SLATEC Common Mathematical Library -- Table of Contents
SECTION II. Subsidiary Routines
Section II contains the names and purposes of all subsidiary CML routines,
arranged in alphabetical order. Usually these routines are not referenced
directly by library users. They are listed here so that users will be able
to avoid duplicating names that are used by the CML and for the benefit of
programmers who may be able to use them in the construction of new routines
for the library.
ASYIK Subsidiary to BESI and BESK
ASYJY Subsidiary to BESJ and BESY
BCRH Subsidiary to CBLKTR
BDIFF Subsidiary to BSKIN
BESKNU Subsidiary to BESK
BESYNU Subsidiary to BESY
BKIAS Subsidiary to BSKIN
BKISR Subsidiary to BSKIN
BKSOL Subsidiary to BVSUP
BLKTR1 Subsidiary to BLKTRI
BNFAC Subsidiary to BINT4 and BINTK
BNSLV Subsidiary to BINT4 and BINTK
BSGQ8 Subsidiary to BFQAD
BSPLVD Subsidiary to FC
BSPLVN Subsidiary to FC
BSRH Subsidiary to BLKTRI
BVDER Subsidiary to BVSUP
BVPOR Subsidiary to BVSUP
C1MERG Merge two strings of complex numbers. Each string is
ascending by the real part.
C9LGMC Compute the log gamma correction factor so that
LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z
+ C9LGMC(Z).
C9LN2R Evaluate LOG(1+Z) from second order relative accuracy so
that LOG(1+Z) = Z - Z**2/2 + Z**3*C9LN2R(Z).
CACAI Subsidiary to CAIRY
CACON Subsidiary to CBESH and CBESK
CASYI Subsidiary to CBESI and CBESK
CBINU Subsidiary to CAIRY, CBESH, CBESI, CBESJ, CBESK and CBIRY
CBKNU Subsidiary to CAIRY, CBESH, CBESI and CBESK
CBLKT1 Subsidiary to CBLKTR
CBUNI Subsidiary to CBESI and CBESK
CBUNK Subsidiary to CBESH and CBESK
CCMPB Subsidiary to CBLKTR
CDCOR Subroutine CDCOR computes corrections to the Y array.
CDCST CDCST sets coefficients used by the core integrator CDSTP.
CDIV Compute the complex quotient of two complex numbers.
CDNTL Subroutine CDNTL is called to set parameters on the first
call to CDSTP, on an internal restart, or when the user has
altered MINT, MITER, and/or H.
CDNTP Subroutine CDNTP interpolates the K-th derivative of Y at
TOUT, using the data in the YH array. If K has a value
greater than NQ, the NQ-th derivative is calculated.
CDPSC Subroutine CDPSC computes the predicted YH values by
effectively multiplying the YH array by the Pascal triangle
matrix when KSGN is +1, and performs the inverse function
when KSGN is -1.
CDPST Subroutine CDPST evaluates the Jacobian matrix of the right
hand side of the differential equations.
CDSCL Subroutine CDSCL rescales the YH array whenever the step
size is changed.
CDSTP CDSTP performs one step of the integration of an initial
value problem for a system of ordinary differential
equations.
CDZRO CDZRO searches for a zero of a function F(N, T, Y, IROOT)
between the given values B and C until the width of the
interval (B, C) has collapsed to within a tolerance
specified by the stopping criterion,
ABS(B - C) .LE. 2.*(RW*ABS(B) + AE).
CFFTB Compute the unnormalized inverse of CFFTF.
CFFTF Compute the forward transform of a complex, periodic
sequence.
CFFTI Initialize a work array for CFFTF and CFFTB.
CFOD Subsidiary to DEBDF
CHFCM Check a single cubic for monotonicity.
CHFIE Evaluates integral of a single cubic for PCHIA
CHKPR4 Subsidiary to SEPX4
CHKPRM Subsidiary to SEPELI
CHKSN4 Subsidiary to SEPX4
CHKSNG Subsidiary to SEPELI
CKSCL Subsidiary to CBKNU, CUNK1 and CUNK2
CMLRI Subsidiary to CBESI and CBESK
CMPCSG Subsidiary to CMGNBN
CMPOSD Subsidiary to CMGNBN
CMPOSN Subsidiary to CMGNBN
CMPOSP Subsidiary to CMGNBN
CMPTR3 Subsidiary to CMGNBN
CMPTRX Subsidiary to CMGNBN
COMPB Subsidiary to BLKTRI
COSGEN Subsidiary to GENBUN
COSQB1 Compute the unnormalized inverse of COSQF1.
COSQF1 Compute the forward cosine transform with odd wave numbers.
CPADD Subsidiary to CBLKTR
CPEVL Subsidiary to CPZERO
CPEVLR Subsidiary to CPZERO
CPROC Subsidiary to CBLKTR
CPROCP Subsidiary to CBLKTR
CPROD Subsidiary to BLKTRI
CPRODP Subsidiary to BLKTRI
CRATI Subsidiary to CBESH, CBESI and CBESK
CS1S2 Subsidiary to CAIRY and CBESK
CSCALE Subsidiary to BVSUP
CSERI Subsidiary to CBESI and CBESK
CSHCH Subsidiary to CBESH and CBESK
CSROOT Compute the complex square root of a complex number.
CUCHK Subsidiary to SERI, CUOIK, CUNK1, CUNK2, CUNI1, CUNI2 and
CKSCL
CUNHJ Subsidiary to CBESI and CBESK
CUNI1 Subsidiary to CBESI and CBESK
CUNI2 Subsidiary to CBESI and CBESK
CUNIK Subsidiary to CBESI and CBESK
CUNK1 Subsidiary to CBESK
CUNK2 Subsidiary to CBESK
CUOIK Subsidiary to CBESH, CBESI and CBESK
CWRSK Subsidiary to CBESI and CBESK
D1MERG Merge two strings of ascending double precision numbers.
D1MPYQ Subsidiary to DNSQ and DNSQE
D1UPDT Subsidiary to DNSQ and DNSQE
D9AIMP Evaluate the Airy modulus and phase.
D9ATN1 Evaluate DATAN(X) from first order relative accuracy so
that DATAN(X) = X + X**3*D9ATN1(X).
D9B0MP Evaluate the modulus and phase for the J0 and Y0 Bessel
functions.
D9B1MP Evaluate the modulus and phase for the J1 and Y1 Bessel
functions.
D9CHU Evaluate for large Z Z**A * U(A,B,Z) where U is the
logarithmic confluent hypergeometric function.
D9GMIC Compute the complementary incomplete Gamma function for A
near a negative integer and X small.
D9GMIT Compute Tricomi's incomplete Gamma function for small
arguments.
D9KNUS Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*
K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.
D9LGIC Compute the log complementary incomplete Gamma function
for large X and for A .LE. X.
D9LGIT Compute the logarithm of Tricomi's incomplete Gamma
function with Perron's continued fraction for large X and
A .GE. X.
D9LGMC Compute the log Gamma correction factor so that
LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X
+ D9LGMC(X).
D9LN2R Evaluate LOG(1+X) from second order relative accuracy so
that LOG(1+X) = X - X**2/2 + X**3*D9LN2R(X)
DASYIK Subsidiary to DBESI and DBESK
DASYJY Subsidiary to DBESJ and DBESY
DBDIFF Subsidiary to DBSKIN
DBKIAS Subsidiary to DBSKIN
DBKISR Subsidiary to DBSKIN
DBKSOL Subsidiary to DBVSUP
DBNFAC Subsidiary to DBINT4 and DBINTK
DBNSLV Subsidiary to DBINT4 and DBINTK
DBOLSM Subsidiary to DBOCLS and DBOLS
DBSGQ8 Subsidiary to DBFQAD
DBSKNU Subsidiary to DBESK
DBSYNU Subsidiary to DBESY
DBVDER Subsidiary to DBVSUP
DBVPOR Subsidiary to DBVSUP
DCFOD Subsidiary to DDEBDF
DCHFCM Check a single cubic for monotonicity.
DCHFIE Evaluates integral of a single cubic for DPCHIA
DCHKW SLAP WORK/IWORK Array Bounds Checker.
This routine checks the work array lengths and interfaces
to the SLATEC error handler if a problem is found.
DCOEF Subsidiary to DBVSUP
DCSCAL Subsidiary to DBVSUP and DSUDS
DDAINI Initialization routine for DDASSL.
DDAJAC Compute the iteration matrix for DDASSL and form the
LU-decomposition.
DDANRM Compute vector norm for DDASSL.
DDASLV Linear system solver for DDASSL.
DDASTP Perform one step of the DDASSL integration.
DDATRP Interpolation routine for DDASSL.
DDAWTS Set error weight vector for DDASSL.
DDCOR Subroutine DDCOR computes corrections to the Y array.
DDCST DDCST sets coefficients used by the core integrator DDSTP.
DDES Subsidiary to DDEABM
DDNTL Subroutine DDNTL is called to set parameters on the first
call to DDSTP, on an internal restart, or when the user has
altered MINT, MITER, and/or H.
DDNTP Subroutine DDNTP interpolates the K-th derivative of Y at
TOUT, using the data in the YH array. If K has a value
greater than NQ, the NQ-th derivative is calculated.
DDOGLG Subsidiary to DNSQ and DNSQE
DDPSC Subroutine DDPSC computes the predicted YH values by
effectively multiplying the YH array by the Pascal triangle
matrix when KSGN is +1, and performs the inverse function
when KSGN is -1.
DDPST Subroutine DDPST evaluates the Jacobian matrix of the right
hand side of the differential equations.
DDSCL Subroutine DDSCL rescales the YH array whenever the step
size is changed.
DDSTP DDSTP performs one step of the integration of an initial
value problem for a system of ordinary differential
equations.
DDZRO DDZRO searches for a zero of a function F(N, T, Y, IROOT)
between the given values B and C until the width of the
interval (B, C) has collapsed to within a tolerance
specified by the stopping criterion,
ABS(B - C) .LE. 2.*(RW*ABS(B) + AE).
DEFCMN Subsidiary to DEFC
DEFE4 Subsidiary to SEPX4
DEFEHL Subsidiary to DERKF
DEFER Subsidiary to SEPELI
DENORM Subsidiary to DNSQ and DNSQE
DERKFS Subsidiary to DERKF
DES Subsidiary to DEABM
DEXBVP Subsidiary to DBVSUP
DFCMN Subsidiary to FC
DFDJC1 Subsidiary to DNSQ and DNSQE
DFDJC3 Subsidiary to DNLS1 and DNLS1E
DFEHL Subsidiary to DDERKF
DFSPVD Subsidiary to DFC
DFSPVN Subsidiary to DFC
DFULMT Subsidiary to DSPLP
DGAMLN Compute the logarithm of the Gamma function
DGAMRN Subsidiary to DBSKIN
DH12 Subsidiary to DHFTI, DLSEI and DWNNLS
DHELS Internal routine for DGMRES.
DHEQR Internal routine for DGMRES.
DHKSEQ Subsidiary to DBSKIN
DHSTRT Subsidiary to DDEABM, DDEBDF and DDERKF
DHVNRM Subsidiary to DDEABM, DDEBDF and DDERKF
DINTYD Subsidiary to DDEBDF
DJAIRY Subsidiary to DBESJ and DBESY
DLPDP Subsidiary to DLSEI
DLSI Subsidiary to DLSEI
DLSOD Subsidiary to DDEBDF
DLSSUD Subsidiary to DBVSUP and DSUDS
DMACON Subsidiary to DBVSUP
DMGSBV Subsidiary to DBVSUP
DMOUT Subsidiary to DBOCLS and DFC
DMPAR Subsidiary to DNLS1 and DNLS1E
DOGLEG Subsidiary to SNSQ and SNSQE
DOHTRL Subsidiary to DBVSUP and DSUDS
DORTH Internal routine for DGMRES.
DORTHR Subsidiary to DBVSUP and DSUDS
DPCHCE Set boundary conditions for DPCHIC
DPCHCI Set interior derivatives for DPCHIC
DPCHCS Adjusts derivative values for DPCHIC
DPCHDF Computes divided differences for DPCHCE and DPCHSP
DPCHKT Compute B-spline knot sequence for DPCHBS.
DPCHNG Subsidiary to DSPLP
DPCHST DPCHIP Sign-Testing Routine
DPCHSW Limits excursion from data for DPCHCS
DPIGMR Internal routine for DGMRES.
DPINCW Subsidiary to DSPLP
DPINIT Subsidiary to DSPLP
DPINTM Subsidiary to DSPLP
DPJAC Subsidiary to DDEBDF
DPLPCE Subsidiary to DSPLP
DPLPDM Subsidiary to DSPLP
DPLPFE Subsidiary to DSPLP
DPLPFL Subsidiary to DSPLP
DPLPMN Subsidiary to DSPLP
DPLPMU Subsidiary to DSPLP
DPLPUP Subsidiary to DSPLP
DPNNZR Subsidiary to DSPLP
DPOPT Subsidiary to DSPLP
DPPGQ8 Subsidiary to DPFQAD
DPRVEC Subsidiary to DBVSUP
DPRWPG Subsidiary to DSPLP
DPRWVR Subsidiary to DSPLP
DPSIXN Subsidiary to DEXINT
DQCHEB This routine computes the CHEBYSHEV series expansion
of degrees 12 and 24 of a function using A
FAST FOURIER TRANSFORM METHOD
F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),
F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),
Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.
DQELG The routine determines the limit of a given sequence of
approximations, by means of the Epsilon algorithm of
P.Wynn. An estimate of the absolute error is also given.
The condensed Epsilon table is computed. Only those
elements needed for the computation of the next diagonal
are preserved.
DQFORM Subsidiary to DNSQ and DNSQE
DQPSRT This routine maintains the descending ordering in the
list of the local error estimated resulting from the
interval subdivision process. At each call two error
estimates are inserted using the sequential search
method, top-down for the largest error estimate and
bottom-up for the smallest error estimate.
DQRFAC Subsidiary to DNLS1, DNLS1E, DNSQ and DNSQE
DQRSLV Subsidiary to DNLS1 and DNLS1E
DQWGTC This function subprogram is used together with the
routine DQAWC and defines the WEIGHT function.
DQWGTF This function subprogram is used together with the
routine DQAWF and defines the WEIGHT function.
DQWGTS This function subprogram is used together with the
routine DQAWS and defines the WEIGHT function.
DREADP Subsidiary to DSPLP
DREORT Subsidiary to DBVSUP
DRKFAB Subsidiary to DBVSUP
DRKFS Subsidiary to DDERKF
DRLCAL Internal routine for DGMRES.
DRSCO Subsidiary to DDEBDF
DSLVS Subsidiary to DDEBDF
DSOSEQ Subsidiary to DSOS
DSOSSL Subsidiary to DSOS
DSTOD Subsidiary to DDEBDF
DSTOR1 Subsidiary to DBVSUP
DSTWAY Subsidiary to DBVSUP
DSUDS Subsidiary to DBVSUP
DSVCO Subsidiary to DDEBDF
DU11LS Subsidiary to DLLSIA
DU11US Subsidiary to DULSIA
DU12LS Subsidiary to DLLSIA
DU12US Subsidiary to DULSIA
DUSRMT Subsidiary to DSPLP
DVECS Subsidiary to DBVSUP
DVNRMS Subsidiary to DDEBDF
DVOUT Subsidiary to DSPLP
DWNLIT Subsidiary to DWNNLS
DWNLSM Subsidiary to DWNNLS
DWNLT1 Subsidiary to WNLIT
DWNLT2 Subsidiary to WNLIT
DWNLT3 Subsidiary to WNLIT
DWRITP Subsidiary to DSPLP
DWUPDT Subsidiary to DNLS1 and DNLS1E
DX Subsidiary to SEPELI
DX4 Subsidiary to SEPX4
DXLCAL Internal routine for DGMRES.
DXPMU To compute the values of Legendre functions for DXLEGF.
Method: backward mu-wise recurrence for P(-MU,NU,X) for
fixed nu to obtain P(-MU2,NU1,X), P(-(MU2-1),NU1,X), ...,
P(-MU1,NU1,X) and store in ascending mu order.
DXPMUP To compute the values of Legendre functions for DXLEGF.
This subroutine transforms an array of Legendre functions
of the first kind of negative order stored in array PQA
into Legendre functions of the first kind of positive
order stored in array PQA. The original array is destroyed.
DXPNRM To compute the values of Legendre functions for DXLEGF.
This subroutine transforms an array of Legendre functions
of the first kind of negative order stored in array PQA
into normalized Legendre polynomials stored in array PQA.
The original array is destroyed.
DXPQNU To compute the values of Legendre functions for DXLEGF.
This subroutine calculates initial values of P or Q using
power series, then performs forward nu-wise recurrence to
obtain P(-MU,NU,X), Q(0,NU,X), or Q(1,NU,X). The nu-wise
recurrence is stable for P for all mu and for Q for mu=0,1.
DXPSI To compute values of the Psi function for DXLEGF.
DXQMU To compute the values of Legendre functions for DXLEGF.
Method: forward mu-wise recurrence for Q(MU,NU,X) for fixed
nu to obtain Q(MU1,NU,X), Q(MU1+1,NU,X), ..., Q(MU2,NU,X).
DXQNU To compute the values of Legendre functions for DXLEGF.
Method: backward nu-wise recurrence for Q(MU,NU,X) for
fixed mu to obtain Q(MU1,NU1,X), Q(MU1,NU1+1,X), ...,
Q(MU1,NU2,X).
DY Subsidiary to SEPELI
DY4 Subsidiary to SEPX4
DYAIRY Subsidiary to DBESJ and DBESY
EFCMN Subsidiary to EFC
ENORM Subsidiary to SNLS1, SNLS1E, SNSQ and SNSQE
EXBVP Subsidiary to BVSUP
EZFFT1 EZFFTI calls EZFFT1 with appropriate work array
partitioning.
FCMN Subsidiary to FC
FDJAC1 Subsidiary to SNSQ and SNSQE
FDJAC3 Subsidiary to SNLS1 and SNLS1E
FULMAT Subsidiary to SPLP
GAMLN Compute the logarithm of the Gamma function
GAMRN Subsidiary to BSKIN
H12 Subsidiary to HFTI, LSEI and WNNLS
HKSEQ Subsidiary to BSKIN
HSTART Subsidiary to DEABM, DEBDF and DERKF
HSTCS1 Subsidiary to HSTCSP
HVNRM Subsidiary to DEABM, DEBDF and DERKF
HWSCS1 Subsidiary to HWSCSP
HWSSS1 Subsidiary to HWSSSP
I1MERG Merge two strings of ascending integers.
IDLOC Subsidiary to DSPLP
INDXA Subsidiary to BLKTRI
INDXB Subsidiary to BLKTRI
INDXC Subsidiary to BLKTRI
INTYD Subsidiary to DEBDF
INXCA Subsidiary to CBLKTR
INXCB Subsidiary to CBLKTR
INXCC Subsidiary to CBLKTR
IPLOC Subsidiary to SPLP
ISDBCG Preconditioned BiConjugate Gradient Stop Test.
This routine calculates the stop test for the BiConjugate
Gradient iteration scheme. It returns a non-zero if the
error estimate (the type of which is determined by ITOL)
is less than the user specified tolerance TOL.
ISDCG Preconditioned Conjugate Gradient Stop Test.
This routine calculates the stop test for the Conjugate
Gradient iteration scheme. It returns a non-zero if the
error estimate (the type of which is determined by ITOL)
is less than the user specified tolerance TOL.
ISDCGN Preconditioned CG on Normal Equations Stop Test.
This routine calculates the stop test for the Conjugate
Gradient iteration scheme applied to the normal equations.
It returns a non-zero if the error estimate (the type of
which is determined by ITOL) is less than the user
specified tolerance TOL.
ISDCGS Preconditioned BiConjugate Gradient Squared Stop Test.
This routine calculates the stop test for the BiConjugate
Gradient Squared iteration scheme. It returns a non-zero
if the error estimate (the type of which is determined by
ITOL) is less than the user specified tolerance TOL.
ISDGMR Generalized Minimum Residual Stop Test.
This routine calculates the stop test for the Generalized
Minimum RESidual (GMRES) iteration scheme. It returns a
non-zero if the error estimate (the type of which is
determined by ITOL) is less than the user specified
tolerance TOL.
ISDIR Preconditioned Iterative Refinement Stop Test.
This routine calculates the stop test for the iterative
refinement iteration scheme. It returns a non-zero if the
error estimate (the type of which is determined by ITOL)
is less than the user specified tolerance TOL.
ISDOMN Preconditioned Orthomin Stop Test.
This routine calculates the stop test for the Orthomin
iteration scheme. It returns a non-zero if the error
estimate (the type of which is determined by ITOL) is
less than the user specified tolerance TOL.
ISSBCG Preconditioned BiConjugate Gradient Stop Test.
This routine calculates the stop test for the BiConjugate
Gradient iteration scheme. It returns a non-zero if the
error estimate (the type of which is determined by ITOL)
is less than the user specified tolerance TOL.
ISSCG Preconditioned Conjugate Gradient Stop Test.
This routine calculates the stop test for the Conjugate
Gradient iteration scheme. It returns a non-zero if the
error estimate (the type of which is determined by ITOL)
is less than the user specified tolerance TOL.
ISSCGN Preconditioned CG on Normal Equations Stop Test.
This routine calculates the stop test for the Conjugate
Gradient iteration scheme applied to the normal equations.
It returns a non-zero if the error estimate (the type of
which is determined by ITOL) is less than the user
specified tolerance TOL.
ISSCGS Preconditioned BiConjugate Gradient Squared Stop Test.
This routine calculates the stop test for the BiConjugate
Gradient Squared iteration scheme. It returns a non-zero
if the error estimate (the type of which is determined by
ITOL) is less than the user specified tolerance TOL.
ISSGMR Generalized Minimum Residual Stop Test.
This routine calculates the stop test for the Generalized
Minimum RESidual (GMRES) iteration scheme. It returns a
non-zero if the error estimate (the type of which is
determined by ITOL) is less than the user specified
tolerance TOL.
ISSIR Preconditioned Iterative Refinement Stop Test.
This routine calculates the stop test for the iterative
refinement iteration scheme. It returns a non-zero if the
error estimate (the type of which is determined by ITOL)
is less than the user specified tolerance TOL.
ISSOMN Preconditioned Orthomin Stop Test.
This routine calculates the stop test for the Orthomin
iteration scheme. It returns a non-zero if the error
estimate (the type of which is determined by ITOL) is
less than the user specified tolerance TOL.
IVOUT Subsidiary to SPLP
J4SAVE Save or recall global variables needed by error
handling routines.
JAIRY Subsidiary to BESJ and BESY
LA05AD Subsidiary to DSPLP
LA05AS Subsidiary to SPLP
LA05BD Subsidiary to DSPLP
LA05BS Subsidiary to SPLP
LA05CD Subsidiary to DSPLP
LA05CS Subsidiary to SPLP
LA05ED Subsidiary to DSPLP
LA05ES Subsidiary to SPLP
LMPAR Subsidiary to SNLS1 and SNLS1E
LPDP Subsidiary to LSEI
LSAME Test two characters to determine if they are the same
letter, except for case.
LSI Subsidiary to LSEI
LSOD Subsidiary to DEBDF
LSSODS Subsidiary to BVSUP
LSSUDS Subsidiary to BVSUP
MACON Subsidiary to BVSUP
MC20AD Subsidiary to DSPLP
MC20AS Subsidiary to SPLP
MGSBV Subsidiary to BVSUP
MINSO4 Subsidiary to SEPX4
MINSOL Subsidiary to SEPELI
MPADD Subsidiary to DQDOTA and DQDOTI
MPADD2 Subsidiary to DQDOTA and DQDOTI
MPADD3 Subsidiary to DQDOTA and DQDOTI
MPBLAS Subsidiary to DQDOTA and DQDOTI
MPCDM Subsidiary to DQDOTA and DQDOTI
MPCHK Subsidiary to DQDOTA and DQDOTI
MPCMD Subsidiary to DQDOTA and DQDOTI
MPDIVI Subsidiary to DQDOTA and DQDOTI
MPERR Subsidiary to DQDOTA and DQDOTI
MPMAXR Subsidiary to DQDOTA and DQDOTI
MPMLP Subsidiary to DQDOTA and DQDOTI
MPMUL Subsidiary to DQDOTA and DQDOTI
MPMUL2 Subsidiary to DQDOTA and DQDOTI
MPMULI Subsidiary to DQDOTA and DQDOTI
MPNZR Subsidiary to DQDOTA and DQDOTI
MPOVFL Subsidiary to DQDOTA and DQDOTI
MPSTR Subsidiary to DQDOTA and DQDOTI
MPUNFL Subsidiary to DQDOTA and DQDOTI
OHTROL Subsidiary to BVSUP
OHTROR Subsidiary to BVSUP
ORTHO4 Subsidiary to SEPX4
ORTHOG Subsidiary to SEPELI
ORTHOL Subsidiary to BVSUP
ORTHOR Subsidiary to BVSUP
PASSB Calculate the fast Fourier transform of subvectors of
arbitrary length.
PASSB2 Calculate the fast Fourier transform of subvectors of
length two.
PASSB3 Calculate the fast Fourier transform of subvectors of
length three.
PASSB4 Calculate the fast Fourier transform of subvectors of
length four.
PASSB5 Calculate the fast Fourier transform of subvectors of
length five.
PASSF Calculate the fast Fourier transform of subvectors of
arbitrary length.
PASSF2 Calculate the fast Fourier transform of subvectors of
length two.
PASSF3 Calculate the fast Fourier transform of subvectors of
length three.
PASSF4 Calculate the fast Fourier transform of subvectors of
length four.
PASSF5 Calculate the fast Fourier transform of subvectors of
length five.
PCHCE Set boundary conditions for PCHIC
PCHCI Set interior derivatives for PCHIC
PCHCS Adjusts derivative values for PCHIC
PCHDF Computes divided differences for PCHCE and PCHSP
PCHKT Compute B-spline knot sequence for PCHBS.
PCHNGS Subsidiary to SPLP
PCHST PCHIP Sign-Testing Routine
PCHSW Limits excursion from data for PCHCS
PGSF Subsidiary to CBLKTR
PIMACH Subsidiary to HSTCSP, HSTSSP and HWSCSP
PINITM Subsidiary to SPLP
PJAC Subsidiary to DEBDF
PNNZRS Subsidiary to SPLP
POISD2 Subsidiary to GENBUN
POISN2 Subsidiary to GENBUN
POISP2 Subsidiary to GENBUN
POS3D1 Subsidiary to POIS3D
POSTG2 Subsidiary to POISTG
PPADD Subsidiary to BLKTRI
PPGQ8 Subsidiary to PFQAD
PPGSF Subsidiary to CBLKTR
PPPSF Subsidiary to CBLKTR
PPSGF Subsidiary to BLKTRI
PPSPF Subsidiary to BLKTRI
PROC Subsidiary to CBLKTR
PROCP Subsidiary to CBLKTR
PROD Subsidiary to BLKTRI
PRODP Subsidiary to BLKTRI
PRVEC Subsidiary to BVSUP
PRWPGE Subsidiary to SPLP
PRWVIR Subsidiary to SPLP
PSGF Subsidiary to BLKTRI
PSIXN Subsidiary to EXINT
PYTHAG Compute the complex square root of a complex number without
destructive overflow or underflow.
QCHEB This routine computes the CHEBYSHEV series expansion
of degrees 12 and 24 of a function using A
FAST FOURIER TRANSFORM METHOD
F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),
F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),
Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.
QELG The routine determines the limit of a given sequence of
approximations, by means of the Epsilon algorithm of
P. Wynn. An estimate of the absolute error is also given.
The condensed Epsilon table is computed. Only those
elements needed for the computation of the next diagonal
are preserved.
QFORM Subsidiary to SNSQ and SNSQE
QPSRT Subsidiary to QAGE, QAGIE, QAGPE, QAGSE, QAWCE, QAWOE and
QAWSE
QRFAC Subsidiary to SNLS1, SNLS1E, SNSQ and SNSQE
QRSOLV Subsidiary to SNLS1 and SNLS1E
QS2I1D Sort an integer array, moving an integer and DP array.
This routine sorts the integer array IA and makes the same
interchanges in the integer array JA and the double pre-
cision array A. The array IA may be sorted in increasing
order or decreasing order. A slightly modified QUICKSORT
algorithm is used.
QS2I1R Sort an integer array, moving an integer and real array.
This routine sorts the integer array IA and makes the same
interchanges in the integer array JA and the real array A.
The array IA may be sorted in increasing order or decreas-
ing order. A slightly modified QUICKSORT algorithm is
used.
QWGTC This function subprogram is used together with the
routine QAWC and defines the WEIGHT function.
QWGTF This function subprogram is used together with the
routine QAWF and defines the WEIGHT function.
QWGTS This function subprogram is used together with the
routine QAWS and defines the WEIGHT function.
R1MPYQ Subsidiary to SNSQ and SNSQE
R1UPDT Subsidiary to SNSQ and SNSQE
R9AIMP Evaluate the Airy modulus and phase.
R9ATN1 Evaluate ATAN(X) from first order relative accuracy so that
ATAN(X) = X + X**3*R9ATN1(X).
R9CHU Evaluate for large Z Z**A * U(A,B,Z) where U is the
logarithmic confluent hypergeometric function.
R9GMIC Compute the complementary incomplete Gamma function for A
near a negative integer and for small X.
R9GMIT Compute Tricomi's incomplete Gamma function for small
arguments.
R9KNUS Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*
K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.
R9LGIC Compute the log complementary incomplete Gamma function
for large X and for A .LE. X.
R9LGIT Compute the logarithm of Tricomi's incomplete Gamma
function with Perron's continued fraction for large X and
A .GE. X.
R9LGMC Compute the log Gamma correction factor so that
LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X
+ R9LGMC(X).
R9LN2R Evaluate LOG(1+X) from second order relative accuracy so
that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X).
RADB2 Calculate the fast Fourier transform of subvectors of
length two.
RADB3 Calculate the fast Fourier transform of subvectors of
length three.
RADB4 Calculate the fast Fourier transform of subvectors of
length four.
RADB5 Calculate the fast Fourier transform of subvectors of
length five.
RADBG Calculate the fast Fourier transform of subvectors of
arbitrary length.
RADF2 Calculate the fast Fourier transform of subvectors of
length two.
RADF3 Calculate the fast Fourier transform of subvectors of
length three.
RADF4 Calculate the fast Fourier transform of subvectors of
length four.
RADF5 Calculate the fast Fourier transform of subvectors of
length five.
RADFG Calculate the fast Fourier transform of subvectors of
arbitrary length.
REORT Subsidiary to BVSUP
RFFTB Compute the backward fast Fourier transform of a real
coefficient array.
RFFTF Compute the forward transform of a real, periodic sequence.
RFFTI Initialize a work array for RFFTF and RFFTB.
RKFAB Subsidiary to BVSUP
RSCO Subsidiary to DEBDF
RWUPDT Subsidiary to SNLS1 and SNLS1E
S1MERG Merge two strings of ascending real numbers.
SBOLSM Subsidiary to SBOCLS and SBOLS
SCHKW SLAP WORK/IWORK Array Bounds Checker.
This routine checks the work array lengths and interfaces
to the SLATEC error handler if a problem is found.
SCLOSM Subsidiary to SPLP
SCOEF Subsidiary to BVSUP
SDAINI Initialization routine for SDASSL.
SDAJAC Compute the iteration matrix for SDASSL and form the
LU-decomposition.
SDANRM Compute vector norm for SDASSL.
SDASLV Linear system solver for SDASSL.
SDASTP Perform one step of the SDASSL integration.
SDATRP Interpolation routine for SDASSL.
SDAWTS Set error weight vector for SDASSL.
SDCOR Subroutine SDCOR computes corrections to the Y array.
SDCST SDCST sets coefficients used by the core integrator SDSTP.
SDNTL Subroutine SDNTL is called to set parameters on the first
call to SDSTP, on an internal restart, or when the user has
altered MINT, MITER, and/or H.
SDNTP Subroutine SDNTP interpolates the K-th derivative of Y at
TOUT, using the data in the YH array. If K has a value
greater than NQ, the NQ-th derivative is calculated.
SDPSC Subroutine SDPSC computes the predicted YH values by
effectively multiplying the YH array by the Pascal triangle
matrix when KSGN is +1, and performs the inverse function
when KSGN is -1.
SDPST Subroutine SDPST evaluates the Jacobian matrix of the right
hand side of the differential equations.
SDSCL Subroutine SDSCL rescales the YH array whenever the step
size is changed.
SDSTP SDSTP performs one step of the integration of an initial
value problem for a system of ordinary differential
equations.
SDZRO SDZRO searches for a zero of a function F(N, T, Y, IROOT)
between the given values B and C until the width of the
interval (B, C) has collapsed to within a tolerance
specified by the stopping criterion,
ABS(B - C) .LE. 2.*(RW*ABS(B) + AE).
SHELS Internal routine for SGMRES.
SHEQR Internal routine for SGMRES.
SLVS Subsidiary to DEBDF
SMOUT Subsidiary to FC and SBOCLS
SODS Subsidiary to BVSUP
SOPENM Subsidiary to SPLP
SORTH Internal routine for SGMRES.
SOSEQS Subsidiary to SOS
SOSSOL Subsidiary to SOS
SPELI4 Subsidiary to SEPX4
SPELIP Subsidiary to SEPELI
SPIGMR Internal routine for SGMRES.
SPINCW Subsidiary to SPLP
SPINIT Subsidiary to SPLP
SPLPCE Subsidiary to SPLP
SPLPDM Subsidiary to SPLP
SPLPFE Subsidiary to SPLP
SPLPFL Subsidiary to SPLP
SPLPMN Subsidiary to SPLP
SPLPMU Subsidiary to SPLP
SPLPUP Subsidiary to SPLP
SPOPT Subsidiary to SPLP
SREADP Subsidiary to SPLP
SRLCAL Internal routine for SGMRES.
STOD Subsidiary to DEBDF
STOR1 Subsidiary to BVSUP
STWAY Subsidiary to BVSUP
SUDS Subsidiary to BVSUP
SVCO Subsidiary to DEBDF
SVD Perform the singular value decomposition of a rectangular
matrix.
SVECS Subsidiary to BVSUP
SVOUT Subsidiary to SPLP
SWRITP Subsidiary to SPLP
SXLCAL Internal routine for SGMRES.
TEVLC Subsidiary to CBLKTR
TEVLS Subsidiary to BLKTRI
TRI3 Subsidiary to GENBUN
TRIDQ Subsidiary to POIS3D
TRIS4 Subsidiary to SEPX4
TRISP Subsidiary to SEPELI
TRIX Subsidiary to GENBUN
U11LS Subsidiary to LLSIA
U11US Subsidiary to ULSIA
U12LS Subsidiary to LLSIA
U12US Subsidiary to ULSIA
USRMAT Subsidiary to SPLP
VNWRMS Subsidiary to DEBDF
WNLIT Subsidiary to WNNLS
WNLSM Subsidiary to WNNLS
WNLT1 Subsidiary to WNLIT
WNLT2 Subsidiary to WNLIT
WNLT3 Subsidiary to WNLIT
XERBLA Error handler for the Level 2 and Level 3 BLAS Routines.
XERCNT Allow user control over handling of errors.
XERHLT Abort program execution and print error message.
XERPRN Print error messages processed by XERMSG.
XERSVE Record that an error has occurred.
XPMU To compute the values of Legendre functions for XLEGF.
Method: backward mu-wise recurrence for P(-MU,NU,X) for
fixed nu to obtain P(-MU2,NU1,X), P(-(MU2-1),NU1,X), ...,
P(-MU1,NU1,X) and store in ascending mu order.
XPMUP To compute the values of Legendre functions for XLEGF.
This subroutine transforms an array of Legendre functions
of the first kind of negative order stored in array PQA
into Legendre functions of the first kind of positive
order stored in array PQA. The original array is destroyed.
XPNRM To compute the values of Legendre functions for XLEGF.
This subroutine transforms an array of Legendre functions
of the first kind of negative order stored in array PQA
into normalized Legendre polynomials stored in array PQA.
The original array is destroyed.
XPQNU To compute the values of Legendre functions for XLEGF.
This subroutine calculates initial values of P or Q using
power series, then performs forward nu-wise recurrence to
obtain P(-MU,NU,X), Q(0,NU,X), or Q(1,NU,X). The nu-wise
recurrence is stable for P for all mu and for Q for mu=0,1.
XPSI To compute values of the Psi function for XLEGF.
XQMU To compute the values of Legendre functions for XLEGF.
Method: forward mu-wise recurrence for Q(MU,NU,X) for fixed
nu to obtain Q(MU1,NU,X), Q(MU1+1,NU,X), ..., Q(MU2,NU,X).
XQNU To compute the values of Legendre functions for XLEGF.
Method: backward nu-wise recurrence for Q(MU,NU,X) for
fixed mu to obtain Q(MU1,NU1,X), Q(MU1,NU1+1,X), ...,
Q(MU1,NU2,X).
YAIRY Subsidiary to BESJ and BESY
ZABS Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
ZBIRY
ZACAI Subsidiary to ZAIRY
ZACON Subsidiary to ZBESH and ZBESK
ZASYI Subsidiary to ZBESI and ZBESK
ZBINU Subsidiary to ZAIRY, ZBESH, ZBESI, ZBESJ, ZBESK and ZBIRY
ZBKNU Subsidiary to ZAIRY, ZBESH, ZBESI and ZBESK
ZBUNI Subsidiary to ZBESI and ZBESK
ZBUNK Subsidiary to ZBESH and ZBESK
ZDIV Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
ZBIRY
ZEXP Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
ZBIRY
ZKSCL Subsidiary to ZBESK
ZLOG Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
ZBIRY
ZMLRI Subsidiary to ZBESI and ZBESK
ZMLT Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
ZBIRY
ZRATI Subsidiary to ZBESH, ZBESI and ZBESK
ZS1S2 Subsidiary to ZAIRY and ZBESK
ZSERI Subsidiary to ZBESI and ZBESK
ZSHCH Subsidiary to ZBESH and ZBESK
ZSQRT Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
ZBIRY
ZUCHK Subsidiary to SERI, ZUOIK, ZUNK1, ZUNK2, ZUNI1, ZUNI2 and
ZKSCL
ZUNHJ Subsidiary to ZBESI and ZBESK
ZUNI1 Subsidiary to ZBESI and ZBESK
ZUNI2 Subsidiary to ZBESI and ZBESK
ZUNIK Subsidiary to ZBESI and ZBESK
ZUNK1 Subsidiary to ZBESK
ZUNK2 Subsidiary to ZBESK
ZUOIK Subsidiary to ZBESH, ZBESI and ZBESK
ZWRSK Subsidiary to ZBESI and ZBESK