このページの内容は最新ではありません。最新版の英語を参照するには、ここをクリックします。
Black Litterman 法を使用してポートフォリオを最適化するコードの生成
この例では、Black Litterman 法を使用して、ポートフォリオの最適化を実行する MATLAB® コードから MEX 関数と C のソース コードを生成する方法を説明します。
必要条件
この例には必要条件はありません。
関数 hlblacklitterman について
関数 hlblacklitterman.m は、ポートフォリオに関する財務情報を読み込み、Black Litterman 法を使用してポートフォリオの最適化を実行します。
type hlblacklittermanfunction [er, ps, w, pw, lambda, theta] = hlblacklitterman(delta, weq, sigma, tau, P, Q, Omega)%#codegen
% hlblacklitterman
% This function performs the Black-Litterman blending of the prior
% and the views into a new posterior estimate of the returns as
% described in the paper by He and Litterman.
% Inputs
% delta - Risk tolerance from the equilibrium portfolio
% weq - Weights of the assets in the equilibrium portfolio
% sigma - Prior covariance matrix
% tau - Coefficiet of uncertainty in the prior estimate of the mean (pi)
% P - Pick matrix for the view(s)
% Q - Vector of view returns
% Omega - Matrix of variance of the views (diagonal)
% Outputs
% Er - Posterior estimate of the mean returns
% w - Unconstrained weights computed given the Posterior estimates
% of the mean and covariance of returns.
% lambda - A measure of the impact of each view on the posterior estimates.
% theta - A measure of the share of the prior and sample information in the
% posterior precision.
% Reverse optimize and back out the equilibrium returns
% This is formula (12) page 6.
pi = weq * sigma * delta;
% We use tau * sigma many places so just compute it once
ts = tau * sigma;
% Compute posterior estimate of the mean
% This is a simplified version of formula (8) on page 4.
er = pi' + ts * P' * inv(P * ts * P' + Omega) * (Q - P * pi');
% We can also do it the long way to illustrate that d1 + d2 = I
d = inv(inv(ts) + P' * inv(Omega) * P);
d1 = d * inv(ts);
d2 = d * P' * inv(Omega) * P;
er2 = d1 * pi' + d2 * pinv(P) * Q;
% Compute posterior estimate of the uncertainty in the mean
% This is a simplified and combined version of formulas (9) and (15)
ps = ts - ts * P' * inv(P * ts * P' + Omega) * P * ts;
posteriorSigma = sigma + ps;
% Compute the share of the posterior precision from prior and views,
% then for each individual view so we can compare it with lambda
theta=zeros(1,2+size(P,1));
theta(1,1) = (trace(inv(ts) * ps) / size(ts,1));
theta(1,2) = (trace(P'*inv(Omega)*P* ps) / size(ts,1));
for i=1:size(P,1)
theta(1,2+i) = (trace(P(i,:)'*inv(Omega(i,i))*P(i,:)* ps) / size(ts,1));
end
% Compute posterior weights based solely on changed covariance
w = (er' * inv(delta * posteriorSigma))';
% Compute posterior weights based on uncertainty in mean and covariance
pw = (pi * inv(delta * posteriorSigma))';
% Compute lambda value
% We solve for lambda from formula (17) page 7, rather than formula (18)
% just because it is less to type, and we've already computed w*.
lambda = pinv(P)' * (w'*(1+tau) - weq)';
end
% Black-Litterman example code for MatLab (hlblacklitterman.m)
% Copyright (c) Jay Walters, blacklitterman.org, 2008.
%
% Redistribution and use in source and binary forms,
% with or without modification, are permitted provided
% that the following conditions are met:
%
% Redistributions of source code must retain the above
% copyright notice, this list of conditions and the following
% disclaimer.
%
% Redistributions in binary form must reproduce the above
% copyright notice, this list of conditions and the following
% disclaimer in the documentation and/or other materials
% provided with the distribution.
%
% Neither the name of blacklitterman.org nor the names of its
% contributors may be used to endorse or promote products
% derived from this software without specific prior written
% permission.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
% CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
% INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
% MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
% DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
% CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
% SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
% BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
% SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
% WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
% NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
% OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
% DAMAGE.
%
% This program uses the examples from the paper "The Intuition
% Behind Black-Litterman Model Portfolios", by He and Litterman,
% 1999. You can find a copy of this paper at the following url.
% http:%papers.ssrn.com/sol3/papers.cfm?abstract_id=334304
%
% For more details on the Black-Litterman model you can also view
% "The BlackLitterman Model: A Detailed Exploration", by this author
% at the following url.
% http:%www.blacklitterman.org/Black-Litterman.pdf
%
%#codegen 命令は、当該の MATLAB コードがコード生成用であることを示します。
検定に使用する MEX 関数の生成
codegen コマンドを使用して MEX 関数を生成します。
codegen hlblacklitterman -args {0, zeros(1, 7), zeros(7,7), 0, zeros(1, 7), 0, 0}
Code generation successful.
C コードを生成する前に、MATLAB で MEX 関数をテストして、その関数が元の MATLAB コードと機能的に等価であることと実行時のエラーが発生しないことを確認しなければなりません。既定で、codegen は、現在のフォルダーに hlblacklitterman_mex という名前の MEX 関数を生成します。これにより、MATLAB コードと MEX 関数をテストして結果を比較することができます。
MEX 関数の実行
生成された MEX 関数の呼び出し
testMex();
View 1 Country P mu w* Australia 0 4.328 1.524 Canada 0 7.576 2.095 France -29.5 9.288 -3.948 Germany 100 11.04 35.41 Japan 0 4.506 11.05 UK -70.5 6.953 -9.462 USA 0 8.069 58.57 q 5 omega/tau 0.0213 lambda 0.317 theta 0.0714 pr theta 0.929 View 1 Country P mu w* Australia 0 4.328 1.524 Canada 0 7.576 2.095 France -29.5 9.288 -3.948 Germany 100 11.04 35.41 Japan 0 4.506 11.05 UK -70.5 6.953 -9.462 USA 0 8.069 58.57 q 5 omega/tau 0.0213 lambda 0.317 theta 0.0714 pr theta 0.929 Execution Time - MATLAB function: 0.022985 seconds Execution Time - MEX function : 0.008042 seconds
C コードの生成
cfg = coder.config('lib'); codegen -config cfg hlblacklitterman -args {0, zeros(1, 7), zeros(7,7), 0, zeros(1, 7), 0, 0}
Code generation successful.
-config cfg オプションを指定して codegen を使用すると、スタンドアロン C ライブラリが生成されます。
生成されたコードの確認
既定では、ライブラリ用に生成されたコードは codegen/lib/hbblacklitterman/ フォルダーにあります。
ファイルは、以下のとおりです。
dir codegen/lib/hlblacklitterman/. .. _clang-format buildInfo.mat codeInfo.mat codedescriptor.dmr compileInfo.mat examples hlblacklitterman.a hlblacklitterman.c hlblacklitterman.h hlblacklitterman.o hlblacklitterman_data.h hlblacklitterman_initialize.c hlblacklitterman_initialize.h hlblacklitterman_initialize.o hlblacklitterman_rtw.mk hlblacklitterman_terminate.c hlblacklitterman_terminate.h hlblacklitterman_terminate.o hlblacklitterman_types.h interface inv.c inv.h inv.o rtGetInf.c rtGetInf.h rtGetInf.o rtGetNaN.c rtGetNaN.h rtGetNaN.o rt_nonfinite.c rt_nonfinite.h rt_nonfinite.o rtw_proj.tmw rtwtypes.h
関数 hlblacklitterman.c の C コードの検査
type codegen/lib/hlblacklitterman/hlblacklitterman.c/*
* Prerelease License - for engineering feedback and testing purposes
* only. Not for sale.
* File: hlblacklitterman.c
*
* MATLAB Coder version : 24.1
* C/C++ source code generated on : 25-Jan-2024 15:05:48
*/
/* Include Files */
#include "hlblacklitterman.h"
#include "inv.h"
#include "rt_nonfinite.h"
#include "rt_nonfinite.h"
#include <emmintrin.h>
#include <math.h>
/* Function Definitions */
/*
* hlblacklitterman
* This function performs the Black-Litterman blending of the prior
* and the views into a new posterior estimate of the returns as
* described in the paper by He and Litterman.
* Inputs
* delta - Risk tolerance from the equilibrium portfolio
* weq - Weights of the assets in the equilibrium portfolio
* sigma - Prior covariance matrix
* tau - Coefficiet of uncertainty in the prior estimate of the mean (pi)
* P - Pick matrix for the view(s)
* Q - Vector of view returns
* Omega - Matrix of variance of the views (diagonal)
* Outputs
* Er - Posterior estimate of the mean returns
* w - Unconstrained weights computed given the Posterior estimates
* of the mean and covariance of returns.
* lambda - A measure of the impact of each view on the posterior estimates.
* theta - A measure of the share of the prior and sample information in the
* posterior precision.
*
* Arguments : double delta
* const double weq[7]
* const double sigma[49]
* double tau
* const double P[7]
* double Q
* double Omega
* double er[7]
* double ps[49]
* double w[7]
* double pw[7]
* double *lambda
* double theta[3]
* Return Type : void
*/
void hlblacklitterman(double delta, const double weq[7], const double sigma[49],
double tau, const double P[7], double Q, double Omega,
double er[7], double ps[49], double w[7], double pw[7],
double *lambda, double theta[3])
{
__m128d r;
__m128d r1;
double b_er_tmp[49];
double dv[49];
double posteriorSigma[49];
double ts[49];
double er_tmp[7];
double pi[7];
double y_tmp[7];
double absxk;
double anrm;
double cfromc;
double ctoc;
double nrm;
double scale;
int br;
int cr;
int exponent;
int ib;
int ic;
int scalarLB;
boolean_T doscale;
/* Reverse optimize and back out the equilibrium returns */
/* This is formula (12) page 6. */
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
scale = 0.0;
for (ib = 0; ib < 7; ib++) {
scale += weq[ib] * sigma[ib + 7 * scalarLB];
}
pi[scalarLB] = scale * delta;
}
/* We use tau * sigma many places so just compute it once */
for (scalarLB = 0; scalarLB <= 46; scalarLB += 2) {
_mm_storeu_pd(&ts[scalarLB],
_mm_mul_pd(_mm_set1_pd(tau), _mm_loadu_pd(&sigma[scalarLB])));
}
ts[48] = tau * sigma[48];
/* Compute posterior estimate of the mean */
/* This is a simplified version of formula (8) on page 4. */
anrm = 0.0;
cfromc = 0.0;
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
scale = 0.0;
absxk = 0.0;
for (ib = 0; ib < 7; ib++) {
nrm = P[ib];
scale += ts[scalarLB + 7 * ib] * nrm;
absxk += nrm * ts[ib + 7 * scalarLB];
}
y_tmp[scalarLB] = absxk;
er_tmp[scalarLB] = scale;
scale = P[scalarLB];
anrm += absxk * scale;
cfromc += scale * pi[scalarLB];
}
ctoc = 1.0 / (anrm + Omega);
absxk = Q - cfromc;
/* We can also do it the long way to illustrate that d1 + d2 = I */
anrm = 1.0 / Omega;
/* Compute posterior estimate of the uncertainty in the mean */
/* This is a simplified and combined version of formulas (9) and (15) */
nrm = 0.0;
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
er[scalarLB] = pi[scalarLB] + er_tmp[scalarLB] * ctoc * absxk;
nrm += y_tmp[scalarLB] * P[scalarLB];
}
ctoc = 1.0 / (nrm + Omega);
r = _mm_set1_pd(ctoc);
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
__m128d r2;
r1 = _mm_loadu_pd(&er_tmp[0]);
scale = P[scalarLB];
r2 = _mm_set1_pd(scale);
_mm_storeu_pd(&b_er_tmp[7 * scalarLB], _mm_mul_pd(_mm_mul_pd(r1, r), r2));
r1 = _mm_loadu_pd(&er_tmp[2]);
_mm_storeu_pd(&b_er_tmp[7 * scalarLB + 2],
_mm_mul_pd(_mm_mul_pd(r1, r), r2));
r1 = _mm_loadu_pd(&er_tmp[4]);
_mm_storeu_pd(&b_er_tmp[7 * scalarLB + 4],
_mm_mul_pd(_mm_mul_pd(r1, r), r2));
b_er_tmp[7 * scalarLB + 6] = er_tmp[6] * ctoc * scale;
}
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
for (ib = 0; ib < 7; ib++) {
scale = 0.0;
for (br = 0; br < 7; br++) {
scale += b_er_tmp[scalarLB + 7 * br] * ts[br + 7 * ib];
}
br = scalarLB + 7 * ib;
ps[br] = ts[br] - scale;
}
}
for (scalarLB = 0; scalarLB <= 46; scalarLB += 2) {
r = _mm_loadu_pd(&ps[scalarLB]);
_mm_storeu_pd(&posteriorSigma[scalarLB],
_mm_add_pd(_mm_loadu_pd(&sigma[scalarLB]), r));
}
posteriorSigma[48] = sigma[48] + ps[48];
/* Compute the share of the posterior precision from prior and views, */
/* then for each individual view so we can compare it with lambda */
inv(ts, dv);
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
for (ib = 0; ib < 7; ib++) {
scale = 0.0;
for (br = 0; br < 7; br++) {
scale += dv[scalarLB + 7 * br] * ps[br + 7 * ib];
}
ts[scalarLB + 7 * ib] = scale;
}
}
cfromc = 0.0;
for (br = 0; br < 7; br++) {
cfromc += ts[br + 7 * br];
}
theta[0] = cfromc / 7.0;
r = _mm_set1_pd(anrm);
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
r1 = _mm_set1_pd(P[scalarLB]);
_mm_storeu_pd(&b_er_tmp[7 * scalarLB],
_mm_mul_pd(_mm_mul_pd(_mm_loadu_pd(&P[0]), r), r1));
_mm_storeu_pd(&b_er_tmp[7 * scalarLB + 2],
_mm_mul_pd(_mm_mul_pd(_mm_loadu_pd(&P[2]), r), r1));
_mm_storeu_pd(&b_er_tmp[7 * scalarLB + 4],
_mm_mul_pd(_mm_mul_pd(_mm_loadu_pd(&P[4]), r), r1));
b_er_tmp[7 * scalarLB + 6] = P[6] * anrm * P[scalarLB];
}
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
for (ib = 0; ib < 7; ib++) {
scale = 0.0;
for (br = 0; br < 7; br++) {
scale += b_er_tmp[scalarLB + 7 * br] * ps[br + 7 * ib];
}
ts[scalarLB + 7 * ib] = scale;
}
}
cfromc = 0.0;
for (br = 0; br < 7; br++) {
cfromc += ts[br + 7 * br];
}
theta[1] = cfromc / 7.0;
r = _mm_set1_pd(anrm);
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
r1 = _mm_set1_pd(P[scalarLB]);
_mm_storeu_pd(&b_er_tmp[7 * scalarLB],
_mm_mul_pd(_mm_mul_pd(_mm_loadu_pd(&P[0]), r), r1));
_mm_storeu_pd(&b_er_tmp[7 * scalarLB + 2],
_mm_mul_pd(_mm_mul_pd(_mm_loadu_pd(&P[2]), r), r1));
_mm_storeu_pd(&b_er_tmp[7 * scalarLB + 4],
_mm_mul_pd(_mm_mul_pd(_mm_loadu_pd(&P[4]), r), r1));
b_er_tmp[7 * scalarLB + 6] = P[6] * anrm * P[scalarLB];
}
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
for (ib = 0; ib < 7; ib++) {
scale = 0.0;
for (br = 0; br < 7; br++) {
scale += b_er_tmp[scalarLB + 7 * br] * ps[br + 7 * ib];
}
ts[scalarLB + 7 * ib] = scale;
}
}
cfromc = 0.0;
for (br = 0; br < 7; br++) {
cfromc += ts[br + 7 * br];
}
theta[2] = cfromc / 7.0;
/* Compute posterior weights based solely on changed covariance */
for (scalarLB = 0; scalarLB <= 46; scalarLB += 2) {
r = _mm_loadu_pd(&posteriorSigma[scalarLB]);
_mm_storeu_pd(&b_er_tmp[scalarLB], _mm_mul_pd(_mm_set1_pd(delta), r));
}
b_er_tmp[48] = delta * posteriorSigma[48];
inv(b_er_tmp, dv);
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
scale = 0.0;
for (ib = 0; ib < 7; ib++) {
scale += er[ib] * dv[ib + 7 * scalarLB];
}
w[scalarLB] = scale;
}
/* Compute posterior weights based on uncertainty in mean and covariance */
for (scalarLB = 0; scalarLB <= 46; scalarLB += 2) {
r = _mm_loadu_pd(&posteriorSigma[scalarLB]);
_mm_storeu_pd(&posteriorSigma[scalarLB], _mm_mul_pd(_mm_set1_pd(delta), r));
}
posteriorSigma[48] *= delta;
inv(posteriorSigma, dv);
/* Compute lambda value */
/* We solve for lambda from formula (17) page 7, rather than formula (18) */
/* just because it is less to type, and we've already computed w*. */
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
scale = 0.0;
for (ib = 0; ib < 7; ib++) {
scale += pi[ib] * dv[ib + 7 * scalarLB];
}
pw[scalarLB] = scale;
er_tmp[scalarLB] = P[scalarLB];
}
doscale = true;
for (br = 0; br < 7; br++) {
pi[br] = 0.0;
if (doscale) {
scale = P[br];
if (rtIsInf(scale) || rtIsNaN(scale)) {
doscale = false;
}
} else {
doscale = false;
}
}
if (!doscale) {
for (scalarLB = 0; scalarLB < 7; scalarLB++) {
pi[scalarLB] = rtNaN;
}
} else {
double cscale;
boolean_T exitg1;
boolean_T guard1;
boolean_T notdone;
doscale = false;
anrm = 0.0;
br = 0;
exitg1 = false;
while ((!exitg1) && (br < 7)) {
absxk = fabs(P[br]);
if (rtIsNaN(absxk)) {
anrm = rtNaN;
exitg1 = true;
} else {
if (absxk > anrm) {
anrm = absxk;
}
br++;
}
}
cscale = anrm;
guard1 = false;
if ((anrm > 0.0) && (anrm < 6.7178761075670888E-139)) {
doscale = true;
cscale = 6.7178761075670888E-139;
guard1 = true;
} else if (anrm > 1.4885657073574029E+138) {
doscale = true;
cscale = 1.4885657073574029E+138;
guard1 = true;
}
if (guard1) {
cfromc = anrm;
ctoc = cscale;
notdone = true;
while (notdone) {
absxk = cfromc * 2.0041683600089728E-292;
nrm = ctoc / 4.9896007738368E+291;
if ((absxk > ctoc) && (ctoc != 0.0)) {
scale = 2.0041683600089728E-292;
cfromc = absxk;
} else if (nrm > cfromc) {
scale = 4.9896007738368E+291;
ctoc = nrm;
} else {
scale = ctoc / cfromc;
notdone = false;
}
r = _mm_loadu_pd(&er_tmp[0]);
r1 = _mm_set1_pd(scale);
_mm_storeu_pd(&er_tmp[0], _mm_mul_pd(r, r1));
r = _mm_loadu_pd(&er_tmp[2]);
_mm_storeu_pd(&er_tmp[2], _mm_mul_pd(r, r1));
r = _mm_loadu_pd(&er_tmp[4]);
_mm_storeu_pd(&er_tmp[4], _mm_mul_pd(r, r1));
er_tmp[6] *= scale;
}
}
nrm = 0.0;
scale = 3.3121686421112381E-170;
for (br = 0; br < 7; br++) {
absxk = fabs(er_tmp[br]);
if (absxk > scale) {
cfromc = scale / absxk;
nrm = nrm * cfromc * cfromc + 1.0;
scale = absxk;
} else {
cfromc = absxk / scale;
nrm += cfromc * cfromc;
}
}
nrm = scale * sqrt(nrm);
if (nrm > 0.0) {
if (er_tmp[0] < 0.0) {
cfromc = -nrm;
} else {
cfromc = nrm;
}
if (fabs(cfromc) >= 1.0020841800044864E-292) {
absxk = 1.0 / cfromc;
r = _mm_loadu_pd(&er_tmp[0]);
r1 = _mm_set1_pd(absxk);
_mm_storeu_pd(&er_tmp[0], _mm_mul_pd(r1, r));
r = _mm_loadu_pd(&er_tmp[2]);
_mm_storeu_pd(&er_tmp[2], _mm_mul_pd(r1, r));
r = _mm_loadu_pd(&er_tmp[4]);
_mm_storeu_pd(&er_tmp[4], _mm_mul_pd(r1, r));
er_tmp[6] *= absxk;
} else {
r = _mm_loadu_pd(&er_tmp[0]);
r1 = _mm_set1_pd(cfromc);
_mm_storeu_pd(&er_tmp[0], _mm_div_pd(r, r1));
r = _mm_loadu_pd(&er_tmp[2]);
_mm_storeu_pd(&er_tmp[2], _mm_div_pd(r, r1));
r = _mm_loadu_pd(&er_tmp[4]);
_mm_storeu_pd(&er_tmp[4], _mm_div_pd(r, r1));
er_tmp[6] /= cfromc;
}
er_tmp[0]++;
cfromc = -cfromc;
} else {
cfromc = 0.0;
}
for (br = 0; br < 7; br++) {
y_tmp[br] = er_tmp[br];
}
if (cfromc != 0.0) {
r = _mm_loadu_pd(&y_tmp[0]);
r1 = _mm_set1_pd(-1.0);
_mm_storeu_pd(&y_tmp[0], _mm_mul_pd(r, r1));
r = _mm_loadu_pd(&y_tmp[2]);
_mm_storeu_pd(&y_tmp[2], _mm_mul_pd(r, r1));
r = _mm_loadu_pd(&y_tmp[4]);
_mm_storeu_pd(&y_tmp[4], _mm_mul_pd(r, r1));
y_tmp[6] = -y_tmp[6];
y_tmp[0]++;
nrm = fabs(cfromc);
absxk = cfromc / nrm;
cfromc = nrm;
r = _mm_loadu_pd(&y_tmp[0]);
r1 = _mm_set1_pd(absxk);
_mm_storeu_pd(&y_tmp[0], _mm_mul_pd(r1, r));
r = _mm_loadu_pd(&y_tmp[2]);
_mm_storeu_pd(&y_tmp[2], _mm_mul_pd(r1, r));
r = _mm_loadu_pd(&y_tmp[4]);
_mm_storeu_pd(&y_tmp[4], _mm_mul_pd(r1, r));
y_tmp[6] *= absxk;
} else {
for (br = 0; br < 7; br++) {
y_tmp[br] = 0.0;
}
y_tmp[0] = 1.0;
}
if (doscale) {
notdone = true;
while (notdone) {
absxk = cscale * 2.0041683600089728E-292;
nrm = anrm / 4.9896007738368E+291;
if ((absxk > anrm) && (anrm != 0.0)) {
scale = 2.0041683600089728E-292;
cscale = absxk;
} else if (nrm > cscale) {
scale = 4.9896007738368E+291;
anrm = nrm;
} else {
scale = anrm / cscale;
notdone = false;
}
cfromc *= scale;
}
}
doscale = (rtIsInf(cfromc) || rtIsNaN(cfromc));
if (doscale) {
absxk = rtNaN;
} else if (cfromc < 4.4501477170144028E-308) {
absxk = 4.94065645841247E-324;
} else {
frexp(cfromc, &exponent);
absxk = ldexp(1.0, exponent - 53);
}
absxk *= 7.0;
if (doscale) {
absxk = 1.7976931348623157E+308;
}
if (cfromc > absxk) {
absxk = 1.0 / cfromc;
for (cr = 0; cr < 7; cr++) {
scalarLB = cr + 1;
for (ic = scalarLB; ic <= scalarLB; ic++) {
pi[ic - 1] = 0.0;
}
}
br = 0;
for (cr = 0; cr < 7; cr++) {
br++;
for (ib = br; ib <= br; ib += 7) {
scalarLB = cr + 1;
exponent = cr - 1;
for (ic = scalarLB; ic <= exponent; ic += 2) {
r = _mm_loadu_pd(&pi[ic - 1]);
_mm_storeu_pd(&pi[ic - 1],
_mm_add_pd(r, _mm_set1_pd(y_tmp[ib - 1] * absxk)));
}
for (ic = scalarLB; ic <= scalarLB; ic++) {
pi[ic - 1] += y_tmp[ib - 1] * absxk;
}
}
}
}
}
*lambda = 0.0;
for (br = 0; br < 7; br++) {
*lambda += pi[br] * (w[br] * (tau + 1.0) - weq[br]);
}
}
/*
* File trailer for hlblacklitterman.c
*
* [EOF]
*/
You can also select a web site from the following list:
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)