MSCS CONVERT THE STORAGE ALLOCATION OF A SYMMETRIC MATRIX FROM A TWO-DIMENSIONAL ARRAY TO A LINEAR ARRAY MSCG CONVERT THE STORAGE ALLOCATION OF A SYMMETRIC MATRIX FROM A LINEAR ARRAY TO A TWO-DIMENSIONAL ARRAY MAGS ADD OR SUBTRACT A SQUARE AND A SYMMETRIC MATRIX MMGG MULTIPLY TWO GENERAL MATRICES MMSS MULTIPLY TWO SYMMETRIC MATRICES STORED IN LINEAR ARRAYS MMGS MULTIPLY A GENERAL WITH A SYMMETRIC MATRIX MMGT MULTIPLY A GENERAL MATRIX WITH ITS TRANSPOSE MPRM PERMUTE THE ROWS OR, IF OPT = 'C', THE COLUMNS OF A MATRIX MTPI CALCULATE PERMUTATION VECTOR (OR ITS INVERSE IF INV ='1') CORRESPONDING TO GIVEN TRANSPOSITION VECTOR MPIT CALCULATE THE INVERSE PERMUTATION VECTOR OR, IF OPT = 'T', THE TRANSPOSITION VECTORS OF THE GIVEN AND INVERSE PERMUTATIONS MFG FACTORIZE A GENERAL NON-SINGULAR MATRIX A INTO A PRODUCT OF A LOWER TRIANGULAR MATRIX L AND AN UPPER TRIANGULAR MATRIX U OVERWRITTEN ON A, OMITTING UNIT DIAGONAL OF U MFS FACTORIZE SYMMETRIC POSITIVE DEFINITE MATRIX MFSB FACTORIZE A GIVEN POSITIVE DEFINITE N BY N MATRIX A WITH SYMMETRIC BAND STRUCTURE (NUD UPPER CODIAGONALS) MFGR FOR A GIVEN M BY N MATRIX A THE FOLLOWING CALCULATIONS ARE PERFORMED (1) DETERMINE RANK AND LINEARLY INDEPENDENT ROWS AND COLUMNS (BASIS) (2) FACTORIZE A SUBMATRIX OF MAXIMAL RANK (3) EXPRESS NON-BASIC ROWS IN TERMS OF BASIC ONES (4) EXPRESS BASIC VARIABLES IN TERMS OF FREE ONES MDLS FOR AN EQUATION SYSTEM A*X=R WITH SYMMETRIC POSITIVE DEFINITE MATRIX A=T*TRANSPOSE(T) CALCULATE OPTIONALLY SOLUTION X INVERSE(T) * R TRANSPOSE(INVERSE(T)) * R FOR GIVEN TRIANGULAR FACTOR T AND RIGHT HAND SIDE MATRIX R MDSB FOR AN EQUATION SYSTEM A*X=R WITH SYMMETRIC POSITIVE DEFINITE BAND MATRIX A=TRANSPOSE(T)*T CALCULATE OPTIONALLY SOLUTION X TRANSPOSE(INVERSE(T)) * R INVERSE(T) * R FOR GIVEN UPPER BAND FACTOR T AND GENERAL RIGHT HAND SIDE MATRIX R MDLG FOR AN EQUATION SYSTEM A*X=R WITH GENERAL NON-SINGULAR MATRIX A=L*U CALCULATE OPTIONALLY SOLUTION X INVERSE(L) * R INVERSE(U) * R FOR GIVEN TRIANGULAR FACTORS L, U AND RIGHT HAND SIDE R MIG INVERT A FACTORIZED GENERAL MATRIX A. A MUST BE FACTORIZED INTO THE FORM A = L*U, WHERE THE UPPER TRIANGULAR MATRIX U CONTAINS THE UNIT DIAGONAL WHICH IS NOT STORED. MIS INVERT SYMMETRIC POSITIVE DEFINITE MATRIX MINV TO INVERT A MATRIX MLSQ LINEAR LEAST SQUARES PROBLEM SOLVED USING HOUSEHOLDER TRANSFORMATIONS MGB FOR AN EQUATION SYSTEM A*X=R WITH BAND MATRIX A=L*U CALCULATE OPTIONALLY UPPER TRIANGULAR FACTOR U AND SOLUTION X, UPPER TRIANGULAR FACTOR U AND INVERSE(L)*R, INVERSE(U)*R FOR GIVEN U,R. MATE REDUCE A REAL MATRIX TO HESSENBERG FORM - ELIMINATION TECHNIQUES MATU REDUCE A REAL MATRIX TO HESSENBERG FORM - HOUSEHOLDER'S TRANSFORMATIONS MSTU REDUCTION OF A SYMMETRIC MATRIX TO SYMMETRIC TRIDIAGONAL FORM MEAT EIGENVALUES OF A REAL HESSENBERG MATRIX MEST EIGENVALUES OF A SYMMETRIC TRIDIAGONAL MATRIX MEBS BOUNDS FOR THE EIGENVALUES OF A SYMMETRIC MATRIX MVST EIGENVECTORS OF A SYMMETRIC TRIDIAGONAL MATRIX MSDU TO COMPUTE EIGENVALUES AND EIGENVECTORS OF A REAL SYMMETRIC MATRIX MGDU TO COMPUTE EIGENVALUES AND EIGENVECTORS OF A REAL NONSYMMETRIC MATRIX OF THE FORM B INVERSE TIMES A. MVAT EIGENVECTORS OF A COMPLEX HESSENBERG MATRIX MVSU BACK TRANSFORMATION OF THE EIGENVECTORS - SYMMETRIC CASE MVUB BACK TRANSFORMATION OF THE EIGENVECTORS - HOUSEHOLDER'S TRANSFORMATIONS MVEB BACK TRANSFORMATION OF THE EIGENVECTORS - ELIMINATION TECHNIQUES POV CALCULATE VALUES OF FIRST N ORTHOGONAL POLYNOMIALS POSV EVALUATE N-TERM SERIES EXPANSION IN ORTHOGONAL POLYNOMIALS PEC POLYNOMIAL ECONOMIZATION OVER THE RANGE (0,A) IF OPT ='S' AND OVER THE RANGE (-A,A) IF OPT ='0' POST TRANSFORM N-TERM SERIES EXPANSION IN ORTHOGONAL POLYNOMIALS PRTC CALCULATE ALL ROOTS OF A COMPLEX POLYNOMIAL QTFG INTEGRATION OF A MONOTONICALLY TABULATED FUNCTION BY TRAPEZOIDAL RULE QSF INTEGRATION OF AN EQUI-DISTANTLY TABULATED FUNCTION BY SIMPSON'S RULE QHFG INTEGRATION OF A MONOTONICALLY TABULATED FUNCTION WITH FIRST DERIVATIVE BY A HERMITIAN FORMULA OF FIRST ORDER QATR INTEGRATION OF A GIVEN FUNCTION BY THE TRAPEZOIDAL RULE TOGETHER WITH ROMBERG'S EXTRAPOLATION METHOD QG2 INTEGRATION OF GIVEN FUNCTION BY 2-POINT GAUSSIAN QUADRATURE FORMULA QG4 INTEGRATION OF A GIVEN FUNCTION BY 4-POINT GAUSSIAN QUADRATURE FORMULA QG8 INTEGRATION OF A GIVEN FUNCTION BY 8-POINT GAUSSIAN QUADRATURE FORMULA QG16 INTEGRATION OF A GIVEN FUNCTION BY 16-POINT GAUSSIAN QUADRATURE FORMULA QG24 INTEGRATION OF A GIVEN FUNCTION BY 24-POINT GAUSSIAN QUADRATURE FORMULA QG32 INTEGRATION OF A GIVEN FUNCTION BY 32-POINT GAUSSIAN QUADRATURE FORMULA QG48 INTEGRATION OF A GIVEN FUNCTION BY 48-POINT GAUSSIAN QUADRATURE FORMULA QL2 INTEGRATION OF A GIVEN FUNCTION BY 2-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA QL4 INTEGRATION OF A GIVEN FUNCTION BY 4-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA QL8 INTEGRATION OF A GIVEN FUNCTION BY 8-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA QL12 INTEGRATION OF A GIVEN FUNCTION BY 12-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA QL16 INTEGRATION OF A GIVEN FUNCTION BY 16-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA QL24 INTEGRATION OF A GIVEN FUNCTION BY 24-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA QH2 INTEGRATION OF A GIVEN FUNCTION BY 2-POINT GAUSSIAN-HERMITE QUADRATURE FORMULA QH4 INTEGRATION OF A GIVEN FUNCTION BY 4-POINT GAUSSIAN-HERMITE QUADRATURE FORMULA QH8 INTEGRATION OF A GIVEN FUNCTION BY 8-POINT GAUSSIAN-HERMITE QUADRATURE FORMULA QH16 INTEGRATION OF A GIVEN FUNCTION BY 16-POINT GAUSSIAN-HERMITE QUADRATURE FORMULA QH24 INTEGRATION OF A GIVEN FUNCTION BY 24-POINT GAUSSIAN-HERMITE QUADRATURE FORMULA QH32 INTEGRATION OF A GIVEN FUNCTION BY 32-POINT GAUSSIAN-HERMITE QUADRATURE FORMULA QH48 INTEGRATION OF A GIVEN FUNCTION BY 48-POINT GAUSSIAN-HERMITE QUADRATURE FORMULA QA2 INTEGRATION OF A GIVEN FUNCTION BY ASSOCIATED 2-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA QA4 INTEGRATION OF A GIVEN FUNCTION BY ASSOCIATED 4-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA QA8 INTEGRATION OF A GIVEN FUNCTION BY ASSOCIATED 8-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA QA12 INTEGRATION OF A GIVEN FUNCTION BY ASSOCIATED 12-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA QA16 INTEGRATION OF A GIVEN FUNCTION BY ASSOCIATED 16-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA QA24 INTEGRATION OF A GIVEN FUNCTION BY ASSOCIATED 24-POINT GAUSSIAN-LAGUERRE QUADRATURE FORMULA DGT3 DIFFERENTIATE A TABLED FUNCTION USING LAGRANGIAN INTERPOLATION FORMULA, DEGREE 2 DET3 DIFFERENTIATE AN EQUIDISTANTLY TABLED FUNCTION USING LAGRANGIAN INTERPOLATION FORMULA, DEGREE 2 DET5 DIFFERENTIATE AN EQUIDISTANTLY TABLED FUNCTION USING LAGRANGIAN INTERPOLATION FORMULA, DEGREE 4 DFEC COMPUTE DERIVATIVE VALUE OF A FUNCTION USING EXTRAPOLATION METHOD ON CENTRAL DIVIDED DIFFERENCES DFEO COMPUTE DERIVATIVE VALUE OF A FUNCTION USING EXTRAPOLATION METHOD ON ONE-SIDED DIVIDED DIFFERENCES ALI AITKEN SCHEME FOR INTERPOLATION OF FUNCTION VALUE FROM GIVEN MONOTONIC TABLE AHI AITKEN HERMITE SCHEME FOR INTERPOLATION OF FUNCTION VALUE FROM GIVEN MONOTONIC TABLE ACFI CONTINUED FRACTION SCHEME FOR INTERPOLATION OF FUNCTION VALUE FROM GIVEN MONOTONIC TABLE FFT FAST FOURIER TRANSFORM FOR ANY ONE-DIMENSIONAL ARRAY FFTM FAST FOURIER TRANSFORM FOR MULTI-DIMENSIONAL ARRAY APLL SET UP NORMAL EQUATIONS FOR A LINEAR LEAST SQUARES FIT TO A GIVEN DISCRETE FUNCTION APC SET UP NORMAL EQUATIONS OF WEIGHTED LEAST SQUARES FIT IN TERMS OF CHEBYSHEV POLINOMIALS FOR A GIVEN DESCRETE FUNCTION ASN SOLUTION OF NORMAL-EQUATIONS UP TO SPECIFIED ORDER OR PRECISION. ALL FITS OF SMALLER ORDER ARE CALCULATED OPTIONALLY. SG13 SMOOTH A TABLED FUNCTION USING A FIRST DEGREE POLYNOMIAL FIT RELEVANT TO THREE POINTS SE15 SMOOTH AN EQUIDISTANTLY TABLED FUNCTION USING A FIRST DEGREE POLYNOMIAL FIT RELEVANT TO FIVE POINTS SE35 SMOOTH AN EQUIDISTANTLY TABLED FUNCTION USING A THIRD DEGREE POLYNOMIAL FIT RELEVANT TO FIVE POINTS EXSM TO FIND THE TRIPLE EXPONENTIAL SMOOTHED SERIES S OF A GIVEN SERIES X. FMFP FIND A LOCAL MINIMUM OF A FUNCTION OF SEVERAL VARIABLES BY THE METHOD OF FLETCHER AND POWELL. RTF CALCULATE ROOT OF GIVEN FUNCTION IF OPT = '0' BY LINEAR INTERPOLATION (SECANT METHOD) IF OPT = '1' BY QUADRATIC INTERPOLATION (MULLER'S METHOD) IF OPT = '2' BY HYPERBOLIC INTERPOLATION (HALLEY'S METHOD) RTFD CALCULATE ROOT OF GIVEN FUNCTION USING DERIVATIVE VALUES IF OPT = '0' BY LINEAR INTERPOLATION (NEWTON METHOD) IF OPT = '1' BY INVERSE QUADRATIC INTERPOLATION IF OPT = '2' BY HYPERBOLIC INTERPOLATION (HALLEY METHOD) DERE PERFORM ONE INTEGRATION STEP FOR A SYSTEM OF ORDINARY DIF- FERENTIAL EQUATIONS USING RATIONAL EXTRAPOLATION TECHNIQUE CEL COMPLETE ELLIPTIC INTEGRAL OF FIRST KIND ELI ELLIPTIC INTEGRAL OF FIRST KIND JELF JACOBIAN ELLIPTIC FUNCTIONS SN, CN, DN LGAM COMPUTES THE DOUBLE PRECISION NATURAL LOGARITHM OF THE GAMMA FUNCTION OF A GIVEN DOUBLE PRECISION ARGUMENT. TALY TO CALCULATE TOTAL, MEAN, STANDARD DEVIATION, MINIMUM, MAXIMUM FOR EACH VARIABLE IN A SET (OR A SUBSET) OF OBSERVATIONS. BOUN TO SELECT FROM A SET (OR A SUBSET) OF OBSERVATIONS THE NUMBER OF OBSERVATIONS UNDER, BETWEEN AND OVER TWO GIVEN BOUNDS FOR EACH VARIABLE. ABST TO TEST MISSING OR ZERO VALUES FOR OBSERVATION MATRIX A. SBST TO DERIVE A SUBSET VECTOR INDICATING WHICH OBSERVATIONS IN A SET HAVE SATISFIED CERTAIN CONDITIONS. TAB1 TO TABULATE FOR ONE VARIABLE IN AN OBSERVATION MATRIX (OR A SUBSET), THE FREQUENCY AND PERCENT FREQUENCY OVER GIVEN CLASS INTERVALS. IN ADDITION, CALCULATE FOR THE SAME VARIABLE THE TOTAL, MEAN, STANDARD DEVIATION, MINIMUM, AND MAXIMUM. TAB2 TO PERFORM A TWO-WAY CLASSIFICATION OF THE FREQUENCY, PERCENT FREQUENCY, AND OTHER STATISTICS, OVER GIVEN CLASS INTERVALS, FOR TWO SELECTED VARIABLES IN AN OBSERVATION MATRIX. SUBM BASED ON VECTOR S DERIVED FROM PROCEDURE SBST OR ABST, THIS PROCEDURE COPIES FROM A LARGER MATRIX OF OBSERVATION DATA A SUBSET MATRIX OF THOSE OBSERVATIONS WHICH HAVE SATISFIED CERTAIN CONDITIONS. MOMN TO FIND THE FIRST FOUR MOMENTS FOR GROUPED DATA ON EQUAL CLASS INTERVALS. TTST TO FIND CERTAIN T-STATISTICS ON THE MEANS OF POPULATIONS. CORR TO COMPUTE MEANS, STANDARD DEVIATIONS, SUMS OF CROSS-PRODUCTS OF DEVIATIONS, AND CORRELATION COEFFICIENTS. ORDR TO CONSTRUCT FROM A LARGER MATRIX OF CORRELATION COEFFICIENTS A SUBSET MATRIX OF INTERCORRELATIONS AMONG INDEPENDENT VAR- IABLES AND A VECTOR OF INTERCORRELATIONS OF INDEPENDENT VARIABLES WITH DEPENDENT VARIABLE. MLTR TO PERFORM A MULTIPLE LINEAR REGRESSION ANALYSIS FOR A DEPENDENT VARIABLE AND A SET OF INDEPENDENT VARIABLES. STRG TO PERFORM A STEP-WISE MULTIPLE REGRESSION ANALYSIS FOR A DEPENDENT VARIABLE AND A SET OF INDEPENDENT VARIABLES. CANC TO COMPUTE THE CANONICAL CORRELATIONS BETWEEN TWO SETS OF VARIABLES. AVAR TO PERFORM AN ANALYSIS OF VARIANCE FOR A COMPLETE FACTORIAL DESIGN. DMTX TO COMPUTE MEANS OF VARIABLES IN EACH GROUP AND A POOLED DISPERSION MATRIX FOR ALL THE GROUPS. DSCR TO COMPUTE A SET OF LINEAR FUNCTIONS WHICH SERVE AS INDICES FOR CLASSIFYING AN INDIVIDUAL INTO ONE OF SEVERAL GROUPS. TRAC TO COMPUTE CUMULATIVE PERCENTAGE OF EIGENVALUES GREATER THAN OR EQUAL TO A CONSTANT SPECIFIED BY THE USER. LOAD TO COMPUTE A FACTOR MATRIX (LOADING) FROM EIGENVALUES AND ASSOCIATED EIGENVECTORS. VRMX TO PERFORM ORTHOGONAL ROTATION OF A FACTOR MATRIX. KLMO TESTS THE DIFFERENCE BETWEEN EMPIRICAL AND THEORETICAL DISTRIBUTIONS USING THE KOLMOGOROV-SMIRNOV TEST KLM2 TESTS THE DIFFERENCE BETWEEN TWO SAMPLE DISTRIBUTION FUNCTIONS USING THE KOLMOGOROV-SMIRNOV TEST. SMIR COMPUTES VALUES OF THE LIMITING DISTRIBUTION FUNCTION FOR THE KOLMOGOROV-SMIRNOV STATISTIC. CHSQ TO COMPUTE CHI-SQUARE FROM A CONTINGENCY TABLE. KRNK TO TEST CORRELATION BETWEEN TWO VARIABLES BY MEANS OF THE KENDALL RANK CORRELATION COEFFICIENT. QTST TO TEST WHETHER THREE OR MORE MATCHED GROUPS OF DICHOTOMOUS DATA DIFFER SIGNIFICANTLY BY THE COCHRAN Q-TEST. RANK TO RANK A VECTOR OF VALUES. SRNK TO TEST CORRELATION BETWEEN TWO VARIABLES BY MEANS OF SPEARMAN RANK CORRELATION COEFFICIENT. TIE TO CALCULATE CORRELATION FACTOR DUE TO TIES. TWAV TO TEST WHETHER A NUMBER OF SAMPLES ARE FROM THE SAME POPULATION BY THE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE TEST. UTST TO TEST WHETHER TWO INDEPENDENT GROUPS ARE FROM THE SAME POPULATION BY MEANS OF A MANN-WHITNEY U-TEST. WTST TO TEST DEGREE OF ASSOCIATION AMONG A NUMBER OF VARIABLES BY THE KENDALL COEFFICIENT OF CONCORDANCE. HTES TO CALCULATE THE KRUSKAL-WALLIS H-STATISTIC FROM THE RANKS OF OBSERVATIONS WHICH ARE OBTAINED FROM THREE OR MORE INDEPENDENT SAMPLES. NDTR COMPUTES Y=P(X)=THE PROBABILITY THAT THE RANDOM VARIABLE U, DISTRIBUTED NORMALLY (0,1) IS LESS THAN OR EQUAL TO X. F(X), THE ORDINATE OF THE NORMAL DENSITY AT X, IS ALSO COMPUTED. BDTR BDTR COMPUTES P(X) = PROBABILITY THAT THE RANDOM VARIABLE DISTRIBUTED ACCORDING TO THE BETA DISTRIBUTION WITH PARAMETERS A AND B, IS LESS THAN OR EQUAL TO X. F(A,B,X), THE ORDINATE OF THE BETA DENSITY AT X, IS ALSO COMPUTED. CDTR COMPUTES P(X)=PROBABILITY THAT THE RANDOM VARIABLE U, DISTRIBUTED ACCORDING TO THE CHI-SQUARE DISTRIBUTION WITH G DEGREES OF FREEDOM, IS LESS THAN OR EQUAL TO X. F(G,X), THE ORDINATE OF THE CHI-SQUARE DENSITY AT X, IS ALSO COMPUTED. NDTI COMPUTES X=P**X(-1)(Y), THE ARGUMENT X SUCH THAT Y=P(X)=THE PROBABILITY THAT THE RANDOM VARIABLE U, DISTRIBUTED NORMALLY (0,1), IS LESS THAN OR EQUAL TO X. F(X) THE ORDINATE OF THE NORMAL DENSITY, AT X, IS ALSO COMPUTED. DACR TO PERFORM DATA SCREENING CALCULATIONS ON A SET OF OBSERVATIONS. SBST TO DERIVE A SUBSET VECTOR INDICATING WHICH OBSERVATIONS IN A SET HAVE SATISFIED CERTAIN CONDITIONS. TAB1 TO TABULATE FOR ONE VARIABLE IN AN OBSERVATION MATRIX (OR A SUBSET), THE FREQUENCY AND PERCENT FREQUENCY OVER GIVEN CLASS INTERVALS. IN ADDITION, CALCULATE FOR THE SAME THE TOTAL, MEAN, STANDARD DEVIATION, MINIMUM, AND MAXIMUM. BOOL TO PERFORM A BOOLEAN OPERATION FOR THE PROCEDURE SBST, WHICH IS USED BY THE DATA SCREENING SAMPLE PROGRAM. HIST TO PLOT A HISTOGRAM OF FREQUENCIES FOR THE DATA SCREENING SAMPLE PROGRAM. DAT1 TO READ FLOATING POINT DATA, ONE OBSERVATION AT A TIME. DATA MAY BE SAVED ON A DATA SET. REGR TO READ THE PROBLEM PARAMETER CARD FOR A MULTIPLE REGRESSION, READ SUBSET SELECTION CARDS, CALL THE PROCEDURES TO CALCULATE MEANS, STANDARD DEVIATIONS, SIMPLE AND MULTIPLE CORRELATION COEFFICIENTS, REGRESSION COEFFICIENTS, T-VALUES, BETA COEFFICIENTS, AND ANALYSIS OF VARIANCE FOR MULTIPLE REGRESSION, AND PRINT THE RESULTS.