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numalinx.txt. May 13, 1992.
numalinx.txt only contains a new, trimmed introduction and the systematic index -- for the history of the NUMAL development, and the KWIC index, see: P.W. Hemker (ed.)[1981]: NUMAL. Numerical Procedures in ALGOL 60. 7 volumes. MC Syllabus 47, Mathematical Centre, Amsterdam.
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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