1 INDEX TO THE LIBRARY NUMAL OF ALGOL 60 PROCEDURES IN NUMERICAL MATHEMATICS *********************************************************************** ON REQUEST OF THE ACADEMIC COMPUTING CENTRE AMSTERDAM ( SARA ) THE LIBRARY NUMAL IS DEVELOPED AND SUPPORTED BY THE NUMERICAL MATHEMATICS DEPARTMENT OF THE MATHEMATICAL CENTRE (AMSTERDAM). THE PRESENT DOCUMENT CONTAINS A SURVEY OF THE PROCEDURES AVAILABLE IN NUMAL FOR ALGOL 60 VERSION 5. MOREOVER, IT DESCRIBES THE WAY IN WHICH ONE CAN OBTAIN FULL DOCUMENTATION OF ALL AVAILABLE PROCEDURES. TO GET ENTRANCE TO THE DOCUMENTATION. CLASSIFIED ACCORDING TO SUBJECT, THE PRESENT INDEX CONTAINS THE NAMES OF THE PROCEDURES, THE CORRESPONDING CODE NUMBERS IN NUMAL5 AND A REFERENCE TO THE DOCUMENTATION. THIS REFERENCE GIVES THE RECORD NUMBER IN THE DOCUMENTATION FILE. IN ORDER TO CONSULT A SPECIFIED RECORD OF DOCUMENTATION, ALL PRECEDING RECORDS HAVE TO BE SKIPPED. EXAMPLE. IN ORDER TO OBTAIN THE DESCRIPTION OF THE PROCEDURE "MULTISTEP" (SECTION 5.2.1.1.1.1.F.; RECORD NUMBER = 211) FROM THE DOCUMENTATION FILE THE FOLLOWING CONTROL CARDS CAN BE USED ...... LABEL,TAPE,R,L=NUMAL5TAPE,ID=NUMAL5MC,D=GE,VSN=T1886H. SKIPF,TAPE,1,17. TO POSITION THE TAPE COMMENT. AT THE DOCUMENT FILE SKIPF,TAPE,210. COPYBR,TAPE,OUTPUT. ...... IN ORDER TO OBTAIN THE SOURCE TEXT, ONE MORE RECORD HAD TO BE SKIPPED. STATUS OF NUMAL AND RESPONSIBILITY. IN 1979 THE INTEREST OF THE MATHEMATICAL CENTRE IN THE CREATION OF GENERAL NUMERICAL SOFTWARE IN ALGOL60 DECREASED AND THE DRAFTING COMMITTEE DECIDED TO CONCLUDE THE NUMAL PROJECT WITH THE PUBLICATION OF A FINAL REVISION OF THE LIBRARY IN BOOK FORM. THIS RESULTED IN THE MATHEMATICAL CENTRE PUBLICATION: P.W. HEMKER (ED.)[1981]: NUMAL. NUMERICAL PROCEDURES IN ALGOL 60. 7 VOLUMES. MC SYLLABUS, MATHEMATICAL CENTRE, AMSTERDAM. IN THIS FORM THE LIBRARY NUMAL CAN BE SEEN AS A DESCRIPTION OF THE STATE-OF-THE-ART OF NUMERICAL ALGOL60 PROGRAMMING AT THE MATHEMATICAL CENTRE AT THE END OF THE 1970-S. IT IS CLAIMED TO CONTAIN A VALUABLE COLLECTION OF ROUTINES IN A LANGUAGE THAT STILL CAN DESCRIBE NUMERICAL PROCEDURES BETTER THAN MANY OTHER PROGRAMMING LANGUAGES CURRENTLY IN USE. 1 IN 1981 A NEW TRANSLATED LIBRARY WAS PRODUCED FOR THE USE OF THE NUMAL PROCEDURES UNDER ALGOL 60 VERSION 5 ( AT THE ACADEMIC COMPUTER CENTRE OF AMSTERDAM ). THIS REQUIRED AN ADAPTATION OF ALL SOURCE TEXTS TO ALGOL 60.1 STANDARD. TO THIS END A COMPLETELY NEW DOCUMENTATION FILE WAS MADE DIFFERING FROM THE FORMER ONE (AND FROM THE ABOVE MENTIONED PUBLICATION) IN THE FOLLOWING WAYS: 1) A FEW CHANGES WERE NECESSARY WHEN THE SOURCE TEXT WAS NOT ACCORDING TO ALGOL 60.1 STANDARD (ESPECIALLY WHEN "INTEGER" AND "REAL" TYPES TYPES WERE INTERCHANGED IN PARAMETER SUBSTITUTION). 2) IN ORDER TO PROCESS THE DOCUMENT FILE AUTOMATICALLY, SEVERAL IRREGULARITIES CONCERNING LAY-OUT WERE CORRECTED. 3) A COUPLE OF ERRORS IN THE SPECIFICATIONS OF THE PROCEDURES WERE DETECTED AND DULY CORRECTED. A RECORD IS KEPT OF ALL CHANGES EXCEPT THOSE OF THE LAY-OUT. ALTHOUGH MUCH EFFORT HAS BEEN SPENT TO KEEP THE NUMBER OF ERRORS TO A MINIMUM, IT IS POSSIBLE THAT SOME MINOR ERRORS STILL REMAIN. THE MATHEMATICAL CENTRE CANNOT BE HELD LIABLE FOR DAMAGE DUE TO ILL-FUNCTIONING OF ANY PROGRAM USING THE NUMAL LIBRARY. THE NUMERICAL MATHEMATICS DEPARTMENT WILL KEEP A LIST OF ALL ERRORS IN THE DOCUMENTATION AND/OR THE PROCEDURES THAT BECOME KNOWN, AND THIS LIST CAN BE OBTAINED ON REQUEST. FOR REMARKS AND REQUESTS: MATHEMATISCH CENTRUM AFDELING NUMERIEKE WISKUNDE KRUISLAAN 413 (ADDRESS FOR VISITS) 1098 SJ AMSTERDAM POSTBUS 4079 (MAILING ADDRESS) 1009 AB AMSTERDAM TEL.: 020 - 592 9333. J. KOK (MATHEMATICAL CENTRE) NO PART OF THE LIBRARY NUMAL MAY BE REPRODUCED, STORED IN A RETRIEVAL SYSTEM OR TRANSMITTED, IN ANY FORM OR BY ANY MEANS, ELECTRONIC, PHOTOCOPYING, RECORDING, OR OTHERWISE, WITHOUT THE PRIOR WRITTEN PERMISSION OF THE ACADEMIC COMPUTING CENTRE AMSTERDAM (SARA) OR THE MATHEMATICAL CENTRE (AMSTERDAM). 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 1.ELEMENTARY PROCEDURES 1.REAL VECT AND MAT OPERATIONS 1.INITIALIZATION INIVEC * 31010 NOV/81 1 INIMAT * 31011 NOV/81 1 INIMATD * 31012 NOV/81 1 INISYMD * 31013 NOV/81 1 INISYMROW * 31014 NOV/81 1 2.DUPLICATION DUPVEC * 31030 NOV/81 3 DUPVECROW * 31031 NOV/81 3 DUPROWVEC * 31032 NOV/81 3 DUPVECCOL * 31033 NOV/81 3 DUPCOLVEC * 31034 NOV/81 3 DUPMAT * 31035 NOV/81 3 3.MULTIPLICATION MULVEC * 31020 NOV/81 5 MULROW * 31021 NOV/81 5 MULCOL * 31022 NOV/81 5 COLCST * 31131 NOV/81 5 ROWCST * 31132 NOV/81 5 4.SCALAR PRODUCTS 1.VECTOR VECTOR PRODUCTS VECVEC * 34010 NOV/81 7 MATVEC * 34011 NOV/81 7 TAMVEC * 34012 NOV/81 7 MATMAT * 34013 NOV/81 7 TAMMAT * 34014 NOV/81 7 MATTAM * 34015 NOV/81 7 SEQVEC * 34016 NOV/81 7 SCAPRD1 * 34017 NOV/81 7 SYMMATVEC * 34018 NOV/81 7 2.MATRIX VECTOR PRODUCTS FULMATVEC * 31500 NOV/81 9 FULTAMVEC * 31501 NOV/81 9 FULSYMMATVEC 31502 NOV/81 9 RESVEC * 31503 NOV/81 9 SYMRESVEC 31504 NOV/81 9 3.MATRIX MATRIX PRODUCTS HSHVECMAT * 31070 NOV/81 11 HSHCOLMAT * 31071 NOV/81 11 HSHROWMAT * 31072 NOV/81 11 HSHVECTAM * 31073 NOV/81 11 HSHCOLTAM * 31074 NOV/81 11 HSHROWTAM * 31075 NOV/81 11 5.ELIMINATION ELMVEC * 34020 NOV/81 13 ELMCOL * 34023 NOV/81 13 ELMROW * 34024 NOV/81 13 ELMVECCOL * 34021 NOV/81 13 ELMCOLVEC * 34022 NOV/81 13 ELMVECROW * 34026 NOV/81 13 ELMROWVEC * 34027 NOV/81 13 ELMCOLROW * 34029 NOV/81 13 1. 1. 5. ELMROWCOL * 34028 NOV/81 13 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 1. 1. 5. MAXELMROW * 34025 NOV/81 13 6.INTERCHANGING ICHVEC * 34030 NOV/81 15 ICHCOL * 34031 NOV/81 15 ICHROW * 34032 NOV/81 15 ICHROWCOL * 34033 NOV/81 15 ICHSEQVEC * 34034 NOV/81 15 ICHSEQ * 34035 NOV/81 15 7.ROTATION ROTCOL * 34040 NOV/81 17 ROTROW * 34041 NOV/81 17 8.NORMS INFNRMVEC * 31061 NOV/81 19 INFNRMROW * 31062 NOV/81 19 INFNRMCOL * 31063 NOV/81 19 INFNRMMAT * 31064 NOV/81 19 ONENRMVEC * 31065 NOV/81 19 ONENRMROW * 31066 NOV/81 19 ONENRMCOL * 31067 NOV/81 19 ONENRMMAT * 31068 NOV/81 19 ABSMAXMAT * 31069 NOV/81 19 9.SCALING REASCL 34183 NOV/81 21 2.COMPL VECT AND MAT OPERATIONS 1. 2. 3.MULTIPLICATION COMCOLCST 34352 NOV/81 23 COMROWCST 34353 NOV/81 23 4.SCALAR PRODUCTS COMMATVEC 34354 NOV/81 25 HSHCOMCOL 34355 NOV/81 25 HSHCOMPRD 34356 NOV/81 25 5.ELIMINATION ELMCOMVECCOL 34376 NOV/81 27 ELMCOMCOL 34377 NOV/81 27 ELMCOMROWVEC 34378 NOV/81 27 6.INTERCHANGING 7.ROTATION ROTCOMCOL 34357 NOV/81 29 ROTCOMROW 34358 NOV/81 29 CHSH2 34611 NOV/81 29 8.NORMS COMEUCNRM 34359 NOV/81 31 9.SCALING COMSCL 34193 NOV/81 33 SCLCOM 34360 NOV/81 33 3.COMPLEX ARITHMETIC 1.MONADIC OPERATIONS COMABS 34340 NOV/81 35 COMSQRT 34343 NOV/81 35 CARPOL 34344 NOV/81 35 2.DYADIC OPERATIONS COMMUL * 34341 NOV/81 37 1. 3. 2. COMDIV * 34342 NOV/81 37 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 1. 4.LONG INTEGER ARITHMETIC LNGINTADD 31200 NOV/81 39 LNGINTSUBTRACT 31201 NOV/81 39 LNGINTMULT 31202 NOV/81 39 LNGINTDIVIDE 31203 NOV/81 39 LNGINTPOWER 31204 NOV/81 39 5.LONG REAL ARITHMETIC 1.ELEM. ARITHMETIC OPERATIONS DP ADD * 31101 NOV/81 41 DP SUB * 31102 NOV/81 41 DP MUL * 31103 NOV/81 41 DP DIV * 31104 NOV/81 41 DP POW 31109 NOV/81 41 LNG ADD * 31105 NOV/81 41 LNG SUB * 31106 NOV/81 41 LNG MUL * 31107 NOV/81 41 LNG DIV * 31108 NOV/81 41 LNG POW 31110 NOV/81 41 2.SCALAR PRODUCTS LNGVECVEC * 34410 NOV/81 43 LNGMATVEC * 34411 NOV/81 43 LNGTAMVEC * 34412 NOV/81 43 LNGMATMAT * 34413 NOV/81 43 LNGTAMMAT * 34414 NOV/81 43 LNGMATTAM * 34415 NOV/81 43 LNGSEQVEC * 34416 NOV/81 43 LNGSCAPRD1 * 34417 NOV/81 43 LNGSYMMATVEC * 34418 NOV/81 43 LNGFULMATVEC * 31505 NOV/81 43 LNGFULTAMVEC * 31506 NOV/81 43 LNGFULSYMMATVEC 31507 NOV/81 43 LNGRESVEC * 31508 NOV/81 43 LNGSYMRESVEC 31509 NOV/81 43 3.CONVERSION LNGREATODECI 31100 NOV/81 45 2.ALGEBRAIC EVALUATIONS 1.EVAL. OF A FINITE SERIES 2.EVAL. OF POLYNOMIALS 1.EVAL. OF GENERAL POLYNOMIALS 1.POLYNOMIALS IN GRUNERT FORM POL 31040 NOV/81 47 TAYPOL 31241 NOV/81 47 NORDERPOL 31242 NOV/81 47 DERPOL 31243 NOV/81 47 2.POLYNOMIALS IN NEWTON FORM 2.EVAL. OF ORTHOGON. POLYNOMIALS 1.GENERAL ORTHOGON. POLYNOMIALS ORTPOL 31044 NOV/81 49 ORTPOLSYM 31048 NOV/81 49 ALLORTPOL 31045 NOV/81 49 ALLORTPOLSYM 31049 NOV/81 49 SUMORTPOL 31047 NOV/81 49 SUMORTPOLSYM 31058 NOV/81 49 2.CHEBYCHEV POLYNOMIALS 2. 2. 2. 2. CHEPOLSUM 31046 NOV/81 51 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 2. 2. 2. 2. ODDCHEPOLSUM 31059 NOV/81 51 CHEPOL 31042 NOV/81 51 ALLCHEPOL 31043 NOV/81 51 3.EVAL. OF TRIGONOM. POLYNOMIALS 1.EVAL. OF FOURIER SERIES SINSER 31090 NOV/81 53 COSSER 31091 NOV/81 53 FOUSER 31092 NOV/81 53 FOUSER1 31093 NOV/81 53 FOUSER2 31094 NOV/81 53 COMFOUSER 31095 NOV/81 53 COMFOUSER1 31096 NOV/81 53 COMFOUSER2 31097 NOV/81 53 3.EVAL. OF CONTINUED FRACTIONS JFRAC 35083 NOV/81 55 4.OPERATIONS ON POLYNOMIALS 1.TRANSF. OF REPRESENTATION POLCHS 31051 NOV/81 57 CHSPOL 31052 NOV/81 57 POLSHTCHS 31053 NOV/81 57 SHTCHSPOL 31054 NOV/81 57 GRNNEW 31055 NOV/81 57 NEWGRN 31050 NOV/81 57 LINTFMPOL 31250 NOV/81 57 2.OP. ON GENERAL POLYNOMIALS 3.OP. ON ORTHOGONAL POLYNOMIALS INTCHS 31248 NOV/81 59 5.FAST FOURIER TRANSFORM 3.LINEAR ALGEBRA 1.LINEAR SYSTEMS 1.FULL MATRICES 1.SQUARE NON-SINGULAR MATRICES 1.REAL MATRICES 1.GENERAL MATRICES 1.PREPARATORY PROCEDURES DEC 34300 NOV/81 61 GSSELM 34231 NOV/81 61 ONENRMINV 34240 NOV/81 61 ERBELM 34241 NOV/81 61 GSSERB 34242 NOV/81 61 GSSNRI 34252 NOV/81 61 2.CALCULATION OF DETERMINANT DETERM 34303 NOV/81 63 3.SOLUTION OF LINEAR EQUATIONS SOL 34051 NOV/81 65 DECSOL 34301 NOV/81 65 SOLELM 34061 NOV/81 65 GSSSOL 34232 NOV/81 65 GSSSOLERB 34243 NOV/81 65 4.MATRIX INVERSION INV 34053 NOV/81 67 DECINV 34302 NOV/81 67 INV1 34235 NOV/81 67 GSSINV 34236 NOV/81 67 3. 1. 1. 1. 1. 1. 4. GSSINVERB 34244 NOV/81 67 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 3. 1. 1. 1. 1. 1. 5.ITERATIVELY IMPROVED SOLUTION ITISOL 34250 NOV/81 69 GSSITISOL 34251 NOV/81 69 ITISOLERB 34253 NOV/81 69 GSSITISOLERB 34254 NOV/81 69 2.SYMMETRIC POS DEF MATRICES 1.PREPARATORY PROCEDURES CHLDEC2 34310 NOV/81 71 CHLDEC1 34311 NOV/81 71 2.CALCULATION OF DETERMINANT CHLDETERM2 34312 NOV/81 73 CHLDETERM1 34313 NOV/81 73 3.SOLUTION OF LINEAR EQUATIONS CHLSOL2 34390 NOV/81 75 CHLSOL1 34391 NOV/81 75 CHLDECSOL2 34392 NOV/81 75 CHLDECSOL1 34393 NOV/81 75 4.MATRIX INVERSION CHLINV2 34400 NOV/81 77 CHLINV1 34401 NOV/81 77 CHLDECINV2 34402 NOV/81 77 CHLDECINV1 34403 NOV/81 77 3.GENERAL SYMMETRIC MATRICES 1.PREPARATORY PROCEDURES DECSYM2 34291 NOV/81 79 2.CALCULATION OF DETERMINANT DETERMSYM2 34294 NOV/81 81 3.SOLUTION OF LINEAR EQUATIONS SOLSYM2 34292 NOV/81 83 DECSOLSYM2 34293 NOV/81 83 2.COMPLEX MATRICES 2.FULL RANK OVERDETERM SYSTEMS 1.REAL MATRICES 1.PREPARATORY PROCEDURES LSQORTDEC 34134 NOV/81 85 LSQDGLINV 34132 NOV/81 85 2.LEAST SQUARES SOLUTION LSQSOL 34131 NOV/81 87 LSQORTDECSOL 34135 NOV/81 87 3.INVERSE MATRIX OF NORMAL EQN. LSQINV 34136 NOV/81 89 4.LEAST SQRS WITH LIN. CONSTR. LSQDECOMP 34137 NOV/81 91 LSQREFSOL 34138 NOV/81 91 2.COMPLEX MATRICES 3.OTHER PROBLEMS 1.REAL MATRICES 1.SOLUTION OVERDETERMINED SYST SOLSVDOVR 34280 NOV/81 93 SOLOVR 34281 NOV/81 93 2.SOLUTION UNDERDETERM SYSTEMS SOLSVDUND 34282 NOV/81 95 SOLUND 34283 NOV/81 95 3.SOLUTION HOMOGENEOUS EQUATION 3. 1. 1. 3. 1. 3. HOMSOLSVD 34284 NOV/81 97 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 3. 1. 1. 3. 1. 3. HOMSOL 34285 NOV/81 97 4.PSEUDO-INVERSION PSDINVSVD 34286 NOV/81 99 PSDINV 34287 NOV/81 99 2.COMPLEX MATRICES 2.SPARSE MATRICES 1.DIRECT METHODS 1.REAL MATRICES 1.NON-SYMMETRIC MATRICES 1.BAND MATRICES 1.PREPARATORY PROCEDURES DECBND 34320 NOV/81 101 2.CALCULATION OF DETERMINANT DETERMBND 34321 NOV/81 103 3.SOLUTION OF LINEAR EQUATIONS SOLBND 34071 NOV/81 105 DECSOLBND 34322 NOV/81 105 2.TRIDIAGONAL MATRICES 1.PREPARATORY PROCEDURES DECTRI 34423 NOV/81 107 DECTRIPIV 34426 NOV/81 107 2.CALCULATION OF DETERMINANT 3.SOLUTION OF LINEAR EQUATIONS SOLTRI 34424 NOV/81 109 DECSOLTRI 34425 NOV/81 109 SOLTRIPIV 34427 NOV/81 109 DECSOLTRIPIV 34428 NOV/81 109 3.BLOC-TRIDIAGONAL MATRICES 2.SYMMETRIC POS DEF MATRICES 1.BAND MATRICES 1.PREPARATORY PROCEDURES CHLDECBND 34330 NOV/81 111 2.CALCULATION OF DETERMINANT CHLDETERMBND 34331 NOV/81 113 3.SOLUTION OF LINEAR EQUATIONS CHLSOLBND 34332 NOV/81 115 CHLDECSOLBND 34333 NOV/81 115 2.TRIDIAGONAL MATRICES 1.PREPARATORY PROCEDURES DECSYMTRI 34420 NOV/81 117 2.CALCULATION OF DETERMINANT 3.SOLUTION OF LINEAR EQUATIONS SOLSYMTRI 34421 NOV/81 119 DECSOLSYMTRI 34422 NOV/81 119 3.BLOC-TRIDIAGONAL MATRICES 2.COMPLEX MATRICES 2.ITERATIVE METHODS 1.REAL MATRICES CONJ GRAD 34220 NOV/81 121 2.COMPLEX MATRICES 2.TRANSFORMATION TO SPECIAL FORM 1.SIMILARITY TRANSFORMATIONS 1.EQUILIBRATION 1.REAL MATRICES 3. 2. 1. 1. 1. EQILBR 34173 NOV/81 123 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 3. 2. 1. 1. 1. BAKLBR 34174 NOV/81 123 2.COMPLEX MATRICES EQILBRCOM 34361 NOV/81 125 BAKLBRCOM 34362 NOV/81 125 2.TRANSF TO HESSENBERG FORM 1.REAL MATRICES 1.SYMMETRIC MATRICES TFMSYMTRI2 34140 NOV/81 127 BAKSYMTRI2 34141 NOV/81 127 TFMPREVEC 34142 NOV/81 127 TFMSYMTRI1 34143 NOV/81 127 BAKSYMTRI1 34144 NOV/81 127 2.ASYMMETRIC MATRICES TFMREAHES 34170 NOV/81 129 BAKREAHES1 34171 NOV/81 129 BAKREAHES2 34172 NOV/81 129 2.COMPLEX MATRICES 1.HERMITIAN MATRICES HSHHRMTRI 34363 NOV/81 131 HSHHRMTRIVAL 34364 NOV/81 131 BAKHRMTRI 34365 NOV/81 131 2.NON-HERMITIAN MATRICES HSHCOMHES 34366 NOV/81 133 BAKCOMHES 34367 NOV/81 133 2.OTHER TRANSFORMATIONS 1.TRANSF TO BIDIAGONAL FORM 1.REAL MATRICES HSHREABID 34260 NOV/81 135 PSTTFMMAT 34261 NOV/81 135 PRETFMMAT 34262 NOV/81 135 2.COMPLEX MATRICES 3.THE (ORDINARY) EIGENV PROBLEM 1.REAL MATRICES 1.SYMMETRIC MATRICES 1.TRIDIAGONAL MATRICES VALSYMTRI 34151 NOV/81 137 VECSYMTRI 34152 NOV/81 137 QRIVALSYMTRI 34160 NOV/81 137 QRISYMTRI 34161 NOV/81 137 2.FULL MATRICES EIGVALSYM2 34153 NOV/81 139 EIGSYM2 34154 NOV/81 139 EIGVALSYM1 34155 NOV/81 139 EIGSYM1 34156 NOV/81 139 QRIVALSYM2 34162 NOV/81 139 QRISYM 34163 NOV/81 139 QRIVALSYM1 34164 NOV/81 139 3.ITERATIVE IMPROVEMENT 1.AUXILIARY PROCEDURES MERGESORT 36405 NOV/81 141 VECPERM 36404 NOV/81 141 ROWPERM 36403 NOV/81 141 2.ORTHOGONALISATION ORTHOG 36402 NOV/81 143 3. 3. 1. 1. 3. 3.IMPROVEMENT AND ERRORBOUNDS 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 3. 3. 1. 1. 3. 3. SYMEIGINP 36401 NOV/81 145 2.ASYMMETRIC MATRICES 1.MATRICES IN HESSENBERG FORM REAVALQRI 34180 NOV/81 147 REAVECHES 34181 NOV/81 147 REAQRI 34186 NOV/81 147 COMVALQRI 34190 NOV/81 147 COMVECHES 34191 NOV/81 147 2.FULL MATRICES REAEIGVAL 34182 NOV/81 149 REAEIG1 34184 NOV/81 149 REAEIG3 34187 NOV/81 149 COMEIGVAL 34192 NOV/81 149 COMEIG1 34194 NOV/81 149 2.COMPLEX MATRICES 1.HERMITIAN MATRICES EIGVALHRM 34368 NOV/81 151 EIGHRM 34369 NOV/81 151 QRIVALHRM 34370 NOV/81 151 QRIHRM 34371 NOV/81 151 2.NON-HERMITIAN MATRICES 1.MATRICES IN HESSENBERG FORM VALQRICOM 34372 NOV/81 153 QRICOM 34373 NOV/81 153 2.FULL MATRICES EIGVALCOM 34374 NOV/81 155 EIGCOM 34375 NOV/81 155 4.THE GENERALIZED EIGENV PROBLEM 1.REAL MATRICES 1.SYMMETRIC MATRICES 2.ASYMMETRIC MATRICES QZIVAL 34600 NOV/81 157 QZI 34601 NOV/81 157 HSHDECMUL 34602 NOV/81 157 HESTGL3 34603 NOV/81 157 HESTGL2 34604 NOV/81 157 HSH2COL 34605 NOV/81 157 HSH3COL 34606 NOV/81 157 HSH2ROW3 34607 NOV/81 157 HSH2ROW2 34608 NOV/81 157 HSH3ROW3 34609 NOV/81 157 HSH3ROW2 34610 NOV/81 157 5.SINGULAR VALUES 1.REAL MATRICES 1.BIDIAGONAL MATRICES QRISNGVALBID 34270 NOV/81 159 QRISNGVALDECBID 34271 NOV/81 159 2.FULL MATRICES QRISNGVAL 34272 NOV/81 161 QRISNGVALDEC 34273 NOV/81 161 2.COMPLEX MATRICES 6.ZEROS OF POLYNOMIALS 1.ZEROS OF GENERAL REAL POLYNOM. ZERPOL 34501 NOV/81 163 3. 6. 1. BOUNDS 34502 NOV/81 163 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 3. 6. 2.ZEROS OF ORTHOGONAL POLYNOM. ALLZERORTPOL 31362 NOV/81 165 LUPZERORTPOL 31363 NOV/81 165 SELZERORTPOL 31364 NOV/81 165 ALLJACZER 31370 NOV/81 165 ALLLAGZER 31371 NOV/81 165 3.ZEROS OF COMPLEX POLYNOMIALS COMKWD 34345 NOV/81 167 4.ANALYTIC EVALUATIONS 1.EVAL. OF AN INFINITE SERIES EULER 32010 NOV/81 169 SUMPOSSERIES 32020 NOV/81 169 2.QUADRATURE 1.ONE-DIMENSIONAL QUADRATURE QADRAT 32070 NOV/81 171 INTEGRAL 32051 NOV/81 173 2.MULTIDIMENSIONAL QUADRATURE TRICUB 32075 NOV/81 175 3.GAUSSIAN QUADRATURE 1.GENERAL WEIGHTS RECCOF 31254 NOV/81 177 GSSWTS 31253 NOV/81 177 GSSWTSSYM 31252 NOV/81 177 2.SPECIAL WEIGHTS GSSJACWGHTS 31425 NOV/81 179 GSSLAGWGHTS 31427 NOV/81 179 3.NUMERICAL DIFFERENTIATION 1.FUNCTIONS OF ONE VARIABLE 2.FUNCTIONS OF MORE VARIABLES 1.CALC. WITH DIFFERENCE FORMULAS JACOBNNF 34437 NOV/81 181 JACOBNMF 34438 NOV/81 181 JACOBNBNDF 34439 NOV/81 181 5.ANALYTICAL PROBLEMS 1.ANALYTICAL EQUATIONS 1.NON-LINEAR EQUATIONS 1.A SINGLE EQUATION 1.NO DERIVATIVE AVAILABLE ZEROIN 34150 NOV/81 183 ZEROINRAT 34436 NOV/81 183 2.DERIVATIVE AVAILABLE ZEROINDER 34453 NOV/81 185 2.A SYSTEM OF EQUATIONS 1.AUXILIARY PROCEDURES 2.JACOBIAN MATRIX NOT AVAILABLE QUANEWBND 34430 NOV/81 187 QUANEWBND1 34431 NOV/81 187 3.JACOBIAN MATRIX AVAILABLE 3.POLYNOMIAL EQUATIONS SEE ALSO SECTION 3.6 2.UNCONSTRAINED OPTIMIZATION 1.FUNCTIONS OF ONE VARIABLE 1.DERIVATIVE NOT AVAILABLE MININ 34433 NOV/81 189 5. 1. 2. 1. 2.DERIVATIVE AVAILABLE 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 5. 1. 2. 1. 2. MININDER 34435 NOV/81 191 2.FUNCTIONS OF MORE VARIABLES 1.AUXILIARY PROCEDURES LINEMIN 34210 NOV/81 193 RNK1UPD 34211 NOV/81 193 DAVUPD 34212 NOV/81 193 FLEUPD 34213 NOV/81 193 2.NO DERIVATIVES AVAILABLE PRAXIS 34432 NOV/81 195 3.GRADIENT AVAILABLE RNK1MIN 34214 NOV/81 197 FLEMIN 34215 NOV/81 197 4.GRADIENT & JACOBIAN AVAILABLE 3.OVERDETERMINED NONLINEAR SYST. 1.LEAST SQUARES SOLUTIONS SEE ALSO SECTION 7. 1.AUXILIARY PROCEDURES 2.JACOBIAN MATRIX NOT AVAILABLE SEE ALSO SECTION 5.1.2.2.2. 3.JACOBIAN MATRIX AVAILABLE MARQUARDT 34440 NOV/81 199 GSSNEWTON 34441 NOV/81 199 2.FUNCTIONAL EQUATIONS 1.DIFFERENTIAL EQUATIONS 1.INITIAL VALUE PROBLEMS 1.FIRST ORDER ORDINARY D.E. 1.NO DERIVATIVES RHS AVAILABLE RK1 33010 NOV/81 201 RKE 33033 NOV/81 203 RK4A 33016 NOV/81 205 RK4NA 33017 NOV/81 207 RK5NA 33018 NOV/81 209 MULTISTEP 33080 NOV/81 211 DIFFSYS 33180 NOV/81 213 ARK 33061 NOV/81 215 EFRK 33070 NOV/81 217 2.JACOBIAN MATRIX AVAILABLE EFSIRK 33160 NOV/81 219 EFERK 33120 NOV/81 221 LINIGER1VS 33132 NOV/81 223 LINIGER2 33131 NOV/81 225 GMS 33191 NOV/81 227 IMPEX 33135 NOV/81 229 SEE ALSO PROC. MULTISTEP (5.2.1.1.1.1) 3.SEVERAL DERIVATIVES AVAILABLE MODIFIED TAYLOR 33040 NOV/81 231 EXPONENTIALLY FITTED TAYLOR 33050 NOV/81 233 2.SECOND ORDER ORDINARY D.E. 1.NO DERIVATIVES RHS AVAILABLE RK2 33012 NOV/81 235 RK2N 33013 NOV/81 237 RK3 33014 NOV/81 239 RK3N 33015 NOV/81 241 2.SEVERAL DERIV. RHS AVAILABLE 5. 2. 1. 1. 3.INITIAL BOUNDARY VALUE PROBLEM 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 5. 2. 1. 1. 3. ARKMAT 33066 NOV/81 243 2.BOUNDARY VALUE PROBLEMS 1.TWO POINT B.V.P. 1.SHOOTING METHODS SEE ALSO SECTION 5.2.1.3.1 2.LINEAR GLOBAL METHODS 1.SECOND ORDER TPBVP 1.SELF ADJOINT TPBVP FEM LAG SYM 33300 NOV/81 245 FEM LAG 33301 NOV/81 245 FEM LAG SPHER 33308 NOV/81 245 2.SKEW ADJOINT TPBVP FEM LAG SKEW 33302 NOV/81 247 2.FOURTH ORDER TPBVP 1.SELF ADJOINT TPBVP FEM HERM SYM 33303 NOV/81 249 2.SKEW ADJOINT TPBVP 3.NON-LINEAR GLOBAL METHODS NON LIN FEM LAG SKEW 33314 NOV/81 251 2.TWO-DIMENSIONAL B.V.P. 1.ELLIPTIC B.V.P.S 1.DISCRETIZATION PROCEDURES 2.SPECIAL LINEAR SYSTEMS RICHARDSON 33170 NOV/81 253 ELIMINATION 33171 NOV/81 253 SEE ALSO SECTION 3.1.2 3.SPECIAL NON-LINEAR SYSTEMS 2.PARABOLIC & HYPERBOLIC B.V.P.S 3.MULTI-DIMENSIONAL B.V.P. 4.OVER-DETERMINED PROBLEMS 3.PARAMETER ESTIMATION IN D.E. 1.P.E. IN INITIAL VALUE PROBLEMS PEIDE 34444 NOV/81 255 2.INTEGRAL EQUATIONS 3.INTEGRO- DIFFERENTIAL EQS 4.DIFFERENCE EQUATIONS 5.CONVOLUTION EQUATIONS 6.SPECIAL FUNCTIONS & CONSTANTS 1.MATHEMATICAL CONSTANTS PI * 30006 NOV/81 257 E * 30007 NOV/81 257 2.MACHINE CONSTANTS MBASE * 30001 NOV/81 259 ARREB * 30002 NOV/81 259 DWARF * 30003 NOV/81 259 GIANT * 30004 NOV/81 259 INTCAP * 30005 NOV/81 259 OVERFLOW * 30008 NOV/81 259 UNDERFLOW * 30009 NOV/81 259 3.RANDOM NUMBERS RANDOM 30010 NOT YET AVAILABLE SETRANDOM 30011 NOT YET AVAILABLE 4.ELEMENTARY FUNCTIONS 1.CIRCULAR FUNCTIONS 6. 4. 1. TAN 35120 NOV/81 261 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 6. 4. 1. ARCSIN 35121 NOV/81 261 ARCCOS 35122 NOV/81 261 2.HYPERBOLIC FUNCTIONS SINH 35111 NOV/81 263 COSH 35112 NOV/81 263 TANH 35113 NOV/81 263 ARCSINH 35114 NOV/81 263 ARCCOSH 35115 NOV/81 263 ARCTANH 35116 NOV/81 263 3.LOGARITHMIC FUNCTION LOG ONE PLUS X 35130 NOV/81 265 5.EXPONENTIAL INTEGRAL, ETC. 1.EXPONENTIAL INTEGRAL EI 35080 NOV/81 267 EI ALPHA 35081 NOV/81 267 ENX 35086 NOV/81 267 NONEXP ENX 35087 NOV/81 267 2.SINE AND COSINE INTEGRAL SINCOSINT 35084 NOV/81 269 SINCOSFG 35085 NOV/81 269 6.GAMMA FUNCTION, ETC. GAMMA 35061 NOV/81 271 RECIP GAMMA 35060 NOV/81 271 LOG GAMMA 35062 NOV/81 271 INCOMGAM 35030 NOV/81 271 INCBETA 35050 NOV/81 271 IBPPLUSN 35051 NOV/81 271 IBQPLUSN 35052 NOV/81 271 IXQFIX 35053 NOV/81 271 IXPFIX 35054 NOV/81 271 FORWARD 35055 NOV/81 271 BACKWARD 35056 NOV/81 271 7.ERROR FUNCTION, ETC. ERRORFUNCTION 35021 NOV/81 273 NONEXPERFC 35022 NOV/81 273 INVERSE ERROR FUNCTION 35023 NOV/81 273 FRESNEL 35027 NOV/81 273 FG 35028 NOV/81 273 8.LEGENDRE FUNCTIONS 9.BESSEL FUNCTIONS OF INT. ORDER 1.BESSEL FUNCTIONS J AND Y BESS J0 35160 NOV/81 275 BESS J1 35161 NOV/81 275 BESS J 35162 NOV/81 275 BESS Y01 35163 NOV/81 275 BESS Y 35164 NOV/81 275 BESS PQ0 35165 NOV/81 275 BESS PQ1 35166 NOV/81 275 2.BESSEL FUNCTIONS I AND K BESS I0 35170 NOV/81 277 BESS I1 35171 NOV/81 277 BESS I 35172 NOV/81 277 BESS K01 35173 NOV/81 277 BESS K 35174 NOV/81 277 6. 9. 2. NONEXP BESS I0 35175 NOV/81 277 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 6. 9. 2. NONEXP BESS I1 35176 NOV/81 277 NONEXP BESS I 35177 NOV/81 277 NONEXP BESS K01 35178 NOV/81 277 NONEXP BESS K 35179 NOV/81 277 3.KELVIN FUNCTIONS 10.BESSEL FUNCTIONS OF REAL ORDER 1.BESSEL FUNCTIONS J AND Y BESS JAPLUSN 35180 NOV/81 279 BESS YA01 35181 NOV/81 279 BESS YAPLUSN 35182 NOV/81 279 BESS PQA01 35183 NOV/81 279 BESS ZEROS 35184 NOV/81 279 START 35185 NOV/81 279 2.BESSEL FUNCTIONS I AND K BESS IAPLUSN 35190 NOV/81 281 BESS KA01 35191 NOV/81 281 BESS KAPLUSN 35192 NOV/81 281 NONEXP BESS IAPLUSN 35193 NOV/81 281 NONEXP BESS KA01 35194 NOV/81 281 NONEXP BESS KAPLUSN 35195 NOV/81 281 3.SPHERICAL BESSEL FUNCTIONS SPHER BESS J 35150 NOV/81 283 SPHER BESS Y 35151 NOV/81 283 SPHER BESS I 35152 NOV/81 283 SPHER BESS K 35153 NOV/81 283 NONEXP SPHER BESS I 35154 NOV/81 283 NONEXP SPHER BESS K 35155 NOV/81 283 4.AIRY FUNCTIONS AIRY 35140 NOV/81 285 AIRYZEROS 35145 NOV/81 285 7.INTERPOLATION & APPROXIMATION 1.REAL DATA IN ONE DIMENSION 1.INTERPOLATION, WITH 1.POLYNOMIALS 1.GENERAL POLYNOMIALS NEWTON 36010 NOV/81 287 2.ORTHOGONAL POLYNOMIALS 2.SPLINES 1.GENERAL SPLINES 2.NATURAL SPLINES 3.TRIGONOMETRIC SERIES 1.FOURIER SERIES 2.SINE SERIES 3.COSINE SERIES 4.RATIONAL FUNCTIONS 5.EXPONENTIAL FUNCTIONS 2.APPROXIMATION IN 2-NORM, WITH 1.GENERAL FUNCTIONS SEE ALSO SECTION 5.1.3.1 2.POLYNOMIALS 1.GENERAL POLYNOMIALS 2.ORTHOGONAL POLYNOMIALS 3.SPLINES 1.GENERAL SPLINES 7. 1. 2. 3. 2.NATURAL SPLINES 1 INDEX PROCEDURE CODE MNT/YR RECORD NUMBER 7. 1. 2. 4.TRIGONOMETRIC SERIES 5.RATIONAL FUNCTIONS 6.EXPONENTIAL FUNCTIONS 3.APPROXIMATION IN INF-NORM,WITH 1.GENERAL FUNCTIONS 2.POLYNOMIALS 1.GENERAL POLYNOMIALS INI 36020 NOV/81 289 SNDREMEZ 36021 NOV/81 289 MINMAXPOL 36022 NOV/81 289 2.ORTHOGONAL POLYNOMIALS 3.TRIGONOMETRIC SERIES 4.RATIONAL FUNCTIONS 4.APPROXIMATION IN 1-NORM, WITH 1.GENERAL FUNCTIONS 2.POLYNOMIALS 2.REAL DATA IN MORE DIMENSIONS 3.REAL FUNCTIONS IN 1 DIMENSION 1.POLYNOMIALS 8.NUMBER THEORY VERSION: 811214 1 OBSOLETE PROCEDURES PROCEDURE CODE WITHDRAWAL EXPIRATION REPLACED BY VERSION: 811214