1CONTENTS OF KWICINDEX 31/12/79 PAGE 1 0 30001 275 MBASE DELIVERS THE BASE OF THE ARITHMETIC OF THE COMPUTOR. 30002 275 ARREB DELIVERS THE ARITHMETIC ERROR BOUND OF THE COMPUTOR. 30003 275 DWARF DELIVERS THE SMALLEST ( IN ABSOLUTE VALUE ) REPRESENTABLE REAL NUMBER. 30004 275 GIANT DELIVERS THE LARGEST REPRESENTABLE REAL NUMBER. 30005 275 INTCAP DELIVERS THE INTEGER CAPACITY. 30006 273 PI DELIVERS A FULL PRECISION APPROXIMATION TO PI= 3.14... 30007 273 E DELIVERS A FULL PRECISION APPROXIMATION TO E= 2.718... 30008 275 OVERFLOW TESTS WHETHER A VALUE IS AN OVERFLOW VALUE. 30009 275 UNDERFLOW TESTS WHETHER A VALUE IS AN UNDERFLOW VALUE. 31010 1 INIVEC INITIALIZES A VECTOR WITH A CONSTANT. 31011 1 INIMAT INITIALIZES A MATRIX WITH A CONSTANT. 31012 1 INIMATD INITIALIZES A (CO)DIAGONAL OF A MATRIX. 31013 1 INISYMD INITIALIZES A (CO)DIAGONAL OF A SYMMETRIC MATRIX, WHOSE UPPERTRIANGLE IS STORED COLUMNWISE IN A ONE-DIMENSIONAL ARRAY. 31014 1 INISYMROW INITIALIZES A ROW OF A SYMMETRIC MATRIX, WHOSE UPPERTRIANGLE IS STORED COLUMNWISE IN A ONE-DIMENSIONAL ARRAY. 31020 5 MULVEC STORES A CONSTANT MULTIPLIED BY A VECTOR INTO A VECTOR. 31021 5 MULROW STORES A CONSTANT MULTIPLIED BY A ROW VECTOR INTO A ROW VECTOR. 31022 5 MULCOL STORES A CONSTANT MULTIPLIED BY A COLUMN VECTOR INTO A COLUMN VECTOR. 31030 3 DUPVEC COPIES A VECTOR INTO ANOTHER VECTOR. 31031 3 DUPVECROW COPIES A ROW VECTOR INTO A VECTOR. 31032 3 DUPROWVEC COPIES A VECTOR INTO A ROW VECTOR. 31033 3 DUPVECCOL COPIES A COLUMN VECTOR INTO A VECTOR. 31034 3 DUPCOLVEC COPIES A VECTOR INTO A COLUMN VECTOR. 31035 3 DUPMAT COPIES A MATRIX INTO ANOTHER MATRIX. 31040 245 POL EVALUATES A POLYNOMIAL. 31042 229 CHEPOL EVALUATES A CHEBYSHEV POLYNOMIAL. 31043 229 ALLCHEPOL EVALUATES ALL CHEBYSHEV POLYNOMIALS UP TO A CERTAIN DEGREE. 31044 293 ORTPOL EVALUATES THE VALUE OF AN N-DEGREE ORTHOGONAL POLYNOMIAL, GIVEN BY A SET OF RECURRENCE COEFFICIENTS. 31045 293 ALLORTPOL EVALUATES THE VALUE OF ALL ORTHOGONAL POLYNOMIALS UP TO A GIVEN DEGREE, GIVEN A SET OF RECURRENCE COEFFICIENTS. 31046 229 CHEPOLSER EVALUATES A CHEBYSHEV SERIES. 31046 229 CHEPOLSUM EVALUATES A FINITE SUM OF CHEBYSHEV POLYNOMIALS. 31047 293 SUMORTPOL EVALUATES A FINITE SERIES EXPRESSED IN ORTHOGONAL POLYNOMIALS, GIVEN BY A SET OF RECURRENCE COEFFICIENTS. 31048 293 ORTPOLSYM EVALUATES THE VALUE OF AN N-DEGREE ORTHOGONAL POLYNOMIAL, GIVEN BY A SET OF RECURRENCE COEFFICIENTS. 31049 293 ALLORTPOLSYM EVALUATES THE VALUE OF ALL ORTHOGONAL POLYNOMIALS UP TO A GIVEN DEGREE, GIVEN A SET OF RECURRENCE COEFFICIENTS. 31050 43 NEWGRN TRANSFORMS A POLYNOMIAL FROM NEWTON SUM INTO POWER SUM FORM. 31051 43 POLCHS TRANSFORMS A POLYNOMIAL FROM POWER SUM INTO CHEBYSHEV SUM FORM. 31052 43 CHSPOL TRANSFORMS A POLYNOMIAL FROM CHEBYSHEV SUM INTO POWER SUM FORM. 31053 43 POLSHTCHS TRANSFORMS A POLYNOMIAL FROM POWER SUM INTO SHIFTED CHEBYSHEV SUM FORM. 31054 43 SHTCHSPOL TRANSFORMS A POLYNOMIAL FROM SHIFTED CHEBYSHEV SUM FORM INTO POWER SUM FORM. 31055 43 GRNNEW TRANSFORMS A POLYNOMIAL FROM POWER SUM INTO NEWTON SUM FORM. 31058 293 SUMORTPOLSYM EVALUATES A FINITE SERIES EXPRESSED IN ORTHOGONAL POLYNOMIALS, GIVEN BY A SET OF RECURRENCE COEFFICIENTS. 31059 229 ODDCHEPOLSUM EVALUATES A FINITE SUM OF CHEBYSHEV POLYNOMIALS OF ODD DEGREE. 31061 241 INFNRMVEC CALCULATES THE INFINITY-NORM OF A VECTOR. 31062 241 INFNRMROW CALCULATES THE INFINITY-NORM OF A ROW VECTOR. 31063 241 INFNRMCOL CALCULATES THE INFINITY-NORM OF A COLUMN VECTOR. 31064 241 INFNRMMAT CALCULATES THE INFINITY-NORM OF A MATRIX. 31065 241 ONENRMVEC CALCULATES THE 1-NORM OF A VECTOR. 31066 241 ONENRMROW CALCULATES THE 1-NORM OF A ROW VECTOR. 31067 241 ONENRMCOL CALCULATES THE 1-NORM OF A COLUMN VECTOR. 31068 241 ONENRMMAT CALCULATES THE 1-NORM OF A MATRIX. 31069 241 ABSMAXMAT CALCULATES THE MODULUS OF THE LARGEST ELEMENT OF A MATRIX AND DELIVERS THE INDICES OF THE MAXIMAL ELEMENT. 31070 269 HSHVECMAT PREMULTIPLIES A MATRIX BY A HOUSEHOLDER MATRIX, THE VECTOR DEFINING THIS HSH MATRIX BEING GIVEN IN A ONE-DIMENSIONAL ARRAY. 31071 269 HSHCOLMAT PREMULTIPLIES A MATRIX BY A HOUSEHOLDER MATRIX, THE VECTOR DEFINING THIS HSH MATRIX BEING GIVEN AS A COLUMN 1CONTENTS OF KWICINDEX 31/12/79 PAGE 2 0 IN A TWO-DIMENSIONAL ARRAY. 31072 269 HSHROWMAT PREMULTIPLIES A MATRIX BY A HOUSEHOLDER MATRIX, THE VECTOR DEFINING THIS HSH MATRIX BEING GIVEN AS A ROW IN A TWO-DIMENSIONAL ARRAY. 31073 269 HSHVECTAM POSTMULTIPLIES A MATRIX BY A HOUSEHOLDER MATRIX, THE VECTOR DEFINING THIS HSH MATRIX BEING GIVEN IN A ONE-DIMENSIONAL ARRAY. 31074 269 HSHCOLTAM POSTMULTIPLIES A MATRIX BY A HOUSEHOLDER MATRIX, THE VECTOR DEFINING THIS HSH MATRIX BEING GIVEN AS A COLUMN IN A TWO-DIMENSIONAL ARRAY. 31075 269 HSHROWTAM POSTMULTIPLIES A MATRIX BY A HOUSEHOLDER MATRIX, THE VECTOR DEFINING THIS HSH MATRIX BEING GIVEN AS A ROW IN A TWO-DIMENSIONAL ARRAY. 31090 203 SINSER EVALUATES A SINE SERIES. 31091 203 COSSER EVALUATES A COSINE SERIES. 31092 203 FOUSER EVALUATES A FOURIER SERIES WITH EQUAL SINE AND COSINE COEFFICIENTS. 31093 203 FOUSER1 EVALUATES A FOURIER SERIES. 31094 203 FOUSER2 EVALUATES A FOURIER SERIES. 31095 203 COMFOUSER EVALUATES A COMPLEX FOURIER SERIES WITH REAL COEFFICIENTS. 31096 203 COMFOUSER1 EVALUATES A COMPLEX FOURIER SERIES. 31097 203 COMFOUSER2 EVALUATES A COMPLEX FOURIER SERIES. 31100 289 LNGREATODECI CONVERTS A DOUBLE PRECISION NUMBER TO ITS DECIMAL REPRESENTATION. 31101 271 DPADD ADDS TWO SINGLE PRECISION NUMBERS TO A DOUBLE PRECISION SUM. 31102 271 DPSUB SUBTRACTS TWO SINGLE PRECISION NUMBERS TO A DOUBLE PRECISION DIFFERENCE. 31103 271 DPMUL MULTIPLIES TWO SINGLE PRECISION NUMBERS TO A DOUBLE PRECISION PRODUCT. 31104 271 DPDIV DIVIDES TWO SINGLE PRECISION NUMBERS TO A DOUBLE PRECISION QUOTIENT. 31105 271 LNGADD ADDS TWO DOUBLE PRECISION NUMBERS. 31106 271 LNGSUB SUBTRACTS TWO DOUBLE PRECISION NUMBERS. 31107 271 LNGMUL MULTIPLIES TWO DOUBLE PRECISION NUMBERS. 31108 271 LNGDIV DIVIDES TWO DOUBLE PRECISION NUMBERS. 31109 271 DPPOW COMPUTES THE DOUBLE PRECISION POWER OF A SINGLE PRECISION NUMBER. 31110 271 LNGPOW COMPUTES THE DOUBLE PRECISION POWER OF A DOUBLE PRECISION NUMBER. 31131 5 COLCST MULTIPLIES A COLUMN VECTOR BY A CONSTANT. 31132 5 ROWCST MULTIPLIES A ROW VECTOR BY A CONSTANT. 31200 201 LNGINTADD COMPUTES THE SUM OF LONG NONNEGATIVE INTEGERS. 31201 201 LNGINTSUBTRACT COMPUTES THE DIFFERENCE OF LONG NONNEGATIVE INTEGERS. 31202 201 LNGINTMULT COMPUTES THE PRODUCT OF LONG NONNEGATIVE INTEGERS. 31203 201 LNGINTDIVIDE COMPUTES THE QUOTIENT WITH REMAINDER OF LONG NONNEGATIVE INTEGERS. 31204 201 LNGINTPOWER COMPUTES U**POWER, WHERE U IS A LONG NONNEGATIVE INTEGER AND POWER IS THE POSITIVE ( SINGLE-LENGTH ) EXPONENT. 31241 245 TAYPOL EVALUATES THE FIRST K TERMS OF A TAYLOR SERIES. 31242 245 NORDERPOL EVALUATES THE FIRST K NORMALIZED DERIVATIVES OF A POLYNOMIAL ( I.E. J-TH DERIVATIVE (J FACTORIAL) ), J=0,1,...,K <= DEGREE. 31243 245 DERPOL EVALUATES THE FIRST K DERIVATIVES OF A POLYNOMIAL. 31248 205 INTCHS COMPUTES THE INDEFINITE INTEGRAL OF A GIVEN CHEBYSHEV SERIES. 31250 43 LINTFMPOL TRANSFORMS A POLYNOMIAL IN X INTO A POLYNOMIAL IN Y (Y = A*X + B). 31252 313 GSSWTSSYM CALCULATES THE GAUSSIAN WEIGHTS OF A WEIGHT FUNCTION, THE RECURRENCE COEFFICIENTS BEING GIVEN. 31253 313 GSSWTS CALCULATES THE GAUSSIAN WEIGHTS OF A WEIGHT FUNCTION, THE RECURRENCE COEFFICIENTS BEING GIVEN. 31254 313 RECCOF CALCULATES RECURRENCE COEFFICIENTS OF AN ORTHOGONAL POLYNOMIAL, A WEIGHT FUNCTION BEING GIVEN. 31362 211 ALLZERORTPOL CALCULATES ALL ZEROS OF AN ORTHOGONAL POLYNOMIAL. 31363 211 LUPZERORTPOL CALCULATES A NUMBER OF ADJACENT UPPER OR LOWER ZEROS OF AN ORTHOGONAL POLYNOMIAL. 31364 211 SELZERORTPOL CALCULATES A NUMBER OF ADJACENT ZEROS OF AN ORTHOGONAL POLYNOMIAL. 31370 211 ALLJACZER CALCULATES THE ZEROS OF A JACOBIAN POLYNOMIAL. 31371 211 ALLLAGZER CALCULATES THE ZEROS OF A LAGUERRE POLYNOMIAL. 31425 291 GSSJACWGHTS COMPUTES THE ABSCISSAE AND WEIGHTS FOR GAUSS- JACOBI QUADRATURE. 31427 291 GSSLAGWGHTS COMPUTES THE ABSCISSAE AND WEIGHTS FOR GAUSS- LAGRANGE QUADRATURE. 31500 15 FULMATVEC CALCULATES THE PRODUCT A * B, WHERE A IS A GIVEN MATRIX AND B IS A VECTOR. 31501 15 FULTAMVEC CALCULATES THE PRODUCT A' * B, WHERE A' IS THE TRANSPOSED OF THE MATRIX A AND B IS A VECTOR. 31502 15 FULSYMMATVEC CALCULATES THE PRODUCT A * B, WHERE A IS A SYMMETRIC MATRIX, WHOSE UPPERTRIANGLE IS STORED COLUMNWISE IN A ONE-DIMENSIONAL ARRAY AND B IS A VECTOR. 1CONTENTS OF KWICINDEX 31/12/79 PAGE 3 0 31503 15 RESVEC CALCULATES THE RESIDUAL VECTOR A * B + X * C, WHERE A IS A GIVEN MATRIX, B AND C ARE VECTORS AND X IS A SCALAR. 31504 15 SYMRESVEC CALCULATES THE RESIDUAL VECTOR A * B + X * C, WHERE A IS A SYMMETRIC MATRIX, WHOSE UPPERTRIANGLE IS STORED COLUMNWISE IN A ONE-DIMENSIONAL ARRAY, B AND C ARE VECTORS AND X IS A SCALAR. 31505 285 LNGFULMATVEC CALCULATES BY DOUBLE PRECISION ARITHMETIC THE PRODUCT A * B, WHERE A IS A GIVEN MATRIX AND B IS A VECTOR. 31506 285 LNGFULTAMVEC CALCULATES BY DOUBLE PRECISION ARITHMETIC THE PRODUCT A' * B, WHERE A' IS THE TRANSPOSED OF THE MATRIX A AND B IS A VECTOR. 31507 285 LNGFULSYMMATVEC CALCULATES BY DOUBLE PRECISION ARITHMETIC THE PRODUCT A * B, WHERE A IS A SYMMETRIC MATRIX, WHOSE UPPERTRIANGLE IS STORED COLUMNWISE IN A ONE-DIMENSIONAL ARRAY AND B IS A VECTOR. 31508 285 LNGRESVEC CALCULATES BY DOUBLE PRECISION ARITHMETIC THE RESIDUAL VECTOR A * B + X * C, WHERE A IS A GIVEN MATRIX, B AND C ARE VECTORS AND X IS A SCALAR. 31509 285 LNGSYMRESVEC CALCULATES BY DOUBLE PRECISION ARITHMETIC THE RESIDUAL VECTOR A * B + X * C, WHERE A IS A SYMMETRIC MATRIX, WHOSE UPPERTRIANGLE IS STORED COLUMNWISE IN A ONE-DIMENSIONAL ARRAY, B AND C ARE VECTORS AND X IS A SCALAR. 32010 131 EULER PERFORMS THE SUMMATION OF AN ALTERNATING INFINITE SERIES. 32020 131 SUMPOSSERIES PERFORMS THE SUMMATION OF A INFINITE SERIES WITH POSITIVE MONOTONICALLY DECREASING TERMS USING THE VAN WIJNGAARDEN TRANSFORMATION. 32051 135 INTEGRAL CALCULATES THE DEFINITE INTEGRAL OF A FUNCTION OF ONE VARIABLE OVER A FINITE OR INFINITE INTERVAL OR OVER A NUMBER OF CONSECUTIVE INTERVALS. 32070 133 QADRAT COMPUTES THE DEFINITE INTEGRAL OF A FUNCTION OF ONE VARIABLE OVER A FINITE INTERVAL. 32075 257 TRICUB COMPUTES THE DEFINITE INTEGRAL OF A FUNCTION OF TWO VARIABLES OVER A TRIANGULAR DOMAIN. 33010 141 RK1 SOLVES A SINGLE 1ST ORDER DIFFERENTIAL EQUATION BY MEANS OF A 5TH ORDER RUNGE-KUTTA METHOD. 33012 171 RK2 INTEGRATES A SINGLE 2ND ORDER DIFFERENTIAL EQUATION ( INITIAL VALUE PROBLEM ) BY MEANS OF A 5TH ORDER RUNGE-KUTTA METHOD. 33013 173 RK2N SOLVES A SYSTEM OF 2ND ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A 5TH ORDER RUNGE-KUTTA METHOD. 33014 175 RK3 SOLVES A SINGLE 2ND ORDER DIFFERENTIAL EQUATION ( INITIAL VALUE PROBLEM ) BY MEANS OF A 5TH ORDER RUNGE-KUTTA METHOD; THIS METHOD CAN ONLY BE USED IF THE RIGHT HAND SIDE OF THE DIFFERENTIAL EQUATION DOES NOT DEPEND ON Y'. 33015 177 RK3N SOLVES A SYSTEM OF 2ND ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A 5TH ORDER RUNGE-KUTTA METHOD; THIS METHOD CAN ONLY BE USED IF THE RIGHT HAND SIDE OF THE DIFFERENTIAL EQUATIONS DOES NOT DEPEND ON Y'. 33016 145 RK4A SOLVES A SINGLE 1ST ORDER DIFFERENTIAL EQUATION BY MEANS OF A 5TH ORDER RUNGE-KUTTA METHOD; THE INTEGRATION IS TERMINATED AS SOON AS A CONDITION ON X AND Y, WHICH IS SUPPLIED BY THE USER, IS SATISFIED. 33017 147 RK4NA SOLVES A SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A 5TH ORDER RUNGE-KUTTA METHOD; THE INTEGRATION IS TERMINATED AS SOON AS A CONDITION ON X[0],...,X[N] , SUPPLIED BY THE USER, IS SATISFIED. 33018 149 RK5NA SOLVES A SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A 5TH ORDER RUNGE-KUTTA METHOD; THE ARC LENGTH IS INTRODUCED AS AN INTEGRATION VARIABLE; THE INTEGRATION IS TERMINATED AS SOON AS A CONDITION ON X[0],...,X[N] , SUPPLIED BY THE USER, IS SATISFIED. 33033 143 RKE SOLVES A SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A 5TH ORDER RUNGE-KUTTA METHOD. 33040 167 MODIFIED TAYLOR SOLVES A SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A 1ST, 2ND OR 3RD ORDER ONE-STEP TAYLOR METHOD; THIS METHOD CAN BE USED TO SOLVE LARGE AND SPARSE SYSTEMS, PROVIDED HIGHER ORDER DERIVATIVES CAN EASILY BE OBTAINED. 33050 169 EXPONENTIALLY FITTED TAYLOR SOLVES A SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A VARIABLE ORDER TAYLOR METHOD; THIS METHOD CAN BE USED TO SOLVE STIFF SYSTEMS, WITH KNOWN EIGEN VALUE SPECTRUM, PROVIDED HIGHER ORDER DERIVATIVES CAN EASILY BE OBTAINED. 33061 155 ARK SOLVES A SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A STABILIZED RUNGE-KUTTA METHOD WITH LIMITED STORAGE REQUIREMENTS. 33066 295 ARKMAT SOLVES A SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL BOUNDARY-VALUE PROBLEM ) BY MEANS OF A STABILIZED RUNGE-KUTTA METHOD, IN PARTICULAR SUITABLE FOR SYSTEMS ARISING FROM TWO-DIMENSIONAL TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS. 33070 157 EFRK SOLVES A SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A 1ST, 2ND OR 3RD ORDER, EXPONENTIONALLY FITTED RUNGE-KUTTA METHOD; AUTOMATIC STEPSIZE CONTROL IS NOT PROVIDED; THIS METHOD CAN BE USED TO SOLVE STIFF SYSTEMS WITH KNOWN EIGENVALUE SPECTRUM. 33080 151 MULTISTEP SOLVES A SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A VARIABLE ORDER MULTISTEP METHOD ADAMS-MOULTON, ADAMS-BASHFORTH OR GEAR'S METHOD; THE ORDER OF ACCURACY IS AUTOMATIC, UP TO 5TH ORDER; THIS METHOD IS SUITABLE FOR STIFF SYSTEMS. 33120 161 EFERK SOLVES AN AUTONOMOUS SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF AN EXPONENTIALLY FITTED, 3RD ORDER RUNGE-KUTTA METHOD; THIS METHOD CAN BE USED TO SOLVE STIFF SYSTEMS WITH KNOWN 1CONTENTS OF KWICINDEX 31/12/79 PAGE 4 0 EIGENVALUE SPECTRUM. 33131 165 LINIGER2 SOLVES AN AUTONOMOUS SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF AN IMPLICIT, EXPONENTIALLY FITTED 1ST ORDER ONE-STEP METHOD; AUTOMATIC STEP-SIZE CONTROL IS NOT PROVIDED; THIS METHOD CAN BE USED TO SOLVE STIFF SYSTEMS. 33132 221 LINIGER1VS SOLVES AN AUTONOMOUS SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF AN IMPLICIT, EXPONENTIALLY FITTED 1ST ORDER ONE-STEP METHOD;THIS METHOD CAN BE USED TO SOLVE STIFF SYSTEMS. 33135 231 IMPEX SOLVES AN AUTONOMOUS SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF THE IMPLICIT MIDPOINT RULE WITH SMOOTHING AND EXTRAPOLATION; THIS METHOD IS SUITABLE FOR THE INTEGRATION OF STIFF DIFFERENTIAL EQUATIONS. 33160 159 EFSIRK SOLVES AN AUTONOMOUS SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A 3RD ORDER, EXPONENTIALLY FITTED, SEMI-IMPLICIT RUNGE-KUTTA METHOD; THIS METHOD CAN BE USED TO SOLVE STIFF SYSTEMS. 33170 225 RICHARDSON SOLVES A SYSTEM OF LINEAR EQUATIONS WITH POSITIVE REAL EIGENVALUES ( ELLIPTIC BOUNDARY VALUE PROBLEM ) BY MEANS OF A NON-STATIONARY 2ND ORDER ITERATIVE METHOD. 33171 225 ELIMINATION SOLVES A SYSTEM OF LINEAR EQUATIONS WITH POSITIVE REAL EIGENVALUES ( ELLIPTIC BOUNDARY VALUE PROBLEM ) BY MEANS OF A NON-STATIONARY 2ND ORDER ITERATIVE METHOD, WHICH IS AN ACCELERATION OF RICHARDSON'S METHOD. 33180 153 DIFFSYS SOLVES A SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ); BY EXTRAPOLATION, APPLIED TO LOW ORDER RESULTS, A HIGH ORDER OF ACCURACY IS OBTAINED; THIS METHOD IS SUITABLE FOR SMOOTH PROBLEMS WHEN HIGH ACCURACY IS REQUIRED. 33191 223 GMS SOLVES AN AUTONOMOUS SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS ( INITIAL VALUE PROBLEM ) BY MEANS OF A 3RD ORDER MULTISTEP METHOD; THIS METHOD CAN BE USED TO SOLVE STIFF SYSTEMS. 33300 261 FEMLAGSYM SOLVES A LINEAR TWO-POINT BOUNDARY-VALUE PROBLEM FOR A SECOND ORDER SELF-ADJOINT DIFFERENTIAL EQUATION BY A RITZ-GALERKIN METHOD. 33301 261 FEMLAG SOLVES A LINEAR TWO-POINT BOUNDARY-VALUE PROBLEM FOR A SECOND ORDER SELF-ADJOINT DIFFERENTIAL EQUATION BY A RITZ-GALERKIN METHOD; THE COEFFICIENT OF Y" IS SUPPOSED TO BE UNITY. 33302 263 FEMLAGSKEW SOLVES A LINEAR TWO-POINT BOUNDARY-VALUE PROBLEM FOR A SECOND ORDER DIFFERENTIAL EQUATION BY A RITZ-GALERKIN METHOD. 33303 265 FEMHERMSYM SOLVES A LINEAR TWO-POINT BOUNDARY-VALUE PROBLEM FOR A FOURTH ORDER SELF-ADJOINT DIFFERENTIAL EQUATION WITH DIRICHLET BOUNDARY CONDITIONS BY A RITZ-GALERKIN METHOD. 33308 261 FEMLAGSPHER SOLVES A LINEAR TWO-POINT BOUNDARY-VALUE PROBLEM FOR A SECON ORDER SELF-ADJOINT DIFFERENTIAL EQUATION WITH SPHERICAL COORDINATES BY A RITZ-GALERKIN METHOD. 33314 317 NONLINFEMLAGSKEW SOLVES A NONLINEAR TWO POINT BOUNDARY VALUE PROBLEM FOR A SECOND ORDER DIFFERENTIAL EQUATION WITH SPHERICAL COORDINATES BY A RITZ-GALERKIN METHOD AND NEWTON ITERATION. 34010 7 VECVEC := SCALAR PRODUCT OF A VECTOR AND A VECTOR. 34011 7 MATVEC := SCALAR PRODUCT OF A ROW VECTOR AND A VECTOR. 34012 7 TAMVEC := SCALAR PRODUCT OF A COLUMN VECTOR AND A VECTOR. 34013 7 MATMAT := SCALAR PRODUCT OF A ROW VECTOR AND A COLUMN VECTOR. 34014 7 TAMMAT := SCALAR PRODUCT OF A COLUMN VECTOR AND A COLUMN VECTOR. 34015 7 MATTAM := SCALAR PRODUCT OF A ROW VECTOR AND A ROW VECTOR. 34016 7 SEQVEC := SCALAR PRODUCT OF TWO VECTORS GIVEN IN ONE-DIMENSIONAL ARRAYS, WHERE THE MUTUAL SPACINGS BETWEEN THE INDICES OF THE 1ST VECTOR CHANGE LINEARLY. 34017 7 SCAPRD1 := SCALAR PRODUCT OF TWO VECTORS GIVEN IN ONE-DIMENSIONAL ARRAYS, WHERE THE SPACINGS OF BOTH VECTORS ARE CONSTANT. 34018 7 SYMMATVEC := SCALAR PRODUCT OF A VECTOR AND A ROW OF A SYMMETRIC MATRIX, WHOSE UPPERTRIANGLE IS GIVEN COLUMNWISE IN A ONE-DIMENSIONAL ARRAY. 34020 9 ELMVEC ADDS A CONSTANT TIMES A VECTOR TO A VECTOR. 34021 9 ELMVECCOL ADDS A CONSTANT TIMES A COLUMN VECTOR TO A VECTOR. 34022 9 ELMCOLVEC ADDS A CONSTANT TIMES A VECTOR TO A COLUMN VECTOR. 34023 9 ELMCOL ADDS A CONSTANT TIMES A COLUMN VECTOR TO A COLUMN VECTOR. 34024 9 ELMROW ADDS A CONSTANT TIMES A ROW VECTOR TO A ROW VECTOR. 34025 9 MAXELMROW ADDS A CONSTANT TIMES A ROW VECTOR TO A ROW VECTOR, MAXELMROW:=THE SUBSCRIPT OF AN ELEMENT OF THE NEW ROW VECTOR WHICH IS OF MAXIMUM ABSOLUTE VALUE. 34026 9 ELMVECROW ADDS A CONSTANT TIMES A ROW VECTOR TO A VECTOR. 34027 9 ELMROWVEC ADDS A CONSTANT TIMES A VECTOR TO A ROW VECTOR. 34028 9 ELMROWCOL ADDS A CONSTANT TIMES A COLUMN VECTOR TO A ROW VECTOR. 34029 9 ELMCOLROW ADDS A CONSTANT TIMES A ROW VECTOR TO A COLUMN VECTOR. 34030 11 ICHVEC INTERCHANGES TWO VECTORS GIVEN IN ARRAY A[L:U] AND ARRAY A[SHIFT + L : SHIFT + U]. 34031 11 ICHCOL INTERCHANGES TWO COLUMNS OF A MATRIX. 34032 11 ICHROW INTERCHANGES TWO ROWS OF MATRIX. 34033 11 ICHROWCOL INTERCHANGES A ROW AND A COLUMN OF A MATRIX. 34034 11 ICHSEQVEC INTERCHANGES A ROW AND A COLUMN OF AN UPPERTRIANGULAR MATRIX, WHICH IS STORED COLUMNWISE IN A ONE-DIMENSIONAL 1CONTENTS OF KWICINDEX 31/12/79 PAGE 5 0 ARRAY. 34035 11 ICHSEQ INTERCHANGES TWO COLUMNS OF AN UPPERTRIANGULAR MATRIX, WHICH IS STORED COLUMNWISE IN A ONE-DIMENSIONAL ARRAY. 34040 13 ROTCOL REPLACES TWO COLUMN VECTORS X AND Y BY TWO VECTORS CX + SY AND CY - SX. 34041 13 ROTROW REPLACES TWO ROW VECTORS X AND Y BY TWO VECTORS CX + SY AND CY - SX. 34051 49 SOL SOLVES THE SYSTEM OF LINEAR EQUATIONS WHOSE MATRIX HAS BEEN TRIANGULARLY DECOMPOSED BY DEC. 34053 51 INV CALCULATES THE INVERSE OF A MATRIX THAT HAS BEEN TRIANGULARLY DECOMPOSED BY DEC. 34061 49 SOLELM SOLVES A SYSTEM OF LINEAR EQUATIONS WHOSE MATRIX HAS BEEN TRIANGULARLY DECOMPOSED BY GSSELM OR GSSERB. 34071 79 SOLBND SOLVES A SYSTEM OF LINEAR EQUATIONS, THE MATRIX BEING DECOMPOSED BY DECBND. 34131 65 LSQSOL SOLVES A LINEAR LEAST SQUARES PROBLEM IF THE COEFFICIENT MATRIX HAS BEEN DECOMPOSED BY LSQORTDEC. 34132 63 LSQDGLINV CALCULATES THE DIAGONAL ELEMENTS OF THE INVERSE OF M'M, WHERE M IS THE COEFFICIENT MATRIX OF A LINEAR LEAST SQUARES PROBLEM. 34134 63 LSQORTDEC DELIVERS THE HOUSEHOLDER TRIANGULARIZATION WITH COLUMN INTERCHANGES OF THE MATRIX OF A LINEAR LEAST SQUARES PROBLEM. 34135 65 LSQORTDECSOL SOLVES A LINEAR LEAST SQUARES PROBLEM BY HOUSEHOLDER TRIANGULARIZATION WITH COLUMN INTERCHANGES AND CALCULATES THE DIAGONAL OF THE INVERSE OF M'M, WHERE M IS THE COEFFICIENT MATRIX. 34136 207 LSQINV CALCULATES THE INVERSE OF THE MATRIX S'S, WHERE S IS THE COEFFICIENT MATRIX OF A LINEAR LEAST SQUARES PROBLEM. 34137 309 LSQDECOMP COMPUTES THE QR- DECOMPOSITION OF A LINEAR LEAST SQUARES PROBLEM WITH LINEAR CONSTRAINTS. 34138 309 LSQREFSOL SOLVES A LINEAR LEAST SQUARES PROBLEM WITH LINEAR CONSTRAINTS, IF THE MATRIX HAS BEEN DECOMPOSED BY LSQDECOMP. 34140 101 TFMSYMTRI2 TRANSFORMS A REAL SYMMETRIC MATRIX INTO A SIMILAR TRIDIAGONAL ONE BY MEANS OF HOUSEHOLDER'S TRANSFORMATION. 34141 101 BAKSYMTRI2 PERFORMS THE BACK TRANSFORMATION CORRESPONDING TO TFMSYMTRI2. 34142 101 TFMPREVEC IN COMBINATION WITH TFMSYMTRI2 CALCULATES THE TRANSFORMING MATRIX. 34143 101 TFMSYMTRI1 TRANSFORMS A REAL SYMMETRIC MATRIX INTO A SIMILAR TRIDIAGONAL ONE BY MEANS OF HOUSEHOLDER'S TRANSFORMATION. 34144 101 BAKSYMTRI1 PERFORMS THE BACK TRANSFORMATION CORRESPONDING TO TFMSYMTRI1. 34150 215 ZEROIN FINDS ( IN A GIVEN INTERVAL ) A ZERO OF A FUNCTION OF ONE VARIABLE. 34151 111 VALSYMTRI CALCULATES ALL, OR SOME CONSECUTIVE, EIGENVALUES OF A SYMMETRIC TRIDIAGONAL MATRIX BY MEANS OF LINEAR INTERPOLATION USING A STURM SEQUENCE. 34152 111 VECSYMTRI CALCULATES EIGENVECTORS OF A SYMMETRIC TRIDIAGONAL MATRIX BY MEANS OF INVERSE ITERATION. 34153 113 EIGVALSYM2 CALCULATES ALL ( OR SOME ) EIGENVALUES OF A SYMMETRIC MATRIX USING LINEAR INTERPOLATION OF A FUNCTION DERIVED FROM A STURM SEQUENCE. 34154 113 EIGSYM2 CALCULATES EIGENVALUES AND EIGENVECTORS BY MEANS OF INVERSE ITERATION. 34155 113 EIGVALSYM1 CALCULATES ALL ( OR SOME ) EIGENVALUES OF A SYMMETRIC MATRIX USING LINEAR INTERPOLATION OF A FUNCTION DERIVED FROM A STURM SEQUENCE. 34156 113 EIGSYM1 CALCULATES EIGENVALUES AND EIGENVECTORS BY MEANS OF INVERSE ITERATION. 34160 111 QRIVALSYMTRI CALCULATES THE EIGENVALUES OF A SYMMETRIC TRIDIAGONAL MATRIX BY MEANS OF QR ITERATION. 34161 111 QRISYMTRI CALCULATES THE EIGENVALUES AND EIGENVECTORS OF A SYMMETRIC TRIDIAGONAL MATRIX BY MEANS OF QR ITERATION. 34162 113 QRIVALSYM2 CALCULATES THE EIGENVALUES OF A SYMMETRIC MATRIX BY MEANS OF QR ITERATION. 34163 113 QRISYM CALCULATES ALL EIGENVALUES AND EIGENVECTORS OF A SYMMETRIC MATRIX BY MEANS OF QR ITERATION. 34164 113 QRIVALSYM1 CALCULATES THE EIGENVALUES OF A SYMMETRIC MATRIX BY MEANS OF QR ITERATION. 34170 103 TFMREAHES TRANSFORMS A MATRIX INTO A SIMILAR UPPER-HESSENBERG MATRIX BY MEANS OF WILKINSON'S TRANSFORMATION. 34171 103 BAKREAHES1 PERFORMS THE BACK TRANSFORMATION ( ON A VECTOR ) CORRESPONDING TO TFMREAHES. 34172 103 BAKREAHES2 PERFORMS THE BACK TRANSFORMATION ( ON COLUMNS ) CORRESPONDING TO TFMREAHES. 34173 97 EQILBR EQUILIBRATES A MATRIX BY MEANS OF A DIAGONAL SIMILARITY TRANSFORMATION. 34174 97 BAKLBR PERFORMS THE BACK TRANSFORMATION CORRESPONDING TO EQILBR. 34180 115 REAVALQRI CALCULATES THE EIGENVALUES OF A REAL UPPER-HESSENBERG MATRIX, PROVIDED THAT ALL EIGENVALUES ARE REAL, BY MEANS OF SINGLE QR ITERATION. 34181 115 REAVECHES CALCULATES AN EIGENVECTOR CORRESPONDING TO A GIVEN REAL EIGENVALUE OF A REAL UPPER-HESSENBERG MATRIX BY MEANS OF INVERSE ITERATION. 34182 117 REAEIGVAL CALCULATES THE EIGENVALUES OF A MATRIX, PROVIDED THAT ALL EIGENVALUES ARE REAL. 34183 17 REASCL NORMALIZES THE COLUMNS OF A TWO-DIMENSIONAL ARRAY. 34184 117 REAEIG1 CALCULATES THE EIGENVECTORS AND EIGENVALUES OF A MATRIX, PROVIDED THAT THEY ARE ALL REAL. 34186 115 REAQRI CALCULATES ALL EIGENVALUES AND EIGENVECTORS OF A REAL UPPER-HESSENBERG MATRIX, PROVIDED THAT ALL EIGENVALUES ARE REAL, BY MEANS OF SINGLE QR ITERATION. 34187 117 REAEIG3 CALCULATES THE EIGENVECTORS AND EIGENVALUES OF A MATRIX, PROVIDED THAT THEY ARE ALL REAL. 34190 115 COMVALQRI CALCULATES THE REAL AND COMPLEX EIGENVALUES OF A REAL UPPER-HESSENBERG MATRIX BY MEANS OF DOUBLE QR ITERATION. 1CONTENTS OF KWICINDEX 31/12/79 PAGE 6 0 34191 115 COMVECHES CALCULATES THE EIGENVECTOR CORRESPONDING TO A GIVEN COMPLEX EIGENVALUE OF A REAL UPPER-HESSENBERG MATRIX BY MEANS OF INVERSE ITERATION. 34192 117 COMEIGVAL CALCULATES THE EIGENVALUES OF A MATRIX. 34193 29 COMSCL NORMALIZES REAL AND COMPLEX EIGENVECTORS. 34194 117 COMEIG1 CALCULATES THE EIGENVALUES AND EIGENVECTORS OF A MATRIX. 34210 139 LINEMIN MINIMIZES A FUNCTION OF SEVERAL VARIABLES IN A GIVEN DIRECTION. 34211 139 RNK1UPD ADDS A RANK-1 MATRIX TO A SYMMETRIC MATRIX. 34212 139 DAVUPD ADDS A RANK-2 MATRIX TO A SYMMETRIC MATRIX. 34213 139 FLEUPD ADDS A RANK-2 MATRIX TO A SYMMETRIC MATRIX. 34214 19 RNK1MIN MINIMIZES A FUNCTION OF SEVERAL VARIABLES. 34215 19 FLEMIN MINIMIZES A FUNCTION OF SEVERAL VARIABLES. 34220 95 CONJ GRAD SOLVES A POSITIVE DEFINITE SYMMETRIC SYSTEM OF LINEAR EQUATIONS BY THE METHOD OF CONJUGATE GRADIENTS. 34231 45 GSSELM PERFORMS A TRIANGULAR DECOMPOSITION WITH A COMBINATION OF PARTIAL AND COMPLETE PIVOTING. 34232 49 GSSSOL SOLVES A SYSTEM OF LINEAR EQUATIONS. 34235 51 INV1 CALCULATES THE INVERSE OF A MATRIX THAT HAS BEEN TRIANGULARLY DECOMPOSED BY GSSELM OR GSSERB.THE 1-NORM OF THE INVERSE MATRIX MIGHT ALSO BE CALCULATED. 34236 51 GSSINV CALCULATES THE INVERSE OF A MATRIX. 34240 45 ONENRMINV CALCULATES THE 1-NORM OF THE INVERSE OF A MATRIX WHOSE TRIANGULARLY DECOMPOSED FORM IS DELIVERED BY GSSELM. 34241 45 ERBELM CALCULATES A ROUGH UPPERBOUND FOR THE ERROR IN THE SOLUTION OF A SYSTEM OF LINEAR EQUATIONS WHOSE MATRIX IS TRIANGULARLY DECOMPOSED BY GSSELM. 34242 45 GSSERB PERFORMS A TRIANGULAR DECOMPOSTION OF THE MATRIX OF A SYSTEM OF LINEAR EQUATIONS AND CALCULATES AN UPPERBOUND FOR THE RELATIVE ERROR IN THE SOLUTION OF THAT SYSTEM. 34243 49 GSSSOLERB SOLVES A SYSTEM OF LINEAR EQUATIONS AND CALCULATES A ROUGH UPPERBOUND FOR THE RELATIVE ERROR IN THE CALCULATED SOLUTION. 34244 51 GSSINVERB CALCULATES THE INVERSE OF A MATRIX AND 1-NORM, AN UPPERBOUND FOR THE ERROR IN THE INVERSE MATRIX IS ALSO GIVEN. 34250 53 ITISOL SOLVES A SYSTEM OF LINEAR EQUATIONS WHOSE MATRIX HAS BEEN TRIANGULARLY DECOMPOSED BY GSSELM OR GSSERB. THIS SOLUTION IS IMPROVED ITERATIVELY. 34251 53 GSSITISOL SOLVES A SYSTEM OF LINEAR EQUATIONS AND THE SOLUTION IS IMPROVED ITERATIVELY. 34252 45 GSSNRI PERFORMS A TRIANGULAR DECOMPOSITION AND CALCULATES THE 1-NORM OF THE INVERSE MATRIX. 34253 53 ITISOLERB SOLVES A SYSTEM OF LINEAR EQUATIONS WHOSE MATRIX HAS TRIANGULARLY DECOMPOSED BY GSSNRI; THIS SOLUTION IS IMPROVED ITERATIVELY AN UPPERBOUND FOR THE ERROR IN THE SOLUTION IS CALCULATED. 34254 53 GSSITISOLERB SOLVES A SYSTEM OF LINEAR EQUATIONS; THIS SOLUTION IS IMPROVED ITERATIVELY AND AN UPPERBOUND FOR THE ERROR IN THE SOLUTION IS CALCULATED. 34260 109 HSHREABID TRANSFORMS A MATRIX TO BIDIAGONAL FORM, BY PREMULTIPLYING AND POSTMULTIPLYING WITH ORTHOGONAL MATRICES. 34261 109 PSTTFMMAT CALCULATES THE POSTMULTIPLYING MATRIX FROM THE DATA GENERATED BY HSHREABID. 34262 109 PRETFMMAT CALCULATES THE PREMULTIPLYING MATRIX FROM THE DATA GENERATED BY HSHREABID. 34270 125 QRISNGVALBID CALCULATES THE SINGULAR VALUES OF A BIDIAGONAL MATRIX. 34271 125 QRISNGVALDECBID CALCULATES THE SINGULAR VALUES DECOMPOSITION OF A MATRIX OF WHICH THE BIDIAGONAL AND THE PRE- AND POSTMULTIPLYING MATRICES ARE GIVEN. 34272 127 QRISNGVAL CALCULATES THE SINGULAR VALUES OF A GIVEN MATRIX. 34273 127 QRISNGVALDEC CALCULATES THE SINGULAR VALUES DECOMPOSITION U * S * V', WITH U AND V ORTHOGONAL AND S POSITIVE DIAGONAL. 34280 67 SOLSVDOVR SOLVES AN OVERDETERMINED SYSTEM OF LINEAR EQUATIONS, MULTIPLYING THE RIGHT-HAND SIDE BY THE PSEUDO-INVERSE OF THE GIVEN MATRIX. 34281 67 SOLOVR CALCULATES THE SINGULAR VALUES DECOMPOSITION AND SOLVES AN OVERDETERMINED SYSTEM OF LINEAR EQUATIONS. 34282 69 SOLSVDUND SOLVES AN UNDERDETERMINED SYSTEM OF LINEAR EQUATIONS, MULTIPLYING THE RIGHT-HAND SIDE BY THE PSEUDO-INVERSE OF THE GIVEN MATRIX. 34283 69 SOLUND CALCULATES THE SINGULAR VALUES DECOMPOSITION AND SOLVES AN UNDERDETERMINED SYSTEM OF LINEAR EQUATIONS. 34284 71 HOMSOLSVD SOLVES THE HOMOGENEOUS SYSTEM OF LINEAR EQUATIONS A * X = 0 AND X' * A = 0, WHERE "A" DENOTES A MATRIX AND "X" A VECTOR; ( THE SINGULAR VALUE DECOMPOSITION BEING GIVEN ). 34285 71 HOMSOL SOLVES THE HOMOGENEOUS SYSTEM OF LINEAR EQUATIONS OF EQUATIONS A * X = 0 AND X' * A = 0, WHERE "A" DENOTES A MATRIX AND "X" A VECTOR. 34286 73 PSDINVSVD CALCULATES THE PSEUDO-INVERSE OF A MATRIX; ( THE SINGULAR VALUE DECOMPOSITION BEING GIVEN ). 34287 73 PSDINV CALCULATES THE PSEUDO-INVERSE OF A MATRIX. 34291 303 DECSYM2 CALCULATES THE SYMMETRIC DECOMPOSITION OF A SYMMETRIC MATRIX. 34292 307 SOLSYM2 SOLVES A SYMMETRIC SYSTEM OF LINEAR EQUATIONS IF THE COEFFICIENT MATRIX HAS BEEN DECOMPOSED BY DECSYM2 OR 1CONTENTS OF KWICINDEX 31/12/79 PAGE 7 0 DECSOLSYM2. 34293 307 DECSOLSYM2 SOLVES A SYMMETRIC SYSTEM OF LINEAR EQUATIONS BY SYMMETRIC DECOMPOSITION. 34294 305 DETERMSYM2 CALCULATES THE DETERMINANT OF A SYMMETRIC MATRIX,THE SYMMETRIC DECOMPOSITION BEING GIVEN. 34300 45 DEC PERFORMS A TRIANGULAR DECOMPOSITION WITH PARTIAL PIVOTING. 34301 49 DECSOL SOLVES A SYSTEM OF LINEAR EQUATIONS WHOSE ORDER IS SMALL RELATIVE TO THE NUMBER OF BINARY DIGITS IN THE NUMBER REPRESENTATION. 34302 51 DECINV CALCULATES THE INVERSE OF A MATRIX WHOSE ORDER IS SMALL RELATIVE TO THE NUMBER OF BINARY DIGITS IN THE NUMBER REPRESENTATION. 34303 47 DETERM CALCULATES THE DETERMINANT OF A TRIANGULARLY DECOMPOSED MATRIX. 34310 55 CHLDEC2 CALCULATES THE CHOLESKY DECOMPOSITION OF A POSITIVE DEFINITE SYMMETRIC MATRIX WH0SE UPPER TRIANGLE IS GIVEN IN A TWO-DIMENSIONAL ARRAY. 34311 55 CHLDEC1 CALCULATES THE CHOLESKY DECOMPOSITION OF A POSITIVE DEFINITE SYMMETRIC MATRIX WHOSE UPPER TRIANGLE IS GIVEN COLUMNWISE IN A ONE-DIMENSIONAL ARRAY. 34312 57 CHLDETERM2 CALCULATES OF THE DETERMINANT OF A POSITIVE DEFINITE SYMMETRIC MATRIX, THE CHOLESKY DECOMPOSITION BEING GIVEN IN A TWO-DIMENSIONAL ARRAY. 34313 57 CHLDETERM1 CALCULATES THE DETERMINANT OF A POSITIVE DEFINITE SYMMETRIC MATRIX, THE CHOLESKY DECOMPOSITION BEING GIVEN COLUMNWISE IN A ONE-DIMENSIONAL ARRAY. 34320 75 DECBND PERFORMS A TRIANGULAR DECOMPOSITION OF A BAND MATRIX, USING PARTIAL PIVOTING. 34321 77 DETERMBND CALCULATES THE DETERMINANT OF A BAND MATRIX. 34322 79 DECSOLBND SOLVES A SYSTEM OF LINEAR EQUATIONS BY GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING IF THE COEFFICIENT MATRIX IS IN BAND FORM AND IS STORED ROWWISE IN A ONE-DIMENSIONAL ARRAY. 34330 85 CHLDECBND PERFORMS THE CHOLESKY DECOMPOSITION OF A POSITIVE DEFINITE SYMMETRIC BAND MATRIX. 34331 87 CHLDETERMBND CALCULATES THE DETERMINANT OF A POSITIVE DEFINITE SYMMETRIC BAND MATRIX. 34332 89 CHLSOLBND SOLVES A POSITIVE DEFINITE SYMMETRIC LINEAR SYSTEM, THE TRIANGULAR DECOMPOSITION BEING GIVEN. 34333 89 CHLDECSOLBND SOLVES A POSITIVE DEFINITE SYMMETRIC LINEAR SYSTEM AND PERFORMS THE TRIANGULAR DECOMPOSITION BY CHOLESKY'S METHOD. 34340 35 COMABS CALCULATES THE MODULUS OF A COMPLEX NUMBER. 34341 37 COMMUL CALCULATES THE PRODUCT OF TWO COMPLEX NUMBERS. 34342 37 COMDIV CALCULATES THE QUOTIENT OF TWO COMPLEX NUMBERS. 34343 35 COMSQRT CALCULATES THE SQUARE ROOT OF A COMPLEX NUMBER. 34344 35 CARPOL TRANSFORMS THE CARTESIAN COORDINATES OF A COMPLEX NUMBER INTO POLAR COORDINATES. 34345 129 COMKWD CALCULATES THE ROOTS OF A QUADRATIC EQUATION WITH COMPLEX COEFFICIENTS. 34352 21 COMCOLCST MULTIPLIES A COMPLEX COLUMN VECTOR BY A COMPLEX NUMBER. 34353 21 COMROWCST MULTIPLIES A COMPLEX ROW VECTOR BY A COMPLEX NUMBER. 34354 23 COMMATVEC CALCULATES THE SCALAR PRODUCT OF A COMPLEX ROW VECTOR AND A COMPLEX VECTOR. 34355 23 HSHCOMCOL TRANSFORMS A COMPLEX VECTOR INTO A VECTOR PROPORTIONAL TO A UNIT VECTOR. 34356 23 HSHCOMPRD PREMULTIPLIES A COMPLEX MATRIX WITH A COMPLEX HOUSEHOLDER MATRIX. 34357 287 ROTCOMCOL REPLACES TWO COMPLEX COLUMN VECTORS X AND Y BY TWO COMPLEX VECTORS CX + SY AND CY - SX. 34358 287 ROTCOMROW REPLACES TWO COMPLEX ROW VECTORS X AND Y BY TWO COMPLEX VECTORS CX + SY AND CY - SX. 34359 31 COMEUCNRM CALCULATES THE EUCLIDEAN NORM OF A COMPLEX MATRIX WITH LW LOWER CODIAGONALS. 34360 29 SCLCOM NORMALIZES THE COLUMNS OF A COMPLEX MATRIX. 34361 99 EQILBRCOM EQUILIBRATES A COMPLEX MATRIX. 34362 99 BAKLBRCOM TRANSFORMS THE EIGENVECTORS OF A COMPLEX EQUILIBRATED ( BY EQILBRCOM ) MATRIX INTO THE EIGENVECTORS OF THE ORIGINAL MATRIX. 34363 105 HSHHRMTRI TRANSFORMS A HERMITIAN MATRIX INTO A SIMILAR REAL SYMMETRIC TRIDIAGONAL MATRIX. 34364 105 HSHHRMTRIVAL DELIVERS THE MAIN DIAGONAL ELEMENTS AND THE SQUARES OF THE CODIAGONAL ELEMENTS OF A HERMITIAN TRIDIAGONAL MATRIX WHICH IS UNITARY SIMILAR WITH A GIVEN HERMITIAN MATRIX. 34365 105 BAKHRMTRI PERFORMS THE BACK TRANSFORMATION CORRESPONDING TO HSHHRMTRI. 34366 107 HSHCOMHES TRANSFORMS A COMPLEX MATRIX BY MEANS OF HOUSEHOLDER'S TRANSFORMATION FOLLOWED BY A COMPLEX DIAGONAL TRANSFORMATION INTO A SIMILAR UNITARY UPPER-HESSENBERG MATRIX WITH A REAL NONNEGATIVE SUBDIAGONAL. 34367 107 BAKCOMHES PERFORMS THE BACK TRANSFORMATION CORRESPONDING TO HSHCOMHES. 34368 119 EIGVALHRM CALCULATES THE EIGENVALUES OF A COMPLEX HERMITIAN MATRIX. 34369 119 EIGHRM CALCULATES THE EIGENVALUES AND EIGENVECTORS OF A COMPLEX HERMITIAN MATRIX. 34370 119 QRIVALHRM CALCULATES THE EIGENVALUES OF A COMPLEX HERMITIAN MATRIX. 34371 119 QRIHRM CALCULATES THE EIGENVALUES AND EIGENVECTORS OF A COMPLEX HERMITIAN MATRIX. 34372 121 VALQRICOM CALCULATES THE EIGENVALUES OF A COMPLEX UPPER-HESSENBERG MATRIX WITH A REAL SUBDIAGONAL. 1CONTENTS OF KWICINDEX 31/12/79 PAGE 8 0 34373 121 QRICOM CALCULATES THE EIGENVECTORS AND THE EIGENVALUES OF A COMPLEX UPPER-HESSENBERG MATRIX. 34374 123 EIGVALCOM CALCULATES THE EIGENVALUES OF A COMPLEX MATRIX. 34375 123 EIGCOM CALCULATES THE EIGENVECTORS AND EIGENVALUES OF A COMPLEX MATRIX. 34376 25 ELMCOMVECCOL ADDS A COMPLEX NUMBER TIMES A COMPLEX COLUMN VECTOR TO A COMPLEX VECTOR. 34377 25 ELMCOMCOL ADDS A COMPLEX NUMBER TIMES A COMPLEX COLUMN VECTOR TO A COMPLEX COLUMN VECTOR. 34378 25 ELMCOMROWVEC ADDS A COMPLEX NUMBER TIMES A COMPLEX VECTOR TO A COMPLEX ROW VECTOR. 34390 59 CHLSOL2 SOLVES A SYSTEM OF LINEAR EQUATIONS IF THE COEFFICIENT MATRIX HAS BEEN DECOMPOSED BY CHLDEC2 OR CHLDECSOL2. 34391 59 CHLSOL1 SOLVES A SYSTEM OF LINEAR EQUATIONS IF THE COEFFICIENT MATRIX HAS BEEN DECOMPOSED BY CHLDEC1 OR CHLDECSOL1. 34392 59 CHLDECSOL2 SOLVES A POSITIVE DEFINITE SYMMETRIC SYSTEM OF LINEAR EQUATIONS BY CHOLESKY'S SQUARE ROOT METHOD; THE COEFFICIENT MATRIX SHOULD BE GIVEN IN THE UPPERTRIANGLE OF A TWO-DIMENSIONAL ARRAY. 34393 59 CHLDECSOL1 SOLVES A POSITIVE DEFINITE SYMMETRIC SYSTEM OF LINEAR EQUATIONS BY CHOLESKY'S SQUARE ROOT METHOD; THE COEFFICIENT MATRIX SHOULD BE GIVEN COLUMNWISE IN A ONE-DIMENSIONAL ARRAY. 34400 61 CHLINV2 CALCULATES THE INVERSE OF A POSITIVE DEFINITE SYMMETRIC MATRIX, IF THE MATRIX HAS BEEN DECOMPOSED BY CHLDEC2 OR CHLDECSOL2. 34401 61 CHLINV1 CALCULATES THE INVERSE OF A POSITIVE DEFINITE SYMMETRIC MATRIX, IF THE MATRIX HAS BEEN DECOMPOSED BY CHLDEC1 OR CHLDECSOL1. 34402 61 CHLDECINV2 CALCULATES THE INVERSE OF A POSITIVE DEFINITE SYMMETRIC MATRIX BY CHOLESKY'S SQUARE ROOT METHOD; THE COEFFICIENT MATRIX GIVEN COLUMNWISE IN A TWO-DIMENSIONAL ARRAY. 34403 61 CHLDECINV1 CALCULATES THE INVERSE OF A POSITIVE DEFINITE SYMMETRIC MATRIX BY CHOLESKY'S SQUARE ROOT METHOD; THE COEFFICIENT MATRIX GIVEN COLUMNWISE IN A ONE-DIMENSIONAL ARRAY. 34410 285 LNGVECVEC CALCULATES THE SCALAR PRODUCT OF TWO VECTORS BY DOUBLE LENTGH ARITHMETIC. 34411 285 LNGMATVEC CALCULATES THE SCALAR PRODUCT OF A VECTOR AND A ROW VECTOR BY DOUBLE PRECISION ARITHMETIC. 34412 285 LNGTAMVEC CALCULATES THE SCALAR PRODUCT OF A VECTOR AND A COLUMN VECTOR BY DOUBLE PRECISION ARITHMETIC. 34413 285 LNGMATMAT CALCULATES THE SCALAR PRODUCT OF A ROW OF A VECTOR AND A COLUMN VECTOR BY DOUBLE PRECISION ARITHMETIC. 34414 285 LNGTAMMAT CALCULATES THE SCALAR PRODUCT OF TWO COLUMN VECTORS BY DOUBLE PRECISION ARITHMETIC. 34415 285 LNGMATTAM CALCULATES THE SCALAR PRODUCT OF TWO ROW VECTORS BY DOUBLE PRECISION ARITHMETIC. 34416 285 LNGSEQVEC CALCULATES THE SCALAR PRODUCT OF TWO VECTORS GIVEN IN ONE-DIMENSIONAL ARRAYS, WHERE THE MUTUAL SPACINGS BETWEEN THE INDICES OF THE 1ST VECTOR CHANGE LINEARLY, BY DOUBLE LENGTH ARITHMETIC. 34417 285 LNGSCAPRD1 CALCULATES THE SCALAR PRODUCT OF TWO VECTORS GIVEN IN ONE-DIMENSIONAL ARRAYS, WHERE THE SPACINGS OF BOTH VECTORS ARE CONSTANT, BY DOUBLE PRECISION ARITHMETIC. 34418 285 LNGSYMMATVEC CALCULATES THE SCALAR PRODUCT OF A VECTOR GIVEN IN A ONE-DIMENSIONAL ARRAY AND A ROW OF A SYMMETRIC MATRIX, WHOSE UPPER TRIANGLE IS STORED COLUMNWISE IN A ONE-DIMENSIONAL ARRAY, BY DOUBLE PRECISION ARITHMETIC. 34420 91 DECSYMTRI PERFORMS THE TRIANGULAR DECOMPOSITION OF A SYMMETRIC TRIDIAGONAL MATRIX. 34421 93 SOLSYMTRI SOLVES A SYMMETRIC TRIDIAGONAL SYSTEM OF LINEAR EQUATIONS, THE TRIANGULAR DECOMPOSITION BEING GIVEN. 34422 93 DECSOLSYMTRI SOLVES A SYMMETRIC TRIDIAGONAL SYSTEM OF LINEAR EQUATIONS AND PERFORMS THE TRIDIAGONAL DECOMPOSITION. 34423 81 DECTRI PERFORMS A TRIANGULAR DECOMPOSITION OF A TRIDIAGONAL MATRIX. 34424 83 SOLTRI SOLVES A TRIDIAGONAL SYSTEM OF LINEAR EQUATIONS THE TRIANGULAR DECOMPOSITION BEING GIVEN. 34425 83 DECSOLTRI SOLVES A TRIDIAGONAL SYSTEM OF LINEAR EQUATIONS AND PERFORMS THE TRIANGULAR DECOMPOSITION WITHOUT PIVOTING. 34426 81 DECTRIPIV PERFORMS A TRIANGULAR DECOMPOSITION OF A TRIDIAGONAL MATRIX, USING PARTIAL PIVOTING. 34427 83 SOLTRIPIV SOLVES A TRIDIAGONAL SYSTEM OF LINEAR EQUATIONS THE TRIANGULAR DECOMPOSITION BEING GIVEN. 34428 83 DECSOLTRIPIV SOLVES A TRIDIAGONAL SYSTEM OF LINEAR EQUATIONS AND PERFORMS THE TRIANGULAR DECOMPOSITION WITH PARTIAL PIVOTING. 34430 217 QUANEWBND SOLVES A SYSTEM OF NON-LINEAR EQUATIONS OF WHICH THE JACOBIAN ( BEING A BAND MATRIX ) IS GIVEN. 34431 217 QUANEWBND1 SOLVES A SYSTEM OF NON-LINEAR EQUATIONS OF WHICH THE JACOBIAN IS A BAND MATRIX. 34432 239 PRAXIS MINIMIZES A FUNCTION OF SEVERAL VARIABLES. 34433 235 MININ MINIMIZES A FUNCTION OF ONE VARIABLE IN A GIVEN INTERVAL. 34435 237 MININDER MINIMIZES A FUNCTION OF ONE VARIABLE IN A GIVEN INTERVAL, USING VALUES OF THE FUNCTION AND OF ITS DERIVATIVE. 34436 215 ZEROINRAT FINDS ( IN A GIVEN INTERVAL ) A ZERO OF A FUNCTION OF ONE VARIABLE. 34437 213 JACOBNNF CALCULATES THE JACOBIAN MATRIX OF AN N-DIMENSIONAL FUNCTION OF N VARIABLES USING FORWARD DIFFERENCES. 34438 213 JACOBNMF CALCULATES THE JACOBIAN MATRIX OF AN N-DIMENSIONAL FUNCTION OF M VARIABLES USING FORWARD DIFFERENCES. 34439 213 JACOBNBNDF CALCULATES THE JACOBIAN MATRIX OF AN N-DIMENSIONAL FUNCTION OF N VARIABLES, IF THE JACOBIAN IS KNOWN TO BE A BAND MATRIX. 34440 219 MARQUARDT CALCULATES THE LEAST SQUARES SOLUTION OF AN OVERDETERMINED SYSTEM OF NON-LINEAR EQUATIONS WITH MARQUARDT'S METHOD. 34441 219 GSSNEWTON CALCULATES THE LEAST SQUARES SOLUTION OF AN OVERDETERMINED SYSTEM OF NON-LINEAR EQUATIONS WITH THE GAUSS-NEWTON METHOD. 1CONTENTS OF KWICINDEX 31/12/79 PAGE 9 0 34444 259 PEIDE ESTIMATES UNKNOWN PARAMETERS IN A SYSTEM OF 1ST ORDER DIFFERENTIAL EQUATIONS; THE UNKNOWN VARIABLES MAY APPEAR NON-LINEARLY BOTH IN THE DIFFERENTIAL EQUATIONS AND ITS INITIAL VALUES; A SET OF OBSERVED VALUES OF SOME COMPONENTS OF THE SOLUTION OF THE DIFFERENTIAL EQUATIONS MUST BE GIVEN. 34453 233 ZEROINDER FINDS ( IN A GIVEN INTERVAL ) A ZERO OF A FUNCTION OF ONE VARIABLE USING VALUES OF THE FUNCTION AND OF ITS DERIVATIVE. 34500 209 POLZEROS CALCULATES ALL ZEROS OF A POLYNOMIAL WITH REAL COEFFICIENTS. 34501 311 ZERPOL CALCULATES ALL ROOTS (ZEROS) OF A POLYNOMIAL WITH REAL COEFFICIENTS BY LAGUERRE'S METHOD. 34502 311 BOUNDS CALCULATES THE ERROR IN APPROXIMATED ZEROS OF A POLYNOMIAL WITH REAL COEFFICIENTS. 34600 267 QZIVAL COMPUTES GENERALIZED EIGENVALUES BY MEANS OF QZ-ITERATION. 34601 267 QZI COMPUTES GENERALIZED EIGENVALUES AND EIGENVECTORS BY MEANS OF QZ-ITERATION. 34602 267 HSHDECMUL IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF GENERALIZED EIGENVALUES. 34603 267 HESTGL3 IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF GENERALIZED EIGENVALUES. 34604 267 HESTGL2 IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF GENERALIZED EIGENVALUES. 34605 267 HSH2COL IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF GENERALIZED EIGENVALUES. 34606 267 HSH3COL IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF GENERALIZED EIGENVALUES. 34607 267 HSH2ROW3 IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF GENERALIZED EIGENVALUES. 34608 267 HSH2ROW2 IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF GENERALIZED EIGENVALUES. 34609 267 HSH3ROW3 IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF GENERALIZED EIGENVALUES. 34610 267 HSH3ROW2 IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF GENERALIZED EIGENVALUES. 34611 287 CHSH2 FINDS A COMPLEX ROTATION MATRIX. 35021 227 ERRORFUNCTION COMPUTES THE ERROR FUNCTION ( ERF ) AND COMPLEMENTARY ERROR FUNCTION ( ERFC ) FOR A REAL ARGUMENT. 35022 227 NONEXPERFC COMPUTES ERFC(X) * EXP(X*X). 35023 227 INVERSE ERROR FUNCTION CALCULATES THE INVERSE ERROR FUNCTION Y = INVERF(X). 35027 227 FRESNEL CALCULATES THE FRESNEL INTEGRALS C(X) AND S(X). 35028 227 FG IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF FRESNEL INTEGRALS. 35030 187 INCOMGAM COMPUTES THE INCOMPLETE GAMMA FUNCTIONS. 35050 187 INCBETA COMPUTES THE INCOMPLETE BETA-FUNCTION I(X,P,Q); 0 <= X <= 1, P > 0, Q > 0. 35051 187 IBPPLUSN COMPUTES INCOMPLETE BETA-FUNCTION RATIOS I(X,P+N,Q) FOR N = 0 (1) NMAX, 0 <= X <= 1, P > 0, Q > 0. 35052 187 IBQPLUSN COMPUTES INCOMPLETE BETA-FUNCTION RATIOS I(X,P,Q+N) FOR N = 0 (1) NMAX, 0 <= X <= 1, P > 0, Q > 0. 35053 187 IXQFIX IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF INCOMPLETE BESSELFUNCTIONS. 35054 187 IXPFIX IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF INCOMPLETE BESSELFUNCTIONS. 35055 187 FORWARD IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF INCOMPLETE BESSELFUNCTIONS. 35056 187 BACKWARD IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF INCOMPLETE BESSELFUNCTIONS. 35060 187 RECIP GAMMA CALCULATES THE RECIPROCAL OF THE GAMMA FUNCTION FOR ARGUMENTS IN THE RANGE [.5,1.5]; MOREOVER ODD AND EVEN PARTS ARE DELIVERED. 35061 187 GAMMA CALCULATES THE GAMMA FUNCTION. 35062 187 LOG GAMMA CALCULATES THE NATURAL LOGARITHM OF THE GAMMA FUNCTION FOR POSITIVE ARGUMENTS. 35080 183 EI CALCULATES THE EXPONENTIAL INTEGRAL . 35081 183 EI ALPHA CALCULATES A SEQUENCE OF INTEGRALS OF THE FORM INTEGRAL (EXP(-X*T)*T**N DT), FROM T=1 TO T=INFINITY. 35083 41 JFRAC CALCULATES A TERMINATING CONTINUED FRACTION. 35084 185 SINCOSINT CALCULATES THE SINE INTEGRAL SI(X) AND THE COSINE INTEGRAL CI(X). 35085 185 SINCOSFG IS AN AUXILIARY PROCEDURE FOR THE SINE AND COSINE INTEGRALS. 35086 183 ENX COMPUTES A SEQUENCE OF EXPONENTIAL INTEGRALS E(N,X) = THE INTEGRAL FROM 1 TO INFINITY OF EXP(-X * T) T**N DT. 35087 183 NONEXP ENX COMPUTES A SEQUENCE OF INTEGRALS EXP(X) * E(N,X). 35111 181 SINH COMPUTES THE HYPERBOLIC SINE FOR A REAL ARGUMENT X. 35112 181 COSH COMPUTES THE HYPERBOLIC COSINE FOR A REAL ARGUMENT X. 35113 181 TANH COMPUTES THE HYPERBOLIC TANGENT FOR A REAL ARGUMENT X. 35114 181 ARCSINH COMPUTES THE INVERSE HYPERBOLIC SINE FOR A REAL ARGUMENT X. 35115 181 ARCCOSH COMPUTES THE INVERSE HYPERBOLIC COSINE FOR A REAL ARGUMENT X. 35116 181 ARCTANH COMPUTES THE INVERSE HYPERBOLIC TANGENT FOR A REAL ARGUMENT X. 35120 179 TAN COMPUTES THE TANGENT FOR A REAL ARGUMENT X. 35121 179 ARCSIN COMPUTES THE ARCSINE FOR A REAL ARGUMENT X. 35122 179 ARCCOS COMPUTES THE ARCCOSINE FOR A REAL ARGUMENT X. 35130 315 LOGONEPLUSX EVALUATES THE LOGARITHMIC FUNCTION LN(1+X). 35140 243 AIRY EVALUATES THE AIRY FUNCTIONS AI(Z) AND BI(Z) AND THEIR DERIVATIVES. 1CONTENTS OF KWICINDEX 31/12/79 PAGE 10 0 35145 243 AIRYZEROS COMPUTES THE ZEROS AND ASSOCIATED VALUES OF THE AIRY FUNCTIONS AI(Z) AND BI(Z) AND THEIR DERIVATIVES. 35150 247 SPHER BESS J CALCULATES THE SPHERICAL BESSEL FUNCTIONS OF THE 1ST KIND: J[K+.5](X)*SQRT(PI (2*X)), K=0,...,N , WHERE J[K+.5](X) DENOTES THE BESSEL FUNCTION OF THE 1ST KIND OF ORDER K+.5. 35151 247 SPHER BESS Y CALCULATES THE SPHERICAL BESSEL FUNCTIONS OF THE 3RD KIND: Y[K+.5](X)*SQRT(PI (2*X)), K=0,...,N , WHERE Y[K+.5](X) DENOTES THE BESSEL FUNCTION OF THE 3RD KIND OF ORDER K+.5. 35152 247 SPHER BESS I CALCULATES THE MODIFIED SPHERICAL BESSEL FUNCTIONS OF THE 1ST KIND: I[K+.5](X)*SQRT(PI (2*X)), K=0,...,N , WHERE I[K+.5](X) DENOTES THE MODIFIED BESSEL FUNCTION OF THE 1ST KIND OF ORDER K+.5. 35153 247 SPHER BESS K CALCULATES THE MODIFIED SPHERICAL BESSEL FUNCTIONS OF THE 3RD KIND: K[I+.5](X)*SQRT(PI (2*X)), I=0,...,N , WHERE K[I+.5](X) DENOTES THE MODIFIED BESSEL FUNCTION OF THE 3RD KIND OF ORDER I+.5. 35154 247 NONEXP SPHER BESS I CALCULATES THE MODIFIED SPHERICAL BESSEL FUNCTIONS OF THE 1ST KIND MULTIPIED BY EXP(-X): I[K+.5](X)*SQRT(PI (2*X))*EXP(-X), K=0,...,N , WHERE I[K+.5](X) DENOTES THE MODIFIED BESSEL FUNCTION OF THE 1ST KIND OF ORDER K+.5. 35155 247 NONEXP SPHER BESS K CALCULATES THE MODIFIED SPHERICAL BESSEL FUNCTIONS OF THE 3RD KIND MULTIPLIED BY EXP(+X): K[I+.5](X)*SQRT(PI (2*X))*EXP(+X) , I=0,...,N , WHERE K[I+.5](X) DENOTES THE MODIFIED BESSEL OF THE 3RD KIND OF ORDER I+.5. 35160 253 BESS J0 CALCULATES THE ORDINARY BESSEL FUNCTION OF THE 1ST KIND OF ORDER ZERO. 35161 253 BESS J1 CALCULATES THE ORDINARY BESSEL FUNCTION OF THE 1ST KIND OF ORDER ONE. 35162 253 BESS J CALCULATES THE ORDINARY BESSEL FUNCTIONS OF THE 1ST KIND OF ORDER L ( L = 0,...,N ). 35163 253 BESS Y01 CALCULATES THE ORDINARY BESSEL FUNCTIONS OF THE 2ND KIND ORDER ZERO AND ONE WITH ARGUMENT X; X > 0. 35164 253 BESS Y CALCULATES THE ORDINARY BESSEL FUNCTIONS OF THE 2ND KIND OF ORDER L ( L = 0,...,N ) WITH ARGUMENT X, X> 0. 35165 253 BESS PQ0 IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF THE ORDINARY BESSEL FUNCTIONS OF ORDER ZERO FOR LARGE VALUES OF THEIR ARGUMENT. 35166 253 BESS PQ1 IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF THE ORDINARY BESSEL FUNCTIONS OF ORDER ONE FOR LARGE VALUES OF THEIR ARGUMENT. 35170 255 BESS I0 CALCULATES THE MODIFIED BESSEL FUNCTION OF THE 1ST KIND OF ORDER ZERO. 35171 255 BESS I1 CALCULATES THE MODIFIED BESSEL FUNCTION OF THE 1ST KIND OF ORDER ONE. 35172 255 BESS I CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 1ST KIND OF ORDER L ( L = 0,...,N ). 35173 255 BESS K01 CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 3RD KIND OF ORDERS ZERO AND ONE WITH ARGUMENT X, X > 0. 35174 255 BESS K CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 3RD KIND OF ORDER L ( L = 0,...,N ) WITH ARGUMENT X, X > 0. 35175 255 NONEXP BESS I0 CALCULATES THE MODIFIED BESSEL FUNCTION OF THE 1ST KIND OF ORDER ZERO; THE RESULT IS MULTIPLIED BY EXP(-ABS(X)). 35176 255 NONEXP BESS I1 CALCULATES THE MODIFIED BESSEL FUNCTION OF THE 1ST KIND OF ORDER ONE; THE RESULT IS MULTIPLIED BY EXP(-ABS(X)) 35177 255 NONEXP BESS I CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 1ST KIND OF ORDER L ( L = 0,...,N ); THE RESULT IS MULTIPLIED BY EXP(-ABS(X)). 35178 255 NONEXP BESS K01 CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 3RD KIND OF ORDER ZERO AND ONE WITH ARGUMENT X, X>0; THE RESULT IS MULTIPLIED BY EXP(X). 35179 255 NONEXP BESS K CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 3RD KIND OF ORDER L ( L = 0,...,N ) WITH ARGUMENT X, X>0; THE RESULT IS MULTIPLIED BY EXP(X). 35180 249 BESS JAPLUSN CALCULATES THE BESSEL FUNCTIONS OF THE 1ST KIND OF ORDER A+K ( 0<=K<=N, 0<=A<1 ). 35181 249 BESS YA01 CALCULATES THE BESSEL FUNCTIONS OF THE 2ND KIND ( ALSO CALLED NEUMANN'S FUNCTIONS ) OF ORDER A AND A+1 ( A>=0 ) AND ARGUMENT X>0. 35182 249 BESS YAPLUSN CALCULATES THE BESSEL FUNCTIONS OF THE 2ND KIND OF ORDER A+N, N=0,...,NMAX , A>=0, AND ARGUMENT X>0. 35183 249 BESS PQA01 IS AN AUXILIARY PROCEDURE FOR THE COMPUTATION OF THE BESSEL FUNCTIONS FOR LARGE VALUES OF THEIR ARGUMENT. 35184 249 BESSZEROS CALCULATES ZEROS OF A BESSELFUNCTION (OF 1ST OR 2ND KIND) AND OF ITS DERIVATIVE. 35185 249 START IS AN AUXILIARY PROCEDURE IN BESSELFUNCTION PROCEDURES. 35190 251 BESS IAPLUSN CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 1ST KIND OF ORDER A+N, N=0,...,NMAX , A>=0 AND ARGUMENT X>=0. 35191 251 BESS KA01 CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 3RD KIND OF ORDER A AND A+1, A>=0, AND ARGUMENT X, X>0. 35192 251 BESS KAPLUSN CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 3RD KIND OF ORDER A+N, N=0,...,NMAX , A>=0, AND ARGUMENT X>0. 35193 251 NONEXP BESS IAPLUSN CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 1ST KIND OF ORDER A+N, N=0,...,NMAX , A>=0 AND ARGUMENT X>=0, MULTIPLIED BY EXP(-X). 35194 251 NONEXP BESS KA01 CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 3RD KIND OF ORDER A AND A+1, A>=0 AND ARGUMENT X, X>0, MULTIPLIED BY THE FACTOR EXP(X). 35195 251 NONEXP BESS KAPLUSN CALCULATES THE MODIFIED BESSEL FUNCTIONS OF THE 3RD KIND OF ORDER A+N, N=0,...,NMAX , A>=0 AND 1CONTENTS OF KWICINDEX 31/12/79 PAGE 11 0 ARGUMENT X>0 MULTIPLIED BY THE FACTOR EXP(X). 36010 195 NEWTON CALCULATES THE COEFFICIENTS OF THE NEWTON POLYNOMIAL THROUGH GIVEN INTERPOLATION POINTS AND CORRESPONDING FUNCTION VALUES. 36020 197 INI SELECTS A (SUB)SET OF INTEGERS OUT OF A GIVEN SET OF INTEGERS; IT IS AN AUXILIARY PROCEDURE FOR MINMAXPOL. 36021 197 SNDREMEZ EXCHANGES AT MOST N+1 NUMBERS WITH NUMBERS OUT OF A REFERENCE SET; IT IS AN AUXILIARY PROCEDURE FOR MINMAXPOL. 36022 197 MINMAXPOL CALCULATES THE COEFFICIENTS OF THE POLYNOMIAL THAT APPROXIMATES A FUNCTION, GIVEN FOR DISCRETE ARGUMENTS, SUCH THAT THE INFINITY NORM OF THE ERROR VECTOR IS MINIMISED. 36401 301 SYMEIGINP IMPROVES AN APPROXIMATION OF A REAL SYMMETRIC EIGENSYSTEM AND CALCULATES ERROR BOUNDS FOR THE EIGENVALUES. 36402 299 ORTHOG OTHOGONALIZES SOME ADJACENT MATRIX COLUMNS ACCORDING TO THE MODIFIED GRAM-SMIDT METHOD. 36403 297 ROWPERM PERMUTES THE ELEMENTS OF A GIVEN ROW OF A MATRIX ACCORDING TO A GIVEN PERMUTATION OF INDICES. 36404 297 VECPERM PERMUTES THE ELEMENTS OF A GIVEN VECTOR ACCORDING TO A GIVEN PERMUTATION OF INDICES. 36405 297 MERGESORT DELIVERS A PERMUTATION OF INDICES CORRESPONDING TO SORTING THE ELEMENTS OF A GIVEN VECTOR INTO NON-DECREASING ORDER.