxXd xy xy rows 1 el : a b c spec . 5 black 1 3 mat : Origin HadCRUt4 a b c spec pts : 5 1 line 1950 2013.8333 2 1 mat

1. Convert Original XY => Cheby domain [±1]

v i 1 XY rows range v i el i : for v 2 v * v Min - v Max - v Max v Min - / : 2 1 line : XY v XY 2 col augment : vx XY 1 col : vy XY 2 col : 4 1 line

2. Create ChebyShev Optimiz: Symbolic

x β p n 0 order range F n 1 + el β n 1 + el n x acos * cos * : for F 2 1 line : β 1 el β 2 el x * β 3 el 2 x acos * cos * β 4 el 3 x acos * cos * β 5 el 4 x acos * cos * β 6 el 5 x acos * cos * 6 1 mat

0. Create the original reserve 1. The original XY is converted in ChebyShev domain. 2. The ChebyShev vector function is created. 3. Collect the model f(x,β). 4. Cheby coefficients are spooled to file. 5. Collocate the "linfitCheby" Colln(x) 6. Reverse back the fit & the data set

Prepare the 'Unary β'

i 1 order 1 + range idx i el 1 : for

3. Collect the model function

x β f x β p n el n 1 order 1 + sum 1 1 line : 1 1 1 1 1 1 1 6 mat

set the 'Unary β' & length 'n' of the vector gradient

<= vector gradient

The "linfit" coefficients

Cheby XY f φ β βlinfit : 1 0.242903 0.530784 0.124906 0.05945 - 0.081141 - 0.013158 6 1 mat

5. Collocate the "linfitCheby"

x Colln c k el x p k el * ( k 1 order sum :

5. Data set & the fit in ChebyShev domain [-1..1]

 data x Colln 2 1 sys

6. reverse scale 'x domain'

ω scale 2 ω * minXd - maxXd - maxXd minXd - / :

6. linfitCheby in the original domain

 HadCRUt4 x scale Colln 10 x D1 * 100 x D2 * 1994 0 + 20 red 1 5 mat 2010 0 + 20 red 1 5 mat 7 1 sys

------------- linfitCheby ------------- HadCRUt4 January 1950 ... November 2013

1994: year the speed global warming started decreasing. 2010: year global warming started cooling down