Guide and Reference

linear algebra subprograms (2975), (3809), (3810) See also vector-scalar linear algebra subprograms, sparse vector-scalar linear algebra subprograms

accuracy considerations (3826)

list of matrix-vector linear algebra subprograms (3820)

list of sparse matrix-vector linear algebra subprograms (3821)

list of sparse vector-scalar linear algebra subprograms (3819)

list of vector-scalar linear algebra subprograms (3818)

overview (3811)

performance considerations (3824)

usage considerations (3822)

linear algebraic equations (3026), (4441), (4442), (4443), (4444) See also dense linear algebraic equation subroutines, banded linear algebraic equation subroutines, sparse linear algebraic equation subroutines, linear least squares subroutines

accuracy considerations (4464)

list of banded linear algebraic equation subroutines (4455)

list of dense linear algebraic equations (4454)

list of linear least squares subroutines (4457)

list of sparse linear algebraic equation subroutines (4456)

overview (4447)

performance considerations (4461)

usage considerations (4458)

linear least squares solution (2918)

preparing for (4801)

QR decomposition with column pivoting (4816)

singular value decomposition (4809)

linear least squares subroutines

SGELLS and DGELLS (4814)

SGESVF and DGESVF (4799)

SGESVS and DGESVS (4806)

linking and loading your program (3002)

under AIX (3691)

loading your program (3003)

logical data (2980)

conventions (3092), (3261)

setting up for C (3627)

setting up for C++ (3663)

long precision (3004)

accuracy statement (3194)

meaning of (3298)

lower band width (3484)

lower storage mode (3422), (3426)

lower-band-packed storage mode (3503)

lower-packed storage mode (3420), (3424)

lower-storage-by-rows for symmetric sparse matrices (3562)

lower-triangular storage mode (3473), (3479)

lower-triangular-band-packed storage mode (3520), (3525)

lower-triangular-packed storage mode (3475), (3477)

mailing list for ESSL customers (3218)

masking underflow (3005)

for performance (3317)

why you should (3305)

math and programming notations (3146)

math background publications (5290) See also references, math background

mathematical expressions, conventions for (3135)

mathematical functions, overview (3174)

matrix (2920), (3454), (4445) See also Toeplitz matrix, general matrix

band matrix (3481)

complex Hermitian band matrix (3509)

complex Hermitian matrix (3436), (3462)

complex Hermitian Toeplitz matrix (3460)

conventions for (3097)

description of (3404)

font for (3083)

full or dense matrix (3548)

general tridiagonal matrix (3527)

leading dimension for (3415)

negative definite complex Hermitian matrix (3445)

negative definite symmetric matrix (3431)

positive definite complex Hermitian matrix (3443)

positive definite symmetric band matrix (3506)

positive definite symmetric matrix (3429)

positive definite symmetric tridiagonal matrix (3540)

sparse matrix (3545)

storage of (3412)

symmetric band matrix (3496)

symmetric matrix (3417)

symmetric tridiagonal matrix (3534)

Toeplitz matrix (3452)

triangular band matrices (3516)

triangular matrices (3469)

matrix operation subroutines

accuracy considerations (4280)

performance considerations (4278)

SGEADD, DGEADD, CGEADD, and ZGEADD (4290)

SGEMM, DGEMM, CGEMM, and ZGEMM (4349)

SGEMMS, DGEMMS, CGEMMS, and ZGEMMS (4333)

SGEMUL, DGEMUL, CGEMUL, and ZGEMUL (4318)

SGESUB, DGESUB, CGESUB, and ZGESUB (4304)

SGETMI, DGETMI, CGETMI, and ZGETMI (4427)

SGETMO, DGETMO, CGETMO, and ZGETMO (4437)

SSYMM, DSYMM, CSYMM, ZSYMM, CHEMM, and ZHEMM (4369)

SSYRK, DSYRK, CSYRK, ZSYRK, CHERK, and ZHERK (4399)

SSYR2K, DSYR2K, CSYR2K, ZSYR2K, CHER2K, and ZHER2K (4415)

STRMM, DTRMM, CTRMM, and ZTRMM (4384)

usage considerations (4276)

matrix-matrix product (2922)

complex Hermitian matrix (4375)

complex symmetric matrix (4374)

general matrices, their transposes, or their conjugate transposes (4351)

real symmetric matrix (4373)

triangular matrix (4386)

matrix-vector linear algebra subprograms (2886)

SGBMV, DGBMV, CGBMV, and ZGBMV (4213)

SGEMX, DGEMX, SGEMTX, DGEMTX, SGEMV, DGEMV, CGEMV, and ZGEMV (4117)

SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC (4132)

SSBMV, DSBMV, CHBMV, and ZHBMV (4224)

SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX and DSLMX (4154)

SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 (4179)

SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2 (4202)

STBMV, DTBMV, CTBMV, and ZTBMV (4256)

STPMV, DTPMV, CTPMV, ZTPMV, STRMV, DTRMV, CTRMV, and ZTRMV (4245)

matrix-vector product (2921)

complex Hermitian band matrix (4228)

complex Hermitian matrix (4158)

general band matrix, its transpose, or its conjugate transpose (4215)

general matrix, its transpose, or its conjugate transpose (4119)

real symmetric band matrix (4227)

real symmetric matrix (4157)

sparse matrix (4263)

sparse matrix or its transpose (4272)

triangular band matrix, its transpose, or its conjugate transpose (4258)

triangular matrix, its transpose, or its conjugate transpose (4247)

max notation and meaning (3127)

maximum (2923)

absolute value (3838)

value (3851)

meanings of words in the Glossary (5276)

messages (2924)

ESSL and attention messages, interpreting (3784)

ESSL informational messages, interpreting (3778)

ESSL miscellaneous messages, interpreting (3790)

ESSL resource messages, interpreting (3772)

list of ESSL messages (3800)

message conventions (3798)

migrating (3006)

from ESSL Version 2 to Version 3 (3709)

from ESSL/370 (3717)

from LAPACK (3725)

from non-IBM libraries (3731)

from other IBM subroutine libraries (3719)

future migration considerations (3713)

programs to ESSL (3705)

RS/6000 processors considerations (3716)

min notation and meaning (3128)

minimum (2925)

absolute value (3845)

value (3857)

miscellaneous error messages, interpreting (3785)

mod notation and meaning (3130)

modification level of ESSL, getting (5249)

Modifying C language AIX commands (3702)

Modifying C++ language AIX commands (3704)

Modifying Fortran language AIX commands (3700)

modulo notation (3143)

multiplying (2926), (2934) See also product

compute SAXPY or DAXPY N times (3910)

general matrices using Strassen's algorithm (4334)

general matrices, their transposes, or their conjugate transposes (4319)

notation (3107)

sparse vector x by a scalar, add sparse vector y, and store in vector y (4086)

vector x by a scalar and store in vector x (3981)

vector x by a scalar and store in vector y (4036)

vector x by a scalar, add to vector y, and store in vector y (3879)

vector x by a scalar, add to vector y, and store in vector z (4046)

vector x by vector y, and store in vector z (4022)

multithreaded (3007)

definition (5283)

ESSL subroutines (3243)

name usage restrictions (3245)

names in ESSL with an underscore (_) prefix, how to interpret (3067)

names of (3008)

products and acronyms (3072)

the eigensystem analysis subroutines (4821)

the Fourier transform, convolution and correlation, and related-computation subroutines (4880)

the interpolation subroutines (5105)

the linear algebra subprograms (3813)

the linear algebraic equations subroutines (4453)

the matrix operations subroutines (4275)

the numerical quadrature subroutines (5142)

the random number generation subroutines (5195)

the sorting and searching subroutines (5053)

the utility subroutines (5221)

National Language Support (3743)

negative definite complex Hermitian matrix

definition of (3444)

negative definite complex Hermitian Toeplitz matrix

definition of (3459)

negative definite Hermitian matrix

storage layout (3448)

negative definite symmetric matrix

definition of (3430)

storage layout (3434)

negative definite symmetric Toeplitz matrix

definition of (3451)

negative stride, for vectors (3395)

NLS, National Language Support (3744)

non-IBM library, migrating from (3729)

norm notation (3118)

normally distributed random numbers, generate (5211)

notations and conventions (3086)

notes, conventions used in the subroutine descriptions (3157)

number of subroutines in each area (3184)

numbers (3222) See also random number generation

accuracy of computations (3304)

accuracy of computations, for ESSL (3197)

numerical quadrature (2927)

accuracy considerations (5147)

performance considerations (5145)

programming considerations for SUBF (5149)

usage considerations (5143)

numerical quadrature performed (2928)

on a function (2929)

using Gauss-Hermite Quadrature (5190)

using Gauss-Laguerre Quadrature (5176)

using Gauss-Legendre Quadrature (5162)

using Gauss-Rational Quadrature (5183)

using two-dimensional Gauss-Legendre Quadrature (5169)

on a set of points (5156)

numerical quadrature subroutines

SGHMQ and DGHMQ (5189)

SGLGQ and DGLGQ (5175)

SGLNQ and DGLNQ (5161)

SGLNQ2 and DGLNQ2 (5168)

SGRAQ and DGRAQ (5182)

SPTNQ and DPTNQ (5155)

objectives for this manual (3056)

one norm notation (3122)

online documentation

online Guide and Reference manual (5312)

required Hypertext Markup Language products (3217)

option table, default values for ESSL errors (3361)

order numbers of the publications (5306)

ordering IBM publications (5307)

output (3009)

accuracy on different processors (3191)

how errors affect output (3326)

output arguments, conventions used in the subroutine descriptions (3156)

overflow, avoiding (3929)

overview

of eigensystem analysis (4820)

of ESSL (3165)

of Fourier transforms, convolutions and correlations, and related computations (4879)

of interpolation (5104)

of linear algebra subprograms (3812)

of linear algebraic equations (4448)

of matrix operations (4274)

of numerical quadrature (5141)

of random number generation (5194)

of sorting and searching (5052)

of the documentation (5296)

of utility subroutines (5220)

packed band storage mode (3486)

packed-Hermitian-Toeplitz storage mode (3467)

packed-symmetric-Toeplitz storage mode (3457)

Parallel Fortran (3011)

parallel processing (2931), (3013)

introduction to (3187)

performance (3010)

achieving better performance in your program (3307)

aspects of parallel processing on the workstations (3186)

coding techniques that affect performance (3314)

considerations for dense and banded linear algebraic equations (4462)

considerations for eigensystem analysis (4823)

considerations for Fourier transforms, convolutions, and correlations (4892)

considerations for interpolation (5109)

considerations for linear algebra subprograms (3825)

considerations for matrix operations (4279)

considerations for numerical quadrature (5146)

considerations for related computations (4905)

considerations for sorting and searching (5057)

how the Fourier transforms achieve high performance (4901)

information on ESSL run-time performance (3320)

tradeoffs for convolution and correlation subroutines (4903)

where to find information on (3319)

pi notation (3102)

PL/I (Programming Language/I) (3041)

coding programs (3685)

handling errors in your program (3640), (3676)

publications (5326)

plane rotation (2932)

applying a (3966)

constructing a Givens (3951)

planning your program (3229)

planning, publications for (5310)

polynomial

evaluating (5020)

interpolating (5117), (5124)

positive definite complex Hermitian matrix

definition of (3442)

positive definite complex Hermitian Toeplitz matrix

definition of (3458)

positive definite Hermitian matrix

storage layout (3446)

positive definite symmetric band matrix

definition of (3505)

storage layout (3507)

positive definite symmetric band matrix subroutines, names of (4451)

positive definite symmetric matrix

definition of (3428)

storage layout (3432)

positive definite symmetric matrix subroutines, names of (4452)

positive definite symmetric Toeplitz matrix

definition of (3450)

positive definite symmetric tridiagonal matrix (3542)

definition of (3541)

storage layout (3543)

positive stride, for vectors (3391)

precision, meaning of (3299)

precision, short and long (3195)

problems, handling (3734) See also diagnosis procedures

problems, IBM support for (3742)

procedures, job processing (3012)

setting up your own AIX (3695)

processing your program (3018)

requirements for ESSL on the workstations (3203)

setting up your AIX procedures (3694)

steps involved in (3686)

using parallel subroutines on the workstations (3188)

processor-independent formulas for auxiliary storage, interpreting (3284)

product (2933), (3880) See also multiplying

matrix-matrix (2937)

complex Hermitian matrix (4372)

complex symmetric matrix (4371)

general matrices, their transposes, or their conjugate transposes (4350)

real symmetric matrix (4370)

triangular matrix (4385)

matrix-vector (2936)

complex Hermitian band matrix (4226)

complex Hermitian matrix (4156)

general band matrix, its transpose, or its conjugate transpose (4214)

general matrix, its transpose, or its conjugate transpose (4118)

real symmetric band matrix (4225)

real symmetric matrix (4155)

sparse matrix (4262)

sparse matrix or its transpose (4271)

triangular band matrix, its transpose, or its conjugate transpose (4257)

triangular matrix, its transpose, or its conjugate transpose (4246)

product names, acronyms for (3071)

products, programming (2970)

migrating from LAPACK (3727)

migrating from other IBM (3721)

required by ESSL on the workstations, programming (3210)

profile-in skyline storage mode (3568)

program (3015)

attention messages, overview (3351)

coding (3578)

computational errors (3341)

design (3231)

errors (3331)

handling errors in your C program (3637)

handling errors in your C++ program (3673)

handling errors in your Fortran program (3602)

input-argument errors, overview (3334)

interface for C programs (3613)

interface for C++ programs (3649)

interface for Fortran programs (3584)

interface for PL/I programs (3684)

migrated to ESSL (3706)

performance, achieving high (3312)

processing your program (3687)

resource errors, overview (3346)

setting up your data structures (3371)

types of data in your program (3253)

when coding large applications (3365)

program exceptions (3014)

description of ESSL (3328)

program exceptions, diagnosing (3748)

program number for ESSL (5305)

programming considerations for SUBF in numerical quadrature (5150)

programming items, font for (3085)

Programming Language/I (3042) See also PL/I (Programming Language/I)

programming products (2971)

required by ESSL on the workstations (3208)

programming publications (5314), (5320)

PTF (2892)

getting the most recent level applied (5246)

publications (2938)

list of ESSL (5299)

math background (5291)

related (5318)

QR decomposition with column pivoting (4815)

quadratic interpolation (5038)

random number generation (2945)

long period uniformly distributed (5217)

normally distributed (5210)

uniformly distributed (5203)

usage considerations (5196)

random number generation subroutines

SNRAND and DNRAND (5209)

SURAND and DURAND (5202)

SURXOR and DURXOR (5216)

rank-k update (2941)

complex Hermitian matrix (4402)

complex symmetric matrix (4401)

real symmetric matrix (4400)

rank-one update (2939)

complex Hermitian matrix (4181)

general matrix (4133)

real symmetric matrix (4180)

rank-two update (2940)

complex Hermitian matrix (4204)

real symmetric matrix (4203)

rank-2k update (2942)

complex Hermitian matrix (4418)

complex symmetric matrix (4417)

real symmetric matrix (4416)

readers of this book (3057)

real and complex array elements (3595)

real data (2978)

conventions (3091), (3260)

real general matrix eigensystem analysis subroutine (4818)

real symmetric matrix eigensystem analysis subroutine (4819)

reciprocal of the condition number (2943)

general matrix (4534), (4591)

positive definite real symmetric matrix (4580), (4604)

recursive filter (3219) See also time-varying recursive filter

reference for ESSL, online (5315)

reference information (3023)

ESSL online information (5316)

math background texts and reports (5294)

organization of (3804)

what is in each subroutine description and the conventions used (3151)

references, math background (3019)

related publications (5317)

related-computation subroutines

accuracy considerations (4906)

CWLEV and ZWLEV (5049)

performance considerations (4904)

SIZC and DIZC (5025)

SPOLY and DPOLY (5019)

SQINT and DQINT (5037)

STREC and DTREC (5031)

SWLEV and DWLEV (5048)

release of ESSL, getting (5247)

reporting problems to IBM (3737)

required publications (5298)

requirements (3020)

auxiliary working storage (3274), (3278)

for ESSL workstation product (3202)

software products on the workstations (3207)

transforms in storage, lengths of (3286)

workstation hardware (3204)

resource error messages, interpreting (3767)

restrictions, ESSL coding (3246)

results (3021)

accuracy on different processors (3196)

how accuracy is affected by the nature of the computation (3302)

in C programs (3620)

in C++ programs (3656)

in Fortran programs (3591)

multiplication of NaN (3303)

results transposed and conjugate transposed for matrix multiplication (4324), (4340), (4356)

results transposed for matrix addition (4295)

results transposed for matrix subtraction (4309)

return code (3022)

in C programs (3644)

in C++ programs (3680)

in Fortran programs (3608)

using during diagnosis (3766)

rotation (2944)

applying a plane (3967)

constructing a Givens plane (3952)

routine names (3247)

row vector (3376)

run-time performance (3016)

optimizing in your program (3311)

run-time problems, diagnosing (3024)

attention error messages, interpreting (3781)

computational errors (3762)

informational error messages, interpreting (3775)

input-argument errors (3756)

miscellaneous error messages, interpreting (3787)

resource error messages, interpreting (3769)

running your program (3017)

SACOR (5006)

SACORF (5011)

SASUM (3862)

SAXPY (3874)

SAXPYI (4081)

SBSRCH (5089)

scalar data (2979)

conventions (3088), (3257)

scalar items, font for (3081)

Scalar Library (2948)

scalar processing (3028)

scale argument used for Fourier transform subroutines (4897)

scaling, when to use (3318)

SCASUM (3864)

scatter vector elements (4056)

SCFT (4910)

SCFT2 (4942)

SCFT3 (4960)

Scientific Subroutine Package (3048) See also SSP (Scientific Subroutine Package)

SCNRM2 (3923)

SCON (4978)

SCOND (4985)

SCONF (4991)

SCOPY (3885)

SCOR (4979)

SCORD (4986)

SCORF (4992)

SCOSF (4928)

SCOSFT, no documentation provided for (4881)

SCRFT (4922)

SCRFT2 (4954)

SCRFT3 (4972)

SCSINT (5128)

SCSIN2 (5135)

SDCON (4999)

SDCOR (5001)

SDOT (3897)

SDOTI (4093)

searching (2947)

binary (5093)

sequential (5102)

selecting an ESSL library (3235)

selecting an ESSL subroutine (3239)

sequences (2882)

conventions for (3098)

description of (3569)

storage layout (3570)

sequential search (5101)

service, IBM (3740)

setting up

AIX procedures (3693)

setting up your data (3254)

SGBF (4646)

SGBMV (4209)

SGBS (4652)

SGEADD (4286)

SGEEV (4829)

SGEF (4481)

SGEFCD (4530)

SGEGV (4863)

SGEICD (4585)

SGELLS (4812)

SGEMM (4345)

SGEMMS (4329)

SGEMTX (4115)

SGEMUL (4314)

SGEMV (4109)

SGEMX (4113)

SGER (4126)

SGES (4491)

SGESM (4501)

SGESUB (4300)

SGESVF (4797)

SGESVS (4804)

SGETMI (4423)

SGETMO (4433)

SGETRF (4511)

SGETRS (4521)

SGHMQ (5187)

SGLGQ (5173)

SGLNQ (5159)

SGLNQ2 (5166)

SGRAQ (5180)

SGTF (4678)

SGTHR (4061)

SGTHRZ (4071)

SGTNP (4692)

SGTNPF (4703)

SGTNPS (4713)

SGTS (4684)

short precision (3027)

accuracy statement (3193)

meaning of (3297)

SIGN notation and meaning (3145)

signal processing subroutines (4882)

simple formulas for auxiliary storage, interpreting (3285)

sin notation (3141)

sine transform (4939)

singular value decomposition for a general matrix (4800), (4808)

SIZC (5023)

size of array (3025)

required for a vector (3386)

skyline solvers

usage considerations (4470)

skyline storage mode for sparse matrices, diagonal-out (3564)

skyline storage mode for sparse matrices, profile-in (3567)

SL MATH (Subroutine Library--Mathematics) (3045)

migrating from (3723)

SLSS (Subscription Library Services System) (5303)

SMP (3043)

definition (5284)

ESSL Library, why use it (3241)

ESSL multithreaded subroutines (3242)

performance (3198)

SNAXPY (3907)

SNDOT (3913)

SNORM2 (3934)

SNRAND (5207)

SNRM2 (3921)

software products

required by ESSL on the workstations (3209)

required by Hypertext Markup Language (3215)

solving (2951)

general band matrix (4655)

general matrix or its transpose (4496), (4526)

general skyline sparse matrix (4753)

general sparse matrix or its transpose (4749)

general tridiagonal matrix (4687), (4698), (4718)

iterative linear system solver (2954)

general sparse matrix (4769), (4788), (4793)

sparse negative definite symmetric matrix (4775), (4782)

sparse positive definite symmetric matrix (4774), (4781)

symmetric sparse matrix (4770)

multiple right-hand sides (2952)

general matrix, its transpose, or its conjugate transpose (4506), (4527)

positive definite complex Hermitian matrix (4568)

positive definite real symmetric matrix (4567)

triangular matrix (4633)

positive definite (2953)

real symmetric matrix (4557)

symmetric band matrix (4675)

symmetric tridiagonal matrix (4730)

symmetric skyline sparse matrix (4760)

triangular band matrix (4740)

triangular matrix (4623)

some eigenvalues and eigenvectors (2950), (4860) See also extreme eigenvalues and eigenvectors

sorting (2946)

elements of a sequence (5067)

index (5075)

stable sort (5083)

sorting and searching subroutines

accuracy considerations (5058)

IBSRCH, SBSRCH, and DBSRCH (5091)

ISORT, SSORT, and DSORT (5066)

ISORTS, SSORTS, and DSORTS (5082)

ISORTX, SSORTX, and DSORTX (5074)

ISSRCH, SSSRCH, and DSSRCH (5100)

performance considerations (5056)

usage considerations (5054)

sparse linear algebraic equation subroutines

DGKFS (4752)

DGSF (4743)

DGSS (4748)

DSDCG (4780)

DSDGCG (4792)

DSKFS (4759)

DSMCG (4773)

DSMGCG (4787)

DSRIS (4766)

sparse matrix subroutines

direct solvers (4465)

iterative linear system solvers (4473)

performance and accuracy considerations (4468), (4472), (4476)

skyline solvers (4469)

sparse matrix-vector linear algebra subprograms (2887)

DSDMX (4270)

DSMMX (4261)

DSMTM (4266)

sparse matrix, definition and storage modes (3546)

sparse vector-scalar linear algebra subprograms (2885)

SAXPYI, DAXPYI, CAXPYI, and ZAXPYI (4085)

SDOTI, DDOTI, CDOTUI, ZDOTUI, CDOTCI, and, ZDOTCI (4099)

SGTHR, DGTHR, CGTHR, and ZGTHR (4065)

SGTHRZ, DGTHRZ, CGTHRZ, and ZGTHRZ (4075)

SSCTR, DSCTR, CSCTR, and ZSCTR (4055)

sparse vector, definition and storage modes (3398)

SPBCHF (4662)

SPBCHS (4672)

SPBF (4660)

SPBS (4670)

special usage (2968)

of matrix addition (4293)

of matrix multiplication (4322), (4338), (4354)

of matrix subtraction (4307)

spectral norm notation (3124)

SPINT (5114)

SPOF (4545)

SPOFCD (4575)

SPOICD (4598)

SPOLY (5017)

SPOSM (4562)

SPPF (4543)

SPPFCD (4573)

SPPICD (4596)

SPPS (4554)

SPTF (4721)

SPTNQ (5153)

SPTS (4727)

SQINT (5035)

square root notation (3104)

SRCFT (4916)

SRCFT2 (4948)

SRCFT3 (4966)

SROT (3959)

SROTG (3945)

SSBMV (4220)

SSCAL (3974)

SSCTR (4051)

SSINF (4935)

SSLMX (4152)

SSLR1 (4169)

SSLR2 (4200)

SSORT (5064)

SSORTS (5080)

SSORTX (5072)

SSP (Scientific Subroutine Package) (3047)

migrating from (3724)

SSPEV (4841)

SSPMV (4144)

SSPR (4171)

SSPR2 (4192)

SSPSV (4852)

SSSRCH (5098)

SSWAP (3986)

SSYGV (4870)

SSYMM (4363)

SSYMV (4148)

SSYR (4175)

SSYRK (4393)

SSYR2 (4196)

SSYR2K (4409)

stable sort (5084)

STBMV (4252)

STBSV (4735)

stepping through storage, for matrices (3410)

stepping through storage, for vectors (3390)

storage (3029)

array storage techniques overview (3251)

auxiliary working storage requirements (3275), (3280)

compressed-diagonal storage mode for sparse matrices (3553)

compressed-matrix storage mode for sparse matrices (3551)

considerations when designing your program (3249)

diagonal-out skyline storage mode for sparse matrices (3563)

for matrices (3411)

for vectors (3383)

layout for a complex Hermitian band matrix (3514)

layout for a complex Hermitian matrix (3441)

layout for a general tridiagonal matrix (3532)

layout for a negative definite Hermitian matrix (3449)

layout for a negative definite symmetric matrix (3435)

layout for a positive definite Hermitian matrix (3447)

layout for a positive definite symmetric matrix (3433)

layout for a positive definite symmetric tridiagonal matrix (3544)

layout for a sequence (3571), (3572), (3573)

layout for a symmetric tridiagonal matrix (3538)

layout for a Toeplitz matrix (3456), (3466)

layout for band matrices (3485), (3489), (3492)

layout for positive definite symmetric band matrices (3508)

layout for sparse matrices (3547)

layout for sparse vectors (3401)

layout for symmetric band matrices (3500)

layout for symmetric matrices (3419)

layout for triangular band matrices (3518), (3521), (3524)

layout for triangular matrices (3471)

list of subroutines using auxiliary storage (3273)

list of subroutines using transforms (3290)

of arrays in Fortran (3594)

profile-in skyline storage mode for sparse matrices (3566)

storage-by-columns for sparse matrices (3557)

storage-by-indices for sparse matrices (3555)

storage-by-rows for sparse matrices (3559)

tradeoffs for input (3316)

transform length requirements (3288)

storage conversion subroutine (2949)

general skyline sparse matrix (5261)

sparse matrix (5257)

symmetric skyline sparse matrix (5265)

storage-by-columns for sparse matrices (3558)

storage-by-indices for sparse matrices (3556)

storage-by-rows for sparse matrices (3560)

STPI (4640)

STPINT (5121)

STPMV (4241)

STPSV (4617)

Strassen's algorithm, multiplying general matrices (4335)

STREC (5029)

STRI (4638)

stride (2955)

defining vectors in arrays (3388)

how it is used in three dimensions (3575)

negative (3396)

optimizing for your Fourier transforms (4896)

positive (3392)

subroutine for optimizing Fourier transforms (5253)

zero (3394)

STRIDE (5251)

STRMM (4380)

STRMV (4237)

STRSM (4628)

STRSV (4613)

structures, data (vectors and matrices) (3374)

subject code for ESSL documentation (5304)

subprogram (3031) See also subroutine

linear algebra (3807)

meaning of (3064), (3814)

subprogram, definition (3066)

subroutine (3030)

calling sequence format for C programs (3612)

calling sequence format for C++ programs (3648)

calling sequence format for Fortran programs (3583)

choose of (3234), (3238)

conventions used in the description of (3149)

overview of ESSL (3183)

Subroutine Library--Mathematics (3046) See also SL MATH (Subroutine Library--Mathematics)

subroutine, definition (3065)

subroutines, ESSL

CAXPY (3872)

CAXPYI (4079)

CCOPY (3883)

CDOTC (3895)

CDOTCI (4091)

CDOTU (3893)

CDOTUI (4089)

CGBMV (4207)

CGEADD (4284)

CGEEV (4827)

CGEF (4479)

CGEMM (4343)

CGEMMS (4327)

CGEMUL (4312)

CGEMV (4103)

CGERC (4124)

CGERU (4122)

CGES (4489)

CGESM (4499)

CGESUB (4298)

CGETMI (4421)

CGETMO (4431)

CGETRF (4509)

CGETRS (4519)

CGTHR (4059)

CGTHRZ (4069)

CGTNP (4690)

CGTNPF (4701)

CGTNPS (4711)

CHBMV (4218)

CHEMM (4361)

CHEMV (4140)

CHER (4165)

CHERK (4391)

CHER2 (4188)

CHER2K (4407)

CHPEV (4839)

CHPMV (4136)

CHPR (4161)

CHPR2 (4184)

CHPSV (4850)

CNORM2 (3932)

CPOF (4541)

CPOSM (4560)

CROT (3955)

CROTG (3943)

CSCAL (3970)

CSCTR (4049)

CSROT (3957)

CSSCAL (3972)

CSWAP (3984)

CSYAX (4027)

CSYMM (4359)

CSYRK (4389)

CSYR2K (4405)

CTBMV (4250)

CTBSV (4733)

CTPMV (4235)

CTPSV (4611)

CTRMM (4378)

CTRMV (4231)

CTRSM (4626)

CTRSV (4607)

CVEA (3995)

CVEM (4015)

CVES (4005)

CWLEV (5042)

CYAX (4025)

CZAXPY (4039)

DASUM (3859)

DAXPY (3871)

DAXPYI (4078)

DBSRCH (5087)

DCFT (4909)

DCFT2 (4941)

DCFT3 (4959)

DCOPY (3882)

DCOSF (4927)

DCRFT (4921)

DCRFT2 (4953)

DCRFT3 (4971)

DCSINT (5127)

DCSIN2 (5134)

DDCON (4996)

DDCOR (4998)

DDOT (3892)

DDOTI (4088)

DGBF (4645)

DGBMV (4206)

DGBS (4651)

DGEADD (4283)

DGEEV (4826)

DGEF (4478)

DGEFCD (4529)

DGEGV (4862)

DGEICD (4584)

DGELLS (4811)

DGEMM (4342)

DGEMMS (4326)

DGEMTX (4108)

DGEMUL (4311)

DGEMV (4102)

DGEMX (4106)

DGER (4121)

DGES (4488)

DGESM (4498)

DGESUB (4297)

DGESVF (4796)

DGESVS (4803)

DGETMI (4420)

DGETMO (4430)

DGETRF (4508)

DGETRS (4518)

DGHMQ (5186)

DGKFS (4750)

DGKTRN (5258)

DGLGQ (5172)

DGLNQ (5158)

DGLNQ2 (5165)

DGRAQ (5179)

DGSF (4741)

DGSS (4746)

DGTF (4677)

DGTHR (4058)

DGTHRZ (4068)

DGTNP (4689)

DGTNPF (4700)

DGTNPS (4710)

DGTS (4683)

DIZC (5022)

DNAXPY (3906)

DNDOT (3912)

DNORM2 (3931)

DNRAND (5206)

DNRM2 (3918)

DPBCHF (4659)

DPBCHS (4669)

DPBF (4657)

DPBS (4667)

DPINT (5113)

DPOF (4540)

DPOFCD (4572)

DPOICD (4595)

DPOLY (5016)

DPOSM (4559)

DPPF (4538)

DPPFCD (4570)

DPPICD (4593)

DPPS (4553)

DPTF (4720)

DPTNQ (5152)

DPTS (4726)

DQINT (5034)

DRCFT (4915)

DRCFT2 (4947)

DRCFT3 (4965)

DROT (3954)

DROTG (3942)

DSBMV (4217)

DSCAL (3969)

DSCTR (4048)

DSDCG (4778)

DSDGCG (4790)

DSDMX (4268)

DSINF (4934)

DSKFS (4757)

DSKTRN (5262)

DSLMX (4143)

DSLR1 (4168)

DSLR2 (4191)

DSMCG (4771)

DSMGCG (4785)

DSMMX (4259)

DSMTM (4264)

DSORT (5062)

DSORTS (5078)

DSORTX (5070)

DSPEV (4838)

DSPMV (4135)

DSPR (4160)

DSPR2 (4183)

DSPSV (4849)

DSRIS (4764)

DSRSM (5254)

DSSRCH (5096)

DSWAP (3983)

DSYGV (4869)

DSYMM (4358)

DSYMV (4139)

DSYR (4164)

DSYRK (4388)

DSYR2 (4187)

DSYR2K (4404)

DTBMV (4249)

DTBSV (4732)

DTPI (4637)

DTPINT (5120)

DTPMV (4234)

DTPSV (4610)

DTREC (5028)

DTRI (4635)

DTRMM (4377)

DTRMV (4230)

DTRSM (4625)

DTRSV (4606)

DURAND (5199)

DURXOR (5213)

DVEA (3994)

DVEM (4014)

DVES (4004)

DWLEV (5041)

DYAX (4024)

DZASUM (3861)

DZAXPY (4038)

DZNRM2 (3920)

EINFO (5226)

ERRSAV (5230)

ERRSET (5234)

ERRSTR (5238)

IBSRCH (5085)

ICAMAX (3830)

IDAMAX (3829)

IDAMIN (3840)

IDMAX (3847)

IDMIN (3853)

IESSL (5242)

ISAMAX (3828)

ISAMIN (3839)

ISMAX (3846)

ISMIN (3852)

ISORT (5060)

ISORTS (5076)

ISORTX (5068)

ISSRCH (5094)

IZAMAX (3831)

SACOR (5005)

SACORF (5010)

SASUM (3858)

SAXPY (3870)

SAXPYI (4077)

SBSRCH (5086)

SCASUM (3860)

SCFT (4908)

SCFT2 (4940)

SCFT3 (4958)

SCNRM2 (3919)

SCON (4976)

SCOND (4983)

SCONF (4989)

SCOPY (3881)

SCOR (4977)

SCORD (4984)

SCORF (4990)

SCOSF (4926)

SCRFT (4920)

SCRFT2 (4952)

SCRFT3 (4970)

SCSINT (5126)

SCSIN2 (5133)

SDCON (4995)

SDCOR (4997)

SDOT (3891)

SDOTI (4087)

SGBF (4644)

SGBMV (4205)

SGBS (4650)

SGEADD (4282)

SGEEV (4825)

SGEF (4477)

SGEFCD (4528)

SGEGV (4861)

SGEICD (4583)

SGELLS (4810)

SGEMM (4341)

SGEMMS (4325)

SGEMTX (4107)

SGEMUL (4310)

SGEMV (4101)

SGEMX (4105)

SGER (4120)

SGES (4487)

SGESM (4497)

SGESUB (4296)

SGESVF (4795)

SGESVS (4802)

SGETMI (4419)

SGETMO (4429)

SGETRF (4507)

SGETRS (4517)

SGHMQ (5185)

SGLGQ (5171)

SGLNQ (5157)

SGLNQ2 (5164)

SGRAQ (5178)

SGTF (4676)

SGTHR (4057)

SGTHRZ (4067)

SGTNP (4688)

SGTNPF (4699)

SGTNPS (4709)

SGTS (4682)

SIZC (5021)

SNAXPY (3905)

SNDOT (3911)

SNORM2 (3930)

SNRAND (5205)

SNRM2 (3917)

SPBCHF (4658)

SPBCHS (4668)

SPBF (4656)

SPBS (4666)

SPINT (5112)

SPOF (4539)

SPOFCD (4571)

SPOICD (4594)

SPOLY (5015)

SPOSM (4558)

SPPF (4537)

SPPFCD (4569)

SPPICD (4592)

SPPS (4552)

SPTF (4719)

SPTNQ (5151)

SPTS (4725)

SQINT (5033)

SRCFT (4914)

SRCFT2 (4946)

SRCFT3 (4964)

SROT (3953)

SROTG (3941)

SSBMV (4216)

SSCAL (3968)

SSCTR (4047)

SSINF (4933)

SSLMX (4142)

SSLR1 (4167)

SSLR2 (4190)

SSORT (5061)

SSORTS (5077)

SSORTX (5069)

SSPEV (4837)

SSPMV (4134)

SSPR (4159)

SSPR2 (4182)

SSPSV (4848)

SSSRCH (5095)

SSWAP (3982)

SSYGV (4868)

SSYMM (4357)

SSYMV (4138)

SSYR (4163)

SSYRK (4387)

SSYR2 (4186)

SSYR2K (4403)

STBMV (4248)

STBSV (4731)

STPI (4636)

STPINT (5119)

STPMV (4233)

STPSV (4609)

STREC (5027)

STRI (4634)

STRIDE (5250)

STRMM (4376)

STRMV (4229)

STRSM (4624)

STRSV (4605)

SURAND (5198)

SURXOR (5212)

SVEA (3993)

SVEM (4013)

SVES (4003)

SWLEV (5040)

SYAX (4023)

SZAXPY (4037)

ZAXPY (3873)

ZAXPYI (4080)

ZCOPY (3884)

ZDOTC (3896)

ZDOTCI (4092)

ZDOTU (3894)

ZDOTUI (4090)

ZDROT (3958)

ZDSCAL (3973)

ZDYAX (4028)

ZGBMV (4208)

ZGEADD (4285)

ZGEEV (4828)

ZGEF (4480)

ZGEMM (4344)

ZGEMMS (4328)

ZGEMUL (4313)

ZGEMV (4104)

ZGERC (4125)

ZGERU (4123)

ZGES (4490)

ZGESM (4500)

ZGESUB (4299)

ZGETMI (4422)

ZGETMO (4432)

ZGETRF (4510)

ZGETRS (4520)

ZGTHR (4060)

ZGTHRZ (4070)

ZGTNP (4691)

ZGTNPF (4702)

ZGTNPS (4712)

ZHBMV (4219)

ZHEMM (4362)

ZHEMV (4141)

ZHER (4166)

ZHERK (4392)

ZHER2 (4189)

ZHER2K (4408)

ZHPEV (4840)

ZHPMV (4137)

ZHPR (4162)

ZHPR2 (4185)

ZHPSV (4851)

ZNORM2 (3933)

ZPOF (4542)

ZPOSM (4561)

ZROT (3956)

ZROTG (3944)

ZSCAL (3971)

ZSCTR (4050)

ZSWAP (3985)

ZSYMM (4360)

ZSYRK (4390)

ZSYR2K (4406)

ZTBMV (4251)

ZTBSV (4734)

ZTPMV (4236)

ZTPSV (4612)

ZTRMM (4379)

ZTRMV (4232)

ZTRSM (4627)

ZTRSV (4608)

ZVEA (3996)

ZVEM (4016)

ZVES (4006)

ZWLEV (5043)

ZYAX (4026)

ZZAXPY (4040)

subscript notation, what it means (3113)

subtracting (2956)

general matrices or their transposes (4305)

vector y from vector x and store in vector z (4012)

sum of (2957) See also adding

absolute values (3869)

summation notation (3140)

superscript notation, what it means (3112)

support, IBM (3741)

SURAND (5200)

SURXOR (5214)

SVEA (3997)

SVEM (4017)

SVES (4007)

swap elements of two vectors (3992)

SWLEV (5044)

SYAX (4029)

symbols, special usage of (3133)

symmetric band matrix

definition of (3495)

storage layout (3499)

symmetric matrix

definition of (3416)

storage layout (3418)

Symmetric Multi-Processing (3044) See also SMP

symmetric tridiagonal matrix (3536)

definition of (3535)

storage layout (3537)

symmetric-tridiagonal storage mode (3539)

symptoms, identifying problem (3747)

syntax rules for call statements and data (3269)

syntax, conventions used in the subroutine descriptions (3152)

SZAXPY (4041)

table, default values for ESSL error option (3362)

termination, program (3033)

attention messages (3353)

computational errors (3337)

input-argument errors (3336)

resource errors (3348)

terminology in the Glossary (5279)

terminology used for Fourier transforms, convolutions, and correlations (4888)

terminology, names of products (3069)

textbooks cited (5289) See also references, math background

thread-safe (3034)

definition (5285)

ESSL Library, why use it (3244)

three-dimensional data structures, how stride is used for (3576)

time-varying recursive filter (5032)

times notation, multiply (3106)

timings, achieving high performance in your program (3310)

Toeplitz matrix

definition of (3453), (3461)

storage layout (3455), (3465)

traceback map, using during diagnosis (3758)

transform lengths, calculating (3289)

transpose (3032), (3054)

conjugate, of a matrix (3408)

conjugate, of a vector (3381)

notation (3139)

of a matrix (3407), (3413)

of a matrix inverse notation (3103)

of a vector (3380), (3387)

of a vector or matrix notation (3115)

of matrix operation results for add (4292)

of matrix operation results for multiply (4320), (4336), (4352)

of matrix operation results for subtract (4306)

transposing (2958)

general matrix (In-Place) (4428)

general matrix (Out-of-Place) (4438)

sparse matrix (4267)

triangular band matrices

storage layout (3517)

triangular band matrices, upper and lower

definition of (3515)

triangular matrices

storage layout (3470)

triangular matrices, upper and lower

definition of (3468)

tridiagonal matrix

definition of (3528)

storage layout (3531)

tridiagonal storage mode (3533)

truncation

how truncation affects output (3301)

type font usage (3080)

underflow (2959)

avoiding underflow (3928)

why mask it (3306)

uniformly distributed random numbers, generate (5204), (5218)

upper band width (3483)

upper storage mode (3423), (3427)

upper-band-packed storage mode (3501)

upper-packed storage mode (3421), (3425)

upper-storage-by-rows for symmetric sparse matrices (3561)

upper-triangular storage mode (3472), (3478)

upper-triangular-band-packed storage mode (3519), (3522)

upper-triangular-packed storage mode (3474), (3476)

usability of subroutines (3170)

usability of the ESSL subroutines (3171)

usage considerations

direct sparse matrix solvers (4467)

for Fourier transforms, convolutions, and correlations (4887)

for interpolation (5107)

for linear algebra subprograms (3823)

for linear algebraic equations (4459)

for matrix operations (4277)

for numerical quadrature (5144)

for random number generation (5197)

for sorting and searching (5055)

for utility subroutines (5223)

sparse matrix subroutines (iterative linear system solvers) (4475)

sparse matrix subroutines (skyline solvers) (4471)

usage, special (2893)

conventions used in the subroutine description (3159)

for matrix addition (4294)

for matrix multiplication (4323), (4339), (4355)

for matrix subtraction (4308)

user applications (3178)

users of ESSL (3058)

using this book (3061), (3063)

utility subroutines (2960)

DGKTRN (5260)

DSKTRN (5264)

DSRSM (5256)

EINFO (5227)

ERRSAV (5232)

ERRSET (5236)

ERRSTR (5240)

IESSL (5244)

STRIDE (5252)

usage considerations (5222)

vector (3036)

compressed vector (3400)

conventions for (3096)

description of (3375)

font for (3082)

full vector (3399)

number of array elements needed for (3385)

sparse vector (3397)

storage of (3384)

stride for (3389)

Vector Library (2961)

vector processing (3037)

Vector Processing Subsystem (3050) See also VPSS (Vector Processing Subsystem)

vector register (3035)

vector-scalar linear algebra subprograms (2884)

ISAMAX, ICAMAX, IDAMAX, and IZAMAX (3836)

ISAMIN and IDAMIN (3843)

ISMAX and IDMAX (3850)

ISMIN and IDMIN (3856)

SASUM, DASUM, SCASUM, and DZASUM (3866)

SAXPY, DAXPY, CAXPY, and ZAXPY (3878)

SCOPY, DCOPY, CCOPY, and ZCOPY (3889)

SDOT, DDOT, CDOTU, ZDOTU, CDOTC, and ZDOTC (3903)

SNAXPY and DNAXPY (3909)

SNDOT and DNDOT (3915)

SNORM2, DNORM2, CNORM2, and ZNORM2 (3938)

SNRM2, DNRM2, SCNRM2, and DZNRM2 (3925)

SROT, DROT, CROT, ZROT, CSROT, and ZDROT (3965)

SROTG, DROTG, CROTG, and ZROTG (3949)

SSCAL, DSCAL, CSCAL, ZSCAL, CSSCAL, and ZDSCAL (3980)

SSWAP, DSWAP, CSWAP, and ZSWAP (3990)

SVEA, DVEA, CVEA, and ZVEA (4001)

SVEM, DVEM, CVEM, and ZVEM (4021)

SVES, DVES, CVES, and ZVES (4011)

SYAX, DYAX, CYAX, ZYAX, CSYAX, and ZDYAX (4035)

SZAXPY, DZAXPY, CZAXPY, and ZZAXPY (4045)

version of ESSL, getting (5248)

versions of subroutines (3182)

VPSS (Vector Processing Subsystem) (3049)

Wiener-Levinson filter coefficients (5050)

words in the Glossary (5274)

working auxiliary storage, list of subroutines using (3272)

working storage for band matrix (3488)

workstations (2969)

migrating between RS/6000 processors (3715)

required for ESSL (3201)

ZAXPY (3877)

ZAXPYI (4084)

ZCOPY (3888)

ZDOTC (3902)

ZDOTCI (4098)

ZDOTU (3900)

ZDOTUI (4096)

ZDROT (3964)

ZDSCAL (3979)

ZDYAX (4034)

zero crossing (4884) See also i-th zero crossing

zero stride, for vectors (3393)

ZGBMV (4212)

ZGEADD (4289)

ZGEEV (4832)

ZGEF (4484)

ZGEMM (4348)

ZGEMMS (4332)

ZGEMUL (4317)

ZGEMV (4112)

ZGERC (4131)

ZGERU (4129)

ZGES (4494)

ZGESM (4504)

ZGESUB (4303)

ZGETMI (4426)

ZGETMO (4436)

ZGETRF (4514)

ZGETRS (4524)

ZGTHR (4064)

ZGTHRZ (4074)

ZGTNP (4695)

ZGTNPF (4706)

ZGTNPS (4716)

ZHBMV (4223)

ZHEMM (4368)

ZHEMV (4151)

ZHER (4178)

ZHERK (4398)

ZHER2 (4199)

ZHER2K (4414)

ZHPEV (4844)

ZHPMV (4147)

ZHPR (4174)

ZHPR2 (4195)

ZHPSV (4855)

ZNORM2 (3937)

ZPOF (4548)

ZPOSM (4565)

ZROT (3962)

ZROTG (3948)

ZSCAL (3977)

ZSCTR (4054)

ZSWAP (3989)

ZSYMM (4366)

ZSYRK (4396)

ZSYR2K (4412)

ZTBMV (4255)

ZTBSV (4738)

ZTPMV (4244)

ZTPSV (4620)

ZTRMM (4383)

ZTRMV (4240)

ZTRSM (4631)

ZTRSV (4616)

ZVEA (4000)

ZVEM (4020)

ZVES (4010)

ZWLEV (5047)

ZYAX (4032)

ZZAXPY (4044)

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