Update a weighted sum of squares matrix with a new observation

はじめる前に
新機能一覧
Maple ワークシートの作成
Mapleワークシートを共有
Maple ウィンドウのカスタマイズ
Maple システムのカスタマイズ
コネクティビティ
Mathematics
数学
物理
プログラミング
グラフィックス
Student パッケージ
Science and Engineering
科学・エンジニアリング
アプリケーションと例題
リファレンス
システム
MapleSim
MapleSim ツールボックス
MapleSim ヘルプ
Tasks
Toolboxes
- BlockImporter
- Global Optimization
- Grid Computing
- Maple-NAG Connector
  - General information
  - Computational Routines
    - a02 (Complex Arithmetic)
    - c02 (Zeros of Polynomials)
    - c05 (Roots of One or More Transcendental Equations)
    - c06 (Fourier Transforms)
    - d01 (Quadrature)
    - d02 (Ordinary Differential Equations)
    - d03 (Partial Differential Equations)
    - d06 (Mesh Generation)
    - e01 (Interpolation)
    - e02 (Curve and Surface Fitting)
    - e04 (Minimizing or Maximizing a Function)
    - f01 (Matrix Factorizations)
    - f02 (Eigenvalues and Eigenvectors)
    - f03 (Determinants)
    - f04 (Simultaneous Linear Equations)
    - f06 (Linear Algebra Support Functions)
    - f07 (Linear Equations (LAPACK))
    - f08 (Least-squares and Eigenvalue Problems (LAPACK))
    - f11 (Large Scale Linear Systems)
    - f16 (NAG Interface to BLAS)
    - g01 (Simple Calculations on Statistical Data)
    - g02 (Correlation and Regression Analysis)
      - g02 Introduction
      - g02brc (nag_ken_spe_corr_coeff)
      - g02btc (nag_sum_sqs_update)
      - g02buc (nag_sum_sqs)
      - g02bwc (nag_cov_to_corr)
      - g02bxc (nag_corr_cov)
      - g02byc (nag_partial_corr)
      - g02cac (nag_simple_linear_regression)
      - g02cbc (nag_regress_confid_interval)
      - g02dac (nag_regsn_mult_linear)
      - g02dcc (nag_regsn_mult_linear_addrem_obs)
      - g02ddc (nag_regsn_mult_linear_upd_model)
      - g02dec (nag_regsn_mult_linear_add_var)
      - g02dfc (nag_regsn_mult_linear_delete_var)
      - g02dgc (nag_regsn_mult_linear_newyvar)
      - g02dkc (nag_regsn_mult_linear_tran_model)
      - g02dnc (nag_regsn_mult_linear_est_func)
      - g02eac (nag_all_regsn)
      - g02ecc (nag_cp_stat)
      - g02eec (nag_step_regsn)
      - g02fac (nag_regsn_std_resid_influence)
      - g02fcc (nag_durbin_watson_stat)
      - g02gac (nag_glm_normal)
      - g02gbc (nag_glm_binomial)
      - g02gcc (nag_glm_poisson)
      - g02gdc (nag_glm_gamma)
      - g02gkc (nag_glm_tran_model)
      - g02gnc (nag_glm_est_func)
      - g02hac (nag_robust_m_regsn_estim)
      - g02hbc (nag_robust_m_regsn_wts)
      - g02hdc (nag_robust_m_regsn_user_fn)
      - g02hfc (nag_robust_m_regsn_param_var)
      - g02hkc (nag_robust_corr_estim)
      - g02hlc (nag_robust_m_corr_user_fn)
      - g02hmc (nag_robust_m_corr_user_fn_no_derr)
    - g03 (Multivariate Methods)
    - g04 (Analysis of Variance)
    - g05 (Random Number Generators)
    - g07 (Univariate Estimation)
    - g08 (Nonparametric Statistics)
    - g10 (Smoothing in Statistics)
    - g11 (Contingency Table Analysis)
    - g12 (Survival Analysis)
    - g13 (Time Series Analysis)
    - h (Operations Research)
    - m01 (Sorting)
    - s (Approximations of Special Functions)
    - x01 (Mathematical Constants)
    - x02 (Machine Constants)
    - x04 (Input-Output Utilities)
  - Getting Started
  - Example Worksheet
エラーメッセージガイド
マニュアル
数学アプリ

NAG[g02btc] NAG[nag_sum_sqs_update] - Update a weighted sum of squares matrix with a new observation

Calling Sequence

g02btc(mean, wt, x, incx, sw, xbar, c, 'm'=m, 'fail'=fail)

nag_sum_sqs_update(. . .)

Parameters

mean - String;

On entry: indicates whether nag_sum_sqs_update (g02btc) is to calculate sums of squares and cross-products, or sums of squares and cross-products of deviations about the mean.

The sums of squares and cross-products of deviations about the mean are calculated.

The sums of squares and cross-products are calculated.

Constraint: "Nag_AboutMean" or "Nag_AboutZero". .

wt - float;

On entry: the weight to use for the current observation, .

For unweighted means and cross-products set . The use of a suitable negative value of wt, e.g., will have the effect of deleting the observation.

x - Vector(1.., datatype=float[8]);

On entry: must contain the value of the th variable for the current observation, .

incx - integer;

On entry: the increment of x.

Constraint: . .

sw - assignable;

Note: On exit the variable sw will have a value of type float.

On entry: the sum of weights for the previous observations, .

The update procedure is initialized.

All elements of xbar and c are set to zero.

Constraint: and . .

On exit: contains the updated sum of weights, .

xbar - Vector(1..m, datatype=float[8]);

On entry: if , xbar is initialized, otherwise must contain the weighted mean of the th variable for the previous observations, , for .

On exit: contains the weighted mean of the th variable, , for .

c - Vector(1.., datatype=float[8]);

Note: the dimension, dim, of the array c must be at least .

On entry: if , c must contain the upper triangular part of the matrix of weighted sums of squares and cross-products or weighted sums of squares and cross-products of deviations about the mean. It is stored packed form by column, i.e., the cross-product between the th and th variable, , is stored in .

On exit: the update sums of squares and cross-products stored as on input.

'm'=m - integer; (optional)

On entry: , the number of variables.

Constraint: . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_sum_sqs_update (g02btc) updates the sample means and sums of squares and cross-products, or sums of squares and cross-products of deviations about the mean, for a new observation. The data may be weighted.

Description

nag_sum_sqs_update (g02btc) is an adaptation of West's WV2 algorithm; see West (1979). This function updates the weighted means of variables and weighted sums of squares and cross-products or weighted sums of squares and cross-products of deviations about the mean for observations on variables , for . For the first observations let the mean of the th variable be , the cross-product about the mean for the th and th variables be and the sum of weights be . These are updated by the th observation, , for , with weight as follows:

W[i]=W[i-1]+w[i] (x)[j](i)=(x)[j](i,-,1)+(w[i])/(W[i])(x[j],-,(x)[j],(i,-,1)) j=1,2,..,m

and

c[jk](i)=c[jk](i,-,1)+(w[i])/(W[i])(x[j],-,(x)[j],(i,-,1))(x[k],-,(x)[k],(i,-,1))W[i-1] j=1,2,..,m k=j,j+1,2,..,m

The algorithm is initialized by taking , the first observation and .

For the unweighted case and for all .

	Error Indicators and Warnings
	"NE_BAD_PARAM" On entry, argument had an illegal value. "NE_INT" On entry, . Constraint: . On entry, . Constraint: . "NE_INTERNAL_ERROR" An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance. "NE_REAL" On entry, . Constraint: . "NE_SUM_WEIGHT" On entry, : .

	Accuracy
	For a detailed discussion of the accuracy of this method see Chan et al. (1982) and West (1979).

	Further Comments
	nag_sum_sqs_update (g02btc) may be used to update the results returned by g02buc (nag_sum_sqs). g02bwc (nag_cov_to_corr) may be used to calculate the correlation matrix from the matrix of sums of squares and cross-products of deviations about the mean .

Examples

>	mean := "Nag_AboutMean": m := 3: wt := 0.13: incx := 1: sw := 0: x := Vector([9.123100000000001, 3.7011, 4.523], datatype=float[8]): xbar := Vector([0, 0, 0], datatype=float[8]): c := Vector([0, 0, 0, 0, 0, 0], datatype=float[8]): NAG:-g02btc(mean, wt, x, incx, sw, xbar, c, 'm' = m):

sw;

xbar;

	See Also
	Chan T F, Golub G H and Leveque R J (1982) Updating Formulae and a Pairwise Algorithm for Computing Sample Variances Compstat, Physica-Verlag West D H D (1979) Updating mean and variance estimates: An improved method Comm. ACM 22 532–555 g02 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.