Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: Guide and Reference

Index

Numerics
A B C D E F G H I L M N O P Q R S T U V W Z

Numerics

3838 Array Processor

general signal processing routines (4833)

3838 Array Processor publications (5276)

abbreviations

for product names (2951)

in the Glossary (5229)

interpreting math and programming (2994)

absolute value

maximum (3734)

minimum (3741)

notation (3015)

sum of all absolute values (3764)

accuracy

considerations for dense and banded linear algebraic equations (4360)

considerations for eigensystem analysis (4774)

considerations for Fourier transforms, convolutions, and correlations (4843)

considerations for interpolation (5062)

considerations for linear algebra subprograms (3724)

considerations for matrix operations (4178)

considerations for numerical quadrature (5099)

considerations for related computations (4858)

considerations for sorting and searching (5010)

error of computation (3178)

of results (3068), (3172)

precisions (3174)

what accuracy means (3171)

where to find information on (3173)

acronyms

associated with programming values (3022)

in the Glossary (5232)

product names (2948)

adding

absolute values (3765)

general matrices or their transposes (4188)

vector x to vector y and store in vector z (3899)

address notation (3001)

advantages of ESSL (3044)

AIX

publications (5273)

algebra (4337)

Announcing ESSL brochure (5252)

ANSI definitions in Glossary (5233)

application programming, publication for (5265)

applications in the industry (3057)

architecture supported by ESSL on the workstations (3084)

arguments

coding rules (3145)

conventions used in the subroutine descriptions (3032)

diagnosing ESSL input-argument errors (3647)

font for ESSL calling (2962)

list of ESSL input-argument errors (3696), (3700)

passing in C++ programs (3541)

passing in C programs (3505)

array

coding in C++ programs (3548)

coding in C programs (3512)

coding in Fortran programs (3474)

conventions for (2977)

definition of (3142)

real and complex elements (3479)

setting up data structures inside (3250)

storage techniques overview (3130)

array data

storage and performance tradeoffs (3193)

arrow notation, what it means (2989)

attention error messages, interpreting (3673)

autocorrelation of one or more sequences (4959), (4964)

auxiliary working storage

calculating (3160)

dynamic allocation (3154)

list of subroutines using (3148)

provided by the user (3159)

background books (5244)

band matrix

definition of (3362)

storage layout (3369), (3373), (3376), (3384), (3386) , (3405), (3408)

band matrix subroutines, names of (4346)

band width (3364), (3379)

banded linear algebraic equation subroutines (4339)

SGBF and DGBF (4589)

SGBS and DGBS (4595)

SGTF and DGTF (4621)

SGTNP, DGTNP, CGTNP, and ZGTNP (4637)

SGTNPF, DGTNPF, CGTNPF, and ZGTNPF (4648)

SGTNPS, DGTNPS, CGTNPS, and ZGTNPS (4658)

SGTS and DGTS (4627)

SPBF, DPBF, SPBCHF, and DPBCHF (4605)

SPBS, DPBS, SPBCHS, and DPBCHS (4615)

SPTF and DPTF (4664)

SPTS and DPTS (4670)

STBSV, DTBSV, CTBSV, and ZTBSV (4680)

base program, processing your

under AIX (3566)

bibliography (5238)

binary search (5043)

BLAS (Basic Linear Algebra Subprograms) (3702)

ESSL subprograms (3703), (5217)

Level 1 (5218)

Level 2 (5220)

Level 3 (5222)

migrating from (3626)

migrating to ESSL (3118)

BLAS-general-band storage mode (3375)

bold letters, usage of (2956)

books (5245)

C++ (C++ programming language)

coding programs (3532)

ESSL header file (3539), (3546)

function reference (3537)

handling errors in your program (3550)

how to code arrays (3549)

modifying procedures for using ESSL (3589)

passing character arguments (3542)

program calling interface (3536)

setting up complex and logical data (3543)

C (C programming language)

coding programs (3496)

ESSL header file (3503), (3510)

function reference (3501)

handling errors in your program (3514)

how to code arrays (3513)

modifying procedures for using ESSL (3584)

passing character arguments (3506)

program calling interface (3500)

setting up complex and logical data (3507)

calculating auxiliary working storage (3157)

calculating transform lengths (3165)

CALL statement (3461)

calling sequence

for C++ programs (3527)

for C programs (3491)

for Fortran programs (3462)

specifying the arguments (3146)

subroutines versus functions (3469), (3498), (3534)

syntax description (3031)

cataloged procedures, ESSL (3569)

CAXPY (3773)

CAXPYI (3980)

CCOPY (3784)

CDOTC (3798)

CDOTCI (3994)

CDOTU (3796)

CDOTUI (3992)

ceiling notation and meaning (3004)

CGBMV (4108)

CGEADD (4185)

CGEEV (4781)

CGEF (4380)

CGEMM (4244)

CGEMMS (4228)

CGEMUL (4213)

CGEMV (4008)

CGERC (4027)

CGERU (4025)

CGES (4390)

CGESM (4400)

CGESUB (4199)

CGETMI (4322)

CGETMO (4332)

CGETRF (4410)

CGETRS (4420)

CGTHR (3960)

CGTHRZ (3970)

CGTNP (4635)

CGTNPF (4646)

CGTNPS (4656)

character data

conventions (2973), (3141)

characters, special usage of (3010)

CHBMV (4119)

CHEMM (4264)

CHEMV (4047)

CHER (4074)

CHER2 (4095)

CHER2K (4310)

CHERK (4294)

choosing the ESSL library (3110)

choosing the ESSL subroutine (3114)

CHPEV (4793)

CHPMV (4043)

CHPR (4070)

CHPR2 (4091)

CHPSV (4804)

citations (5240)

CNORM2 (3833)

coding your program

arguments in ESSL calling sequences (3144)

CALL sequence for C++ programs (3528)

CALL sequence for C programs (3492)

CALL sequence for Fortran programs (3463)

calls to ESSL in C++ programs (3533)

calls to ESSL in C programs (3497)

calls to ESSL in Fortran programs (3468)

data types used in your program (3133)

handling errors with ERRSET, EINFO, ERRSAV, ERRSTR, and return codes (3485), (3520), (3556)

restrictions for application programs (3126)

techniques that affect performance (3191)

column vector (3255)

comparison of accuracy for libraries (3070)

compilers, required by ESSL on the workstations (3089)

compiling your program

C++ programs (3588)

C programs (3583)

Fortran programs (3578)

under AIX (3567)

complex and real array elements (3478)

complex conjugate notation (2998)

complex data

conventions (2971), (3140)

setting up for C (3508)

setting up for C++ (3544)

complex Hermitian band matrix

definition of (3393)

storage layout (3394)

complex Hermitian matrix

definition of (3320)

storage layout (3321)

complex Hermitian Toeplitz matrix

definition of (3346)

complex matrix (3284)

complex vector (3257)

compressed-diagonal storage mode for sparse matrices (3436)

compressed-matrix storage mode for sparse matrices (3434)

compressed-vector, definition and storage mode (3281)

computational areas, overview (3054)

computational errors

diagnosing (3653)

list of messages for (3697)

overview (3216)

condition number, reciprocal of

general matrix (4432), (4519)

positive definite real symmetric matrix (4494), (4536)

conjugate notation (2999)

conjugate transpose

of matrix operation results for multiply (4218), (4234), (4250)

conjugate transpose of a matrix (3287)

conjugate transpose of a vector (3260)

continuation, convention for numerical data (2972)

conventions (2965)

for messages (3691)

mathematical and programming notations (2983)

subroutine descriptions (3026)

convolution and correlation

autocorrelation of one or more sequences (4960)

direct method

one sequence with another sequence (4939)

with decimated output (4955)

mixed radix Fourier method

autocorrelation of one or more sequences (4965)

one sequence with one or more sequences (4945)

one sequence with one or more sequences (4932)

convolution and correlation subroutines

accuracy considerations (4845)

performance and accuracy considerations (4853)

performance considerations (4841)

SACOR (4958)

SACORF (4963)

SCON and SCOR (4931)

SCOND and SCORD (4938)

SCONF and SCORF (4944)

SDCON, DDCON, SDCOR, and DDCOR (4954)

usage considerations (4836)

copy a vector (3787)

correlation (4933)

cosine notation (3020)

cosine transform (4883)

courier font usage (2955)

CPOF (4448)

CPOSM (4473)

CPOTRF (4452)

CPOTRS (4477)

CROT (3858)

CROTG (3844)

CSCAL (3873)

CSCTR (3950)

CSROT (3860)

CSSCAL (3875)

CSWAP (3885)

CSYAX (3930)

CSYMM (4262)

CSYR2K (4308)

CSYRK (4292)

CTBMV (4151)

CTBSV (4678)

CTPMV (4140)

CTPSV (4552)

CTRMM (4279)

CTRMV (4136)

CTRSM (4563)

CTRSV (4548)

cubic spline interpolating (5082), (5089)

customer service, IBM (3632)

customer support, IBM (3633)

CVEA (3896)

CVEM (3916)

CVES (3906)

CWLEV (4997)

CYAX (3928)

CZAXPY (3940)

DASUM (3760)

data

array data (3143)

conventions for scalar data (2967), (3136)

data structures (vectors and matrices) (3251)

DAXPY (3772)

DAXPYI (3979)

DBSRCH (5041)

DBSSV (4497)

DBSTRF (4501)

DBSTRS (4505)

DCFT (4862)

DCFT2 (4894)

DCFT3 (4912)

DCOPY (3783)

DCOSF (4880)

DCRFT (4874)

DCRFT2 (4906)

DCRFT3 (4924)

DCSIN2 (5087)

DCSINT (5080)

DDCON (4951)

DDCOR (4953)

DDOT (3795)

DDOTI (3991)

default values in the ESSL error option table (3232)

definitions of terms in the Glossary (5230)

dense and banded subroutines

performance and accuracy considerations (4357)

dense linear algebraic equation subroutines (4338)

DBSSV (4498)

DBSTRF (4502)

DBSTRS (4506)

SGEF, DGEF, CGEF, and ZGEF (4382)

SGEFCD and DGEFCD (4429)

SGEICD, DGEICD, SGETRI, and DGETRI (4516)

SGES, DGES, CGES, and ZGES (4392)

SGESM, DGESM, CGESM, and ZGESM (4402)

SGETRF, DGETRF, CGETRF and ZGETRF (4412)

SGETRS, DGETRS, CGETRS, and ZGETRS (4422)

SPOFCD and DPOFCD (4491)

SPOSM, DPOSM, CPOSM, ZPOSM, SPOTRS, DPOTRS, CPOTRS, and ZPOTRS (4479)

SPPF, DPPF, SPOF, DPOF, CPOF, ZPOF, SPOTRF, DPOTRF, CPOTRF, ZPOTRF (4454)

SPPFCD and DPPFCD (4490)

SPPICD, DPPICD, SPOICD, DPOICD, SPOTRI, and DPOTRI (4533)

SPPS and DPPS (4461)

STPSV, DTPSV, CTPSV, and ZTPSV (4555)

STRI, DTRI, STPI, DPTI, STRTRI, DTRTRI, STPTRI, DTPTRI (4583)

STRSM, DTRSM, CTRSM, and ZTRSM (4565)

STRSV, DTRSV, CTRSV, and ZTRSV (4554)

dense matrix, definition (3432)

descriptions, conventions used in the subroutine (3028)

designing your program

accuracy of results (3170)

choosing the ESSL library (3111)

choosing the ESSL subroutine (3115)

error considerations (3200)

performance considerations (3186)

storage considerations (3128)

determinant

general matrix (4433), (4518)

general skyline sparse matrix (4695)

matrix notation (2992)

positive definite real symmetric matrix (4495), (4535)

symmetric skyline sparse matrix (4702)

DGBF (4588)

DGBMV (4107)

DGBS (4594)

DGEADD (4184)

DGEEV (4780)

DGEF (4379)

DGEFCD (4428)

DGEGV (4814)

DGEICD (4513)

DGELLS (4763)

DGELS (4755)

DGEMM (4243)

DGEMMS (4227)

DGEMTX (4013)

DGEMUL (4212)

DGEMV (4007)

DGEMX (4011)

DGEQRF (4752)

DGER (4024)

DGES (4389)

DGESM (4399)

DGESUB (4198)

DGESVF (4739)

DGESVS (4746)

DGETMI (4321)

DGETMO (4331)

DGETRF (4409)

DGETRI (4515)

DGETRS (4419)

DGHMQ (5139)

DGKFS (4692)

DGKTRN (5210)

DGLGQ (5125)

DGLNQ (5111)

DGLNQ2 (5118)

DGRAQ (5132)

DGSF (4683)

DGSS (4688)

DGTF (4620)

DGTHR (3959)

DGTHRZ (3969)

DGTNP (4634)

DGTNPF (4645)

DGTNPS (4655)

DGTS (4626)

diagnosis procedures

attention error messages (3674)

computational errors (3654)

ESSL messages, list of (3685)

in your program (3630)

informational error messages (3668)

initial problem diagnosis procedures (symptom index) (3639)

input-argument errors (3648)

miscellaneous error messages (3680)

program exceptions (3643)

resource error messages (3662)

diagnostics (3689)

diagonal-out skyline storage mode (3447)

dimensions of arrays

storage layout (3475)

direct method

general skyline sparse matrix (4697)

general sparse matrix (4686)

symmetric skyline sparse matrix (4704)

direct sparse matrix solvers

usage considerations (4363)

DIZC (4975)

DNAXPY (3805)

DNDOT (3811)

DNORM2 (3832)

DNRAND (5159)

DNRM2 (3819)

documentation (5239)

dot product

notation (3016)

of dense vectors (3801)

of sparse vectors (3997)

special (compute N times) (3813)

DPBCHF (4604)

DPBCHS (4614)

DPBF (4602)

DPBS (4612)

DPINT (5066)

DPOF (4447)

DPOFCD (4489)

DPOICD (4530)

DPOLY (4969)

DPOSM (4472)

DPOTRF (4451)

DPOTRI (4532)

DPOTRS (4476)

DPPF (4445)

DPPFCD (4487)

DPPICD (4528)

DPPS (4460)

DPTF (4663)

DPTNQ (5105)

DPTS (4669)

DQINT (4987)

DRCFT (4868)

DRCFT2 (4900)

DRCFT3 (4918)

DROT (3857)

DROTG (3843)

DSBMV (4118)

DSCAL (3872)

DSCTR (3949)

DSDCG (4720)

DSDGCG (4732)

DSDMX (4166)

DSINF (4887)

DSKFS (4699)

DSKTRN (5214)

DSLMX (4050)

DSLR1 (4067)

DSLR2 (4098)

DSMCG (4713)

DSMGCG (4727)

DSMMX (4157)

DSMTM (4162)

DSORT (5016)

DSORTS (5032)

DSORTX (5024)

DSPEV (4792)

DSPMV (4042)

DSPR (4069)

DSPR2 (4090)

DSPSV (4803)

DSRIS (4706)

DSRSM (5206)

DSSRCH (5050)

DSWAP (3884)

DSYGV (4821)

DSYMM (4261)

DSYMV (4046)

DSYR (4073)

DSYR2 (4094)

DSYR2K (4307)

DSYRK (4291)

DTBMV (4150)

DTBSV (4677)

DTPI (4578)

DTPINT (5073)

DTPMV (4139)

DTPSV (4551)

DTPTRI (4582)

DTREC (4981)

DTRI (4576)

DTRMM (4278)

DTRMV (4135)

DTRSM (4562)

DTRSV (4547)

DTRTRI (4580)

DURAND (5152)

DURXOR (5166)

DVEA (3895)

DVEM (3915)

DVES (3905)

DWLEV (4996)

DYAX (3927)

dynamic allocation of auxiliary working storage (3155)

dynamic linking versus static linking (3573)

DZASUM (3762)

DZAXPY (3939)

DZNRM2 (3821)

efficiency of your program (3187)

eigensystem analysis subroutines

performance and accuracy considerations (4772)

SGEEV, DGEEV, CGEEV, and ZGEEV (4783)

SGEGV and DGEGV (4815)

SSPEV, DSPEV, CHPEV, and ZHPEV (4795)

SSPSV, DSPSV, CHPSV, and ZHPSV (4806)

SSYGV and DSYGV (4822)

eigenvalues and eigenvectors (4786)

complex Hermitian matrix (4797)

general matrix (4784)

real general matrices (4816)

real symmetric matrix (4796), (4823)

real symmetric positive definite matrix (4824)

EINFO, ESSL error information-handler

considerations when designing your program (3221)

diagnosis procedures using (3659)

subroutine description (5179)

using EINFO in C++ programs (3560)

using EINFO in C programs (3524)

using EINFO in Fortran programs (3488)

element of a matrix notation (2987)

element of a vector notation (2986)

error conditions, conventions used in the subroutine descriptions (3038)

error-handling subroutines

EINFO (5180)

ERRSAV (5184)

ERRSET (5188)

ERRSTR (5192)

error messages (3687)

error option table default values (3237)

errors

attention error messages, interpreting (3676)

attention messages, overview (3227)

calculating auxiliary storage (3149)

computational errors (3217), (3655)

EINFO subroutine description (5175)

extended error-handling subroutines (3103)

handling errors in your C++ program (3553)

handling errors in your C program (3517)

handling errors in your Fortran program (3480)

how errors affect output (3202)

informational error messages, interpreting (3670)

input-argument errors (3649)

input-argument errors, overview (3210)

miscellaneous error messages, interpreting (3682)

overview of (3199)

program exceptions (3207), (3644)

resource error messages, interpreting (3664)

resource errors, overview (3222)

types of errors that you can encounter (3201)

using ERRSAV and ERRSTR (3241)

values returned for EINFO error codes (5176)

when to use ERRSET (3238)

where to find information on (3203)

ERRSAV

in workstation environment (3106)

subroutine description (5182)

using with large applications (3245)

ERRSET

diagnosis procedures using (3658)

ESSL default values for (3234)

handling errors in C (3515)

handling errors in C++ (3551)

in workstation environment (3104)

subroutine description (5186)

using EINFO in C++ programs (3561)

using EINFO in C programs (3525)

using EINFO in Fortran programs (3489)

using ERRSET, EINFO, and return codes in C (3523)

using ERRSET, EINFO, and return codes in C++ (3559)

using ERRSET, EINFO, and return codes in Fortran (3487)

when to use (3220), (3233)

when to use ERRSAV and ERRSTR with ERRSET (3244)

ERRSTR

in workstation environment (3105)

subroutine description (5190)

using with large applications (3246)

ESSL (Engineering and Scientific Subroutine Library)

advantages of (3045)

attention error messages, interpreting (3677)

attention messages, overview (3228)

coding your program (3459)

computational areas, overview (3053)

computational errors (3218)

computational errors, diagnosing (3657)

designing your program (3108)

diagnosis procedures for ESSL errors (3627)

dynamic linking versus static linking (3574)

eigensystem analysis subroutines (4767)

error option table default values (3235)

extended error-handling subroutines (3101)

Fourier transform, convolutions and correlations, and related-computation subroutines (4828)

functional capability (3051)

informational error messages, interpreting (3671)

input-argument errors, diagnosing (3645)

input-argument errors, overview (3211)

installation requirements (3091)

interpolation subroutines (5054)

introduction to (3042)

languages supported (3078)

linear algebra subprograms (3705)

linear algebraic equations subroutines (4343)

matrix operation subroutines (4170)

message conventions (3693)

messages, list of (3686)

migrating between IBM

pSeries and RS/6000 processors (3607)

migrating programs (3592)

migrating to future releases or future hardware (3604)

miscellaneous error messages, interpreting (3683)

name (2952)

names with an underscore, interpreting (2946)

number of subroutines in each area (3059)

numerical quadrature subroutines (5091)

ordering publications (5254)

overview (3046)

overview of the subroutines (3058)

packaging characteristics (3092)

parallel processing subroutines on the workstations (3067)

processing your program (3565)

program exceptions (3208)

program number for (5260)

publications overview (5247)

random number generation subroutines (5143)

reference information conventions (3025)

related publications (5271)

resource error messages, interpreting (3665)

resource errors, overview (3223)

setting up your data structures (3248)

sorting and searching subroutines (5002)

usability of subroutines (3047)

utility subroutines (5170)

when coding large applications (3242)

when to use ERRSET for ESSL errors (3236)

ESSL/370, migrating from (3612)

ESSL messages (3688)

ESSLPARM file

migrating programs to use (3603)

Euclidean length

with no scaling of input (3836)

with scaling of input (3823)

Euclidean norm notation (2997)

evaluation and planning, publications for (5261)

examples, conventions used in the subroutine descriptions (3039)

examples of matrices (3283)

examples of vectors (3256)

exponential function notation (2995)

expressions, special usage of (3012)

extended error-handling subroutines

handling errors in C (3516)

handling errors in C++ (3552)

handling errors in your Fortran program (3481)

how they work (3205), (3247)

in ESSL and in Fortran, list of (3102)

using them in diagnosing problems (3651)

extended-error-handling subroutines, using

in your C++ program (3557)

in your C program (3521)

in your Fortran program (3483)

extreme eigenvalues and eigenvectors (4785), (4809), (4825)

complex Hermitian matrix (4808)

real symmetric matrix (4807)

factoring

general band matrix (4590)

general matrix (4383), (4413), (4430)

general skyline sparse matrix (4696)

general sparse matrix (4685)

general tridiagonal matrix (4622)

positive definite

complex Hermitian matrix (4456)

real symmetric indefinite matrix (4503), (4507)

real symmetric matrix (4455), (4492)

symmetric band matrix (4606)

symmetric tridiagonal matrix (4665)

symmetric skyline sparse matrix (4703)

tridiagonal matrix (4638), (4649)

fast Fourier transform (FFT) (4848)

FFT (4849)

floor notation and meaning (3003)

fonts used in this book (2953)

formula for transform lengths, interpreting (3169)

formulas for auxiliary storage, interpreting (3161)

Fortran

languages required by ESSL on the workstations (3090)

modifying procedures for using ESSL (3579)

publications (5274)

Fortran considerations

coding programs (3467)

function reference (3712)

handling errors in your program (3486)

Fortran function reference (3472)

Fortran program calling interface (3471)

Fourier transform (4850)

one dimension

complex (4864)

complex-to-real (4876)

cosine transform (4882)

real-to-complex (4870)

sine transform (4889)

three dimensions

complex (4914)

complex-to-real (4926)

real-to-complex (4920)

two dimensions

complex (4896)

complex-to-real (4908)

real-to-complex (4902)

fourier transform subroutines

accuracy considerations (4844)

how they achieve high performance (4851)

performance considerations (4840)

SCFT and DCFT (4863)

SCFT2 and DCFT2 (4895)

SCFT3 and DCFT3 (4913)

SCOSF and DCOSF (4881)

SCRFT and DCRFT (4875)

SCRFT2 and DCRFT2 (4907)

SCRFT3 and DCRFT3 (4925)

SRCFT and DRCFT (4869)

SRCFT2 and DRCFT2 (4901)

SRCFT3 and DRCFT3 (4919)

SSINF and DSINF (4888)

terminology used for (4839)

usage considerations (4835)

Fourier transform subroutines

Frobenius norm notation (3009)

full-matrix storage mode (3431)

full-vector, definition and storage mode (3280)

function

calling sequence in C++ programs (3535)

calling sequence in C programs (3499)

calling sequence in Fortran programs (3470)

function reference (3714)

functional capability of the ESSL subroutines (3050)

functional description, conventions used in the subroutine descriptions (3036)

functions, ESSL (3713)

future migration considerations (3605)

gather vector elements (3963), (3973)

Gaussian quadrature methods

Gauss-Hermite Quadrature (5142)

Gauss-Laguerre Quadrature (5128)

Gauss-Legendre Quadrature (5114)

Gauss-Rational Quadrature (5135)

two-dimensional Gauss-Legendre Quadrature (5121)

general-band storage mode (3372)

general matrix (4342)

general matrix subroutines, names of (4347)

general tridiagonal matrix

definition of (3411)

storage layout (3412)

generalized eigensystem

real general matrices (4817)

real symmetric matrix (4826)

real symmetric positive definite matrix (4827)

generation of random numbers (5144)

Givens plane rotation, constructing (3847)

Glossary (5227)

greek letters notation (3014)

guide information (3040)

guidelines for handling problems (3629)

half band width (3380)

handling errors

in your C++ program (3554)

in your C program (3518)

in your Fortran program (3482)

hardware

required on the workstations (3083)

header file, ESSL, for C (3504), (3511)

header file, ESSL, for C++ (3540), (3547)

Hermitian band matrix

definition of (3392)

storage layout (3395)

Hermitian matrix

definition of (3319)

definition of, complex (3345)

storage layout (3322)

how to use this book (2938), (2940)

Hypertext Markup Language, required products (3094)

i-th zero crossing (4834), (4977)

IBM products, migrating from (3614)

IBM publications (5249)

IBSRCH (5039)

ICAMAX (3731)

IDAMAX (3730)

IDAMIN (3739)

identifying problems (3640)

IDMAX (3746)

IDMIN (3752)

IESSL (5194)

industry areas (3055)

infinity notation (2978)

informational error messages, interpreting (3667)

informational messages, for ESSL (3690)

input-argument errors

diagnosing (3646)

list of messages for (3695), (3699)

overview (3213), (3225), (3230)

input arguments, conventions used in the subroutine descriptions (3033)

input data, conventions for (3134)

installation documentation, Program Directory (5263)

int notation and meaning (3007)

integer data

conventions (2968), (3137)

integral notation (2979)

interchange elements of two vectors (3888)

interface, ESSL

for C++ programs (3529)

for C programs (3493)

for Fortran programs (3464)

interpolating

cubic spline (5083)

local polynomial (5076)

polynomial (5069)

quadratic (4990)

two-dimensional cubic spline (5090)

interpolation subroutines

accuracy considerations (5061)

performance considerations (5059)

SCSIN2 and DCSIN2 (5088)

SCSINT and DCSINT (5081)

SPINT and DPINT (5067)

STPINT and DTPINT (5074)

usage considerations (5057)

introduction to ESSL (3041)

inverse

general matrix (4517)

matrix notation (2988)

positive definite real symmetric matrix (4534)

triangular matrix (4584)

ISAMAX (3729)

ISAMIN (3738)

ISMAX (3745)

ISMIN (3751)

ISO definitions in Glossary (5234)

ISORT (5014)

ISORTS (5030)

ISORTX (5022)

ISSRCH (5048)

italic font usage (2954)

iterative linear system solver

general sparse matrix (4708), (4730), (4735)

sparse negative definite symmetric matrix (4718), (4725)

sparse positive definite symmetric matrix (4717), (4724)

symmetric sparse matrix (4709)

usage considerations (4371)

IZAMAX (3732)

l(2) norm

with no scaling of input (3837)

with scaling of input (3824)

languages supported by ESSL (3077)

LAPACK

ESSL subprograms (5224)

LAPACK, migrating from (3620)

leading dimension for matrices

how it is used for matrices (3292)

how it is used in three dimensions (3456)

least squares solution (4748), (4754)

letters, fonts of (2957)

Level 1 BLAS (5219)

Level 2 BLAS (5221)

Level 3 BLAS (5223)

level of ESSL, getting (5196)

library

migrating from a non-IBM (3624)

migrating from another IBM (3616)

migrating from ESSL Version 2 to Version 3 (3601)

migrating from ESSL Version 3 to Version 3 Release 1.1 (3599)

migrating from ESSL Version 3 to Version 3 Release 1.2 (3597)

migrating from ESSL Version 3 to Version 3 Release 2 (3595)

migrating from ESSL Version 3 to Version 3 Release 3 (3593)

migrating from LAPACK (3622)

overview (3063)

Licensed Program Specification, ESSL (5253)

linear algebra (4336)

linear algebra subprograms (3706), (3707)

accuracy considerations (3723)

list of matrix-vector linear algebra subprograms (3717)

list of sparse matrix-vector linear algebra subprograms (3718)

list of sparse vector-scalar linear algebra subprograms (3716)

list of vector-scalar linear algebra subprograms (3715)

overview (3708)

performance considerations (3721)

usage considerations (3719)

linear algebraic equations

accuracy considerations (4361)

list of banded linear algebraic equation subroutines (4352)

list of dense linear algebraic equations (4351)

list of linear least squares subroutines (4354)

list of sparse linear algebraic equation subroutines (4353)

overview (4344)

performance considerations (4358)

usage considerations (4355)

linear least squares solution

preparing for (4742)

QR decomposition with column pivoting (4766)

QR factorization (4759)

singular value decomposition (4750)

linear least squares subroutines (4341)

DGELS (4757)

DGEQRF (4753)

SGELLS and DGELLS (4764)

SGESVF and DGESVF (4740)

SGESVS and DGESVS (4747)

linking (3571)

C++ programs (3586)

C programs (3581)

dynamic versus static (3572)

Fortran programs (3576)

linking and loading your program

under AIX (3568)

logical data

conventions (2970), (3139)

setting up for C (3509)

setting up for C++ (3545)

long precision

accuracy statement (3072)

meaning of (3176)

lower-band-packed storage mode (3385)

lower band width (3366)

lower-packed storage mode (3298), (3302)

lower-storage-by-rows for symmetric sparse matrices (3444)

lower storage mode (3300), (3304)

lower-triangular-band-packed storage mode (3402), (3407)

lower-triangular-packed storage mode (3357), (3359)

lower-triangular storage mode (3355), (3361)

mailing list for ESSL customers (3096)

masking underflow

for performance (3195)

why you should (3183)

math and programming notations (3024)

math background publications (5242)

mathematical expressions, conventions for (3013)

mathematical functions, overview (3052)

matrix

band matrix (3363)

complex Hermitian band matrix (3391)

complex Hermitian matrix (3318), (3344)

complex Hermitian Toeplitz matrix (3342)

conventions for (2975)

description of (3282)

font for (2961)

full or dense matrix (3430)

general tridiagonal matrix (3409)

leading dimension for (3293)

negative definite complex Hermitian matrix (3327)

negative definite symmetric matrix (3309)

positive definite complex Hermitian matrix (3325)

positive definite symmetric band matrix (3388)

positive definite symmetric matrix (3307)

positive definite symmetric tridiagonal matrix (3422)

sparse matrix (3427)

storage of (3290)

symmetric band matrix (3378)

symmetric matrix (3295)

symmetric tridiagonal matrix (3416)

Toeplitz matrix (3334)

triangular band matrices (3398)

triangular matrices (3351)

matrix-matrix product

complex Hermitian matrix (4272)

complex symmetric matrix (4271)

general matrices, their transposes, or their conjugate transposes (4248)

real symmetric matrix (4270)

triangular matrix (4283)

matrix operation subroutines

accuracy considerations (4177)

performance considerations (4175)

SGEADD, DGEADD, CGEADD, and ZGEADD (4187)

SGEMM, DGEMM, CGEMM, and ZGEMM (4246)

SGEMMS, DGEMMS, CGEMMS, and ZGEMMS (4230)

SGEMUL, DGEMUL, CGEMUL, and ZGEMUL (4215)

SGESUB, DGESUB, CGESUB, and ZGESUB (4201)

SGETMI, DGETMI, CGETMI, and ZGETMI (4324)

SGETMO, DGETMO, CGETMO, and ZGETMO (4334)

SSYMM, DSYMM, CSYMM, ZSYMM, CHEMM, and ZHEMM (4266)

SSYR2K, DSYR2K, CSYR2K, ZSYR2K, CHER2K, and ZHER2K (4312)

SSYRK, DSYRK, CSYRK, ZSYRK, CHERK, and ZHERK (4296)

STRMM, DTRMM, CTRMM, and ZTRMM (4281)

usage considerations (4173)

matrix-vector linear algebra subprograms

SGBMV, DGBMV, CGBMV, and ZGBMV (4110)

SGEMX, DGEMX, SGEMTX, DGEMTX, SGEMV, DGEMV, CGEMV, and ZGEMV (4014)

SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC (4029)

SSBMV, DSBMV, CHBMV, and ZHBMV (4121)

SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX and DSLMX (4051)

SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 (4076)

SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2 (4099)

STBMV, DTBMV, CTBMV, and ZTBMV (4153)

STPMV, DTPMV, CTPMV, ZTPMV, STRMV, DTRMV, CTRMV, and ZTRMV (4142)

matrix-vector product

complex Hermitian band matrix (4125)

complex Hermitian matrix (4055)

general band matrix, its transpose, or its conjugate transpose (4112)

general matrix, its transpose, or its conjugate transpose (4016)

real symmetric band matrix (4124)

real symmetric matrix (4054)

sparse matrix (4160)

sparse matrix or its transpose (4169)

triangular band matrix, its transpose, or its conjugate transpose (4155)

triangular matrix, its transpose, or its conjugate transpose (4144)

max notation and meaning (3005)

maximum

absolute value (3735)

value (3748)

meanings of words in the Glossary (5228)

messages

ESSL and attention messages, interpreting (3678)

ESSL informational messages, interpreting (3672)

ESSL miscellaneous messages, interpreting (3684)

ESSL resource messages, interpreting (3666)

list of ESSL messages (3694), (3698)

message conventions (3692)

migrating

from ESSL/370 (3611)

from ESSL Version 2 to Version 3 (3602)

from ESSL Version 3 to Version 3 Release 1.1 (3600)

from ESSL Version 3 to Version 3 Release 1.2 (3598)

from ESSL Version 3 to Version 3 Release 2 (3596)

from ESSL Version 3 to Version 3 Release 3 (3594)

from LAPACK (3619)

from non-IBM libraries (3625)

from other IBM subroutine libraries (3613)

future migration considerations (3606)

IBM

pSeries and RS/6000 processors considerations (3609)

programs to ESSL (3590)

RS/6000 and IBM

pSeries processors considerations (3610)

min notation and meaning (3006)

minimum

absolute value (3742)

value (3754)

miscellaneous error messages, interpreting (3679)

mod notation and meaning (3008)

modification level of ESSL, getting (5200)

modifying

C++ programs, for using Parallel ESSL (3585)

C programs, for using ESSL (3580)

Fortran programs, for using ESSL (3575)

modulo notation (3021)

multiplying

compute SAXPY or DAXPY N times (3807)

general matrices, their transposes, or their conjugate transposes (4216)

general matrices using Strassen's algorithm (4231)

notation (2985)

sparse vector x by a scalar, add sparse vector y, and store in vector y (3983)

vector x by a scalar, add to vector y, and store in vector y (3776)

vector x by a scalar, add to vector y, and store in vector z (3943)

vector x by a scalar and store in vector x (3878)

vector x by a scalar and store in vector y (3933)

vector x by vector y, and store in vector z (3919)

multithreaded

definition (5235)

ESSL subroutines (3121)

name usage restrictions (3123)

names in ESSL with an underscore (_) prefix, how to interpret (2945)

names of

products and acronyms (2950)

the eigensystem analysis subroutines (4771)

the Fourier transform, convolution and correlation, and related-computation subroutines (4830)

the interpolation subroutines (5056)

the linear algebra subprograms (3710)

the linear algebraic equations subroutines (4350)

the matrix operations subroutines (4172)

the numerical quadrature subroutines (5093)

the random number generation subroutines (5146)

the sorting and searching subroutines (5004)

the utility subroutines (5172)

National Language Support (3637)

negative definite complex Hermitian matrix

definition of (3326)

negative definite complex Hermitian Toeplitz matrix

definition of (3341)

negative definite Hermitian matrix

storage layout (3330)

negative definite symmetric matrix

definition of (3308)

storage layout (3312)

negative definite symmetric Toeplitz matrix

definition of (3333)

negative stride, for vectors (3273)

NLS, National Language Support (3638)

non-IBM library, migrating from (3623)

norm notation (2996)

normally distributed random numbers, generate (5162)

notations and conventions (2964)

notes, conventions used in the subroutine descriptions (3035)

number of subroutines in each area (3062)

numbers (3100)

accuracy of computations (3182)

accuracy of computations, for ESSL (3075)

numerical quadrature

accuracy considerations (5098)

performance considerations (5096)

programming considerations for SUBF (5100)

usage considerations (5094)

numerical quadrature performed

on a function

using Gauss-Hermite Quadrature (5141)

using Gauss-Laguerre Quadrature (5127)

using Gauss-Legendre Quadrature (5113)

using Gauss-Rational Quadrature (5134)

using two-dimensional Gauss-Legendre Quadrature (5120)

on a set of points (5107)

numerical quadrature subroutines

SGHMQ and DGHMQ (5140)

SGLGQ and DGLGQ (5126)

SGLNQ and DGLNQ (5112)

SGLNQ2 and DGLNQ2 (5119)

SGRAQ and DGRAQ (5133)

SPTNQ and DPTNQ (5106)

one norm notation (3000)

online documentation

online Guide and Reference manual (5264)

required Hypertext Markup Language products (3095)

option table, default values for ESSL errors (3239)

order numbers of the publications (5258)

ordering IBM publications (5259)

output

accuracy on different processors (3069)

how errors affect output (3204)

output arguments, conventions used in the subroutine descriptions (3034)

overflow, avoiding (3826)

overview

of eigensystem analysis (4770)

of ESSL (3043)

of Fourier transforms, convolutions and correlations, and related computations (4829)

of interpolation (5055)

of linear algebra subprograms (3709)

of linear algebraic equations (4345)

of matrix operations (4171)

of numerical quadrature (5092)

of random number generation (5145)

of sorting and searching (5003)

of the documentation (5248)

of utility subroutines (5171)

packed band storage mode (3368)

packed-Hermitian-Toeplitz storage mode (3349)

packed-symmetric-Toeplitz storage mode (3339)

parallel processing

introduction to (3065)

performance

achieving better performance in your program (3185)

aspects of parallel processing on the workstations (3064)

coding techniques that affect performance (3192)

considerations for dense and banded linear algebraic equations (4359)

considerations for eigensystem analysis (4773)

considerations for Fourier transforms, convolutions, and correlations (4842)

considerations for interpolation (5060)

considerations for linear algebra subprograms (3722)

considerations for matrix operations (4176)

considerations for numerical quadrature (5097)

considerations for related computations (4856)

considerations for sorting and searching (5008)

how the Fourier transforms achieve high performance (4852)

information on ESSL run-time performance (3198)

tradeoffs for convolution and correlation subroutines (4854)

where to find information on (3197)

pi notation (2980)

PL/I

publications (5275)

PL/I (Programming Language/I)

handling errors in your program (3522), (3558)

plane rotation

applying a (3863)

constructing a Givens (3848)

planning, publications for (5262)

planning your program (3107)

polynomial

evaluating (4971)

interpolating (5068), (5075)

positive definite complex Hermitian matrix

definition of (3324)

positive definite complex Hermitian Toeplitz matrix

definition of (3340)

positive definite Hermitian matrix

storage layout (3328)

positive definite symmetric band matrix

definition of (3387)

storage layout (3389)

positive definite symmetric band matrix subroutines, names of (4348)

positive definite symmetric matrix

definition of (3306)

storage layout (3310)

positive definite symmetric matrix subroutines, names of (4349)

positive definite symmetric Toeplitz matrix

definition of (3332)

positive definite symmetric tridiagonal matrix (3424)

definition of (3423)

storage layout (3425)

positive stride, for vectors (3269)

precision, meaning of (3177)

precision, short and long (3073)

problems, handling (3628)

problems, IBM support for (3636)

processing your program

requirements for ESSL on the workstations (3081)

steps involved in (3563)

using parallel subroutines on the workstations (3066)

processor-independent formulas for auxiliary storage, interpreting (3162)

product (3777)

matrix-matrix

complex Hermitian matrix (4269)

complex symmetric matrix (4268)

general matrices, their transposes, or their conjugate transposes (4247)

real symmetric matrix (4267)

triangular matrix (4282)

matrix-vector

complex Hermitian band matrix (4123)

complex Hermitian matrix (4053)

general band matrix, its transpose, or its conjugate transpose (4111)

general matrix, its transpose, or its conjugate transpose (4015)

real symmetric band matrix (4122)

real symmetric matrix (4052)

sparse matrix (4159)

sparse matrix or its transpose (4168)

triangular band matrix, its transpose, or its conjugate transpose (4154)

triangular matrix, its transpose, or its conjugate transpose (4143)

product names, acronyms for (2949)

products, programming

migrating from LAPACK (3621)

migrating from other IBM (3615)

required by ESSL on the workstations, programming (3088)

profile-in skyline storage mode (3450)

program

attention messages, overview (3229)

coding (3460)

computational errors (3219)

design (3109)

errors (3209)

handling errors in your C++ program (3555)

handling errors in your C program (3519)

handling errors in your Fortran program (3484)

input-argument errors, overview (3212)

interface for C++ programs (3531)

interface for C programs (3495)

interface for Fortran programs (3466)

migrated to ESSL (3591)

performance, achieving high (3190)

processing your program (3564)

resource errors, overview (3224)

setting up your data structures (3249)

types of data in your program (3131)

when coding large applications (3243)

program exceptions

description of ESSL (3206)

program exceptions, diagnosing (3642)

program number for ESSL (5257)

programming considerations for SUBF in numerical quadrature (5101)

programming items, font for (2963)

programming products

required by ESSL on the workstations (3086)

programming publications (5266), (5272)

PTF

getting the most recent level applied (5197)

publications

list of ESSL (5251)

math background (5243)

related (5270)

QR decomposition with column pivoting (4765)

QR factorization (4758)

quadratic interpolation (3099), (4989)

random number generation

long period uniformly distributed (5168)

normally distributed (5161)

uniformly distributed (5154)

usage considerations (5147)

random number generation subroutines

SNRAND and DNRAND (5160)

SURAND and DURAND (5153)

SURXOR and DURXOR (5167)

rank-2k update

complex Hermitian matrix (4315)

complex symmetric matrix (4314)

real symmetric matrix (4313)

rank-k update

complex Hermitian matrix (4299)

complex symmetric matrix (4298)

real symmetric matrix (4297)

rank-one update

complex Hermitian matrix (4078)

general matrix (4030)

real symmetric matrix (4077)

rank-two update

complex Hermitian matrix (4101)

real symmetric matrix (4100)

real and complex array elements (3477)

real data

conventions (2969), (3138)

real general matrix eigensystem analysis subroutine (4768)

real symmetric matrix eigensystem analysis subroutine (4769)

reciprocal of the condition number

general matrix (4431), (4520)

positive definite real symmetric matrix (4493), (4537)

reference for ESSL, online (5267)

reference information

ESSL online information (5268)

math background texts and reports (5246)

organization of (3701)

what is in each subroutine description and the conventions used (3029)

related-computation subroutines

accuracy considerations (4857)

CWLEV and ZWLEV (5000)

performance considerations (4855)

SIZC and DIZC (4976)

SPOLY and DPOLY (4970)

SQINT and DQINT (4988)

STREC and DTREC (4982)

SWLEV and DWLEV (4999)

related publications (5269)

release of ESSL, getting (5198)

reporting problems to IBM (3631)

required publications (5250)

requirements

auxiliary working storage (3152), (3156)

for ESSL workstation product (3080)

software products on the workstations (3085)

transforms in storage, lengths of (3164)

workstation hardware (3082)

resource error messages, interpreting (3661)

restrictions, ESSL coding (3124)

results

accuracy on different processors (3074)

how accuracy is affected by the nature of the computation (3180)

in C++ programs (3538)

in C programs (3502)

in Fortran programs (3473)

multiplication of NaN (3181)

results transposed and conjugate transposed for matrix multiplication (4221), (4237), (4253)

results transposed for matrix addition (4192)

results transposed for matrix subtraction (4206)

return code

in C++ programs (3562)

in C programs (3526)

in Fortran programs (3490)

using during diagnosis (3660)

rotation

applying a plane (3864)

constructing a Givens plane (3849)

routine names (3125)

row vector (3254)

run-time performance

optimizing in your program (3189)

run-time problems, diagnosing

attention error messages, interpreting (3675)

computational errors (3656)

informational error messages, interpreting (3669)

input-argument errors (3650)

miscellaneous error messages, interpreting (3681)

resource error messages, interpreting (3663)

running your program

C++ programs (3587)

C programs (3582)

Fortran programs (3577)

SACOR (4957)

SACORF (4962)

SASUM (3759)

SAXPY (3771)

SAXPYI (3978)

SBSRCH (5040)

scalar data

conventions (2966), (3135)

scalar items, font for (2959)

scale argument used for Fourier transform subroutines (4847)

scaling, when to use (3196)

SCASUM (3761)

scatter vector elements (3953)

SCFT (4861)

SCFT2 (4893)

SCFT3 (4911)

SCNRM2 (3820)

SCON (4929)

SCOND (4936)

SCONF (4942)

SCOPY (3782)

SCOR (4930)

SCORD (4937)

SCORF (4943)

SCOSF (4879)

SCOSFT, no documentation provided for (4831)

SCRFT (4873)

SCRFT2 (4905)

SCRFT3 (4923)

SCSIN2 (5086)

SCSINT (5079)

SDCON (4950)

SDCOR (4952)

SDOT (3794)

SDOTI (3990)

searching

binary (5044)

sequential (5053)

selecting an ESSL library (3113)

selecting an ESSL subroutine (3117)

sequences

conventions for (2976)

description of (3451)

storage layout (3452)

sequential search (5052)

service, IBM (3634)

setting up

AIX procedures (3570)

setting up your data (3132)

SGBF (4587)

SGBMV (4106)

SGBS (4593)

SGEADD (4183)

SGEEV (4779)

SGEF (4378)

SGEFCD (4427)

SGEGV (4813)

SGEICD (4512)

SGELLS (4762)

SGEMM (4242)

SGEMMS (4226)

SGEMTX (4012)

SGEMUL (4211)

SGEMV (4006)

SGEMX (4010)

SGER (4023)

SGES (4388)

SGESM (4398)

SGESUB (4197)

SGESVF (4738)

SGESVS (4745)

SGETMI (4320)

SGETMO (4330)

SGETRF (4408)

SGETRI (4514)

SGETRS (4418)

SGHMQ (5138)

SGLGQ (5124)

SGLNQ (5110)

SGLNQ2 (5117)

SGRAQ (5131)

SGTF (4619)

SGTHR (3958)

SGTHRZ (3968)

SGTNP (4633)

SGTNPF (4644)

SGTNPS (4654)

SGTS (4625)

short precision

accuracy statement (3071)

meaning of (3175)

SIGN notation and meaning (3023)

signal processing subroutines (4832)

simple formulas for auxiliary storage, interpreting (3163)

sin notation (3019)

sine transform (4890)

singular value decomposition for a general matrix (4741), (4749)

SIZC (4974)

size of array

required for a vector (3264)

skyline solvers

usage considerations (4367)

skyline storage mode for sparse matrices, diagonal-out (3446)

skyline storage mode for sparse matrices, profile-in (3449)

SL MATH (Subroutine Library--Mathematics)

migrating from (3617)

SLSS (Subscription Library Services System) (5255)

SMP

definition (5236)

ESSL Library, why use it (3119)

ESSL multithreaded subroutines (3120)

performance (3076)

SNAXPY (3804)

SNDOT (3810)

SNORM2 (3831)

SNRAND (5158)

SNRM2 (3818)

software products

required by ESSL on the workstations (3087)

required by Hypertext Markup Language (3093)

solving

general band matrix (4596)

general matrix or its transpose (4393), (4423)

general skyline sparse matrix (4694)

general sparse matrix or its transpose (4690)

general tridiagonal matrix (4628), (4639), (4659)

iterative linear system solver

general sparse matrix (4710), (4729), (4734)

sparse negative definite symmetric matrix (4716), (4723)

sparse positive definite symmetric matrix (4715), (4722)

symmetric sparse matrix (4711)

multiple right-hand sides

general matrix, its transpose, or its conjugate transpose (4403), (4424)

positive definite complex Hermitian matrix (4481)

positive definite real symmetric matrix (4480)

triangular matrix (4566)

positive definite

real symmetric matrix (4462)

symmetric band matrix (4616)

symmetric tridiagonal matrix (4671)

symmetric skyline sparse matrix (4701)

triangular band matrix (4681)

triangular matrix (4556)

some eigenvalues and eigenvectors (4810)

sorting

elements of a sequence (5018)

index (5026)

stable sort (5034)

sorting and searching subroutines

accuracy considerations (5009)

IBSRCH, SBSRCH, and DBSRCH (5042)

ISORT, SSORT, and DSORT (5017)

ISORTS, SSORTS, and DSORTS (5033)

ISORTX, SSORTX, and DSORTX (5025)

ISSRCH, SSSRCH, and DSSRCH (5051)

performance considerations (5007)

usage considerations (5005)

sparse linear algebraic equation subroutines (4340)

DGKFS (4693)

DGSF (4684)

DGSS (4689)

DSDCG (4721)

DSDGCG (4733)

DSKFS (4700)

DSMCG (4714)

DSMGCG (4728)

DSRIS (4707)

sparse matrix, definition and storage modes (3428)

sparse matrix subroutines

direct solvers (4362)

iterative linear system solvers (4370)

performance and accuracy considerations (4365), (4369), (4373)

skyline solvers (4366)

sparse matrix-vector linear algebra subprograms

DSDMX (4167)

DSMMX (4158)

DSMTM (4163)

sparse vector, definition and storage modes (3276)

sparse vector-scalar linear algebra subprograms

SAXPYI, DAXPYI, CAXPYI, and ZAXPYI (3982)

SDOTI, DDOTI, CDOTUI, ZDOTUI, CDOTCI, and, ZDOTCI (3996)

SGTHR, DGTHR, CGTHR, and ZGTHR (3962)

SGTHRZ, DGTHRZ, CGTHRZ, and ZGTHRZ (3972)

SSCTR, DSCTR, CSCTR, and ZSCTR (3952)

SPBCHF (4603)

SPBCHS (4613)

SPBF (4601)

SPBS (4611)

special usage

of matrix addition (4190)

of matrix multiplication (4219), (4235), (4251)

of matrix subtraction (4204)

spectral norm notation (3002)

SPINT (5065)

SPOF (4446)

SPOFCD (4488)

SPOICD (4529)

SPOLY (4968)

SPOSM (4471)

SPOTRF (4450)

SPOTRI (4531)

SPOTRS (4475)

SPPF (4444)

SPPFCD (4486)

SPPICD (4527)

SPPS (4459)

SPTF (4662)

SPTNQ (5104)

SPTS (4668)

SQINT (4986)

square root notation (2982)

SRCFT (4867)

SRCFT2 (4899)

SRCFT3 (4917)

SROT (3856)

SROTG (3842)

SSBMV (4117)

SSCAL (3871)

SSCTR (3948)

SSINF (4886)

SSLMX (4049)

SSLR1 (4066)

SSLR2 (4097)

SSORT (5015)

SSORTS (5031)

SSORTX (5023)

SSP (Scientific Subroutine Package)

migrating from (3618)

SSPEV (4791)

SSPMV (4041)

SSPR (4068)

SSPR2 (4089)

SSPSV (4802)

SSSRCH (5049)

SSWAP (3883)

SSYGV (4820)

SSYMM (4260)

SSYMV (4045)

SSYR (4072)

SSYR2 (4093)

SSYR2K (4306)

SSYRK (4290)

stable sort (5035)

STBMV (4149)

STBSV (4676)

stepping through storage, for matrices (3288)

stepping through storage, for vectors (3268)

storage

array storage techniques overview (3129)

auxiliary working storage requirements (3153), (3158)

compressed-diagonal storage mode for sparse matrices (3435)

compressed-matrix storage mode for sparse matrices (3433)

considerations when designing your program (3127)

diagonal-out skyline storage mode for sparse matrices (3445)

for matrices (3289)

for vectors (3261)

layout for a complex Hermitian band matrix (3396)

layout for a complex Hermitian matrix (3323)

layout for a general tridiagonal matrix (3414)

layout for a negative definite Hermitian matrix (3331)

layout for a negative definite symmetric matrix (3313)

layout for a positive definite Hermitian matrix (3329)

layout for a positive definite symmetric matrix (3311)

layout for a positive definite symmetric tridiagonal matrix (3426)

layout for a sequence (3453), (3454), (3455)

layout for a symmetric indefinite matrix (3317)

layout for a symmetric tridiagonal matrix (3420)

layout for a Toeplitz matrix (3338), (3348)

layout for band matrices (3367), (3371), (3374)

layout for positive definite symmetric band matrices (3390)

layout for sparse matrices (3429)

layout for sparse vectors (3279)

layout for symmetric band matrices (3382)

layout for symmetric matrices (3297)

layout for triangular band matrices (3400), (3403), (3406)

layout for triangular matrices (3353)

list of subroutines using auxiliary storage (3151)

list of subroutines using transforms (3168)

of arrays in Fortran (3476)

profile-in skyline storage mode for sparse matrices (3448)

storage-by-columns for sparse matrices (3439)

storage-by-indices for sparse matrices (3437)

storage-by-rows for sparse matrices (3441)

tradeoffs for input (3194)

transform length requirements (3166)

storage-by-columns for sparse matrices (3440)

storage-by-indices for sparse matrices (3438)

storage-by-rows for sparse matrices (3442)

storage conversion subroutine

general skyline sparse matrix (5212)

sparse matrix (5208)

symmetric skyline sparse matrix (5216)

STPI (4577)

STPINT (5072)

STPMV (4138)

STPSV (4550)

STPTRI (4581)

Strassen's algorithm, multiplying general matrices (4232)

STREC (4980)

STRI (4575)

stride

defining vectors in arrays (3266)

how it is used in three dimensions (3457)

negative (3274)

optimizing for your Fourier transforms (4846)

positive (3270)

subroutine for optimizing Fourier transforms (5204)

zero (3272)

STRIDE (5202)

STRMM (4277)

STRMV (4134)

STRSM (4561)

STRSV (4546)

STRTRI (4579)

structures, data (vectors and matrices) (3252)

subject code for ESSL documentation (5256)

subprogram

linear algebra (3704)

meaning of (2942), (3711)

subprogram, definition (2944)

subroutine

calling sequence format for C++ programs (3530)

calling sequence format for C programs (3494)

calling sequence format for Fortran programs (3465)

choose of (3112), (3116)

conventions used in the description of (3027)

overview of ESSL (3061)

subroutine, definition (2943)

subroutines, ESSL

CAXPY (3769)

CAXPYI (3976)

CCOPY (3780)

CDOTC (3792)

CDOTCI (3988)

CDOTU (3790)

CDOTUI (3986)

CGBMV (4104)

CGEADD (4181)

CGEEV (4777)

CGEF (4376)

CGEMM (4240)

CGEMMS (4224)

CGEMUL (4209)

CGEMV (4000)

CGERC (4021)

CGERU (4019)

CGES (4386)

CGESM (4396)

CGESUB (4195)

CGETMI (4318)

CGETMO (4328)

CGETRF (4406)

CGETRS (4416)

CGTHR (3956)

CGTHRZ (3966)

CGTNP (4631)

CGTNPF (4642)

CGTNPS (4652)

CHBMV (4115)

CHEMM (4258)

CHEMV (4037)

CHER (4062)

CHER2 (4085)

CHER2K (4304)

CHERK (4288)

CHPEV (4789)

CHPMV (4033)

CHPR (4058)

CHPR2 (4081)

CHPSV (4800)

CNORM2 (3829)

CPOF (4438)

CPOSM (4465)

CPOTRF (4442)

CPOTRS (4469)

CROT (3852)

CROTG (3840)

CSCAL (3867)

CSCTR (3946)

CSROT (3854)

CSSCAL (3869)

CSWAP (3881)

CSYAX (3924)

CSYMM (4256)

CSYR2K (4302)

CSYRK (4286)

CTBMV (4147)

CTBSV (4674)

CTPMV (4132)

CTPSV (4544)

CTRMM (4275)

CTRMV (4128)

CTRSM (4559)

CTRSV (4540)

CVEA (3892)

CVEM (3912)

CVES (3902)

CWLEV (4993)

CYAX (3922)

CZAXPY (3936)

DASUM (3756)

DAXPY (3768)

DAXPYI (3975)

DBSRCH (5038)

DBSSV (4496)

DBSTRF (4500)

DBSTRS (4504)

DCFT (4860)

DCFT2 (4892)

DCFT3 (4910)

DCOPY (3779)

DCOSF (4878)

DCRFT (4872)

DCRFT2 (4904)

DCRFT3 (4922)

DCSIN2 (5085)

DCSINT (5078)

DDCON (4947)

DDCOR (4949)

DDOT (3789)

DDOTI (3985)

DGBF (4586)

DGBMV (4103)

DGBS (4592)

DGEADD (4180)

DGEEV (4776)

DGEF (4375)

DGEFCD (4426)

DGEGV (4812)

DGEICD (4509)

DGELLS (4761)

DGELS (4756)

DGEMM (4239)

DGEMMS (4223)

DGEMTX (4005)

DGEMUL (4208)

DGEMV (3999)

DGEMX (4003)

DGEQRF (4751)

DGER (4018)

DGES (4385)

DGESM (4395)

DGESUB (4194)

DGESVF (4737)

DGESVS (4744)

DGETMI (4317)

DGETMO (4327)

DGETRF (4405)

DGETRI (4511)

DGETRS (4415)

DGHMQ (5137)

DGKFS (4691)

DGKTRN (5209)

DGLGQ (5123)

DGLNQ (5109)

DGLNQ2 (5116)

DGRAQ (5130)

DGSF (4682)

DGSS (4687)

DGTF (4618)

DGTHR (3955)

DGTHRZ (3965)

DGTNP (4630)

DGTNPF (4641)

DGTNPS (4651)

DGTS (4624)

DIZC (4973)

DNAXPY (3803)

DNDOT (3809)

DNORM2 (3828)

DNRAND (5157)

DNRM2 (3815)

DPBCHF (4600)

DPBCHS (4610)

DPBF (4598)

DPBS (4608)

DPINT (5064)

DPOF (4437)

DPOFCD (4485)

DPOICD (4524)

DPOLY (4967)

DPOSM (4464)

DPOTRF (4441)

DPOTRI (4526)

DPOTRS (4468)

DPPF (4435)

DPPFCD (4483)

DPPICD (4522)

DPPS (4458)

DPTF (4661)

DPTNQ (5103)

DPTS (4667)

DQINT (4985)

DRCFT (4866)

DRCFT2 (4898)

DRCFT3 (4916)

DROT (3851)

DROTG (3839)

DSBMV (4114)

DSCAL (3866)

DSCTR (3945)

DSDCG (4719)

DSDGCG (4731)

DSDMX (4165)

DSINF (4885)

DSKFS (4698)

DSKTRN (5213)

DSLMX (4040)

DSLR1 (4065)

DSLR2 (4088)

DSMCG (4712)

DSMGCG (4726)

DSMMX (4156)

DSMTM (4161)

DSORT (5013)

DSORTS (5029)

DSORTX (5021)

DSPEV (4788)

DSPMV (4032)

DSPR (4057)

DSPR2 (4080)

DSPSV (4799)

DSRIS (4705)

DSRSM (5205)

DSSRCH (5047)

DSWAP (3880)

DSYGV (4819)

DSYMM (4255)

DSYMV (4036)

DSYR (4061)

DSYR2 (4084)

DSYR2K (4301)

DSYRK (4285)

DTBMV (4146)

DTBSV (4673)

DTPI (4570)

DTPINT (5071)

DTPMV (4131)

DTPSV (4543)

DTPTRI (4574)

DTREC (4979)

DTRI (4568)

DTRMM (4274)

DTRMV (4127)

DTRSM (4558)

DTRSV (4539)

DTRTRI (4572)

DURAND (5150)

DURXOR (5164)

DVEA (3891)

DVEM (3911)

DVES (3901)

DWLEV (4992)

DYAX (3921)

DZASUM (3758)

DZAXPY (3935)

DZNRM2 (3817)

EINFO (5177)

ERRSAV (5181)

ERRSET (5185)

ERRSTR (5189)

IBSRCH (5036)

ICAMAX (3727)

IDAMAX (3726)

IDAMIN (3737)

IDMAX (3744)

IDMIN (3750)

IESSL (5193)

ISAMAX (3725)

ISAMIN (3736)

ISMAX (3743)

ISMIN (3749)

ISORT (5011)

ISORTS (5027)

ISORTX (5019)

ISSRCH (5045)

IZAMAX (3728)

SACOR (4956)

SACORF (4961)

SASUM (3755)

SAXPY (3767)

SAXPYI (3974)

SBSRCH (5037)

SCASUM (3757)

SCFT (4859)

SCFT2 (4891)

SCFT3 (4909)

SCNRM2 (3816)

SCON (4927)

SCOND (4934)

SCONF (4940)

SCOPY (3778)

SCOR (4928)

SCORD (4935)

SCORF (4941)

SCOSF (4877)

SCRFT (4871)

SCRFT2 (4903)

SCRFT3 (4921)

SCSIN2 (5084)

SCSINT (5077)

SDCON (4946)

SDCOR (4948)

SDOT (3788)

SDOTI (3984)

SGBF (4585)

SGBMV (4102)

SGBS (4591)

SGEADD (4179)

SGEEV (4775)

SGEF (4374)

SGEFCD (4425)

SGEGV (4811)

SGEICD (4508)

SGELLS (4760)

SGEMM (4238)

SGEMMS (4222)

SGEMTX (4004)

SGEMUL (4207)

SGEMV (3998)

SGEMX (4002)

SGER (4017)

SGES (4384)

SGESM (4394)

SGESUB (4193)

SGESVF (4736)

SGESVS (4743)

SGETMI (4316)

SGETMO (4326)

SGETRF (4404)

SGETRI (4510)

SGETRS (4414)

SGHMQ (5136)

SGLGQ (5122)

SGLNQ (5108)

SGLNQ2 (5115)

SGRAQ (5129)

SGTF (4617)

SGTHR (3954)

SGTHRZ (3964)

SGTNP (4629)

SGTNPF (4640)

SGTNPS (4650)

SGTS (4623)

SIZC (4972)

SNAXPY (3802)

SNDOT (3808)

SNORM2 (3827)

SNRAND (5156)

SNRM2 (3814)

SPBCHF (4599)

SPBCHS (4609)

SPBF (4597)

SPBS (4607)

SPINT (5063)

SPOF (4436)

SPOFCD (4484)

SPOICD (4523)

SPOLY (4966)

SPOSM (4463)

SPOTRF (4440)

SPOTRI (4525)

SPOTRS (4467)

SPPF (4434)

SPPFCD (4482)

SPPICD (4521)

SPPS (4457)

SPTF (4660)

SPTNQ (5102)

SPTS (4666)

SQINT (4984)

SRCFT (4865)

SRCFT2 (4897)

SRCFT3 (4915)

SROT (3850)

SROTG (3838)

SSBMV (4113)

SSCAL (3865)

SSCTR (3944)

SSINF (4884)

SSLMX (4039)

SSLR1 (4064)

SSLR2 (4087)

SSORT (5012)

SSORTS (5028)

SSORTX (5020)

SSPEV (4787)

SSPMV (4031)

SSPR (4056)

SSPR2 (4079)

SSPSV (4798)

SSSRCH (5046)

SSWAP (3879)

SSYGV (4818)

SSYMM (4254)

SSYMV (4035)

SSYR (4060)

SSYR2 (4083)

SSYR2K (4300)

SSYRK (4284)

STBMV (4145)

STBSV (4672)

STPI (4569)

STPINT (5070)

STPMV (4130)

STPSV (4542)

STPTRI (4573)

STREC (4978)

STRI (4567)

STRIDE (5201)

STRMM (4273)

STRMV (4126)

STRSM (4557)

STRSV (4538)

STRTRI (4571)

SURAND (5149)

SURXOR (5163)

SVEA (3890)

SVEM (3910)

SVES (3900)

SWLEV (4991)

SYAX (3920)

SZAXPY (3934)

ZAXPY (3770)

ZAXPYI (3977)

ZCOPY (3781)

ZDOTC (3793)

ZDOTCI (3989)

ZDOTU (3791)

ZDOTUI (3987)

ZDROT (3855)

ZDSCAL (3870)

ZDYAX (3925)

ZGBMV (4105)

ZGEADD (4182)

ZGEEV (4778)

ZGEF (4377)

ZGEMM (4241)

ZGEMMS (4225)

ZGEMUL (4210)

ZGEMV (4001)

ZGERC (4022)

ZGERU (4020)

ZGES (4387)

ZGESM (4397)

ZGESUB (4196)

ZGETMI (4319)

ZGETMO (4329)

ZGETRF (4407)

ZGETRS (4417)

ZGTHR (3957)

ZGTHRZ (3967)

ZGTNP (4632)

ZGTNPF (4643)

ZGTNPS (4653)

ZHBMV (4116)

ZHEMM (4259)

ZHEMV (4038)

ZHER (4063)

ZHER2 (4086)

ZHER2K (4305)

ZHERK (4289)

ZHPEV (4790)

ZHPMV (4034)

ZHPR (4059)

ZHPR2 (4082)

ZHPSV (4801)

ZNORM2 (3830)

ZPOF (4439)

ZPOSM (4466)

ZPOTRF (4443)

ZPOTRS (4470)

ZROT (3853)

ZROTG (3841)

ZSCAL (3868)

ZSCTR (3947)

ZSWAP (3882)

ZSYMM (4257)

ZSYR2K (4303)

ZSYRK (4287)

ZTBMV (4148)

ZTBSV (4675)

ZTPMV (4133)

ZTPSV (4545)

ZTRMM (4276)

ZTRMV (4129)

ZTRSM (4560)

ZTRSV (4541)

ZVEA (3893)

ZVEM (3913)

ZVES (3903)

ZWLEV (4994)

ZYAX (3923)

ZZAXPY (3937)

subscript notation, what it means (2991)

subtracting

general matrices or their transposes (4202)

vector y from vector x and store in vector z (3909)

sum, calculating

absolute values (3766)

summation notation (3018)

superscript notation, what it means (2990)

support, IBM (3635)

SURAND (5151)

SURXOR (5165)

SVEA (3894)

SVEM (3914)

SVES (3904)

swap elements of two vectors (3889)

SWLEV (4995)

SYAX (3926)

symbols, special usage of (3011)

symmetric band matrix

definition of (3377)

storage layout (3381)

symmetric indefinite matrix

definition of (3314)

storage layout (3316)

symmetric indefinite matrix (3315)

real symmetric indefinite matrix (4499)

symmetric matrix

definition of (3294)

storage layout (3296)

symmetric tridiagonal matrix (3418)

definition of (3417)

storage layout (3419)

symmetric-tridiagonal storage mode (3421)

symptoms, identifying problem (3641)

syntax, conventions used in the subroutine descriptions (3030)

syntax rules for call statements and data (3147)

SZAXPY (3938)

table, default values for ESSL error option (3240)

termination, program

attention messages (3231)

computational errors (3215)

input-argument errors (3214)

resource errors (3226)

terminology, names of products (2947)

terminology in the Glossary (5231)

terminology used for Fourier transforms, convolutions, and correlations (4838)

textbooks cited (5241)

thread-safe

definition (5237)

ESSL Library, why use it (3122)

three-dimensional data structures, how stride is used for (3458)

time-varying recursive filter (3097), (4983)

times notation, multiply (2984)

timings, achieving high performance in your program (3188)

Toeplitz matrix (3336)

definition of (3335), (3343)

storage layout (3337), (3347)

traceback map, using during diagnosis (3652)

trademarks (5225)

transform lengths, calculating (3167)

transpose

conjugate, of a matrix (3286)

conjugate, of a vector (3259)

notation (3017)

of a matrix (3285), (3291)

of a matrix inverse notation (2981)

of a vector (3258), (3265)

of a vector or matrix notation (2993)

of matrix operation results for add (4189)

of matrix operation results for multiply (4217), (4233), (4249)

of matrix operation results for subtract (4203)

transposing

general matrix (In-Place) (4325)

general matrix (Out-of-Place) (4335)

sparse matrix (4164)

triangular band matrices

storage layout (3399)

triangular band matrices, upper and lower

definition of (3397)

triangular matrices

storage layout (3352)

triangular matrices, upper and lower

definition of (3350)

tridiagonal matrix

definition of (3410)

storage layout (3413)

tridiagonal storage mode (3415)

truncation

how truncation affects output (3179)

type font usage (2958)

underflow

avoiding underflow (3825)

why mask it (3184)

uniformly distributed random numbers, generate (5155), (5169)

upper-band-packed storage mode (3383)

upper band width (3365)

upper-packed storage mode (3299), (3303)

upper-storage-by-rows for symmetric sparse matrices (3443)

upper storage mode (3301), (3305)

upper-triangular-band-packed storage mode (3401), (3404)

upper-triangular-packed storage mode (3356), (3358)

upper-triangular storage mode (3354), (3360)

usability of subroutines (3048)

usability of the ESSL subroutines (3049)

usage, special

conventions used in the subroutine description (3037)

for matrix addition (4191)

for matrix multiplication (4220), (4236), (4252)

for matrix subtraction (4205)

usage considerations

direct sparse matrix solvers (4364)

for Fourier transforms, convolutions, and correlations (4837)

for interpolation (5058)

for linear algebra subprograms (3720)

for linear algebraic equations (4356)

for matrix operations (4174)

for numerical quadrature (5095)

for random number generation (5148)

for sorting and searching (5006)

for utility subroutines (5174)

sparse matrix subroutines (iterative linear system solvers) (4372)

sparse matrix subroutines (skyline solvers) (4368)

user applications (3056)

using this book (2939), (2941)

utility subroutines

DGKTRN (5211)

DSKTRN (5215)

DSRSM (5207)

EINFO (5178)

ERRSAV (5183)

ERRSET (5187)

ERRSTR (5191)

IESSL (5195)

STRIDE (5203)

usage considerations (5173)

vector

compressed vector (3278)

conventions for (2974)

description of (3253)

font for (2960)

full vector (3277)

number of array elements needed for (3263)

sparse vector (3275)

storage of (3262)

stride for (3267)

vector-scalar linear algebra subprograms

ISAMAX, ICAMAX, IDAMAX, and IZAMAX (3733)

ISAMIN and IDAMIN (3740)

ISMAX and IDMAX (3747)

ISMIN and IDMIN (3753)

SASUM, DASUM, SCASUM, and DZASUM (3763)

SAXPY, DAXPY, CAXPY, and ZAXPY (3775)

SCOPY, DCOPY, CCOPY, and ZCOPY (3786)

SDOT, DDOT, CDOTU, ZDOTU, CDOTC, and ZDOTC (3800)

SNAXPY and DNAXPY (3806)

SNDOT and DNDOT (3812)

SNORM2, DNORM2, CNORM2, and ZNORM2 (3835)

SNRM2, DNRM2, SCNRM2, and DZNRM2 (3822)

SROT, DROT, CROT, ZROT, CSROT, and ZDROT (3862)

SROTG, DROTG, CROTG, and ZROTG (3846)

SSCAL, DSCAL, CSCAL, ZSCAL, CSSCAL, and ZDSCAL (3877)

SSWAP, DSWAP, CSWAP, and ZSWAP (3887)

SVEA, DVEA, CVEA, and ZVEA (3898)

SVEM, DVEM, CVEM, and ZVEM (3918)

SVES, DVES, CVES, and ZVES (3908)

SYAX, DYAX, CYAX, ZYAX, CSYAX, and ZDYAX (3932)

SZAXPY, DZAXPY, CZAXPY, and ZZAXPY (3942)

version of ESSL, getting (5199)

versions of subroutines (3060)

Wiener-Levinson filter coefficients (5001)

Wiener-Levinson filter coefficients subroutine (3098)

words in the Glossary (5226)

working auxiliary storage, list of subroutines using (3150)

working storage for band matrix (3370)

workstations

migrating between IBM

pSeries and RS/6000 processors (3608)

required for ESSL (3079)

ZAXPY (3774)

ZAXPYI (3981)

ZCOPY (3785)

ZDOTC (3799)

ZDOTCI (3995)

ZDOTU (3797)

ZDOTUI (3993)

ZDROT (3861)

ZDSCAL (3876)

ZDYAX (3931)

zero stride, for vectors (3271)

ZGBMV (4109)

ZGEADD (4186)

ZGEEV (4782)

ZGEF (4381)

ZGEMM (4245)

ZGEMMS (4229)

ZGEMUL (4214)

ZGEMV (4009)

ZGERC (4028)

ZGERU (4026)

ZGES (4391)

ZGESM (4401)

ZGESUB (4200)

ZGETMI (4323)

ZGETMO (4333)

ZGETRF (4411)

ZGETRS (4421)

ZGTHR (3961)

ZGTHRZ (3971)

ZGTNP (4636)

ZGTNPF (4647)

ZGTNPS (4657)

ZHBMV (4120)

ZHEMM (4265)

ZHEMV (4048)

ZHER (4075)

ZHER2 (4096)

ZHER2K (4311)

ZHERK (4295)

ZHPEV (4794)

ZHPMV (4044)

ZHPR (4071)

ZHPR2 (4092)

ZHPSV (4805)

ZNORM2 (3834)

ZPOF (4449)

ZPOSM (4474)

ZPOTRF (4453)

ZPOTRS (4478)

ZROT (3859)

ZROTG (3845)

ZSCAL (3874)

ZSCTR (3951)

ZSWAP (3886)

ZSYMM (4263)

ZSYR2K (4309)

ZSYRK (4293)

ZTBMV (4152)

ZTBSV (4679)

ZTPMV (4141)

ZTPSV (4553)

ZTRMM (4280)

ZTRMV (4137)

ZTRSM (4564)

ZTRSV (4549)

ZVEA (3897)

ZVEM (3917)

ZVES (3907)

ZWLEV (4998)

ZYAX (3929)

ZZAXPY (3941)

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