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IDL Analyst Reference Guide IDL Version 7.0 November 2007 Edition Copyright © ITT Visual Information Solutions All Rights Reserved 1107IDL70AN Restricted Rights Notice The IDL®, IDL Analyst™, ENVI®, and ENVI Zoom™ software programs and the accompanying procedures, functions, and documentation described herein are sold under license agreement. Their use, duplication, and disclosure are subject to the restrictions stated in the license agreement. ITT Visual Information Solutions reserves the right to make changes to this document at any time and without notice. Limitation of Warranty ITT Visual Information Solutions makes no warranties, either express or implied, as to any matter not expressly set forth in the license agreement, including without limitation the condition of the software, merchantability, or fitness for any particular purpose. ITT Visual Information Solutions shall not be liable for any direct, consequential, or other damages suffered by the Licensee or any others resulting from use of the software packages or their documentation. Permission to Reproduce this Manual If you are a licensed user of these products, ITT Visual Information Solutions grants you a limited, nontransferable license to reproduce this particular document provided such copies are for your use only and are not sold or distributed to third parties. All such copies must contain the title page and this notice page in their entirety. Export Control Information This software and its associated documentation are subject to the controls of the Export Administration Regulations (EAR). It has been determined that this software is classified as EAR99 under U.S. Export Control laws and regulations, and may not be re- transferred to any destination expressly prohibited by U.S. laws and regulations. The recipient is responsible for ensuring compliance to all applicable U.S. Export Control laws and regulations. Acknowledgments ENVI® and IDL® are registered trademarks of ITT Corporation, registered in the United States Patent and Trademark Office. ION™, ION Script™, ION Java™, and ENVI Zoom™ are trademarks of ITT Visual Information Solutions. Numerical Recipes™ is a trademark of Numerical Recipes Software. Numerical Recipes routines are used by permission. GRG2™ is a trademark of Windward Technologies, Inc. The GRG2 software for nonlinear optimization is used by permission. NCSA Hierarchical Data Format (HDF) Software Library and Utilities. Copyright © 1988-2001, The Board of Trustees of the University of Illinois. All rights reserved. NCSA HDF5 (Hierarchical Data Format 5) Software Library and Utilities. Copyright © 1998-2002, by the Board of Trustees of the University of Illinois. All rights reserved. CDF Library. Copyright © 2002, National Space Science Data Center, NASA/Goddard Space Flight Center. NetCDF Library. Copyright © 1993-1999, University Corporation for Atmospheric Research/Unidata. HDF EOS Library. Copyright © 1996, Hughes and Applied Research Corporation. SMACC. Copyright © 2000-2004, Spectral Sciences, Inc. and ITT Visual Information Solutions. All rights reserved. This software is based in part on the work of the Independent JPEG Group. Portions of this software are copyrighted by DataDirect Technologies, © 1991-2003. BandMax®. Copyright © 2003, The Galileo Group Inc. Portions of this computer program are copyright © 1995-1999, LizardTech, Inc. All rights reserved. MrSID is protected by U.S. Patent No. 5,710,835. Foreign Patents Pending. Portions of this software were developed using Unisearch’s Kakadu software, for which ITT has a commercial license. Kakadu Software. Copyright © 2001. The University of New South Wales, UNSW, Sydney NSW 2052, Australia, and Unisearch Ltd, Australia. This product includes software developed by the Apache Software Foundation (www.apache.org/). MODTRAN is licensed from the United States of America under U.S. Patent No. 5,315,513 and U.S. Patent No. 5,884,226. FLAASH is licensed from Spectral Sciences, Inc. under a U.S. Patent Pending. Portions of this software are copyrighted by Merge Technologies Incorporated. Support Vector Machine (SVM) is based on the LIBSVM library written by Chih-Chung Chang and Chih-Jen Lin (www.csie.ntu.edu.tw/~cjlin/libsvm), adapted by ITT Visual Information Solutions for remote sensing image supervised classification purposes. IDL Wavelet Toolkit Copyright © 2002, Christopher Torrence. IMSL is a trademark of Visual Numerics, Inc. Copyright © 1970-2006 by Visual Numerics, Inc. All Rights Reserved. Other trademarks and registered trademarks are the property of the respective trademark holders. Contents Chapter 1 Preface ................................................................................................... 13 About IDL Analyst .......................................................................................................... 14 Licensing ................................................................................................................... 14 Using the IDL Analyst Documentation ........................................................................... 15 Rows versus Columns ............................................................................................... 15 Error Handling ................................................................................................................. 17 Underflow and Overflow .......................................................................................... 17 Missing Values ......................................................................................................... 17 Errors in User Code .................................................................................................. 17 Chapter 2 Functional List of IMSL Routines ....................................................................................... 21 Linear Systems ................................................................................................................ 23 Eigensystem Analysis ...................................................................................................... 25 IDL Analyst Reference Guide 3 4 Interpolation and Approximation ..................................................................................... 26 Quadrature ........................................................................................................................ 27 Differential Equations ...................................................................................................... 28 Transforms ....................................................................................................................... 29 Nonlinear Equations ......................................................................................................... 30 Optimization .................................................................................................................... 31 Special Functions ............................................................................................................. 32 Basic Statistics and Random Number Generators ........................................................... 34 Regression ........................................................................................................................ 35 Correlation and Covariance ............................................................................................. 37 Analysis of Variance ........................................................................................................ 38 Categorical and Discrete Data Analysis .......................................................................... 39 Nonparametric Statistics .................................................................................................. 40 Goodness of Fit ................................................................................................................ 41 Time Series and Forecasting ............................................................................................ 42 Multivariate Analysis ....................................................................................................... 43 Survival Analysis ............................................................................................................. 44 Probability Distribution Functions and Inverses .............................................................. 45 Random Number Generation ........................................................................................... 46 Math and Statistics Utilities ............................................................................................. 48 Chapter 3 Alphabetical Listing of IMSL Routines ............................................... 49 Part I: Mathematics Routines Chapter 4 Linear Systems ..................................................................................... 65 Overview: Linear Systems ............................................................................................... 66 Linear Systems Routines .................................................................................................. 77 IMSL_INV ....................................................................................................................... 79 IMSL_LUSOL ................................................................................................................. 81 IMSL_LUFAC ................................................................................................................. 87 IMSL_CHSOL ................................................................................................................. 91 IMSL_CHFAC ................................................................................................................. 95 IMSL_QRSOL ................................................................................................................. 98 IMSL_QRFAC ............................................................................................................... 102 IMSL_SVDCOMP ......................................................................................................... 106 Contents IDL Analyst Reference Guide 5 IMSL_CHNNDSOL ...................................................................................................... 110 IMSL_CHNNDFAC ..................................................................................................... 114 IMSL_LINLSQ ............................................................................................................. 118 IMSL_SP_LUSOL ........................................................................................................ 123 IMSL_SP_LUFAC ........................................................................................................ 129 IMSL_SP_BDSOL ........................................................................................................ 136 IMSL_SP_BDFAC ........................................................................................................ 140 IMSL_SP_PDSOL ........................................................................................................ 144 IMSL_SP_PDFAC ........................................................................................................ 149 IMSL_SP_BDPDSOL ................................................................................................... 153 IMSL_SP_BDPDFAC ................................................................................................... 156 IMSL_SP_GMRES ....................................................................................................... 160 IMSL_SP_CG ............................................................................................................... 164 IMSL_SP_MVMUL ...................................................................................................... 168 Chapter 5 Eigensystem Analysis ........................................................................ 173 Overview: Eigensystem Analysis .................................................................................. 174 Eigensystem Routines ................................................................................................... 177 IMSL_EIG ..................................................................................................................... 178 IMSL_EIGSYMGEN .................................................................................................... 183 IMSL_GENEIG ............................................................................................................. 186 Chapter 6 Interpolation and Approximation ....................................................... 191 Overview: Interpolation and Approximation ................................................................ 192 Interpolation and Approximation Routines ................................................................... 199 IMSL_CSINTERP ......................................................................................................... 200 IMSL_CSSHAPE .......................................................................................................... 205 IMSL_BSINTERP ......................................................................................................... 210 IMSL_BSKNOTS ......................................................................................................... 219 IMSL_SPVALUE ......................................................................................................... 224 IMSL_SPINTEG ........................................................................................................... 230 IMSL_FCNLSQ ............................................................................................................ 234 IMSL_BSLSQ ............................................................................................................... 238 IMSL_CONLSQ ........................................................................................................... 248 IMSL_CSSMOOTH ...................................................................................................... 254 IDL Analyst Reference Guide Contents 6 IMSL_SMOOTHDATA1D ........................................................................................... 258 IMSL_SCAT2DINTERP ............................................................................................... 262 IMSL_RADBF ............................................................................................................... 266 IMSL_RADBE .............................................................................................................. 277 Chapter 7 Quadrature .......................................................................................... 279 Overview: Quadrature .................................................................................................... 280 Quadrature Routines ...................................................................................................... 283 IMSL_INTFCN .............................................................................................................. 284 IMSL_INTFCNHYPER ................................................................................................ 315 IMSL_INTFCN_QMC .................................................................................................. 319 IMSL_GQUAD .............................................................................................................. 322 IMSL_FCN_DERIV ...................................................................................................... 326 Chapter 8 Differential Equations ........................................................................ 329 Overview: Differential Equations .................................................................................. 330 Differential Equations Routines ..................................................................................... 332 IMSL_ODE .................................................................................................................... 333 IMSL_PDE_MOL .......................................................................................................... 351 IMSL_POISSON2D ...................................................................................................... 366 Chapter 9 Transforms .......................................................................................... 373 Overview: Transforms ................................................................................................... 374 Transforms Routines ...................................................................................................... 376 IMSL_FFTCOMP .......................................................................................................... 377 IMSL_FFTINIT ............................................................................................................. 387 IMSL_CONVOL1D ...................................................................................................... 390 IMSL_CORR1D ............................................................................................................ 395 IMSL_LAPLACE_INV ................................................................................................. 398 Chapter 10 Nonlinear Equations ........................................................................... 407 Overview: Nonlinear Equations ..................................................................................... 408 Nonlinear Equations Routines ....................................................................................... 409 IMSL_ZEROPOLY ....................................................................................................... 410 Contents IDL Analyst Reference Guide 7 IMSL_ZEROFCN ......................................................................................................... 413 IMSL_ZEROSYS .......................................................................................................... 418 Chapter 11 Optimization ........................................................................................ 421 Overview: Optimization ................................................................................................ 422 Optimization Routines ................................................................................................... 424 IMSL_FMIN ................................................................................................................. 425 IMSL_FMINV ............................................................................................................... 433 IMSL_NLINLSQ .......................................................................................................... 441 IMSL_LINPROG .......................................................................................................... 449 IMSL_QUADPROG ..................................................................................................... 454 IMSL_MINCONGEN ................................................................................................... 458 IMSL_CONSTRAINED_NLP ...................................................................................... 465 Chapter 12 Special Functions .............................................................................. 473 Overview: Special Functions ......................................................................................... 474 Special Functions Routines ........................................................................................... 475 IMSL_ERF .................................................................................................................... 477 IMSL_ERFC ................................................................................................................. 480 IMSL_BETA ................................................................................................................. 484 IMSL_LNBETA ............................................................................................................ 487 IMSL_BETAI ................................................................................................................ 489 IMSL_LNGAMMA ...................................................................................................... 491 IMSL_GAMMA_ADV ................................................................................................. 493 IMSL_GAMMAI .......................................................................................................... 495 IMSL_BESSI ................................................................................................................. 498 IMSL_BESSJ ................................................................................................................ 500 IMSL_BESSK ............................................................................................................... 502 IMSL_BESSY ............................................................................................................... 504 IMSL_BESSI_EXP ....................................................................................................... 506 IMSL_BESSK_EXP ..................................................................................................... 508 IMSL_ELK .................................................................................................................... 510 IMSL_ELE .................................................................................................................... 512 IMSL_ELRF .................................................................................................................. 514 IMSL_ELRD ................................................................................................................. 516 IDL Analyst Reference Guide Contents 8 IMSL_ELRJ ................................................................................................................... 518 IMSL_ELRC .................................................................................................................. 520 IMSL_FRESNEL_COSINE .......................................................................................... 522 IMSL_FRESNEL_SINE ................................................................................................ 524 IMSL_AIRY_AI ............................................................................................................ 526 IMSL_AIRY_BI ............................................................................................................ 528 IMSL_KELVIN_BER0 ................................................................................................. 531 IMSL_KELVIN_BEI0 ................................................................................................... 533 IMSL_KELVIN_KER0 ................................................................................................. 535 IMSL_KELVIN_KEI0 .................................................................................................. 537 Part II: Statistics Routines Chapter 13 Basic Statistics ................................................................................... 541 Overview: Basic Statistics ............................................................................................. 542 Basic Statistics Routines ................................................................................................ 543 IMSL_SIMPLESTAT .................................................................................................... 544 IMSL_NORM1SAMP ................................................................................................... 550 IMSL_NORM2SAMP ................................................................................................... 555 IMSL_FREQTABLE ..................................................................................................... 563 IMSL_SORTDATA ....................................................................................................... 570 IMSL_RANKS .............................................................................................................. 577 Chapter 14 Regression .......................................................................................... 585 Overview: Regression .................................................................................................... 586 Regression Routines ....................................................................................................... 599 IMSL_REGRESSORS ................................................................................................... 600 IMSL_MULTIREGRESS .............................................................................................. 607 IMSL_MULTIPREDICT ............................................................................................... 622 IMSL_ALLBEST .......................................................................................................... 630 IMSL_STEPWISE ......................................................................................................... 639 IMSL_POLYREGRESS ................................................................................................ 649 IMSL_POLYPREDICT ................................................................................................. 657 IMSL_NONLINREGRESS ........................................................................................... 665 IMSL_HYPOTH_PARTIAL ......................................................................................... 675 Contents IDL Analyst Reference Guide 9 IMSL_HYPOTH_SCPH ............................................................................................... 681 IMSL_HYPOTH_TEST ................................................................................................ 686 IMSL_NONLINOPT ..................................................................................................... 693 IMSL_LNORMREGRESS ........................................................................................... 702 Chapter 15 Correlation and Covariance ............................................................... 719 Overview: Correlation and Covariance ......................................................................... 720 Correlation and Covariance Routines ............................................................................ 721 IMSL_COVARIANCES ............................................................................................... 722 IMSL_PARTIAL_COV ................................................................................................ 728 IMSL_POOLED_COV ................................................................................................. 734 IMSL_ROBUST_COV ................................................................................................. 738 Chapter 16 Analysis of Variance ........................................................................... 747 Overview: Analysis of Variance ................................................................................... 748 Analysis of Variance Routines ...................................................................................... 749 IMSL_ANOVA1 ........................................................................................................... 750 IMSL_ANOVAFACT ................................................................................................... 760 IMSL_MULTICOMP ................................................................................................... 769 IMSL_ANOVANESTED .............................................................................................. 772 IMSL_ANOVABALANCED ....................................................................................... 781 Chapter 17 Categorical and Discrete Data Analysis ........................................... 793 Overview: Categorical and Discrete Data Analysis ...................................................... 794 Categorical and Discrete Data Analysis Routines ......................................................... 795 IMSL_CONTINGENCY ............................................................................................... 796 IMSL_EXACT_ENUM ................................................................................................ 809 IMSL_EXACT_NETWORK ........................................................................................ 812 IMSL_CAT_GLM ......................................................................................................... 817 Chapter 18 Nonparametric Statistics .................................................................... 831 Overview ....................................................................................................................... 832 Nonparametric Statistics Routines ................................................................................ 833 IMSL_SIGNTEST ......................................................................................................... 834 IDL Analyst Reference Guide Contents 10 IMSL_WILCOXON ...................................................................................................... 837 IMSL_NCTRENDS ....................................................................................................... 846 IMSL_CSTRENDS ........................................................................................................ 849 IMSL_TIE_STATS ........................................................................................................ 855 IMSL_KW_TEST .......................................................................................................... 857 IMSL_FRIEDMANS_TEST ......................................................................................... 860 IMSL_COCHRANQ ...................................................................................................... 865 IMSL_KTRENDS .......................................................................................................... 868 Chapter 19 Goodness of Fit .................................................................................. 873 Overview: Goodness of Fit ............................................................................................ 874 Goodness of Fit Routines ............................................................................................... 875 IMSL_CHISQTEST ...................................................................................................... 876 IMSL_NORMALITY .................................................................................................... 882 IMSL_KOLMOGOROV1 ............................................................................................. 886 IMSL_KOLMOGOROV2 ............................................................................................. 889 IMSL_MVAR_NORMALITY ...................................................................................... 892 IMSL_RANDOMNESS_TEST ..................................................................................... 897 Chapter 20 Time Series and Forecasting ............................................................. 909 Overview: Time Series and Forecasting ........................................................................ 910 Time Series and Forecasting Routines ........................................................................... 912 IMSL_ARMA ................................................................................................................ 913 IMSL_DIFFERENCE .................................................................................................... 929 IMSL_BOXCOXTRANS .............................................................................................. 935 IMSL_AUTOCORRELATION ..................................................................................... 940 IMSL_PARTIAL_AC .................................................................................................... 945 IMSL_LACK_OF_FIT .................................................................................................. 948 IMSL_GARCH .............................................................................................................. 952 IMSL_KALMAN .......................................................................................................... 957 Chapter 21 Multivariate Analysis .......................................................................... 967 Overview: Multivariate Analysis ................................................................................... 968 Multivariate Analysis Routines ...................................................................................... 970 Contents IDL Analyst Reference Guide

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