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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_correg_pls_wold (g02lb)

Purpose

nag_correg_pls_wold (g02lb) fits an orthogonal scores partial least squares (PLS) regression by using Wold's iterative method.

Syntax

[xbar, ybar, xstd, ystd, xres, yres, w, p, t, c, u, xcv, ycv, ifail] = g02lb(x, isx, y, iscale, xstd, ystd, maxfac, 'n', n, 'mx', mx, 'ip', ip, 'my', my, 'maxit', maxit, 'tau', tau)
[xbar, ybar, xstd, ystd, xres, yres, w, p, t, c, u, xcv, ycv, ifail] = nag_correg_pls_wold(x, isx, y, iscale, xstd, ystd, maxfac, 'n', n, 'mx', mx, 'ip', ip, 'my', my, 'maxit', maxit, 'tau', tau)
Note: the interface to this routine has changed since earlier releases of the toolbox:
Mark 24: tau, maxit optional
.

Description

Let X1X1 be the mean-centred nn by mm data matrix XX of nn observations on mm predictor variables. Let Y1Y1 be the mean-centred nn by rr data matrix YY of nn observations on rr response variables.
The first of the kk factors PLS methods extract from the data predicts both X1X1 and Y1Y1 by regressing on a t1t1 column vector of nn scores:
1 = t1 p1T
1 = t1 c1T , with ​ t1T t1 = 1 ,
X^1 = t1 p1T Y^1 = t1 c1T , with ​ t1T t1 = 1 ,
where the column vectors of mm xx-loadings p1p1 and rr yy-loadings c1c1 are calculated in the least squares sense:
p1T = t1T X1
c1T = t1T Y1 .
p1T = t1T X1 c1T = t1T Y1 .
The xx-score vector t1 = X1w1t1=X1w1 is the linear combination of predictor data X1X1 that has maximum covariance with the yy-scores u1 = Y1c1u1=Y1c1, where the xx-weights vector w1w1 is the normalised first left singular vector of X1T Y1X1T Y1.
The method extracts subsequent PLS factors by repeating the above process with the residual matrices:
Xi = Xi1 i1
Yi = Yi1 i1 , i = 2,3,,k ,
Xi = Xi-1 - X^ i-1 Yi = Yi-1 - Y^ i-1 , i=2,3,,k ,
and with orthogonal scores:
tiT tj = 0 , j = 1,2,,i1 .
tiT tj = 0 , j=1,2,,i-1 .
Optionally, in addition to being mean-centred, the data matrices X1X1 and Y1Y1 may be scaled by standard deviations of the variables. If data are supplied mean-centred, the calculations are not affected within numerical accuracy.

References

Wold H (1966) Estimation of principal components and related models by iterative least squares In: Multivariate Analysis (ed P R Krishnaiah) 391–420 Academic Press NY

Parameters

Compulsory Input Parameters

1:     x(ldx,mx) – double array
ldx, the first dimension of the array, must satisfy the constraint ldxnldxn.
x(i,j)xij must contain the iith observation on the jjth predictor variable, for i = 1,2,,ni=1,2,,n and j = 1,2,,mxj=1,2,,mx.
2:     isx(mx) – int64int32nag_int array
mx, the dimension of the array, must satisfy the constraint mx > 1mx>1.
Indicates which predictor variables are to be included in the model.
isx(j) = 1isxj=1
The jjth predictor variable (with variates in the jjth column of XX) is included in the model.
isx(j) = 0isxj=0
Otherwise.
Constraint: the sum of elements in isx must equal ip.
3:     y(ldy,my) – double array
ldy, the first dimension of the array, must satisfy the constraint ldynldyn.
y(i,j)yij must contain the iith observation for the jjth response variable, for i = 1,2,,ni=1,2,,n and j = 1,2,,myj=1,2,,my.
4:     iscale – int64int32nag_int scalar
Indicates how predictor variables are scaled.
iscale = 1iscale=1
Data are scaled by the standard deviation of variables.
iscale = 2iscale=2
Data are scaled by user-supplied scalings.
iscale = -1iscale=-1
No scaling.
Constraint: iscale = -1iscale=-1, 11 or 22.
5:     xstd(ip) – double array
ip, the dimension of the array, must satisfy the constraint 1 < ipmx1<ipmx.
If iscale = 2iscale=2, xstd(j)xstdj must contain the user-supplied scaling for the jjth predictor variable in the model, for j = 1,2,,ipj=1,2,,ip. Otherwise xstd need not be set.
6:     ystd(my) – double array
my, the dimension of the array, must satisfy the constraint my1my1.
If iscale = 2iscale=2, ystd(j)ystdj must contain the user-supplied scaling for the jjth response variable in the model, for j = 1,2,,myj=1,2,,my. Otherwise ystd need not be set.
7:     maxfac – int64int32nag_int scalar
kk, the number of latent variables to calculate.
Constraint: 1maxfacip1maxfacip.

Optional Input Parameters

1:     n – int64int32nag_int scalar
Default: The first dimension of the arrays x, y. (An error is raised if these dimensions are not equal.)
nn, the number of observations.
Constraint: n > 1n>1.
2:     mx – int64int32nag_int scalar
Default: The dimension of the array isx and the second dimension of the array x. (An error is raised if these dimensions are not equal.)
The number of predictor variables.
Constraint: mx > 1mx>1.
3:     ip – int64int32nag_int scalar
Default: The dimension of the array xstd.
mm, the number of predictor variables in the model.
Constraint: 1 < ipmx1<ipmx.
4:     my – int64int32nag_int scalar
Default: The dimension of the array ystd and the second dimension of the array y. (An error is raised if these dimensions are not equal.)
rr, the number of response variables.
Constraint: my1my1.
5:     maxit – int64int32nag_int scalar
If my = 1my=1, maxit is not referenced; otherwise the maximum number of iterations used to calculate the xx-weights.
Default: maxit = 200maxit=200
Constraint: if my > 1my>1, maxit > 1maxit>1.
6:     tau – double scalar
If my = 1my=1, tau is not referenced; otherwise the iterative procedure used to calculate the xx-weights will halt if the Euclidean distance between two subsequent estimates is less than or equal to tau.
Default: tau = 1.0e−4tau=1.0e−4
Constraint: if my > 1my>1, tau > 0.0tau>0.0.

Input Parameters Omitted from the MATLAB Interface

ldx ldy ldxres ldyres ldw ldp ldt ldc ldu ldycv

Output Parameters

1:     xbar(ip) – double array
Mean values of predictor variables in the model.
2:     ybar(my) – double array
The mean value of each response variable.
3:     xstd(ip) – double array
If iscale = 1iscale=1, standard deviations of predictor variables in the model. Otherwise xstd is not changed.
4:     ystd(my) – double array
If iscale = 1iscale=1, the standard deviation of each response variable. Otherwise ystd is not changed.
5:     xres(ldxres,ip) – double array
ldxresnldxresn.
The predictor variables' residual matrix XkXk.
6:     yres(ldyres,my) – double array
ldyresnldyresn.
The residuals for each response variable, YkYk.
7:     w(ldw,maxfac) – double array
ldwipldwip.
The jjth column of WW contains the xx-weights wjwj, for j = 1,2,,maxfacj=1,2,,maxfac.
8:     p(ldp,maxfac) – double array
ldpipldpip.
The jjth column of PP contains the xx-loadings pjpj, for j = 1,2,,maxfacj=1,2,,maxfac.
9:     t(ldt,maxfac) – double array
ldtnldtn.
The jjth column of TT contains the xx-scores tjtj, for j = 1,2,,maxfacj=1,2,,maxfac.
10:   c(ldc,maxfac) – double array
ldcmyldcmy.
The jjth column of CC contains the yy-loadings cjcj, for j = 1,2,,maxfacj=1,2,,maxfac.
11:   u(ldu,maxfac) – double array
ldunldun.
The jjth column of UU contains the yy-scores ujuj, for j = 1,2,,maxfacj=1,2,,maxfac.
12:   xcv(maxfac) – double array
xcv(j)xcvj contains the cumulative percentage of variance in the predictor variables explained by the first jj factors, for j = 1,2,,maxfacj=1,2,,maxfac.
13:   ycv(ldycv,my) – double array
ldycvmaxfacldycvmaxfac.
ycv(i,j)ycvij is the cumulative percentage of variance of the jjth response variable explained by the first ii factors, for i = 1,2,,maxfaci=1,2,,maxfac and j = 1,2,,myj=1,2,,my.
14:   ifail – int64int32nag_int scalar
ifail = 0ifail=0 unless the function detects an error (see [Error Indicators and Warnings]).

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
On entry,n < 2n<2,
ormx < 2mx<2,
oran element of isx0isx0 or 11,
ormy < 1my<1,
oriscale-1iscale-1, 11 or 22.
  ifail = 2ifail=2
On entry,ldx < nldx<n,
orip < 2ip<2 or ip > mxip>mx,
orldy < nldy<n,
ormaxfac < 1maxfac<1 or maxfac > ipmaxfac>ip,
ormy > 1my>1 and maxit1maxit1,
ormy > 1my>1 and tau0.0tau0.0,
orldxres < nldxres<n,
orldyres < nldyres<n,
orldw < ipldw<ip,
orldp < ipldp<ip,
orldc < myldc<my,
orldt < nldt<n,
orldu < nldu<n,
orldycv < maxfacldycv<maxfac.
  ifail = 3ifail=3
ip does not equal the sum of elements in isx.

Accuracy

In general, the iterative method used in the calculations is less accurate (but faster) than the singular value decomposition approach adopted by nag_correg_pls_svd (g02la).

Further Comments

nag_correg_pls_wold (g02lb) allocates internally (n + rn+r) elements of double storage.

Example

function nag_correg_pls_wold_example
x = [-2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 1.9607, -1.6324, ...
     0.5746, 1.9607, -1.6324, 0.574, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 1.9607, -1.6324, ...
     0.5746, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 1.9607, -1.6324, 0.5746, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 2.8369, 1.4092, -3.1398, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, -4.7548, 3.6521, ...
     0.8524, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, -1.2201, 0.8829, 2.2253;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 2.4064, 1.7438, ...
     1.1057, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 0.0744, -1.7333, 0.0902, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     2.2261, -5.3648, 0.3049, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -4.1921, -1.0285, -0.9801, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -4.9217, 1.2977, 0.4473, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 2.2261, -5.3648, ...
     0.3049, 2.2261, -5.3648, 0.3049, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, -4.9217, 1.2977, ...
     0.4473, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, -4.1921, -1.0285, ...
     -0.9801, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398];
isx = ones(15, 1, 'int64');
y = [0;0.28;0.2;0.51;0.11;2.73;0.18;1.53;-0.1;-0.52;0.4;0.3;-1;1.57;0.59];
iscale = int64(1);
xstd = zeros(15, 1);
ystd = [0];
maxfac = int64(4);
[xbar, ybar, xstdOut, ystdOut, xres, yres, w, p, t, c, u, xcv, ycv, ifail] = ...
         nag_correg_pls_wold(x, isx, y, iscale, xstd, ystd, maxfac)
 

xbar =

   -2.6137
   -2.3614
   -1.0449
    2.8614
    0.3156
   -0.2641
   -0.3146
   -1.1221
    0.2401
    0.4694
   -1.9619
    0.1691
    2.5664
    1.3741
   -2.7821


ybar =

    0.4520


xstdOut =

    1.4956
    1.3233
    0.5829
    0.7735
    0.6247
    0.7966
    2.4113
    2.0421
    0.4678
    0.8197
    0.9420
    0.1735
    1.0475
    0.1359
    1.3853


ystdOut =

    0.9062


xres =

  Columns 1 through 9

    0.5270   -0.3689    0.3559   -0.4126   -0.5572    0.4198   -0.2773    0.2477   -0.0704
    0.1973   -0.3392   -0.3323    0.0646   -0.2604    0.6403    0.5212   -0.2744    0.5535
    0.3314   -0.2623    0.1522   -0.2158   -0.3327    0.3034   -0.7904    0.2199   -0.8792
    0.0014   -0.2325   -0.5365    0.2618   -0.0356    0.5239    0.0088   -0.3024   -0.2548
    0.0294   -0.4945   -1.0686   -0.0484    1.2332   -2.5880   -0.4220   -0.0115    0.0186
    0.3074   -0.1970    0.2558   -0.0378    0.2148   -0.5015   -0.0146    0.1862    0.2950
   -0.2382    0.3952    0.3257    0.5963    0.7523   -0.4992   -0.1086   -0.0605   -0.0371
    0.4495   -0.3948    0.1230   -0.1885   -0.2942    0.2724    1.4126    0.4280    1.0781
   -0.6352    0.1862   -1.0409   -2.9900   -2.6946    0.3145    0.4281    0.1827    0.5372
    2.5029   -2.0193    1.2074    1.0321    0.6477    0.4653    0.2246    0.5833    0.8890
   -0.9517    0.8371   -0.0396    0.2151   -0.1179    0.6105    0.0327   -0.3922   -0.3070
   -1.7120    2.6260    1.8591    0.4847    0.0285    0.7783    0.1958   -0.1668    0.1312
   -0.5133    0.4067   -0.2509    0.4074    0.6723   -0.6626    0.3226   -0.2405    0.3010
    0.1209   -0.1562   -0.0813    0.1489    0.2406   -0.2318   -0.5985   -0.2699   -0.1218
   -0.4166    0.0136   -0.9291    0.6822    0.5033    0.1549   -0.9350   -0.1297   -2.1334

  Columns 10 through 15

    0.3304    0.6297    0.6994    0.1694    0.1694   -0.1694
   -0.4342   -0.3245   -0.6752    0.2816    0.2816   -0.2816
    0.5204    0.8023    1.0133    0.1221    0.1221   -0.1221
   -0.2433   -0.1521   -0.3638    0.2343    0.2343   -0.2343
    0.0245   -0.6582   -0.2927   -0.4687   -0.4687    0.4687
    0.1176    0.0341    0.1566   -0.1477   -0.1477    0.1477
   -0.0019   -0.2597   -0.1292   -0.3225   -0.3225    0.3225
   -0.4030   -0.3317   -0.6416    0.0873    0.0873   -0.0873
    0.0951    0.4746    0.3451    0.6324    0.6324   -0.6324
    0.1566    0.5175    0.4393    0.0685    0.0685   -0.0685
   -0.2088   -0.2336   -0.3626    0.0384    0.0384   -0.0384
    0.0648   -0.0903    0.0329   -0.4937   -0.4937    0.4937
   -0.3409   -0.7200   -0.7578   -0.2528   -0.2528    0.2528
    0.0951    0.0428    0.1340   -0.0127   -0.0127    0.0127
    0.2275    0.2691    0.4022    0.0640    0.0640   -0.0640


yres =

   -0.1254
   -0.1776
    0.1312
    0.1119
    0.0637
    0.1753
    0.0335
    0.1365
   -0.0169
   -0.0214
   -0.1004
    0.0689
    0.0095
   -0.3242
    0.0355


w =

   -0.1576   -0.1594    0.1777    0.0540
    0.0857   -0.0002   -0.1218    0.1099
   -0.1693   -0.3743    0.0943    0.3188
    0.1215    0.2059   -0.1814   -0.0446
    0.0711    0.0559   -0.2692    0.0549
    0.0652    0.2417    0.2336   -0.1885
   -0.4248   -0.0019   -0.3241   -0.1160
    0.6537    0.1672    0.2191    0.2546
    0.2850    0.3655   -0.1924   -0.1543
   -0.2934    0.5046   -0.0110    0.1388
    0.2983   -0.3698   -0.4994   -0.4936
   -0.2031    0.4195   -0.2568   -0.0756
    0.0569   -0.0232   -0.3050    0.3967
    0.0569   -0.0232   -0.3050    0.3967
   -0.0569    0.0232    0.3050   -0.3967


p =

   -0.6708   -1.0047    0.6505    0.6169
    0.4943    0.1355   -0.9010   -0.2388
   -0.4167   -1.9983   -0.5538    0.8474
    0.3930    1.2441   -0.6967   -0.4336
    0.3267    0.5838   -1.4088   -0.6323
    0.0145    0.9607    1.6594    0.5361
   -2.4471    0.3532   -1.1321   -1.3554
    3.5198    0.6005    0.2191    0.0380
    1.0973    2.0635   -0.4074   -0.3522
   -2.4466    2.5640   -0.4806    0.3819
    2.2732   -1.3110   -0.7686   -1.8959
   -1.7987    2.4088   -0.9475   -0.4727
    0.3629    0.2241   -2.6332    2.3739
    0.3629    0.2241   -2.6332    2.3739
   -0.3629   -0.2241    2.6332   -2.3739


t =

   -0.1896    0.3898   -0.2502   -0.2479
    0.0201   -0.0013   -0.1726   -0.2042
   -0.1889    0.3141   -0.1727   -0.1350
    0.0210   -0.0773   -0.0950   -0.0912
   -0.0090   -0.2649   -0.4195   -0.1327
    0.5479    0.2843    0.1914    0.2727
   -0.0937   -0.0579    0.6799   -0.6129
    0.2500    0.2033   -0.1046   -0.1014
   -0.1005   -0.2992    0.2131    0.1223
   -0.1810   -0.4427    0.0559    0.2114
    0.0497   -0.0762   -0.1526   -0.0771
    0.0173   -0.2517   -0.2104    0.1044
   -0.6002    0.3596    0.1876    0.4812
    0.3796    0.1338    0.1410    0.1999
    0.0773   -0.2139    0.1085    0.2106


c =

    3.5425    1.0475    0.2548    0.1866


u =

   -1.7670    0.1812   -0.0600   -0.0320
   -0.6724   -0.2735   -0.0662   -0.0402
   -0.9852    0.4097    0.0158    0.0198
    0.2267   -0.0107    0.0180    0.0177
   -1.3370   -0.3619   -0.0173    0.0073
    8.9056    0.6000    0.0701    0.0422
   -1.0634    0.0332    0.0235   -0.0151
    4.2143    0.3184    0.0232    0.0219
   -2.1580   -0.2652    0.0153    0.0011
   -3.7999   -0.4520    0.0082    0.0034
   -0.2033   -0.2446   -0.0392   -0.0214
   -0.5942   -0.2398    0.0089    0.0165
   -5.6764    0.5487    0.0375    0.0185
    4.3707   -0.1161   -0.0639   -0.0535
    0.5395   -0.1274    0.0261    0.0139


xcv =

   16.9021
   29.6743
   44.3324
   56.1720


ycv =

   89.6381
   97.4763
   97.9398
   98.1885


ifail =

                    0


function g02lb_example
x = [-2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 1.9607, -1.6324, ...
     0.5746, 1.9607, -1.6324, 0.574, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 1.9607, -1.6324, ...
     0.5746, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 1.9607, -1.6324, 0.5746, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 2.8369, 1.4092, -3.1398, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, -4.7548, 3.6521, ...
     0.8524, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, -1.2201, 0.8829, 2.2253;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 2.4064, 1.7438, ...
     1.1057, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 0.0744, -1.7333, 0.0902, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     2.2261, -5.3648, 0.3049, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -4.1921, -1.0285, -0.9801, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -4.9217, 1.2977, 0.4473, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333, ...
     0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 2.2261, -5.3648, ...
     0.3049, 2.2261, -5.3648, 0.3049, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, -4.9217, 1.2977, ...
     0.4473, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398;
     -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, -4.1921, -1.0285, ...
     -0.9801, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398];
isx = ones(15, 1, 'int64');
y = [0;0.28;0.2;0.51;0.11;2.73;0.18;1.53;-0.1;-0.52;0.4;0.3;-1;1.57;0.59];
iscale = int64(1);
xstd = zeros(15, 1);
ystd = [0];
maxfac = int64(4);
[xbar, ybar, xstdOut, ystdOut, xres, yres, w, p, t, c, u, xcv, ycv, ifail] = ...
         g02lb(x, isx, y, iscale, xstd, ystd, maxfac)
 

xbar =

   -2.6137
   -2.3614
   -1.0449
    2.8614
    0.3156
   -0.2641
   -0.3146
   -1.1221
    0.2401
    0.4694
   -1.9619
    0.1691
    2.5664
    1.3741
   -2.7821


ybar =

    0.4520


xstdOut =

    1.4956
    1.3233
    0.5829
    0.7735
    0.6247
    0.7966
    2.4113
    2.0421
    0.4678
    0.8197
    0.9420
    0.1735
    1.0475
    0.1359
    1.3853


ystdOut =

    0.9062


xres =

  Columns 1 through 9

    0.5270   -0.3689    0.3559   -0.4126   -0.5572    0.4198   -0.2773    0.2477   -0.0704
    0.1973   -0.3392   -0.3323    0.0646   -0.2604    0.6403    0.5212   -0.2744    0.5535
    0.3314   -0.2623    0.1522   -0.2158   -0.3327    0.3034   -0.7904    0.2199   -0.8792
    0.0014   -0.2325   -0.5365    0.2618   -0.0356    0.5239    0.0088   -0.3024   -0.2548
    0.0294   -0.4945   -1.0686   -0.0484    1.2332   -2.5880   -0.4220   -0.0115    0.0186
    0.3074   -0.1970    0.2558   -0.0378    0.2148   -0.5015   -0.0146    0.1862    0.2950
   -0.2382    0.3952    0.3257    0.5963    0.7523   -0.4992   -0.1086   -0.0605   -0.0371
    0.4495   -0.3948    0.1230   -0.1885   -0.2942    0.2724    1.4126    0.4280    1.0781
   -0.6352    0.1862   -1.0409   -2.9900   -2.6946    0.3145    0.4281    0.1827    0.5372
    2.5029   -2.0193    1.2074    1.0321    0.6477    0.4653    0.2246    0.5833    0.8890
   -0.9517    0.8371   -0.0396    0.2151   -0.1179    0.6105    0.0327   -0.3922   -0.3070
   -1.7120    2.6260    1.8591    0.4847    0.0285    0.7783    0.1958   -0.1668    0.1312
   -0.5133    0.4067   -0.2509    0.4074    0.6723   -0.6626    0.3226   -0.2405    0.3010
    0.1209   -0.1562   -0.0813    0.1489    0.2406   -0.2318   -0.5985   -0.2699   -0.1218
   -0.4166    0.0136   -0.9291    0.6822    0.5033    0.1549   -0.9350   -0.1297   -2.1334

  Columns 10 through 15

    0.3304    0.6297    0.6994    0.1694    0.1694   -0.1694
   -0.4342   -0.3245   -0.6752    0.2816    0.2816   -0.2816
    0.5204    0.8023    1.0133    0.1221    0.1221   -0.1221
   -0.2433   -0.1521   -0.3638    0.2343    0.2343   -0.2343
    0.0245   -0.6582   -0.2927   -0.4687   -0.4687    0.4687
    0.1176    0.0341    0.1566   -0.1477   -0.1477    0.1477
   -0.0019   -0.2597   -0.1292   -0.3225   -0.3225    0.3225
   -0.4030   -0.3317   -0.6416    0.0873    0.0873   -0.0873
    0.0951    0.4746    0.3451    0.6324    0.6324   -0.6324
    0.1566    0.5175    0.4393    0.0685    0.0685   -0.0685
   -0.2088   -0.2336   -0.3626    0.0384    0.0384   -0.0384
    0.0648   -0.0903    0.0329   -0.4937   -0.4937    0.4937
   -0.3409   -0.7200   -0.7578   -0.2528   -0.2528    0.2528
    0.0951    0.0428    0.1340   -0.0127   -0.0127    0.0127
    0.2275    0.2691    0.4022    0.0640    0.0640   -0.0640


yres =

   -0.1254
   -0.1776
    0.1312
    0.1119
    0.0637
    0.1753
    0.0335
    0.1365
   -0.0169
   -0.0214
   -0.1004
    0.0689
    0.0095
   -0.3242
    0.0355


w =

   -0.1576   -0.1594    0.1777    0.0540
    0.0857   -0.0002   -0.1218    0.1099
   -0.1693   -0.3743    0.0943    0.3188
    0.1215    0.2059   -0.1814   -0.0446
    0.0711    0.0559   -0.2692    0.0549
    0.0652    0.2417    0.2336   -0.1885
   -0.4248   -0.0019   -0.3241   -0.1160
    0.6537    0.1672    0.2191    0.2546
    0.2850    0.3655   -0.1924   -0.1543
   -0.2934    0.5046   -0.0110    0.1388
    0.2983   -0.3698   -0.4994   -0.4936
   -0.2031    0.4195   -0.2568   -0.0756
    0.0569   -0.0232   -0.3050    0.3967
    0.0569   -0.0232   -0.3050    0.3967
   -0.0569    0.0232    0.3050   -0.3967


p =

   -0.6708   -1.0047    0.6505    0.6169
    0.4943    0.1355   -0.9010   -0.2388
   -0.4167   -1.9983   -0.5538    0.8474
    0.3930    1.2441   -0.6967   -0.4336
    0.3267    0.5838   -1.4088   -0.6323
    0.0145    0.9607    1.6594    0.5361
   -2.4471    0.3532   -1.1321   -1.3554
    3.5198    0.6005    0.2191    0.0380
    1.0973    2.0635   -0.4074   -0.3522
   -2.4466    2.5640   -0.4806    0.3819
    2.2732   -1.3110   -0.7686   -1.8959
   -1.7987    2.4088   -0.9475   -0.4727
    0.3629    0.2241   -2.6332    2.3739
    0.3629    0.2241   -2.6332    2.3739
   -0.3629   -0.2241    2.6332   -2.3739


t =

   -0.1896    0.3898   -0.2502   -0.2479
    0.0201   -0.0013   -0.1726   -0.2042
   -0.1889    0.3141   -0.1727   -0.1350
    0.0210   -0.0773   -0.0950   -0.0912
   -0.0090   -0.2649   -0.4195   -0.1327
    0.5479    0.2843    0.1914    0.2727
   -0.0937   -0.0579    0.6799   -0.6129
    0.2500    0.2033   -0.1046   -0.1014
   -0.1005   -0.2992    0.2131    0.1223
   -0.1810   -0.4427    0.0559    0.2114
    0.0497   -0.0762   -0.1526   -0.0771
    0.0173   -0.2517   -0.2104    0.1044
   -0.6002    0.3596    0.1876    0.4812
    0.3796    0.1338    0.1410    0.1999
    0.0773   -0.2139    0.1085    0.2106


c =

    3.5425    1.0475    0.2548    0.1866


u =

   -1.7670    0.1812   -0.0600   -0.0320
   -0.6724   -0.2735   -0.0662   -0.0402
   -0.9852    0.4097    0.0158    0.0198
    0.2267   -0.0107    0.0180    0.0177
   -1.3370   -0.3619   -0.0173    0.0073
    8.9056    0.6000    0.0701    0.0422
   -1.0634    0.0332    0.0235   -0.0151
    4.2143    0.3184    0.0232    0.0219
   -2.1580   -0.2652    0.0153    0.0011
   -3.7999   -0.4520    0.0082    0.0034
   -0.2033   -0.2446   -0.0392   -0.0214
   -0.5942   -0.2398    0.0089    0.0165
   -5.6764    0.5487    0.0375    0.0185
    4.3707   -0.1161   -0.0639   -0.0535
    0.5395   -0.1274    0.0261    0.0139


xcv =

   16.9021
   29.6743
   44.3324
   56.1720


ycv =

   89.6381
   97.4763
   97.9398
   98.1885


ifail =

                    0



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