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Posted to commits@systemml.apache.org by mb...@apache.org on 2017/02/27 18:36:09 UTC
[7/9] incubator-systemml git commit: [SYSTEMML-1286] Code generator
compiler integration, incl tests
http://git-wip-us.apache.org/repos/asf/incubator-systemml/blob/bbefe96b/src/test/scripts/functions/codegen/Algorithm_GLM.dml
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diff --git a/src/test/scripts/functions/codegen/Algorithm_GLM.dml b/src/test/scripts/functions/codegen/Algorithm_GLM.dml
new file mode 100644
index 0000000..d8eb966
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+++ b/src/test/scripts/functions/codegen/Algorithm_GLM.dml
@@ -0,0 +1,1053 @@
+#-------------------------------------------------------------
+#
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements. See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership. The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied. See the License for the
+# specific language governing permissions and limitations
+# under the License.
+#
+#-------------------------------------------------------------
+
+X = read ($1);
+Y = read ($2);
+
+fileO = " ";
+fileLog = " ";
+
+intercept_status = $3
+eps = $4
+max_iteration_IRLS = $5;
+max_iteration_CG = $5;
+
+distribution_type = $6;
+variance_as_power_of_the_mean = $7;
+link_type = $8;
+
+if( distribution_type != 1 ) {
+ link_as_power_of_the_mean = $9;
+ bernoulli_No_label = 0.0;
+} else {
+ link_as_power_of_the_mean = 1.0;
+ bernoulli_No_label = $9;
+}
+
+dispersion = 0.0;
+regularization = 0.001;
+
+
+variance_as_power_of_the_mean = as.double (variance_as_power_of_the_mean);
+link_as_power_of_the_mean = as.double (link_as_power_of_the_mean);
+bernoulli_No_label = as.double (bernoulli_No_label);
+dispersion = as.double (dispersion);
+eps = as.double (eps);
+
+
+# Default values for output statistics:
+
+termination_code = 0;
+min_beta = 0.0 / 0.0;
+i_min_beta = 0.0 / 0.0;
+max_beta = 0.0 / 0.0;
+i_max_beta = 0.0 / 0.0;
+intercept_value = 0.0 / 0.0;
+dispersion = 0.0 / 0.0;
+estimated_dispersion = 0.0 / 0.0;
+deviance_nodisp = 0.0 / 0.0;
+deviance = 0.0 / 0.0;
+
+print("BEGIN GLM SCRIPT");
+
+num_records = nrow (X);
+num_features = ncol (X);
+zeros_r = matrix (0, rows = num_records, cols = 1);
+ones_r = 1 + zeros_r;
+
+# Introduce the intercept, shift and rescale the columns of X if needed
+
+if (intercept_status == 1 | intercept_status == 2) # add the intercept column
+{
+ X = append (X, ones_r);
+ num_features = ncol (X);
+}
+
+scale_lambda = matrix (1, rows = num_features, cols = 1);
+if (intercept_status == 1 | intercept_status == 2)
+{
+ scale_lambda [num_features, 1] = 0;
+}
+
+if (intercept_status == 2) # scale-&-shift X columns to mean 0, variance 1
+{ # Important assumption: X [, num_features] = ones_r
+ avg_X_cols = t(colSums(X)) / num_records;
+ var_X_cols = (t(colSums (X ^ 2)) - num_records * (avg_X_cols ^ 2)) / (num_records - 1);
+ is_unsafe = ppred (var_X_cols, 0.0, "<=");
+ scale_X = 1.0 / sqrt (var_X_cols * (1 - is_unsafe) + is_unsafe);
+ scale_X [num_features, 1] = 1;
+ shift_X = - avg_X_cols * scale_X;
+ shift_X [num_features, 1] = 0;
+ rowSums_X_sq = (X ^ 2) %*% (scale_X ^ 2) + X %*% (2 * scale_X * shift_X) + sum (shift_X ^ 2);
+} else {
+ scale_X = matrix (1, rows = num_features, cols = 1);
+ shift_X = matrix (0, rows = num_features, cols = 1);
+ rowSums_X_sq = rowSums (X ^ 2);
+}
+
+# Henceforth we replace "X" with "X %*% (SHIFT/SCALE TRANSFORM)" and rowSums(X ^ 2)
+# with "rowSums_X_sq" in order to preserve the sparsity of X under shift and scale.
+# The transform is then associatively applied to the other side of the expression,
+# and is rewritten via "scale_X" and "shift_X" as follows:
+#
+# ssX_A = (SHIFT/SCALE TRANSFORM) %*% A --- is rewritten as:
+# ssX_A = diag (scale_X) %*% A;
+# ssX_A [num_features, ] = ssX_A [num_features, ] + t(shift_X) %*% A;
+#
+# tssX_A = t(SHIFT/SCALE TRANSFORM) %*% A --- is rewritten as:
+# tssX_A = diag (scale_X) %*% A + shift_X %*% A [num_features, ];
+
+# Initialize other input-dependent parameters
+
+lambda = scale_lambda * regularization;
+if (max_iteration_CG == 0) {
+ max_iteration_CG = num_features;
+}
+
+# In Bernoulli case, convert one-column "Y" into two-column
+
+if (distribution_type == 2 & ncol(Y) == 1)
+{
+ is_Y_negative = ppred (Y, bernoulli_No_label, "==");
+ Y = append (1 - is_Y_negative, is_Y_negative);
+ count_Y_negative = sum (is_Y_negative);
+ if (count_Y_negative == 0) {
+ stop ("GLM Input Error: all Y-values encode Bernoulli YES-label, none encode NO-label");
+ }
+ if (count_Y_negative == nrow(Y)) {
+ stop ("GLM Input Error: all Y-values encode Bernoulli NO-label, none encode YES-label");
+ }
+}
+
+# Set up the canonical link, if requested [Then we have: Var(mu) * (d link / d mu) = const]
+
+if (link_type == 0)
+{
+ if (distribution_type == 1) {
+ link_type = 1;
+ link_as_power_of_the_mean = 1.0 - variance_as_power_of_the_mean;
+ } else { if (distribution_type == 2) {
+ link_type = 2;
+} } }
+
+# For power distributions and/or links, we use two constants,
+# "variance as power of the mean" and "link_as_power_of_the_mean",
+# to specify the variance and the link as arbitrary powers of the
+# mean. However, the variance-powers of 1.0 (Poisson family) and
+# 2.0 (Gamma family) have to be treated as special cases, because
+# these values integrate into logarithms. The link-power of 0.0
+# is also special as it represents the logarithm link.
+
+num_response_columns = ncol (Y);
+
+is_supported = check_if_supported (num_response_columns, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean);
+if (is_supported == 1)
+{
+
+##### INITIALIZE THE BETAS #####
+
+[beta, saturated_log_l, isNaN] =
+ glm_initialize (X, Y, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean, intercept_status, max_iteration_CG);
+if (isNaN == 0)
+{
+
+##### START OF THE MAIN PART #####
+
+sum_X_sq = sum (rowSums_X_sq);
+trust_delta = 0.5 * sqrt (num_features) / max (sqrt (rowSums_X_sq));
+### max_trust_delta = trust_delta * 10000.0;
+log_l = 0.0;
+deviance_nodisp = 0.0;
+new_deviance_nodisp = 0.0;
+isNaN_log_l = 2;
+newbeta = beta;
+g = matrix (0.0, rows = num_features, cols = 1);
+g_norm = sqrt (sum ((g + lambda * beta) ^ 2));
+accept_new_beta = 1;
+reached_trust_boundary = 0;
+neg_log_l_change_predicted = 0.0;
+i_IRLS = 0;
+
+print ("BEGIN IRLS ITERATIONS...");
+
+ssX_newbeta = diag (scale_X) %*% newbeta;
+ssX_newbeta [num_features, ] = ssX_newbeta [num_features, ] + t(shift_X) %*% newbeta;
+all_linear_terms = X %*% ssX_newbeta;
+
+[new_log_l, isNaN_new_log_l] = glm_log_likelihood_part
+ (all_linear_terms, Y, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean);
+
+if (isNaN_new_log_l == 0) {
+ new_deviance_nodisp = 2.0 * (saturated_log_l - new_log_l);
+ new_log_l = new_log_l - 0.5 * sum (lambda * newbeta ^ 2);
+}
+
+if (fileLog != " ") {
+ log_str = "POINT_STEP_NORM," + i_IRLS + "," + sqrt (sum (beta ^ 2));
+ log_str = append (log_str, "OBJECTIVE," + i_IRLS + "," + (- new_log_l));
+ log_str = append (log_str, "LINEAR_TERM_MIN," + i_IRLS + "," + min (all_linear_terms));
+ log_str = append (log_str, "LINEAR_TERM_MAX," + i_IRLS + "," + max (all_linear_terms));
+} else {
+ log_str = " ";
+}
+
+# set w to avoid 'Initialization of w depends on if-else/while execution' warnings
+w = matrix (0.0, rows=1, cols=1);
+while (termination_code == 0)
+{
+ accept_new_beta = 1;
+
+ if (i_IRLS > 0)
+ {
+ if (isNaN_log_l == 0) {
+ accept_new_beta = 0;
+ }
+
+# Decide whether to accept a new iteration point and update the trust region
+# See Alg. 4.1 on p. 69 of "Numerical Optimization" 2nd ed. by Nocedal and Wright
+
+ rho = (- new_log_l + log_l) / neg_log_l_change_predicted;
+ if (rho < 0.25 | isNaN_new_log_l == 1) {
+ trust_delta = 0.25 * trust_delta;
+ }
+ if (rho > 0.75 & isNaN_new_log_l == 0 & reached_trust_boundary == 1) {
+ trust_delta = 2 * trust_delta;
+
+### if (trust_delta > max_trust_delta) {
+### trust_delta = max_trust_delta;
+### }
+
+ }
+ if (rho > 0.1 & isNaN_new_log_l == 0) {
+ accept_new_beta = 1;
+ }
+ }
+
+ if (fileLog != " ") {
+ log_str = append (log_str, "IS_POINT_UPDATED," + i_IRLS + "," + accept_new_beta);
+ log_str = append (log_str, "TRUST_DELTA," + i_IRLS + "," + trust_delta);
+ }
+ if (accept_new_beta == 1)
+ {
+ beta = newbeta; log_l = new_log_l; deviance_nodisp = new_deviance_nodisp; isNaN_log_l = isNaN_new_log_l;
+
+ [g_Y, w] = glm_dist (all_linear_terms, Y, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean);
+
+ # We introduced these variables to avoid roundoff errors:
+ # g_Y = y_residual / (y_var * link_grad);
+ # w = 1.0 / (y_var * link_grad * link_grad);
+
+ gXY = - t(X) %*% g_Y;
+ g = diag (scale_X) %*% gXY + shift_X %*% gXY [num_features, ];
+ g_norm = sqrt (sum ((g + lambda * beta) ^ 2));
+
+ if (fileLog != " ") {
+ log_str = append (log_str, "GRADIENT_NORM," + i_IRLS + "," + g_norm);
+ }
+ }
+
+ [z, neg_log_l_change_predicted, num_CG_iters, reached_trust_boundary] =
+ get_CG_Steihaug_point (X, scale_X, shift_X, w, g, beta, lambda, trust_delta, max_iteration_CG);
+
+ newbeta = beta + z;
+
+ ssX_newbeta = diag (scale_X) %*% newbeta;
+ ssX_newbeta [num_features, ] = ssX_newbeta [num_features, ] + t(shift_X) %*% newbeta;
+ all_linear_terms = X %*% ssX_newbeta;
+
+ [new_log_l, isNaN_new_log_l] = glm_log_likelihood_part
+ (all_linear_terms, Y, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean);
+
+ if (isNaN_new_log_l == 0) {
+ new_deviance_nodisp = 2.0 * (saturated_log_l - new_log_l);
+ new_log_l = new_log_l - 0.5 * sum (lambda * newbeta ^ 2);
+ }
+
+ log_l_change = new_log_l - log_l; # R's criterion for termination: |dev - devold|/(|dev| + 0.1) < eps
+
+ if (reached_trust_boundary == 0 & isNaN_new_log_l == 0 &
+ (2.0 * abs (log_l_change) < eps * (deviance_nodisp + 0.1) | abs (log_l_change) < (abs (log_l) + abs (new_log_l)) * 0.00000000000001) )
+ {
+ termination_code = 1;
+ }
+ rho = - log_l_change / neg_log_l_change_predicted;
+ z_norm = sqrt (sum (z * z));
+
+ [z_norm_m, z_norm_e] = round_to_print (z_norm);
+ [trust_delta_m, trust_delta_e] = round_to_print (trust_delta);
+ [rho_m, rho_e] = round_to_print (rho);
+ [new_log_l_m, new_log_l_e] = round_to_print (new_log_l);
+ [log_l_change_m, log_l_change_e] = round_to_print (log_l_change);
+ [g_norm_m, g_norm_e] = round_to_print (g_norm);
+
+ i_IRLS = i_IRLS + 1;
+ print ("Iter #" + i_IRLS + " completed"
+ + ", ||z|| = " + z_norm_m + "E" + z_norm_e
+ + ", trust_delta = " + trust_delta_m + "E" + trust_delta_e
+ + ", reached = " + reached_trust_boundary
+ + ", ||g|| = " + g_norm_m + "E" + g_norm_e
+ + ", new_log_l = " + new_log_l_m + "E" + new_log_l_e
+ + ", log_l_change = " + log_l_change_m + "E" + log_l_change_e
+ + ", rho = " + rho_m + "E" + rho_e);
+
+ if (fileLog != " ") {
+ log_str = append (log_str, "NUM_CG_ITERS," + i_IRLS + "," + num_CG_iters);
+ log_str = append (log_str, "IS_TRUST_REACHED," + i_IRLS + "," + reached_trust_boundary);
+ log_str = append (log_str, "POINT_STEP_NORM," + i_IRLS + "," + z_norm);
+ log_str = append (log_str, "OBJECTIVE," + i_IRLS + "," + (- new_log_l));
+ log_str = append (log_str, "OBJ_DROP_REAL," + i_IRLS + "," + log_l_change);
+ log_str = append (log_str, "OBJ_DROP_PRED," + i_IRLS + "," + (- neg_log_l_change_predicted));
+ log_str = append (log_str, "OBJ_DROP_RATIO," + i_IRLS + "," + rho);
+ log_str = append (log_str, "LINEAR_TERM_MIN," + i_IRLS + "," + min (all_linear_terms));
+ log_str = append (log_str, "LINEAR_TERM_MAX," + i_IRLS + "," + max (all_linear_terms));
+ }
+
+ if (i_IRLS == max_iteration_IRLS) {
+ termination_code = 2;
+ }
+}
+
+beta = newbeta;
+log_l = new_log_l;
+deviance_nodisp = new_deviance_nodisp;
+
+if (termination_code == 1) {
+ print ("Converged in " + i_IRLS + " steps.");
+} else {
+ print ("Did not converge.");
+}
+
+ssX_beta = diag (scale_X) %*% beta;
+ssX_beta [num_features, ] = ssX_beta [num_features, ] + t(shift_X) %*% beta;
+if (intercept_status == 2) {
+ beta_out = append (ssX_beta, beta);
+} else {
+ beta_out = ssX_beta;
+}
+
+write (beta_out, $10);
+
+if (intercept_status == 1 | intercept_status == 2) {
+ intercept_value = as.scalar (beta_out [num_features, 1]);
+ beta_noicept = beta_out [1 : (num_features - 1), 1];
+} else {
+ beta_noicept = beta_out [1 : num_features, 1];
+}
+min_beta = min (beta_noicept);
+max_beta = max (beta_noicept);
+tmp_i_min_beta = rowIndexMin (t(beta_noicept))
+i_min_beta = as.scalar (tmp_i_min_beta [1, 1]);
+tmp_i_max_beta = rowIndexMax (t(beta_noicept))
+i_max_beta = as.scalar (tmp_i_max_beta [1, 1]);
+
+##### OVER-DISPERSION PART #####
+
+all_linear_terms = X %*% ssX_beta;
+[g_Y, w] = glm_dist (all_linear_terms, Y, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean);
+
+pearson_residual_sq = g_Y ^ 2 / w;
+pearson_residual_sq = replace (target = pearson_residual_sq, pattern = 0.0/0.0, replacement = 0);
+# pearson_residual_sq = (y_residual ^ 2) / y_var;
+
+if (num_records > num_features) {
+ estimated_dispersion = sum (pearson_residual_sq) / (num_records - num_features);
+}
+if (dispersion <= 0.0) {
+ dispersion = estimated_dispersion;
+}
+deviance = deviance_nodisp / dispersion;
+
+##### END OF THE MAIN PART #####
+
+} else { print ("Input matrices are out of range. Terminating the DML."); termination_code = 3; }
+} else { print ("Distribution/Link not supported. Terminating the DML."); termination_code = 4; }
+
+str = "TERMINATION_CODE," + termination_code;
+str = append (str, "BETA_MIN," + min_beta);
+str = append (str, "BETA_MIN_INDEX," + i_min_beta);
+str = append (str, "BETA_MAX," + max_beta);
+str = append (str, "BETA_MAX_INDEX," + i_max_beta);
+str = append (str, "INTERCEPT," + intercept_value);
+str = append (str, "DISPERSION," + dispersion);
+str = append (str, "DISPERSION_EST," + estimated_dispersion);
+str = append (str, "DEVIANCE_UNSCALED," + deviance_nodisp);
+str = append (str, "DEVIANCE_SCALED," + deviance);
+print (str);
+
+
+
+
+check_if_supported =
+ function (int ncol_y, int dist_type, double var_power, int link_type, double link_power)
+ return (int is_supported)
+{
+ is_supported = 0;
+ if (ncol_y == 1 & dist_type == 1 & link_type == 1)
+ { # POWER DISTRIBUTION
+ is_supported = 1;
+ if (var_power == 0.0 & link_power == -1.0) {print ("Gaussian.inverse"); } else {
+ if (var_power == 0.0 & link_power == 0.0) {print ("Gaussian.log"); } else {
+ if (var_power == 0.0 & link_power == 0.5) {print ("Gaussian.sqrt"); } else {
+ if (var_power == 0.0 & link_power == 1.0) {print ("Gaussian.id"); } else {
+ if (var_power == 0.0 ) {print ("Gaussian.power_nonlog"); } else {
+ if (var_power == 1.0 & link_power == -1.0) {print ("Poisson.inverse"); } else {
+ if (var_power == 1.0 & link_power == 0.0) {print ("Poisson.log"); } else {
+ if (var_power == 1.0 & link_power == 0.5) {print ("Poisson.sqrt"); } else {
+ if (var_power == 1.0 & link_power == 1.0) {print ("Poisson.id"); } else {
+ if (var_power == 1.0 ) {print ("Poisson.power_nonlog"); } else {
+ if (var_power == 2.0 & link_power == -1.0) {print ("Gamma.inverse"); } else {
+ if (var_power == 2.0 & link_power == 0.0) {print ("Gamma.log"); } else {
+ if (var_power == 2.0 & link_power == 0.5) {print ("Gamma.sqrt"); } else {
+ if (var_power == 2.0 & link_power == 1.0) {print ("Gamma.id"); } else {
+ if (var_power == 2.0 ) {print ("Gamma.power_nonlog"); } else {
+ if (var_power == 3.0 & link_power == -2.0) {print ("InvGaussian.1/mu^2"); } else {
+ if (var_power == 3.0 & link_power == -1.0) {print ("InvGaussian.inverse"); } else {
+ if (var_power == 3.0 & link_power == 0.0) {print ("InvGaussian.log"); } else {
+ if (var_power == 3.0 & link_power == 0.5) {print ("InvGaussian.sqrt"); } else {
+ if (var_power == 3.0 & link_power == 1.0) {print ("InvGaussian.id"); } else {
+ if (var_power == 3.0 ) {print ("InvGaussian.power_nonlog");}else{
+ if ( link_power == 0.0) {print ("PowerDist.log"); } else {
+ print ("PowerDist.power_nonlog");
+ } }}}}} }}}}} }}}}} }}}}} }}
+ if (ncol_y == 1 & dist_type == 2)
+ {
+ print ("Error: Bernoulli response matrix has not been converted into two-column format.");
+ }
+ if (ncol_y == 2 & dist_type == 2 & link_type >= 1 & link_type <= 5)
+ { # BINOMIAL/BERNOULLI DISTRIBUTION
+ is_supported = 1;
+ if (link_type == 1 & link_power == -1.0) {print ("Binomial.inverse"); } else {
+ if (link_type == 1 & link_power == 0.0) {print ("Binomial.log"); } else {
+ if (link_type == 1 & link_power == 0.5) {print ("Binomial.sqrt"); } else {
+ if (link_type == 1 & link_power == 1.0) {print ("Binomial.id"); } else {
+ if (link_type == 1) {print ("Binomial.power_nonlog"); } else {
+ if (link_type == 2) {print ("Binomial.logit"); } else {
+ if (link_type == 3) {print ("Binomial.probit"); } else {
+ if (link_type == 4) {print ("Binomial.cloglog"); } else {
+ if (link_type == 5) {print ("Binomial.cauchit"); }
+ } }}}}} }}}
+ if (is_supported == 0) {
+ print ("Response matrix with " + ncol_y + " columns, distribution family (" + dist_type + ", " + var_power
+ + ") and link family (" + link_type + ", " + link_power + ") are NOT supported together.");
+ }
+}
+
+glm_initialize = function (Matrix[double] X, Matrix[double] Y, int dist_type, double var_power, int link_type, double link_power, int icept_status, int max_iter_CG)
+return (Matrix[double] beta, double saturated_log_l, int isNaN)
+{
+ saturated_log_l = 0.0;
+ isNaN = 0;
+ y_corr = Y [, 1];
+ if (dist_type == 2) {
+ n_corr = rowSums (Y);
+ is_n_zero = ppred (n_corr, 0.0, "==");
+ y_corr = Y [, 1] / (n_corr + is_n_zero) + (0.5 - Y [, 1]) * is_n_zero;
+ }
+ linear_terms = y_corr;
+ if (dist_type == 1 & link_type == 1) { # POWER DISTRIBUTION
+ if (link_power == 0.0) {
+ if (sum (ppred (y_corr, 0.0, "<")) == 0) {
+ is_zero_y_corr = ppred (y_corr, 0.0, "==");
+ linear_terms = log (y_corr + is_zero_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr);
+ } else { isNaN = 1; }
+ } else { if (link_power == 1.0) {
+ linear_terms = y_corr;
+ } else { if (link_power == -1.0) {
+ linear_terms = 1.0 / y_corr;
+ } else { if (link_power == 0.5) {
+ if (sum (ppred (y_corr, 0.0, "<")) == 0) {
+ linear_terms = sqrt (y_corr);
+ } else { isNaN = 1; }
+ } else { if (link_power > 0.0) {
+ if (sum (ppred (y_corr, 0.0, "<")) == 0) {
+ is_zero_y_corr = ppred (y_corr, 0.0, "==");
+ linear_terms = (y_corr + is_zero_y_corr) ^ link_power - is_zero_y_corr;
+ } else { isNaN = 1; }
+ } else {
+ if (sum (ppred (y_corr, 0.0, "<=")) == 0) {
+ linear_terms = y_corr ^ link_power;
+ } else { isNaN = 1; }
+ }}}}}
+ }
+ if (dist_type == 2 & link_type >= 1 & link_type <= 5)
+ { # BINOMIAL/BERNOULLI DISTRIBUTION
+ if (link_type == 1 & link_power == 0.0) { # Binomial.log
+ if (sum (ppred (y_corr, 0.0, "<")) == 0) {
+ is_zero_y_corr = ppred (y_corr, 0.0, "==");
+ linear_terms = log (y_corr + is_zero_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr);
+ } else { isNaN = 1; }
+ } else { if (link_type == 1 & link_power > 0.0) { # Binomial.power_nonlog pos
+ if (sum (ppred (y_corr, 0.0, "<")) == 0) {
+ is_zero_y_corr = ppred (y_corr, 0.0, "==");
+ linear_terms = (y_corr + is_zero_y_corr) ^ link_power - is_zero_y_corr;
+ } else { isNaN = 1; }
+ } else { if (link_type == 1) { # Binomial.power_nonlog neg
+ if (sum (ppred (y_corr, 0.0, "<=")) == 0) {
+ linear_terms = y_corr ^ link_power;
+ } else { isNaN = 1; }
+ } else {
+ is_zero_y_corr = ppred (y_corr, 0.0, "<=");
+ is_one_y_corr = ppred (y_corr, 1.0, ">=");
+ y_corr = y_corr * (1.0 - is_zero_y_corr) * (1.0 - is_one_y_corr) + 0.5 * (is_zero_y_corr + is_one_y_corr);
+ if (link_type == 2) { # Binomial.logit
+ linear_terms = log (y_corr / (1.0 - y_corr))
+ + is_one_y_corr / (1.0 - is_one_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr);
+ } else { if (link_type == 3) { # Binomial.probit
+ y_below_half = y_corr + (1.0 - 2.0 * y_corr) * ppred (y_corr, 0.5, ">");
+ t = sqrt (- 2.0 * log (y_below_half));
+ approx_inv_Gauss_CDF = - t + (2.515517 + t * (0.802853 + t * 0.010328)) / (1.0 + t * (1.432788 + t * (0.189269 + t * 0.001308)));
+ linear_terms = approx_inv_Gauss_CDF * (1.0 - 2.0 * ppred (y_corr, 0.5, ">"))
+ + is_one_y_corr / (1.0 - is_one_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr);
+ } else { if (link_type == 4) { # Binomial.cloglog
+ linear_terms = log (- log (1.0 - y_corr))
+ - log (- log (0.5)) * (is_zero_y_corr + is_one_y_corr)
+ + is_one_y_corr / (1.0 - is_one_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr);
+ } else { if (link_type == 5) { # Binomial.cauchit
+ linear_terms = tan ((y_corr - 0.5) * 3.1415926535897932384626433832795)
+ + is_one_y_corr / (1.0 - is_one_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr);
+ }} }}}}}
+ }
+
+ if (isNaN == 0) {
+ [saturated_log_l, isNaN] =
+ glm_log_likelihood_part (linear_terms, Y, dist_type, var_power, link_type, link_power);
+ }
+
+ if ((dist_type == 1 & link_type == 1 & link_power == 0.0) |
+ (dist_type == 2 & link_type >= 2))
+ {
+ desired_eta = 0.0;
+ } else { if (link_type == 1 & link_power == 0.0) {
+ desired_eta = log (0.5);
+ } else { if (link_type == 1) {
+ desired_eta = 0.5 ^ link_power;
+ } else {
+ desired_eta = 0.5;
+ }}}
+
+ beta = matrix (0.0, rows = ncol(X), cols = 1);
+
+ if (desired_eta != 0.0) {
+ if (icept_status == 1 | icept_status == 2) {
+ beta [nrow(beta), 1] = desired_eta;
+ } else {
+ # We want: avg (X %*% ssX_transform %*% beta) = desired_eta
+ # Note that "ssX_transform" is trivial here, hence ignored
+
+ beta = straightenX (X, 0.000001, max_iter_CG);
+ beta = beta * desired_eta;
+} } }
+
+
+glm_dist = function (Matrix[double] linear_terms, Matrix[double] Y,
+ int dist_type, double var_power, int link_type, double link_power)
+ return (Matrix[double] g_Y, Matrix[double] w)
+ # ORIGINALLY we returned more meaningful vectors, namely:
+ # Matrix[double] y_residual : y - y_mean, i.e. y observed - y predicted
+ # Matrix[double] link_gradient : derivative of the link function
+ # Matrix[double] var_function : variance without dispersion, i.e. the V(mu) function
+ # BUT, this caused roundoff errors, so we had to compute "directly useful" vectors
+ # and skip over the "meaningful intermediaries". Now we output these two variables:
+ # g_Y = y_residual / (var_function * link_gradient);
+ # w = 1.0 / (var_function * link_gradient ^ 2);
+{
+ num_records = nrow (linear_terms);
+ zeros_r = matrix (0.0, rows = num_records, cols = 1);
+ ones_r = 1 + zeros_r;
+ g_Y = zeros_r;
+ w = zeros_r;
+
+ # Some constants
+
+ one_over_sqrt_two_pi = 0.39894228040143267793994605993438;
+ ones_2 = matrix (1.0, rows = 1, cols = 2);
+ p_one_m_one = ones_2;
+ p_one_m_one [1, 2] = -1.0;
+ m_one_p_one = ones_2;
+ m_one_p_one [1, 1] = -1.0;
+ zero_one = ones_2;
+ zero_one [1, 1] = 0.0;
+ one_zero = ones_2;
+ one_zero [1, 2] = 0.0;
+ flip_pos = matrix (0, rows = 2, cols = 2);
+ flip_neg = flip_pos;
+ flip_pos [1, 2] = 1;
+ flip_pos [2, 1] = 1;
+ flip_neg [1, 2] = -1;
+ flip_neg [2, 1] = 1;
+
+ if (dist_type == 1 & link_type == 1) { # POWER DISTRIBUTION
+ y_mean = zeros_r;
+ if (link_power == 0.0) {
+ y_mean = exp (linear_terms);
+ y_mean_pow = y_mean ^ (1 - var_power);
+ w = y_mean_pow * y_mean;
+ g_Y = y_mean_pow * (Y - y_mean);
+ } else { if (link_power == 1.0) {
+ y_mean = linear_terms;
+ w = y_mean ^ (- var_power);
+ g_Y = w * (Y - y_mean);
+ } else {
+ y_mean = linear_terms ^ (1.0 / link_power);
+ c1 = (1 - var_power) / link_power - 1;
+ c2 = (2 - var_power) / link_power - 2;
+ g_Y = (linear_terms ^ c1) * (Y - y_mean) / link_power;
+ w = (linear_terms ^ c2) / (link_power ^ 2);
+ } }}
+ if (dist_type == 2 & link_type >= 1 & link_type <= 5)
+ { # BINOMIAL/BERNOULLI DISTRIBUTION
+ if (link_type == 1) { # BINOMIAL.POWER LINKS
+ if (link_power == 0.0) { # Binomial.log
+ vec1 = 1 / (exp (- linear_terms) - 1);
+ g_Y = Y [, 1] - Y [, 2] * vec1;
+ w = rowSums (Y) * vec1;
+ } else { # Binomial.nonlog
+ vec1 = zeros_r;
+ if (link_power == 0.5) {
+ vec1 = 1 / (1 - linear_terms ^ 2);
+ } else { if (sum (ppred (linear_terms, 0.0, "<")) == 0) {
+ vec1 = linear_terms ^ (- 2 + 1 / link_power) / (1 - linear_terms ^ (1 / link_power));
+ } else {isNaN = 1;}}
+ # We want a "zero-protected" version of
+ # vec2 = Y [, 1] / linear_terms;
+ is_y_0 = ppred (Y [, 1], 0.0, "==");
+ vec2 = (Y [, 1] + is_y_0) / (linear_terms * (1 - is_y_0) + is_y_0) - is_y_0;
+ g_Y = (vec2 - Y [, 2] * vec1 * linear_terms) / link_power;
+ w = rowSums (Y) * vec1 / link_power ^ 2;
+ }
+ } else {
+ is_LT_pos_infinite = ppred (linear_terms, 1.0/0.0, "==");
+ is_LT_neg_infinite = ppred (linear_terms, -1.0/0.0, "==");
+ is_LT_infinite = is_LT_pos_infinite %*% one_zero + is_LT_neg_infinite %*% zero_one;
+ finite_linear_terms = replace (target = linear_terms, pattern = 1.0/0.0, replacement = 0);
+ finite_linear_terms = replace (target = finite_linear_terms, pattern = -1.0/0.0, replacement = 0);
+ if (link_type == 2) { # Binomial.logit
+ Y_prob = exp (finite_linear_terms) %*% one_zero + ones_r %*% zero_one;
+ Y_prob = Y_prob / (rowSums (Y_prob) %*% ones_2);
+ Y_prob = Y_prob * ((1.0 - rowSums (is_LT_infinite)) %*% ones_2) + is_LT_infinite;
+ g_Y = rowSums (Y * (Y_prob %*% flip_neg)); ### = y_residual;
+ w = rowSums (Y * (Y_prob %*% flip_pos) * Y_prob); ### = y_variance;
+ } else { if (link_type == 3) { # Binomial.probit
+ is_lt_pos = ppred (linear_terms, 0.0, ">=");
+ t_gp = 1.0 / (1.0 + abs (finite_linear_terms) * 0.231641888); # 0.231641888 = 0.3275911 / sqrt (2.0)
+ pt_gp = t_gp * ( 0.254829592
+ + t_gp * (-0.284496736 # "Handbook of Mathematical Functions", ed. by M. Abramowitz and I.A. Stegun,
+ + t_gp * ( 1.421413741 # U.S. Nat-l Bureau of Standards, 10th print (Dec 1972), Sec. 7.1.26, p. 299
+ + t_gp * (-1.453152027
+ + t_gp * 1.061405429))));
+ the_gauss_exp = exp (- (linear_terms ^ 2) / 2.0);
+ vec1 = 0.25 * pt_gp * (2 - the_gauss_exp * pt_gp);
+ vec2 = Y [, 1] - rowSums (Y) * is_lt_pos + the_gauss_exp * pt_gp * rowSums (Y) * (is_lt_pos - 0.5);
+ w = the_gauss_exp * (one_over_sqrt_two_pi ^ 2) * rowSums (Y) / vec1;
+ g_Y = one_over_sqrt_two_pi * vec2 / vec1;
+ } else { if (link_type == 4) { # Binomial.cloglog
+ the_exp = exp (linear_terms)
+ the_exp_exp = exp (- the_exp);
+ is_too_small = ppred (10000000 + the_exp, 10000000, "==");
+ the_exp_ratio = (1 - is_too_small) * (1 - the_exp_exp) / (the_exp + is_too_small) + is_too_small * (1 - the_exp / 2);
+ g_Y = (rowSums (Y) * the_exp_exp - Y [, 2]) / the_exp_ratio;
+ w = the_exp_exp * the_exp * rowSums (Y) / the_exp_ratio;
+ } else { if (link_type == 5) { # Binomial.cauchit
+ Y_prob = 0.5 + (atan (finite_linear_terms) %*% p_one_m_one) / 3.1415926535897932384626433832795;
+ Y_prob = Y_prob * ((1.0 - rowSums (is_LT_infinite)) %*% ones_2) + is_LT_infinite;
+ y_residual = Y [, 1] * Y_prob [, 2] - Y [, 2] * Y_prob [, 1];
+ var_function = rowSums (Y) * Y_prob [, 1] * Y_prob [, 2];
+ link_gradient_normalized = (1 + linear_terms ^ 2) * 3.1415926535897932384626433832795;
+ g_Y = rowSums (Y) * y_residual / (var_function * link_gradient_normalized);
+ w = (rowSums (Y) ^ 2) / (var_function * link_gradient_normalized ^ 2);
+ }}}}
+ }
+ }
+}
+
+
+glm_log_likelihood_part = function (Matrix[double] linear_terms, Matrix[double] Y,
+ int dist_type, double var_power, int link_type, double link_power)
+ return (double log_l, int isNaN)
+{
+ isNaN = 0;
+ log_l = 0.0;
+ num_records = nrow (Y);
+ zeros_r = matrix (0.0, rows = num_records, cols = 1);
+
+ if (dist_type == 1 & link_type == 1)
+ { # POWER DISTRIBUTION
+ b_cumulant = zeros_r;
+ natural_parameters = zeros_r;
+ is_natural_parameter_log_zero = zeros_r;
+ if (var_power == 1.0 & link_power == 0.0) { # Poisson.log
+ b_cumulant = exp (linear_terms);
+ is_natural_parameter_log_zero = ppred (linear_terms, -1.0/0.0, "==");
+ natural_parameters = replace (target = linear_terms, pattern = -1.0/0.0, replacement = 0);
+ } else { if (var_power == 1.0 & link_power == 1.0) { # Poisson.id
+ if (sum (ppred (linear_terms, 0.0, "<")) == 0) {
+ b_cumulant = linear_terms;
+ is_natural_parameter_log_zero = ppred (linear_terms, 0.0, "==");
+ natural_parameters = log (linear_terms + is_natural_parameter_log_zero);
+ } else {isNaN = 1;}
+ } else { if (var_power == 1.0 & link_power == 0.5) { # Poisson.sqrt
+ if (sum (ppred (linear_terms, 0.0, "<")) == 0) {
+ b_cumulant = linear_terms ^ 2;
+ is_natural_parameter_log_zero = ppred (linear_terms, 0.0, "==");
+ natural_parameters = 2.0 * log (linear_terms + is_natural_parameter_log_zero);
+ } else {isNaN = 1;}
+ } else { if (var_power == 1.0 & link_power > 0.0) { # Poisson.power_nonlog, pos
+ if (sum (ppred (linear_terms, 0.0, "<")) == 0) {
+ is_natural_parameter_log_zero = ppred (linear_terms, 0.0, "==");
+ b_cumulant = (linear_terms + is_natural_parameter_log_zero) ^ (1.0 / link_power) - is_natural_parameter_log_zero;
+ natural_parameters = log (linear_terms + is_natural_parameter_log_zero) / link_power;
+ } else {isNaN = 1;}
+ } else { if (var_power == 1.0) { # Poisson.power_nonlog, neg
+ if (sum (ppred (linear_terms, 0.0, "<=")) == 0) {
+ b_cumulant = linear_terms ^ (1.0 / link_power);
+ natural_parameters = log (linear_terms) / link_power;
+ } else {isNaN = 1;}
+ } else { if (var_power == 2.0 & link_power == -1.0) { # Gamma.inverse
+ if (sum (ppred (linear_terms, 0.0, "<=")) == 0) {
+ b_cumulant = - log (linear_terms);
+ natural_parameters = - linear_terms;
+ } else {isNaN = 1;}
+ } else { if (var_power == 2.0 & link_power == 1.0) { # Gamma.id
+ if (sum (ppred (linear_terms, 0.0, "<=")) == 0) {
+ b_cumulant = log (linear_terms);
+ natural_parameters = - 1.0 / linear_terms;
+ } else {isNaN = 1;}
+ } else { if (var_power == 2.0 & link_power == 0.0) { # Gamma.log
+ b_cumulant = linear_terms;
+ natural_parameters = - exp (- linear_terms);
+ } else { if (var_power == 2.0) { # Gamma.power_nonlog
+ if (sum (ppred (linear_terms, 0.0, "<=")) == 0) {
+ b_cumulant = log (linear_terms) / link_power;
+ natural_parameters = - linear_terms ^ (- 1.0 / link_power);
+ } else {isNaN = 1;}
+ } else { if (link_power == 0.0) { # PowerDist.log
+ natural_parameters = exp (linear_terms * (1.0 - var_power)) / (1.0 - var_power);
+ b_cumulant = exp (linear_terms * (2.0 - var_power)) / (2.0 - var_power);
+ } else { # PowerDist.power_nonlog
+ if (-2 * link_power == 1.0 - var_power) {
+ natural_parameters = 1.0 / (linear_terms ^ 2) / (1.0 - var_power);
+ } else { if (-1 * link_power == 1.0 - var_power) {
+ natural_parameters = 1.0 / linear_terms / (1.0 - var_power);
+ } else { if ( link_power == 1.0 - var_power) {
+ natural_parameters = linear_terms / (1.0 - var_power);
+ } else { if ( 2 * link_power == 1.0 - var_power) {
+ natural_parameters = linear_terms ^ 2 / (1.0 - var_power);
+ } else {
+ if (sum (ppred (linear_terms, 0.0, "<=")) == 0) {
+ power = (1.0 - var_power) / link_power;
+ natural_parameters = (linear_terms ^ power) / (1.0 - var_power);
+ } else {isNaN = 1;}
+ }}}}
+ if (-2 * link_power == 2.0 - var_power) {
+ b_cumulant = 1.0 / (linear_terms ^ 2) / (2.0 - var_power);
+ } else { if (-1 * link_power == 2.0 - var_power) {
+ b_cumulant = 1.0 / linear_terms / (2.0 - var_power);
+ } else { if ( link_power == 2.0 - var_power) {
+ b_cumulant = linear_terms / (2.0 - var_power);
+ } else { if ( 2 * link_power == 2.0 - var_power) {
+ b_cumulant = linear_terms ^ 2 / (2.0 - var_power);
+ } else {
+ if (sum (ppred (linear_terms, 0.0, "<=")) == 0) {
+ power = (2.0 - var_power) / link_power;
+ b_cumulant = (linear_terms ^ power) / (2.0 - var_power);
+ } else {isNaN = 1;}
+ }}}}
+ }}}}} }}}}}
+ if (sum (is_natural_parameter_log_zero * abs (Y)) > 0.0) {
+ log_l = -1.0 / 0.0;
+ isNaN = 1;
+ }
+ if (isNaN == 0)
+ {
+ log_l = sum (Y * natural_parameters - b_cumulant);
+ if (log_l != log_l | (log_l == log_l + 1.0 & log_l == log_l * 2.0)) {
+ log_l = -1.0 / 0.0;
+ isNaN = 1;
+ } } }
+
+ if (dist_type == 2 & link_type >= 1 & link_type <= 5)
+ { # BINOMIAL/BERNOULLI DISTRIBUTION
+
+ [Y_prob, isNaN] = binomial_probability_two_column (linear_terms, link_type, link_power);
+
+ if (isNaN == 0) {
+ does_prob_contradict = ppred (Y_prob, 0.0, "<=");
+ if (sum (does_prob_contradict * abs (Y)) == 0.0) {
+ log_l = sum (Y * log (Y_prob * (1 - does_prob_contradict) + does_prob_contradict));
+ if (log_l != log_l | (log_l == log_l + 1.0 & log_l == log_l * 2.0)) {
+ isNaN = 1;
+ }
+ } else {
+ log_l = -1.0 / 0.0;
+ isNaN = 1;
+ } } }
+
+ if (isNaN == 1) {
+ log_l = - 1.0 / 0.0;
+ }
+}
+
+
+
+binomial_probability_two_column =
+ function (Matrix[double] linear_terms, int link_type, double link_power)
+ return (Matrix[double] Y_prob, int isNaN)
+{
+ isNaN = 0;
+ num_records = nrow (linear_terms);
+
+ # Define some auxiliary matrices
+
+ ones_2 = matrix (1.0, rows = 1, cols = 2);
+ p_one_m_one = ones_2;
+ p_one_m_one [1, 2] = -1.0;
+ m_one_p_one = ones_2;
+ m_one_p_one [1, 1] = -1.0;
+ zero_one = ones_2;
+ zero_one [1, 1] = 0.0;
+ one_zero = ones_2;
+ one_zero [1, 2] = 0.0;
+
+ zeros_r = matrix (0.0, rows = num_records, cols = 1);
+ ones_r = 1.0 + zeros_r;
+
+ # Begin the function body
+
+ Y_prob = zeros_r %*% ones_2;
+ if (link_type == 1) { # Binomial.power
+ if (link_power == 0.0) { # Binomial.log
+ Y_prob = exp (linear_terms) %*% p_one_m_one + ones_r %*% zero_one;
+ } else { if (link_power == 0.5) { # Binomial.sqrt
+ Y_prob = (linear_terms ^ 2) %*% p_one_m_one + ones_r %*% zero_one;
+ } else { # Binomial.power_nonlog
+ if (sum (ppred (linear_terms, 0.0, "<")) == 0) {
+ Y_prob = (linear_terms ^ (1.0 / link_power)) %*% p_one_m_one + ones_r %*% zero_one;
+ } else {isNaN = 1;}
+ }}
+ } else { # Binomial.non_power
+ is_LT_pos_infinite = ppred (linear_terms, 1.0/0.0, "==");
+ is_LT_neg_infinite = ppred (linear_terms, -1.0/0.0, "==");
+ is_LT_infinite = is_LT_pos_infinite %*% one_zero + is_LT_neg_infinite %*% zero_one;
+ finite_linear_terms = replace (target = linear_terms, pattern = 1.0/0.0, replacement = 0);
+ finite_linear_terms = replace (target = finite_linear_terms, pattern = -1.0/0.0, replacement = 0);
+ if (link_type == 2) { # Binomial.logit
+ Y_prob = exp (finite_linear_terms) %*% one_zero + ones_r %*% zero_one;
+ Y_prob = Y_prob / (rowSums (Y_prob) %*% ones_2);
+ } else { if (link_type == 3) { # Binomial.probit
+ lt_pos_neg = ppred (finite_linear_terms, 0.0, ">=") %*% p_one_m_one + ones_r %*% zero_one;
+ t_gp = 1.0 / (1.0 + abs (finite_linear_terms) * 0.231641888); # 0.231641888 = 0.3275911 / sqrt (2.0)
+ pt_gp = t_gp * ( 0.254829592
+ + t_gp * (-0.284496736 # "Handbook of Mathematical Functions", ed. by M. Abramowitz and I.A. Stegun,
+ + t_gp * ( 1.421413741 # U.S. Nat-l Bureau of Standards, 10th print (Dec 1972), Sec. 7.1.26, p. 299
+ + t_gp * (-1.453152027
+ + t_gp * 1.061405429))));
+ the_gauss_exp = exp (- (finite_linear_terms ^ 2) / 2.0);
+ Y_prob = lt_pos_neg + ((the_gauss_exp * pt_gp) %*% ones_2) * (0.5 - lt_pos_neg);
+ } else { if (link_type == 4) { # Binomial.cloglog
+ the_exp = exp (finite_linear_terms);
+ the_exp_exp = exp (- the_exp);
+ is_too_small = ppred (10000000 + the_exp, 10000000, "==");
+ Y_prob [, 1] = (1 - is_too_small) * (1 - the_exp_exp) + is_too_small * the_exp * (1 - the_exp / 2);
+ Y_prob [, 2] = the_exp_exp;
+ } else { if (link_type == 5) { # Binomial.cauchit
+ Y_prob = 0.5 + (atan (finite_linear_terms) %*% p_one_m_one) / 3.1415926535897932384626433832795;
+ } else {
+ isNaN = 1;
+ }}}}
+ Y_prob = Y_prob * ((1.0 - rowSums (is_LT_infinite)) %*% ones_2) + is_LT_infinite;
+} }
+
+
+# THE CG-STEIHAUG PROCEDURE SCRIPT
+
+# Apply Conjugate Gradient - Steihaug algorithm in order to approximately minimize
+# 0.5 z^T (X^T diag(w) X + diag (lambda)) z + (g + lambda * beta)^T z
+# under constraint: ||z|| <= trust_delta.
+# See Alg. 7.2 on p. 171 of "Numerical Optimization" 2nd ed. by Nocedal and Wright
+# IN THE ABOVE, "X" IS UNDERSTOOD TO BE "X %*% (SHIFT/SCALE TRANSFORM)"; this transform
+# is given separately because sparse "X" may become dense after applying the transform.
+#
+get_CG_Steihaug_point =
+ function (Matrix[double] X, Matrix[double] scale_X, Matrix[double] shift_X, Matrix[double] w,
+ Matrix[double] g, Matrix[double] beta, Matrix[double] lambda, double trust_delta, int max_iter_CG)
+ return (Matrix[double] z, double neg_log_l_change, int i_CG, int reached_trust_boundary)
+{
+ trust_delta_sq = trust_delta ^ 2;
+ size_CG = nrow (g);
+ z = matrix (0.0, rows = size_CG, cols = 1);
+ neg_log_l_change = 0.0;
+ reached_trust_boundary = 0;
+ g_reg = g + lambda * beta;
+ r_CG = g_reg;
+ p_CG = -r_CG;
+ rr_CG = sum(r_CG * r_CG);
+ eps_CG = rr_CG * min (0.25, sqrt (rr_CG));
+ converged_CG = 0;
+ if (rr_CG < eps_CG) {
+ converged_CG = 1;
+ }
+
+ max_iteration_CG = max_iter_CG;
+ if (max_iteration_CG <= 0) {
+ max_iteration_CG = size_CG;
+ }
+ i_CG = 0;
+ while (converged_CG == 0)
+ {
+ i_CG = i_CG + 1;
+ ssX_p_CG = diag (scale_X) %*% p_CG;
+ ssX_p_CG [size_CG, ] = ssX_p_CG [size_CG, ] + t(shift_X) %*% p_CG;
+ temp_CG = t(X) %*% (w * (X %*% ssX_p_CG));
+ q_CG = (lambda * p_CG) + diag (scale_X) %*% temp_CG + shift_X %*% temp_CG [size_CG, ];
+ pq_CG = sum (p_CG * q_CG);
+ if (pq_CG <= 0) {
+ pp_CG = sum (p_CG * p_CG);
+ if (pp_CG > 0) {
+ [z, neg_log_l_change] =
+ get_trust_boundary_point (g_reg, z, p_CG, q_CG, r_CG, pp_CG, pq_CG, trust_delta_sq);
+ reached_trust_boundary = 1;
+ } else {
+ neg_log_l_change = 0.5 * sum (z * (r_CG + g_reg));
+ }
+ converged_CG = 1;
+ }
+ if (converged_CG == 0) {
+ alpha_CG = rr_CG / pq_CG;
+ new_z = z + alpha_CG * p_CG;
+ if (sum(new_z * new_z) >= trust_delta_sq) {
+ pp_CG = sum (p_CG * p_CG);
+ [z, neg_log_l_change] =
+ get_trust_boundary_point (g_reg, z, p_CG, q_CG, r_CG, pp_CG, pq_CG, trust_delta_sq);
+ reached_trust_boundary = 1;
+ converged_CG = 1;
+ }
+ if (converged_CG == 0) {
+ z = new_z;
+ old_rr_CG = rr_CG;
+ r_CG = r_CG + alpha_CG * q_CG;
+ rr_CG = sum(r_CG * r_CG);
+ if (i_CG == max_iteration_CG | rr_CG < eps_CG) {
+ neg_log_l_change = 0.5 * sum (z * (r_CG + g_reg));
+ reached_trust_boundary = 0;
+ converged_CG = 1;
+ }
+ if (converged_CG == 0) {
+ p_CG = -r_CG + (rr_CG / old_rr_CG) * p_CG;
+} } } } }
+
+
+# An auxiliary function used twice inside the CG-STEIHAUG loop:
+get_trust_boundary_point =
+ function (Matrix[double] g, Matrix[double] z, Matrix[double] p,
+ Matrix[double] q, Matrix[double] r, double pp, double pq,
+ double trust_delta_sq)
+ return (Matrix[double] new_z, double f_change)
+{
+ zz = sum (z * z); pz = sum (p * z);
+ sq_root_d = sqrt (pz * pz - pp * (zz - trust_delta_sq));
+ tau_1 = (- pz + sq_root_d) / pp;
+ tau_2 = (- pz - sq_root_d) / pp;
+ zq = sum (z * q); gp = sum (g * p);
+ f_extra = 0.5 * sum (z * (r + g));
+ f_change_1 = f_extra + (0.5 * tau_1 * pq + zq + gp) * tau_1;
+ f_change_2 = f_extra + (0.5 * tau_2 * pq + zq + gp) * tau_2;
+ if (f_change_1 < f_change_2) {
+ new_z = z + (tau_1 * p);
+ f_change = f_change_1;
+ }
+ else {
+ new_z = z + (tau_2 * p);
+ f_change = f_change_2;
+ }
+}
+
+
+# Computes vector w such that ||X %*% w - 1|| -> MIN given avg(X %*% w) = 1
+# We find z_LS such that ||X %*% z_LS - 1|| -> MIN unconditionally, then scale
+# it to compute w = c * z_LS such that sum(X %*% w) = nrow(X).
+straightenX =
+ function (Matrix[double] X, double eps, int max_iter_CG)
+ return (Matrix[double] w)
+{
+ w_X = t(colSums(X));
+ lambda_LS = 0.000001 * sum(X ^ 2) / ncol(X);
+ eps_LS = eps * nrow(X);
+
+ # BEGIN LEAST SQUARES
+
+ r_LS = - w_X;
+ z_LS = matrix (0.0, rows = ncol(X), cols = 1);
+ p_LS = - r_LS;
+ norm_r2_LS = sum (r_LS ^ 2);
+ i_LS = 0;
+ while (i_LS < max_iter_CG & i_LS < ncol(X) & norm_r2_LS >= eps_LS)
+ {
+ q_LS = t(X) %*% X %*% p_LS;
+ q_LS = q_LS + lambda_LS * p_LS;
+ alpha_LS = norm_r2_LS / sum (p_LS * q_LS);
+ z_LS = z_LS + alpha_LS * p_LS;
+ old_norm_r2_LS = norm_r2_LS;
+ r_LS = r_LS + alpha_LS * q_LS;
+ norm_r2_LS = sum (r_LS ^ 2);
+ p_LS = -r_LS + (norm_r2_LS / old_norm_r2_LS) * p_LS;
+ i_LS = i_LS + 1;
+ }
+
+ # END LEAST SQUARES
+
+ w = (nrow(X) / sum (w_X * z_LS)) * z_LS;
+}
+
+
+round_to_print = function (double x_to_truncate)
+return (double mantissa, int eee)
+{
+ mantissa = 1.0;
+ eee = 0;
+ positive_infinity = 1.0 / 0.0;
+ x = abs (x_to_truncate);
+ if (x != x / 2.0) {
+ log_ten = log (10.0);
+ d_eee = round (log (x) / log_ten - 0.5);
+ mantissa = round (x * exp (log_ten * (4.0 - d_eee))) / 10000;
+ if (mantissa == 10.0) {
+ mantissa = 1.0;
+ d_eee = d_eee + 1;
+ }
+ if (x_to_truncate < 0.0) {
+ mantissa = - mantissa;
+ }
+ eee = 0;
+ pow_two = 1;
+ res_eee = abs (d_eee);
+ while (res_eee != 0.0) {
+ new_res_eee = round (res_eee / 2.0 - 0.3);
+ if (new_res_eee * 2.0 < res_eee) {
+ eee = eee + pow_two;
+ }
+ res_eee = new_res_eee;
+ pow_two = 2 * pow_two;
+ }
+ if (d_eee < 0.0) {
+ eee = - eee;
+ }
+ } else { mantissa = x_to_truncate; }
+}
http://git-wip-us.apache.org/repos/asf/incubator-systemml/blob/bbefe96b/src/test/scripts/functions/codegen/Algorithm_Kmeans.dml
----------------------------------------------------------------------
diff --git a/src/test/scripts/functions/codegen/Algorithm_Kmeans.dml b/src/test/scripts/functions/codegen/Algorithm_Kmeans.dml
new file mode 100644
index 0000000..9bdfab0
--- /dev/null
+++ b/src/test/scripts/functions/codegen/Algorithm_Kmeans.dml
@@ -0,0 +1,243 @@
+#-------------------------------------------------------------
+#
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements. See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership. The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied. See the License for the
+# specific language governing permissions and limitations
+# under the License.
+#
+#-------------------------------------------------------------
+
+X = read($1)
+num_centroids = $2
+num_runs = $3
+eps = $4;
+max_iter = $5;
+
+is_write_Y = 0;
+is_verbose = 0;
+avg_sample_size_per_centroid = 50;
+
+print ("BEGIN K-MEANS SCRIPT");
+print ("Reading X...");
+num_records = nrow (X);
+num_features = ncol (X);
+
+sumXsq = sum (X ^ 2);
+# Remark - A useful rewrite: sum (A %*% B) = sum (t(colSums(A)) * rowSums(B))
+
+# STEP 1: INITIALIZE CENTROIDS FOR ALL RUNS FROM DATA SAMPLES:
+
+print ("Taking data samples for initialization...");
+
+[sample_maps, samples_vs_runs_map, sample_block_size] =
+ get_sample_maps (num_records, num_runs, num_centroids * avg_sample_size_per_centroid);
+
+is_row_in_samples = rowSums (sample_maps);
+X_samples = sample_maps %*% X;
+X_samples_sq_norms = rowSums (X_samples ^ 2);
+
+print ("Initializing the centroids for all runs...");
+All_Centroids = matrix (0, rows = (num_runs * num_centroids), cols = num_features);
+
+# We select centroids according to the k-Means++ heuristic applied to a sample of X
+# Loop invariant: min_distances ~ sq.distances from X_sample rows to nearest centroids,
+# with the out-of-range X_sample positions in min_distances set to 0.0
+
+min_distances = is_row_in_samples; # Pick the 1-st centroids uniformly at random
+
+for (i in 1 : num_centroids)
+{
+ # "Matricize" and prefix-sum to compute the cumulative distribution function:
+ min_distances_matrix_form =
+ matrix (min_distances, rows = sample_block_size, cols = num_runs, byrow = FALSE);
+ cdf_min_distances = cumsum (min_distances_matrix_form);
+
+ # Select the i-th centroid in each sample as a random sample row id with
+ # probability ~ min_distances:
+ random_row = Rand (rows = 1, cols = num_runs, min = 0.0, max = 1.0);
+ threshold_matrix = random_row * cdf_min_distances [sample_block_size, ];
+ centroid_ids = t(colSums (cdf_min_distances < threshold_matrix)) + 1;
+
+ # Place the selected centroids together, one per run, into a matrix:
+ centroid_placer = matrix (0, rows = num_runs, cols = (sample_block_size * num_runs));
+ centroid_placer_raw =
+ table (seq (1, num_runs, 1), sample_block_size * seq (0, num_runs - 1, 1) + centroid_ids);
+ centroid_placer [, 1 : ncol (centroid_placer_raw)] = centroid_placer_raw;
+ centroids = centroid_placer %*% X_samples;
+
+ # Place the selected centroids into their appropriate slots in All_Centroids:
+ centroid_placer = matrix (0, rows = nrow (All_Centroids), cols = num_runs);
+ centroid_placer_raw =
+ table (seq (i, num_centroids * (num_runs - 1) + i, num_centroids), seq (1, num_runs, 1));
+ centroid_placer [1 : nrow (centroid_placer_raw), ] = centroid_placer_raw;
+ All_Centroids = All_Centroids + centroid_placer %*% centroids;
+
+ # Update min_distances to preserve the loop invariant:
+ distances = X_samples_sq_norms + samples_vs_runs_map %*% rowSums (centroids ^ 2)
+ - 2 * rowSums (X_samples * (samples_vs_runs_map %*% centroids));
+ if (i == 1) {
+ min_distances = is_row_in_samples * distances;
+ } else {
+ min_distances = min (min_distances, distances);
+} }
+
+# STEP 2: PERFORM K-MEANS ITERATIONS FOR ALL RUNS:
+
+termination_code = matrix (0, rows = num_runs, cols = 1);
+final_wcss = matrix (0, rows = num_runs, cols = 1);
+num_iterations = matrix (0, rows = num_runs, cols = 1);
+
+print ("Performing k-means iterations for all runs...");
+
+parfor (run_index in 1 : num_runs, check = 0)
+{
+ C = All_Centroids [(num_centroids * (run_index - 1) + 1) : (num_centroids * run_index), ];
+ C_old = C;
+ iter_count = 0;
+ term_code = 0;
+ wcss = 0;
+
+ while (term_code == 0)
+ {
+ # Compute Euclidean squared distances from records (X rows) to centroids (C rows)
+ # without the C-independent term, then take the minimum for each record
+ D = -2 * (X %*% t(C)) + t(rowSums (C ^ 2));
+ minD = rowMins (D);
+ # Compute the current centroid-based within-cluster sum of squares (WCSS)
+ wcss_old = wcss;
+ wcss = sumXsq + sum (minD);
+ if (is_verbose == 1) {
+ if (iter_count == 0) {
+ print ("Run " + run_index + ", At Start-Up: Centroid WCSS = " + wcss);
+ } else {
+ print ("Run " + run_index + ", Iteration " + iter_count + ": Centroid WCSS = " + wcss
+ + "; Centroid change (avg.sq.dist.) = " + (sum ((C - C_old) ^ 2) / num_centroids));
+ } }
+ # Check if convergence or maximum iteration has been reached
+ if (wcss_old - wcss < eps * wcss & iter_count > 0) {
+ term_code = 1; # Convergence is reached
+ } else {
+ if (iter_count >= max_iter) {
+ term_code = 2; # Maximum iteration is reached
+ } else {
+ iter_count = iter_count + 1;
+ # Find the closest centroid for each record
+ P = (D <= minD);
+ # If some records belong to multiple centroids, share them equally
+ P = P / rowSums (P);
+ # Compute the column normalization factor for P
+ P_denom = colSums (P);
+ if (sum (P_denom <= 0.0) > 0) {
+ term_code = 3; # There is a "runaway" centroid with 0.0 denominator
+ } else {
+ C_old = C;
+ # Compute new centroids as weighted averages over the records
+ C = (t(P) %*% X) / t(P_denom);
+ } } } }
+ print ("Run " + run_index + ", Iteration " + iter_count + ": Terminated with code = " + term_code + ", Centroid WCSS = " + wcss);
+ All_Centroids [(num_centroids * (run_index - 1) + 1) : (num_centroids * run_index), ] = C;
+ final_wcss [run_index, 1] = wcss;
+ termination_code [run_index, 1] = term_code;
+ num_iterations [run_index, 1] = iter_count;
+}
+
+# STEP 3: SELECT THE RUN WITH BEST CENTROID-WCSS AND OUTPUT ITS CENTROIDS:
+
+termination_bitmap = matrix (0, rows = num_runs, cols = 3);
+termination_bitmap_raw = table (seq (1, num_runs, 1), termination_code);
+termination_bitmap [, 1 : ncol(termination_bitmap_raw)] = termination_bitmap_raw;
+termination_stats = colSums (termination_bitmap);
+print ("Number of successful runs = " + as.integer (as.scalar (termination_stats [1, 1])));
+print ("Number of incomplete runs = " + as.integer (as.scalar (termination_stats [1, 2])));
+print ("Number of failed runs (with lost centroids) = " + as.integer (as.scalar (termination_stats [1, 3])));
+
+num_successful_runs = as.scalar (termination_stats [1, 1]);
+if (num_successful_runs > 0) {
+ final_wcss_successful = final_wcss * termination_bitmap [, 1];
+ worst_wcss = max (final_wcss_successful);
+ best_wcss = min (final_wcss_successful + (10 * worst_wcss + 10) * (1 - termination_bitmap [, 1]));
+ avg_wcss = sum (final_wcss_successful) / num_successful_runs;
+ best_index_vector = (final_wcss_successful == best_wcss);
+ aggr_best_index_vector = cumsum (best_index_vector);
+ best_index = as.integer (sum (aggr_best_index_vector == 0) + 1);
+ print ("Successful runs: Best run is " + best_index + " with Centroid WCSS = " + best_wcss
+ + "; Avg WCSS = " + avg_wcss + "; Worst WCSS = " + worst_wcss);
+ C = All_Centroids [(num_centroids * (best_index - 1) + 1) : (num_centroids * best_index), ];
+ print ("Writing out the best-WCSS centroids...");
+ write (C, $6, format="text");
+ print ("DONE.");
+} else {
+ stop ("No output is produced. Try increasing the number of iterations and/or runs.");
+}
+
+
+
+get_sample_maps = function (int num_records, int num_samples, int approx_sample_size)
+ return (Matrix[double] sample_maps, Matrix[double] sample_col_map, int sample_block_size)
+{
+ if (approx_sample_size < num_records) {
+ # Input value "approx_sample_size" is the average sample size; increase it by ~10 std.dev's
+ # to get the sample block size (to allocate space):
+ sample_block_size = as.integer (approx_sample_size + round (10 * sqrt (approx_sample_size)));
+ num_rows = sample_block_size * num_samples;
+
+ # Generate all samples in parallel by converting uniform random values into random
+ # integer skip-ahead intervals and prefix-summing them:
+ sample_rec_ids = Rand (rows = sample_block_size, cols = num_samples, min = 0.0, max = 1.0);
+ sample_rec_ids = round (log (sample_rec_ids) / log (1.0 - approx_sample_size / num_records) + 0.5);
+ # Prob [k-1 < log(uniform)/log(1-p) < k] = p*(1-p)^(k-1) = Prob [k-1 zeros before a one]
+ sample_rec_ids = cumsum (sample_rec_ids); # (skip to next one) --> (skip to i-th one)
+
+ # Replace all sample record ids over "num_records" (i.e. out of range) by "num_records + 1":
+ is_sample_rec_id_within_range = (sample_rec_ids <= num_records);
+ sample_rec_ids = sample_rec_ids * is_sample_rec_id_within_range
+ + (num_records + 1) * (1 - is_sample_rec_id_within_range);
+
+ # Rearrange all samples (and their out-of-range indicators) into one column-vector:
+ sample_rec_ids =
+ matrix (sample_rec_ids, rows = num_rows, cols = 1, byrow = FALSE);
+ is_row_in_samples =
+ matrix (is_sample_rec_id_within_range, rows = num_rows, cols = 1, byrow = FALSE);
+
+ # Use contingency table to create the "sample_maps" matrix that is a vertical concatenation
+ # of 0-1-matrices, one per sample, each with 1s at (i, sample_record[i]) and 0s elsewhere:
+ sample_maps_raw = table (seq (1, num_rows), sample_rec_ids);
+ max_rec_id = ncol (sample_maps_raw);
+ if (max_rec_id >= num_records) {
+ sample_maps = sample_maps_raw [, 1 : num_records];
+ } else {
+ sample_maps = matrix (0, rows = num_rows, cols = num_records);
+ sample_maps [, 1 : max_rec_id] = sample_maps_raw;
+ }
+
+ # Create a 0-1-matrix that maps each sample column ID into all row positions of the
+ # corresponding sample; map out-of-sample-range positions to row id = num_rows + 1:
+ sample_positions = (num_rows + 1) - is_row_in_samples * seq (num_rows, 1, -1);
+ # Column ID positions = 1, 1, ..., 1, 2, 2, ..., 2, . . . , n_c, n_c, ..., n_c:
+ col_positions = round (0.5 + seq (0, num_rows - 1, 1) / sample_block_size);
+ sample_col_map = table (sample_positions, col_positions);
+ # Remove the out-of-sample-range positions by cutting off the last row:
+ sample_col_map = sample_col_map [1 : (num_rows), ];
+
+ } else {
+ one_per_record = matrix (1, rows = num_records, cols = 1);
+ sample_block_size = num_records;
+ sample_maps = matrix (0, rows = (num_records * num_samples), cols = num_records);
+ sample_col_map = matrix (0, rows = (num_records * num_samples), cols = num_samples);
+ for (i in 1:num_samples) {
+ sample_maps [(num_records * (i - 1) + 1) : (num_records * i), ] = diag (one_per_record);
+ sample_col_map [(num_records * (i - 1) + 1) : (num_records * i), i] = one_per_record;
+} } }
+
http://git-wip-us.apache.org/repos/asf/incubator-systemml/blob/bbefe96b/src/test/scripts/functions/codegen/Algorithm_L2SVM.R
----------------------------------------------------------------------
diff --git a/src/test/scripts/functions/codegen/Algorithm_L2SVM.R b/src/test/scripts/functions/codegen/Algorithm_L2SVM.R
new file mode 100644
index 0000000..36e844e
--- /dev/null
+++ b/src/test/scripts/functions/codegen/Algorithm_L2SVM.R
@@ -0,0 +1,98 @@
+#-------------------------------------------------------------
+#
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements. See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership. The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied. See the License for the
+# specific language governing permissions and limitations
+# under the License.
+#
+#-------------------------------------------------------------
+
+args <- commandArgs(TRUE)
+library("Matrix")
+
+X = readMM(paste(args[1], "X.mtx", sep=""));
+Y = readMM(paste(args[1], "Y.mtx", sep=""));
+intercept = as.integer(args[2]);
+epsilon = as.double(args[3]);
+lambda = 0.001;
+maxiterations = as.integer(args[4]);
+
+check_min = min(Y)
+check_max = max(Y)
+num_min = sum(Y == check_min)
+num_max = sum(Y == check_max)
+if(num_min + num_max != nrow(Y)){
+ print("please check Y, it should contain only 2 labels")
+}else{
+ if(check_min != -1 | check_max != +1)
+ Y = 2/(check_max - check_min)*Y - (check_min + check_max)/(check_max - check_min)
+}
+
+N = nrow(X)
+D = ncol(X)
+
+if (intercept == 1) {
+ ones = matrix(1,N,1)
+ X = cbind(X, ones);
+}
+
+num_rows_in_w = D
+if(intercept == 1){
+ num_rows_in_w = num_rows_in_w + 1
+}
+w = matrix(0, num_rows_in_w, 1)
+
+g_old = t(X) %*% Y
+s = g_old
+
+Xw = matrix(0,nrow(X),1)
+iter = 0
+continue = TRUE
+while(continue && iter < maxiterations){
+ t = 0
+ Xd = X %*% s
+ wd = lambda * sum(w * s)
+ dd = lambda * sum(s * s)
+ continue1 = TRUE
+ while(continue1){
+ tmp_Xw = Xw + t*Xd
+ out = 1 - Y * (tmp_Xw)
+ sv = which(out > 0)
+ g = wd + t*dd - sum(out[sv] * Y[sv] * Xd[sv])
+ h = dd + sum(Xd[sv] * Xd[sv])
+ t = t - g/h
+ continue1 = (g*g/h >= 1e-10)
+ }
+
+ w = w + t*s
+ Xw = Xw + t*Xd
+
+ out = 1 - Y * (X %*% w)
+ sv = which(out > 0)
+ obj = 0.5 * sum(out[sv] * out[sv]) + lambda/2 * sum(w * w)
+ g_new = t(X[sv,]) %*% (out[sv] * Y[sv]) - lambda * w
+
+ print(paste("OBJ : ", obj))
+
+ continue = (t*sum(s * g_old) >= epsilon*obj)
+
+ be = sum(g_new * g_new)/sum(g_old * g_old)
+ s = be * s + g_new
+ g_old = g_new
+
+ iter = iter + 1
+}
+
+writeMM(as(w,"CsparseMatrix"), paste(args[5], "w", sep=""));
http://git-wip-us.apache.org/repos/asf/incubator-systemml/blob/bbefe96b/src/test/scripts/functions/codegen/Algorithm_L2SVM.dml
----------------------------------------------------------------------
diff --git a/src/test/scripts/functions/codegen/Algorithm_L2SVM.dml b/src/test/scripts/functions/codegen/Algorithm_L2SVM.dml
new file mode 100644
index 0000000..9a6a631
--- /dev/null
+++ b/src/test/scripts/functions/codegen/Algorithm_L2SVM.dml
@@ -0,0 +1,106 @@
+#-------------------------------------------------------------
+#
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements. See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership. The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied. See the License for the
+# specific language governing permissions and limitations
+# under the License.
+#
+#-------------------------------------------------------------
+
+X = read($1)
+Y = read($2)
+intercept = $3;
+eps = $4;
+maxiter = $5;
+
+check_min = min(Y)
+check_max = max(Y)
+num_min = sum(ppred(Y, check_min, "=="))
+num_max = sum(ppred(Y, check_max, "=="))
+if(num_min + num_max != nrow(Y)) print("please check Y, it should contain only 2 labels")
+else{
+ if(check_min != -1 | check_max != +1)
+ Y = 2/(check_max - check_min)*Y - (check_min + check_max)/(check_max - check_min)
+}
+
+epsilon = eps
+lambda = 0.001
+maxiterations = maxiter
+num_samples = nrow(X)
+dimensions = ncol(X)
+
+if (intercept == 1) {
+ ones = matrix(1, rows=num_samples, cols=1)
+ X = append(X, ones);
+}
+
+num_rows_in_w = dimensions
+if(intercept == 1){
+ num_rows_in_w = num_rows_in_w + 1
+}
+w = matrix(0, rows=num_rows_in_w, cols=1)
+
+g_old = t(X) %*% Y
+s = g_old
+
+Xw = matrix(0, rows=nrow(X), cols=1)
+debug_str = "# Iter, Obj"
+iter = 0
+continue = 1
+while(continue == 1 & iter < maxiterations) {
+ # minimizing primal obj along direction s
+ step_sz = 0
+ Xd = X %*% s
+ wd = lambda * sum(w * s)
+ dd = lambda * sum(s * s)
+ continue1 = 1
+ while(continue1 == 1){
+ tmp_Xw = Xw + step_sz*Xd
+ out = 1 - Y * (tmp_Xw)
+ sv = ppred(out, 0, ">")
+ out = out * sv
+ g = wd + step_sz*dd - sum(out * Y * Xd)
+ h = dd + sum(Xd * sv * Xd)
+ step_sz = step_sz - g/h
+ if (g*g/h < 0.0000000001){
+ continue1 = 0
+ }
+ }
+
+ #update weights
+ w = w + step_sz*s
+ Xw = Xw + step_sz*Xd
+
+ out = 1 - Y * Xw
+ sv = ppred(out, 0, ">")
+ out = sv * out
+ obj = 0.5 * sum(out * out) + lambda/2 * sum(w * w)
+ g_new = t(X) %*% (out * Y) - lambda * w
+
+ print("OBJ = " + obj)
+ tmp = sum(s * g_old)
+ if(step_sz*tmp < epsilon*obj){
+ continue = 0
+ }
+
+ #non-linear CG step
+ be = sum(g_new * g_new)/sum(g_old * g_old)
+ s = be * s + g_new
+ g_old = g_new
+
+ iter = iter + 1
+}
+
+write(w, $6, format="text")
http://git-wip-us.apache.org/repos/asf/incubator-systemml/blob/bbefe96b/src/test/scripts/functions/codegen/Algorithm_LinregCG.R
----------------------------------------------------------------------
diff --git a/src/test/scripts/functions/codegen/Algorithm_LinregCG.R b/src/test/scripts/functions/codegen/Algorithm_LinregCG.R
new file mode 100644
index 0000000..5dcad95
--- /dev/null
+++ b/src/test/scripts/functions/codegen/Algorithm_LinregCG.R
@@ -0,0 +1,57 @@
+#-------------------------------------------------------------
+#
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements. See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership. The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied. See the License for the
+# specific language governing permissions and limitations
+# under the License.
+#
+#-------------------------------------------------------------
+
+
+args <- commandArgs(TRUE)
+options(digits=22)
+library("Matrix")
+
+X = readMM(paste(args[1], "X.mtx", sep=""))
+y = readMM(paste(args[1], "y.mtx", sep=""))
+
+intercept = as.integer(args[2]);
+eps = as.double(args[3]);
+maxiter = as.double(args[4]);
+
+if( intercept == 1 ){
+ ones = matrix(1, nrow(X), 1);
+ X = cbind(X, ones);
+}
+
+r = -(t(X) %*% y);
+p = -r;
+norm_r2 = sum(r * r);
+w = matrix(0, ncol(X), 1);
+
+i = 0;
+while(i < maxiter) {
+ q = ((t(X) %*% (X %*% p)) + eps * p);
+ alpha = norm_r2 / ((t(p) %*% q)[1:1]);
+ w = w + alpha * p;
+ old_norm_r2 = norm_r2;
+ r = r + alpha * q;
+ norm_r2 = sum(r * r);
+ beta = norm_r2 / old_norm_r2;
+ p = -r + beta * p;
+ i = i + 1;
+}
+
+writeMM(as(w,"CsparseMatrix"), paste(args[5], "w", sep=""))
http://git-wip-us.apache.org/repos/asf/incubator-systemml/blob/bbefe96b/src/test/scripts/functions/codegen/Algorithm_LinregCG.dml
----------------------------------------------------------------------
diff --git a/src/test/scripts/functions/codegen/Algorithm_LinregCG.dml b/src/test/scripts/functions/codegen/Algorithm_LinregCG.dml
new file mode 100644
index 0000000..92f15d7
--- /dev/null
+++ b/src/test/scripts/functions/codegen/Algorithm_LinregCG.dml
@@ -0,0 +1,56 @@
+#-------------------------------------------------------------
+#
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements. See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership. The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied. See the License for the
+# specific language governing permissions and limitations
+# under the License.
+#
+#-------------------------------------------------------------
+
+
+X = read($1);
+y = read($2);
+intercept = $3;
+eps = $4;
+maxiter = $5;
+
+if( intercept == 1 ){
+ ones = matrix(1, nrow(X), 1);
+ X = append(X, ones);
+}
+
+r = -(t(X) %*% y);
+p = -r;
+norm_r2 = sum(r * r);
+w = matrix(0, rows = ncol(X), cols = 1);
+
+i = 0;
+while(i < maxiter) {
+ q = ((t(X) %*% (X %*% p)) + eps * p);
+ alpha = norm_r2 / as.scalar(t(p) %*% q);
+ w = w + alpha * p;
+ old_norm_r2 = norm_r2;
+ r = r + alpha * q;
+ norm_r2 = sum(r * r);
+ beta = norm_r2 / old_norm_r2;
+ p = -r + beta * p;
+ i = i + 1;
+}
+
+write(w, $6);
+
+
+
+
http://git-wip-us.apache.org/repos/asf/incubator-systemml/blob/bbefe96b/src/test/scripts/functions/codegen/Algorithm_MLogreg.R
----------------------------------------------------------------------
diff --git a/src/test/scripts/functions/codegen/Algorithm_MLogreg.R b/src/test/scripts/functions/codegen/Algorithm_MLogreg.R
new file mode 100644
index 0000000..121aba7
--- /dev/null
+++ b/src/test/scripts/functions/codegen/Algorithm_MLogreg.R
@@ -0,0 +1,278 @@
+#-------------------------------------------------------------
+#
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements. See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership. The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied. See the License for the
+# specific language governing permissions and limitations
+# under the License.
+#
+#-------------------------------------------------------------
+
+args <- commandArgs(TRUE)
+library("Matrix")
+library("matrixStats")
+
+X = readMM(paste(args[1], "X.mtx", sep=""));
+Y_vec = readMM(paste(args[1], "Y.mtx", sep=""));
+intercept = as.integer(args[2]);
+tol = as.double(args[3]);
+maxiter = as.integer(args[4]);
+
+intercept_status = intercept;
+regularization = 0.001;
+maxinneriter = 0;
+
+print ("BEGIN MULTINOMIAL LOGISTIC REGRESSION SCRIPT");
+
+eta0 = 0.0001;
+eta1 = 0.25;
+eta2 = 0.75;
+sigma1 = 0.25;
+sigma2 = 0.5;
+sigma3 = 4.0;
+psi = 0.1;
+
+N = nrow (X);
+D = ncol (X);
+
+# Introduce the intercept, shift and rescale the columns of X if needed
+if (intercept_status == 1 | intercept_status == 2) # add the intercept column
+{
+ X = cbind (X, matrix (1, N, 1));
+ D = ncol (X);
+}
+
+scale_lambda = matrix (1, D, 1);
+if (intercept_status == 1 | intercept_status == 2)
+{
+ scale_lambda [D, 1] = 0;
+}
+
+if (intercept_status == 2) # scale-&-shift X columns to mean 0, variance 1
+{ # Important assumption: X [, D] = matrix (1, rows = N, cols = 1)
+ avg_X_cols = t(colSums(X)) / N;
+ var_X_cols = (t(colSums (X ^ 2)) - N * (avg_X_cols ^ 2)) / (N - 1);
+ is_unsafe = (var_X_cols <= 0.0);
+ scale_X = 1.0 / sqrt (var_X_cols * (1 - is_unsafe) + is_unsafe);
+ scale_X [D, 1] = 1;
+ shift_X = - avg_X_cols * scale_X;
+ shift_X [D, 1] = 0;
+ rowSums_X_sq = (X ^ 2) %*% (scale_X ^ 2) + X %*% (2 * scale_X * shift_X) + sum (shift_X ^ 2);
+} else {
+ scale_X = matrix (1, D, 1);
+ shift_X = matrix (0, D, 1);
+ rowSums_X_sq = rowSums (X ^ 2);
+}
+
+# Henceforth we replace "X" with "X %*% (SHIFT/SCALE TRANSFORM)" and rowSums(X ^ 2)
+# with "rowSums_X_sq" in order to preserve the sparsity of X under shift and scale.
+# The transform is then associatively applied to the other side of the expression,
+# and is rewritten via "scale_X" and "shift_X" as follows:
+#
+# ssX_A = (SHIFT/SCALE TRANSFORM) %*% A --- is rewritten as:
+# ssX_A = diag (scale_X) %*% A;
+# ssX_A [D, ] = ssX_A [D, ] + t(shift_X) %*% A;
+#
+# tssX_A = t(SHIFT/SCALE TRANSFORM) %*% A --- is rewritten as:
+# tssX_A = diag (scale_X) %*% A + shift_X %*% A [D, ];
+
+# Convert "Y_vec" into indicator matrice:
+if (min (Y_vec) <= 0) {
+ # Category labels "0", "-1" etc. are converted into the largest label
+ max_y = max (Y_vec);
+ Y_vec = Y_vec + (- Y_vec + max_y + 1) * (Y_vec <= 0.0);
+}
+Y = table (seq (1, N, 1), as.vector(Y_vec));
+Y = as.matrix(as.data.frame.matrix(Y)) #this is required due to different table semantics
+
+K = ncol (Y) - 1; # The number of non-baseline categories
+
+lambda = (scale_lambda %*% matrix (1, 1, K)) * regularization;
+delta = 0.5 * sqrt (D) / max (sqrt (rowSums_X_sq));
+
+B = matrix (0, D, K); ### LT = X %*% (SHIFT/SCALE TRANSFORM) %*% B;
+ ### LT = append (LT, matrix (0, rows = N, cols = 1));
+ ### LT = LT - rowMaxs (LT) %*% matrix (1, rows = 1, cols = K+1);
+P = matrix (1, N, K+1); ### exp_LT = exp (LT);
+P = P / (K + 1); ### P = exp_LT / (rowSums (exp_LT) %*% matrix (1, rows = 1, cols = K+1));
+obj = N * log (K + 1); ### obj = - sum (Y * LT) + sum (log (rowSums (exp_LT))) + 0.5 * sum (lambda * (B_new ^ 2));
+
+Grad = t(X) %*% (P [, 1:K] - Y [, 1:K]);
+if (intercept_status == 2) {
+ Grad = diag (scale_X) %*% Grad + shift_X %*% Grad [D, ];
+}
+Grad = Grad + lambda * B;
+norm_Grad = sqrt (sum (Grad ^ 2));
+norm_Grad_initial = norm_Grad;
+
+if (maxinneriter == 0) {
+ maxinneriter = D * K;
+}
+iter = 1;
+
+# boolean for convergence check
+converge = (norm_Grad < tol) | (iter > maxiter);
+
+print (paste("-- Initially: Objective = ", obj, ", Gradient Norm = ", norm_Grad , ", Trust Delta = " , delta));
+
+while (! converge)
+{
+ # SOLVE TRUST REGION SUB-PROBLEM
+ S = matrix (0, D, K);
+ R = - Grad;
+ V = R;
+ delta2 = delta ^ 2;
+ inneriter = 1;
+ norm_R2 = sum (R ^ 2);
+ innerconverge = (sqrt (norm_R2) <= psi * norm_Grad);
+ is_trust_boundary_reached = 0;
+
+ while (! innerconverge)
+ {
+ if (intercept_status == 2) {
+ ssX_V = diag (scale_X) %*% V;
+ ssX_V [D, ] = ssX_V [D, ] + t(shift_X) %*% V;
+ } else {
+ ssX_V = V;
+ }
+ Q = P [, 1:K] * (X %*% ssX_V);
+ HV = t(X) %*% (Q - P [, 1:K] * (rowSums (Q) %*% matrix (1, 1, K)));
+ if (intercept_status == 2) {
+ HV = diag (scale_X) %*% HV + shift_X %*% HV [D, ];
+ }
+ HV = HV + lambda * V;
+ alpha = norm_R2 / sum (V * HV);
+ Snew = S + alpha * V;
+ norm_Snew2 = sum (Snew ^ 2);
+ if (norm_Snew2 <= delta2)
+ {
+ S = Snew;
+ R = R - alpha * HV;
+ old_norm_R2 = norm_R2
+ norm_R2 = sum (R ^ 2);
+ V = R + (norm_R2 / old_norm_R2) * V;
+ innerconverge = (sqrt (norm_R2) <= psi * norm_Grad);
+ } else {
+ is_trust_boundary_reached = 1;
+ sv = sum (S * V);
+ v2 = sum (V ^ 2);
+ s2 = sum (S ^ 2);
+ rad = sqrt (sv ^ 2 + v2 * (delta2 - s2));
+ if (sv >= 0) {
+ alpha = (delta2 - s2) / (sv + rad);
+ } else {
+ alpha = (rad - sv) / v2;
+ }
+ S = S + alpha * V;
+ R = R - alpha * HV;
+ innerconverge = TRUE;
+ }
+ inneriter = inneriter + 1;
+ innerconverge = innerconverge | (inneriter > maxinneriter);
+ }
+
+ # END TRUST REGION SUB-PROBLEM
+
+ # compute rho, update B, obtain delta
+ gs = sum (S * Grad);
+ qk = - 0.5 * (gs - sum (S * R));
+ B_new = B + S;
+ if (intercept_status == 2) {
+ ssX_B_new = diag (scale_X) %*% B_new;
+ ssX_B_new [D, ] = ssX_B_new [D, ] + t(shift_X) %*% B_new;
+ } else {
+ ssX_B_new = B_new;
+ }
+
+ LT = as.matrix(cbind ((X %*% ssX_B_new), matrix (0, N, 1)));
+ LT = LT - rowMaxs (LT) %*% matrix (1, 1, K+1);
+ exp_LT = exp (LT);
+ P_new = exp_LT / (rowSums (exp_LT) %*% matrix (1, 1, K+1));
+ obj_new = - sum (Y * LT) + sum (log (rowSums (exp_LT))) + 0.5 * sum (lambda * (B_new ^ 2));
+
+ # Consider updating LT in the inner loop
+ # Consider the big "obj" and "obj_new" rounding-off their small difference below:
+
+ actred = (obj - obj_new);
+
+ rho = actred / qk;
+ is_rho_accepted = (rho > eta0);
+ snorm = sqrt (sum (S ^ 2));
+
+ if (iter == 1) {
+ delta = min (delta, snorm);
+ }
+
+ alpha2 = obj_new - obj - gs;
+ if (alpha2 <= 0) {
+ alpha = sigma3;
+ }
+ else {
+ alpha = max (sigma1, -0.5 * gs / alpha2);
+ }
+
+ if (rho < eta0) {
+ delta = min (max (alpha, sigma1) * snorm, sigma2 * delta);
+ }
+ else {
+ if (rho < eta1) {
+ delta = max (sigma1 * delta, min (alpha * snorm, sigma2 * delta));
+ }
+ else {
+ if (rho < eta2) {
+ delta = max (sigma1 * delta, min (alpha * snorm, sigma3 * delta));
+ }
+ else {
+ delta = max (delta, min (alpha * snorm, sigma3 * delta));
+ }
+ }
+ }
+
+ if (is_trust_boundary_reached == 1)
+ {
+ print (paste("-- Outer Iteration " , iter , ": Had " , (inneriter - 1) , " CG iterations, trust bound REACHED"));
+ } else {
+ print (paste("-- Outer Iteration " , iter , ": Had " , (inneriter - 1) , " CG iterations"));
+ }
+ print (paste(" -- Obj.Reduction: Actual = " , actred , ", Predicted = " , qk ,
+ " (A/P: " , (round (10000.0 * rho) / 10000.0) , "), Trust Delta = " , delta));
+
+ if (is_rho_accepted)
+ {
+ B = B_new;
+ P = P_new;
+ Grad = t(X) %*% (P [, 1:K] - Y [, 1:K]);
+ if (intercept_status == 2) {
+ Grad = diag (scale_X) %*% Grad + shift_X %*% Grad [D, ];
+ }
+ Grad = Grad + lambda * B;
+ norm_Grad = sqrt (sum (Grad ^ 2));
+ obj = obj_new;
+ print (paste(" -- New Objective = " , obj , ", Beta Change Norm = " , snorm , ", Gradient Norm = " , norm_Grad));
+ }
+
+ iter = iter + 1;
+ converge = ((norm_Grad < (tol * norm_Grad_initial)) | (iter > maxiter) |
+ ((is_trust_boundary_reached == 0) & (abs (actred) < (abs (obj) + abs (obj_new)) * 0.00000000000001)));
+ if (converge) { print ("Termination / Convergence condition satisfied."); } else { print (" "); }
+}
+
+if (intercept_status == 2) {
+ B_out = diag (scale_X) %*% B;
+ B_out [D, ] = B_out [D, ] + t(shift_X) %*% B;
+} else {
+ B_out = B;
+}
+
+writeMM(as(B_out,"CsparseMatrix"), paste(args[5], "w", sep=""));