INTRO_LAPACK(3S)INTRO_LAPACK(3S)NAMEINTRO_LAPACK - Introduction to LAPACK solvers for dense linear systems
IMPLEMENTATION
See individual man pages for implementation details
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
DESCRIPTION
The preferred solvers for dense linear systems are those parts of the
LAPACK package that are included in the current version of the SGI
Scientific Computing Software Library (SCSL).
LAPACK Routines
LAPACK is a public domain library of subroutines for solving dense linear
algebra problems, including the following:
* Systems of linear equations
* Linear least squares problems
* Eigenvalue problems
* Singular value decomposition (SVD) problems
For details about which routines are supported, see "LAPACK Routines
Contained in the Scientific Library," which follows.
The LAPACK package is designed to be the successor to the older LINPACK
and EISPACK packages. It uses today's high-performance computers more
efficiently than the older packages. It also extends the functionality
of these packages by including equilibration, iterative refinement, error
bounds, and driver routines for linear systems, routines for computing
and reordering the Schur factorization, and condition estimation routines
for eigenvalue problems.
Performance issues are addressed by implementing the most
computationally-intensive algorithms by using the Level 2 and 3 Basic
Linear Algebra Subprograms (BLAS). Because most of the BLAS were
optimized in single- and multiple-processor environments, these
algorithms give near optimal performance.
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INTRO_LAPACK(3S)INTRO_LAPACK(3S)
The original Fortran programs are described in the LAPACK User's Guide by
E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A.
Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen,
published by the Society for Industrial and Applied Mathematics (SIAM),
Philadelphia, 1992. The manual is also available online at
http://www.netlib.org/lapack/lug/index.html.
LAPACK Routines Contained in the Scientific Library
All of the real and complex routines from LAPACK 3.0 are supported in
SCSL. This includes driver routines and computational routines for
solving linear systems, least squares problems, and eigenvalue and
singular value problems. Selected auxiliary routines for generating and
manipulating elementary orthogonal transformations are also supported.
The LAPACK routines in SCSL are described online in man pages. For
example, to see a description of the arguments to the expert driver
routine for solving a general system of equations, enter the following
command:
% man sgesvx
The user interface to all supported LAPACK routines is exactly the same
as the standard LAPACK interface.
Tuning parameters for the block algorithms provided in the SCSL are set
within the LAPACK routine ILAENV(3S). ILAENV(3S) is an integer function
subprogram that accepts information about the problem type and
dimensions, and it returns one integer parameter, such as the optimal
block size, the minimum block size for which a block algorithm should be
used, or the crossover point (the problem size at which it becomes more
efficient to switch to an unblocked algorithm). The setting of tuning
parameters occurs without user intervention, but users may call
ILAENV(3S) directly to discover the values that will be used (for
example, to determine how much workspace to provide).
Calling LAPACK Routines from C
Although LAPACK is a library of Fortran 77 subroutines, C and C++ users
have full access to LAPACK functionality provided that they follow
conventions documented in Chapter 8 of the MIPSpro 7 Fortran 90 Commands
and Directives Reference Manual, "Interlanguage Calling" (available from
http://techpubs.sgi.com/). The large majority of LAPACK routines can be
called from C/C++ using the following four rules:
* The name of the LAPACK subprogram must be declared in the C/C++
program using all lowercase letters, appended with a trailing
underscore.
* The correspondence between Fortran and C data types is as follows:
Fortran C/C++
------------
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INTRO_LAPACK(3S)INTRO_LAPACK(3S)
INTEGER int (32-bit integer library)
long long (64-bit integer library)
LOGICAL int (32-bit integer library)
long long (64-bit integer library)
REAL float
DOUBLE PRECISION double
COMPLEX struct{float real, imag;};
DOUBLE COMPLEX struct{double real, imag;};
CHARACTER char
* All subroutine arguments should be passed by reference.
* The LAPACK routines expect multidimensional arrays to be stored in
column-major format in a contiguous region of memory.
Note that the list above represents a subset of the general set of
interlanguage calling conventions described in the Fortran 90 reference
manual. Character strings, in particular, require special handling when
passed as subroutine arguments or when returned from a function: if a
string is longer than one character in extent, its length must be passed
as an additional argument. Since most LAPACK subprograms employ
character strings of length one, however, this special case can usually
be ignored. Two important exceptions, ILAENV(3S) and XERBLA(3S), are
discussed more fully below.
To call the double precision Cholesky factorization routine DPOTRF(3S),
for example, the following prototype and code might apply:
void dpotrf_(char *, int *, double *, int *, int *);
char uplo;
int info, lda, n;
double a[1000][1001];
uplo = 'U';
lda = 1001;
n = 1000;
dpotrf_(&uplo, &n, (double *) a, &lda, &info);
Or, to calculate the eigenvalues and eigenvectors of a double complex
Hermitian matrix using ZHEEVD(3S) from the 64-bit integer version of
SCSL, one might have:
typedef struct {double real, imag;} zomplex;
void zheevd_(char *, char *, long long *, zomplex *,
long long *, double *, zomplex *, long long *,
double *, long long *, long long *, long long *,
long long *);
char jobz, uplo;
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INTRO_LAPACK(3S)INTRO_LAPACK(3S)
long long info, lda, liwork, lrwork, lwork, n;
long long *iwork;
double *rwork, *w;
zomplex *a, *work;
...
(array allocations and variable assignments)
...
zheevd_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, rwork,
&lrwork iwork, &liwork, &info);
Two LAPACK routines involving character string arguments are XERBLA(3S)
and ILAENV(3S). The corresponding C/C++ prototypes, assuming 32-bit
integers in the former case and 64-bit integers in the latter, would be
void xerbla_(char *, int *, const int);
long long ilaenv_(long long *, char *str1, char *str2, long long *,
long long *, long long *, long long *,
const int len_str1, const int len_str2);
Here the lengths of the strings are passed as implicit arguments, in
order of use, following the explicit argument list. Note that,
regardless of the default integer size in the version of SCSL one uses,
the length of the character string is always passed as type int.
Naming Scheme
The name of each LAPACK routine is a coded specification of its function
(within the limits of the FORTRAN 77 standard for six-character names).
All driver and computational routines have five- or six-character names
of the form XYYZZ or XYYZZZ.
The first letter in each name, X, indicates the data type, as follows:
S REAL
D DOUBLE PRECISION
C COMPLEX
Z DOUBLE COMPLEX
The next two letters, YY, indicate the type of matrix (or the
most-significant matrix). Most of these two-letter codes apply to both
real and complex matrices, but a few apply specifically to only one or
the other. The matrix types are as follows:
BD BiDiagonal
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INTRO_LAPACK(3S)INTRO_LAPACK(3S)
DI Diagonal
GB General Band
GE GEneral (nonsymmetric)
GG General matrices, Generalized problem
GT General Tridiagonal
HB Hermitian Band (complex only)
HE HErmitian (possibly indefinite) (complex only)
HG Hessenberg matrix, Generalized problem
HP Hermitian Packed (possibly indefinite) (complex only)
HS upper HeSsenberg
OP Orthogonal Packed (real only)
OR ORthogonal (real only)
PB Positive definite Band (symmetric or Hermitian)
PO POsitive definite (symmetric or Hermitian)
PP Positive definite Packed (symmetric or Hermitian)
PT Positive definite Tridiagonal (symmetric or Hermitian)
SB Symmetric Band (real only)
SP Symmetric Packed (possibly indefinite)
ST Symmetric Tridiagonal
SY SYmmetric (possibly indefinite)
TB Triangular Band
TG Triangular matrices, Generalized problem
TP Triangular Packed
TR TRiangular
TZ TrapeZoidal
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INTRO_LAPACK(3S)INTRO_LAPACK(3S)
UN UNitary (complex only)
UP Unitary Packed (complex only)
The last two or three letters, ZZ or ZZZ, indicate the computation
performed. For example, SGETRF performs a TRiangular Factorization of a
Single-precision (real) GEneral matrix; CGETRF performs the factorization
of a Complex GEneral matrix.
Lists of Available LAPACK Routines
The following pages contain lists of driver and computational routines
from LAPACK available in the SCSL Scientific Library. For details about
the argument lists and usage of these routines, see the individual online
man pages or the LAPACK User's Guide.
These routines are listed in alphabetical order.
* CHESV, ZHESV: Solves a complex Hermitian indefinite system of linear
equations AX = B.
* CHESVX, ZHESVX: Solves a complex Hermitian indefinite system of
linear equations AX = B and provides an estimate of the condition
number and error bounds on the solution.
* CHPSV, ZHPSV: Solves a complex Hermitian indefinite system of linear
equations AX = B; A is held in packed storage.
* CHPSVX, ZHPSVX: Solves a complex Hermitian indefinite system of
linear equations AX = B (A is held in packed storage) and provides an
estimate of the condition number and error bounds on the solution.
* SGBSV, DGBSV, CGBSV, ZGBSV: Solves a general banded system of linear
equations AX = B.
* SGBSVX, DGBSVX, CGBSVX, ZGBSVX: Solves any of the following general
banded systems of linear equations and provides an estimate of the
condition number and error bounds on the solution.
A X = B
T
A = B
H
A X = B
* SGEES, DGEES, CGEES, ZGEES: Computes eigenvalues, Schur form, and
Schur vectors of a general matrix.
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* SGEESX, DGEESX, CGEESX, ZGEESX: Computes eigenvalues, Schur form,
Schur vectors, and condition numbers of a general matrix.
* SGEEV, DGEEV, CGEEV, ZGEEV: Computes eigenvalues and eigenvectors of
a general matrix.
* SGEEVX, DGEEVX, CGEEVX, ZGEEVX: Compute eigenvalues, eigenvectors,
and condition numbers of a general matrix.
* SGEGS, DGEGS, CGEGS, ZGEGS: Computes the generalized Schur
factorization of a matrix pair (A,B).
* SGEGV, DGEGV, CGEGV, ZGEGV: Computes the eigenvalues and
eigenvectors of a matrix pair (A,B).
* SGELS, DGELS, CGELS, ZGELS: Finds a least squares or minimum norm
solution of an overdetermined or underdetermined linear. system.
* SGELSD, DGELSD, CGELSD, ZGELSD: Solves linear least squares problem
using divide-and-conquer.
* SGELSS, DGELSS, CGELSS, ZGELSS: Solves linear least squares problem
using SVD.
* SGELSY, DGELSY, CGELSY, ZGELSY: Computes a minimum norm solution of
a linear least squares problem using a complete orthogonal
factorization.
* SGESDD, DGESDD, CGESDD, ZGESDD: Computes the singular value
decomposition (SVD) of a general matrix using divide-and-conquer.
* SGESV, DGESV, CGESV, ZGESV: Solves a general system of linear
equations AX = B.
* SGESVD, DGESVD, CGESVD, ZGESVD: Computes the singular value
decomposition (SVD) of a general matrix.
* SGESVX, DGESVX, CGESVX, ZGESVX: Solves any of the following general
systems of linear equations and provides an estimate of the condition
number and error bounds on the solution.
A X = B
T
A X = B
H
A X = B
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* SGGES, DGGES, CGGES, ZGGES: Computes the generalized Schur
factorization of a matrix pair (A,B).
* SGGESX, DGGESX, CGGESX, ZGGESX: Computes the generalized Schur
factorization of a matrix pair (A,B), expert driver.
* SGGEV, DGGEV, CGGEV, ZGGEV: Computes the eigenvalues and eigenvectors
of a matrix pair (A,B).
* SGGEVX, DGGEVX, CGGEVX, ZGGEVX: Computes the eigenvalues and
eigenvectors of a matrix pair (A,B), expert driver.
* SGGLSE, DGGLSE, CGGLSE, ZGGLSE: Solves a linear equality-constrained
least squares problem (LSE) using GRQ.
* SGGGLM, DGGGLM, CGGGLM, ZGGGLM: Solves a general (Gauss-Markov)
linear model problem (GLM) using GQR.
* SGGSVD, DGGSVD, CGGSVD, ZGGSVD: Computes the generalized singular
value decomposition (SVD) of a matrix pair (A,B).
* SGTSV, DGTSV, CGTSV, ZGTSV: Solves a general tridiagonal system of
linear equations AX = B.
* SGTSVX, DGTSVX, CGTSVX, ZGTSVX: Solves any of the following general
tridiagonal systems of linear equations and provides an estimate of
the condition number and error bounds on the solution.
A X = B
T
A = B
H
A X = B
* SPBSV, DPBSV, CPBSV, ZPBSV: Solves a symmetric or Hermitian positive
definite banded system of linear equations AX = B.
* SPBSVX, DPBSVX, CPBSVX, ZPBSVX: Solves a symmetric or Hermitian
positive definite banded system of linear equations AX = B and
provides an estimate of the condition number and error bounds on the
solution.
* SPOSV, DPOSV, CPOSV, ZPOSV: Solves a symmetric or Hermitian positive
definite system of linear equations AX = B.
* SPOSVX, DPOSVX, CPOSVX, ZPOSVX: Solves a symmetric or Hermitian
positive definite system of linear equations AX = B and provides an
estimate of the condition number and error bounds on the solution.
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INTRO_LAPACK(3S)INTRO_LAPACK(3S)
* SPPSV, DPPSV, CPPSV, ZPPSV: Solves a symmetric or Hermitian positive
definite system of linear equations AX = B; A is held in packed
storage.
* SPPSVX, DPPSVX, CPPSVX, ZPPSVX: Solves a symmetric or Hermitian
positive definite system of linear equations AX = B (A is held in
packed storage) and provides an estimate of the condition number and
error bounds on the solution.
* SPTSV, DPTSV, CPTSV, ZPTSV: Solves a symmetric or Hermitian positive
definite tridiagonal system of linear equations AX = B.
* SPTSVX, DPTSVX, CPTSVX, ZPTSVX: Solves a symmetric or Hermitian
positive definite tridiagonal system of linear equations AX = B and
provides an estimate of the condition number and error bounds on the
solution.
* SSBEV, DSBEV, CHBEV, ZHBEV: Compute all eigenvalues and eigenvectors
of a symmetric or Hermitian band matrix.
* SSBEVD, DSBEVD, CHBEVD, ZHBEVD: Compute all eigenvalues and
eigenvectors of a symmetric or Hermitian band matrix using divide-
and-conquer.
* SSBEVX, DSBEVX, CHBEVX, ZHBEVX: Compute selected eigenvalues and
eigenvectors of a symmetric or Hermitian band matrix.
* SSBGV, DSBGV, CHBGV, ZHBGV: Computes all eigenvalues and
eigenvectors of a generalized symmetric-definite or Hermitian-
definite banded eigenproblem.
* SSBGVD, DSBGVD, CHBGVD, ZHBGVD: Computes all eigenvalues and
eigenvectors of a generalized symmetric-definite or Hermitian-
definite banded eigenproblem using divide-and-conquer.
* SSBGVX, DSBGVX, CHBGVX, ZHBGVX: Computes all eigenvalues and
eigenvectors of a generalized symmetric-definite or Hermitian-
definite banded eigenproblem expert driver.
* SSPEV, DSPEV, CHPEV, ZHPEV: Computes all eigenvalues and
eigenvectors of a symmetric or Hermitian packed matrix.
* SSPEVD, DSPEVD, CHPEVD, ZHPEVD: Computes all eigenvalues and
eigenvectors of a symmetric or Hermitian packed matrix using divide-
and-conquer.
* SSPEVX, DSPEVX, CHPEVX, ZHPEVX: Computes selected eigenvalues and
eigenvectors of a symmetric or Hermitian packed matrix.
* SSPGV, DSPGV, CHPGV, ZHPGV: Computes all eigenvalues and
eigenvectors of a generalized symmetric-definite or
Hermitian-definite packed eigenproblem.
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* SSPSV, DSPSV, CSPSV, ZSPSV: Solves a real or complex symmetric
indefinite system of linear equations AX = B; A is held in packed
storage.
* SSPSVX, DSPSVX, CSPSVX, ZSPSVX: Solves a real or complex symmetric
indefinite system of linear equations AX = B (A is held in packed
storage) and provides an estimate of the condition number and error
bounds on the solution.
* SSTEV, DSTEV: Compute all eigenvalues and eigenvectors of a real
symmetric tridiagonal matrix.
* SSTEVD, DSTEVD: Compute all eigenvalues and eigenvectors of a real
symmetric tridiagonal matrix using divide-and-conquer.
* SSTEVR, DSTEVR: Compute all eigenvalues and eigenvectors of a real
symmetric tridiagonal matrix using RRR (relatively robust
representation).
* SSTEVX, DSTEVX: Computes selected eigenvalues and eigenvectors of a
real symmetric tridiagonal matrix.
* SSYEV, DSYEV, CHEEV, ZHEEV: Computes all eigenvalues and
eigenvectors of a symmetric or Hermitian matrix.
* SSYEVD, DSYEVD, CHEEVD, ZHEEVD: Computes all eigenvalues and
eigenvectors of a symmetric or Hermitian matrix using divide-and-
conquer.
* SSYEVR, DSYEVR, CHEEVR, ZHEEVR: Computes all eigenvalues and
eigenvectors of a symmetric or Hermitian matrix using RRR (relatively
robust representation).
* SSYEVX, DSYEVX, CHEEVX, ZHEEVX: Computes selected eigenvalues and
eigenvectors of a symmetric or Hermitian matrix.
* SSYGV, DSYGV, CHEGV, ZHEGV: Computes all eigenvalues and
eigenvectors of a generalized symmetric-definite or
Hermitian-definite eigenproblem.
* SSYGVD, DSYGVD, CHEGVD, ZHEGVD: Computes all eigenvalues and
eigenvectors of a generalized symmetric-definite or Hermitian-
definite eigenproblem using divide-and-conquer.
* SSYGVX, DSYGVX, CHEGVX, ZHEGVX: Computes all eigenvalues and
eigenvectors of a generalized symmetric-definite or Hermitian-
definite eigenproblem expert driver.
* SSYSV, DSYSV, CSYSV, ZSYSV: Solves a real or complex symmetric
indefinite system of linear equations AX = B.
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INTRO_LAPACK(3S)INTRO_LAPACK(3S)
* SSYSVX, DSYSVX, CSYSVX, ZSYSVX: Solves a real or complex symmetric
indefinite system of linear equations AX = B and provides an estimate
of the condition number and error bounds on the solution.
These computational routines are listed in alphabetical order, with real
matrix routines and complex matrix routines grouped together as
appropriate.
* CHECON, ZHECON: Estimates the reciprocal of the condition number of
a complex Hermitian indefinite matrix, using the factorization
computed by CHETRF.
* CHERFS, ZHERFS: Improves the computed solution to a complex
Hermitian indefinite system of linear equations AX = B and provides
error bounds for the solution.
* CHETRF, ZHETRF: Computes the factorization of a complex Hermitian
indefinite matrix, using the diagonal pivoting method.
* CHETRI, ZHETRI: Computes the inverse of a complex Hermitian
indefinite matrix, using the factorization computed by CHETRF.
* CHETRS, ZHETRS: Solves a complex Hermitian indefinite system of
linear equations AX = B, using the factorization computed by CHETRF.
* CHPCON, ZHPCON: Estimates the reciprocal of the condition number of
a complex Hermitian indefinite matrix in packed storage, using the
factorization computed by CHPTRF.
* CHPRFS, ZHPRFS: Improves the computed solution to a complex
Hermitian indefinite system of linear equations AX = B (A is held in
packed storage) and provides error bounds for the solution.
* CHPTRF, ZHPTRF: Computes the factorization of a complex Hermitian
indefinite matrix in packed storage, using the diagonal pivoting
method.
* CHPTRI, ZHPTRI: Computes the inverse of a complex Hermitian
indefinite matrix in packed storage, using the factorization computed
by CHPTRF.
* CHPTRS, ZHPTRS: Solves a complex Hermitian indefinite system of
linear equations AX = B (A is held in packed storage) using the
factorization computed by CHPTRF.
* ILAENV: Determines tuning parameters (such as the block size).
* SBDSDC, DBDSDC, CBDSDC, ZBDSDC: Compute the singular value
decomposition of a general matrix reduced to bidiagonal form using
divide-and-conquer.
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* SBDSQR, DBDSQR, CBDSQR, ZBDSQR: Compute the singular value
decomposition of a general matrix reduced to bidiagonal form
* SDISNA, DDISNA, CDISNA, ZDISNA: Computes the reciprocal condition
numbers for the eigenvectors of a real symmetric or complex Hermitian
matrix or for the left or right singular vectors of a general matrix.
* SGBBRD, DGBBRD, CGBBRD, ZGBBRD: Reduces a general band matrix to real
upper bidiagonal form by an orthogonal/unitary transformation.
* SGBCON, DGBCON, CGBCON, ZGBCON: Estimates the reciprocal of the
condition number of a general band matrix, in either the 1-norm or
the infinity-norm, using the LU factorization computed by SGBTRF or
CGBTRF.
* SGBEQU, DGBEQU, CGBEQU, ZGBEQU: Computes row and column scalings to
equilibrate a general band matrix and reduce its condition number.
Does not multiprocess or call any multiprocessing routines.
* SGBRFS, DGBRFS, CGBRFS, ZGBRFS: Improves the computed solution to
any of the following general banded systems of linear equations and
provides error bounds for the solution.
A X = B
T
A X = B
H
A X = B
* SGBTRF, DGBTRF, CGBTRF, ZGBTRF: Computes an LU factorization of a
general band matrix, using partial pivoting with row interchanges.
* SGBTRS, DGBTRS, CGBTRS, ZGBTRS: Solves any of the following general
banded systems of linear equations using the LU factorization
computed by SGBTRF or CGBTRF.
A X = B
T
A X = B
H
A X = B
* SGEBAK, DGEBAK, CGEBAK, ZGEBAK: Back transform the eigenvectors of a
matrix transformed by SGEBAL/CGEBAL.
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* SGEBAL, DGEBAL, CGEBAL, ZGEBAL: Balances a general matrix A.
* SGEBRD, DGEBRD, CGEBRD, ZGEBRD: Reduces a general matrix to upper or
lower bidiagonal form by an orthogonal/unitary transformation.
* SGECON, DGECON, CGECON, ZGECON: Estimates the reciprocal of the
condition number of a general matrix, in either the 1-norm or the
infinity-norm, using the LU factorization computed by SGETRF or
CGETRF.
* SGEEQU, DGEEQU, CGEEQU, ZGEEQU: Computes row and column scalings to
equilibrate a general rectangular matrix and to reduce its condition
number.
* SGEHRD, DGEHRD, CGEHRD, ZGEHRD: Reduces a general matrix to upper
Hessenberg form by an orthogonal/unitary transformation.
* SGELQF, DGELQF, CGELQF, ZGELQF: Computes an LQ factorization of a
general rectangular matrix.
* SGEQLF, DGEQLF, CGEQLF, ZGEQLF: Computes a QL factorization of a
general rectangular matrix.
* SGEQP3, DGEQP3, CGEQP3, ZGEQP3: Computes a QR factorization with
column pivoting of a general rectangular matrix using level-3 BLAS.
* SGEQPF, DGEQPF, CGEQPF, ZGEQPF: Computes a QR factorization with
column pivoting of a general rectangular matrix.
* SGEQRF, DGEQRF, CGEQRF, ZGEQRF: Computes a QR factorization of a
general rectangular matrix.
* SGERFS, DGERFS, CGERFS, ZGERFS: Improves the computed solution to
any of the following general systems of linear equations and provides
error bounds for the solution.
A X = B
T
A X = B
H
A X = B
* SGERQF, DGERQF, CGERQF, ZGERQF: Computes an RQ factorization of a
general rectangular matrix.
* SGETRF, DGETRF, CGETRF, ZGETRF: Computes an LU factorization of a
general matrix, using partial pivoting with row interchanges.
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* SGETRI, DGETRI, CGETRI, ZGETRI: Computes the inverse of a general
matrix, using the LU factorization computed by SGETRF or CGETRF.
* SGETRS, DGETRS, CGETRS, ZGETRS: Solves any of the following general
systems of linear equations using the LU factorization computed by
SGETRF or CGETRF.
A X = B
T
A X = B
H
A X = B
* SGGBAK, DGGBAK, CGGBAK, ZGGBAK: Back transform the eigenvectors of a
generalized eigenvalue problem transformed by SGGBAL
* SGGBAL, DGGBAL, CGGBAL, ZGGBAL: Balance a pair of general matrices
(A,B)
* SGGHRD, DGGHRD, CGGHRD, ZGGHRD: Reduce a pair of matrices (A,B) to
generalized upper Hessenberg form
* SGGQRF, DGGQRF, CGGQRF, ZGGQRF: Computes a generalized QR
factorization of a pair of matrices (A,B).
* SGGRQF, DGGRQF, CGGRQF, ZGGRQF: Computes a generalized RQ
factorization of a pair of matrices (A,B).
* SGGSVP, DGGSVP, CGGSVP, ZGGSVP: Computes orthogonal/unitary matrices
U, V, and Q as the preprocessing step for computing the generalized
singular value decomposition (GSVD).
* SGTCON, DGTCON, CGTCON, ZGTCON: Estimates the reciprocal of the
condition number of a general tridiagonal matrix, in either the 1-
norm or the infinity-norm, using the LU factorization computed by
SGTTRF or CGTTRF.
* SGTRFS, DGTRFS, CGTRFS, ZGTRFS: Improves the computed solution to
any of the following general tridiagonal systems of linear equations
and provides error bounds for the solution.
A X = B
T
A X = B
H
A X = B
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INTRO_LAPACK(3S)INTRO_LAPACK(3S)
* SGTTRF, DGTTRF, CGTTRF, ZGTTRF: Computes an LU factorization of a
general tridiagonal matrix, using partial pivoting with row
interchanges.
* SGTTRS, DGTTRS, CGTTRS, ZGTTRS: Solves a general tridiagonal system
of linear equations using the LU factorization computed by SGTTRF or
CGTTRF.
A X = B
T
A X = B
H
A X = B
* SHGEQZ, DHGEQZ, CHGEQZ, ZHGEQZ: Compute the eigenvalues of a matrix
pair (A,B) in generalized upper Hessenberg form using the QZ method
* SHSEIN, DHSEIN, CHSEIN, ZHSEIN: Compute eigenvectors of a upper
Hessenberg matrix by inverse iteration
* SHSEQR, DHSEQR, CHSEQR, ZHSEQR: Compute eigenvalues, Schur form, and
Schur vectors of a upper Hessenberg matrix
* SLAMCH, DLAMCH: Computes machine-specific constants.
* SLARF, DLARF, CLARF, ZLARF: Applies an elementary reflector.
* SLARFB, DLARFB, CLARFB, ZLARFB: Applies a block reflector.
* SLARFG, DLARFG, CLARFG, ZLARFG: Generates an elementary reflector.
* SLARFT, DLARFT, CLARFT, ZLARFT: Forms the triangular factor of a
block reflector.
* SLARGV, DLARGV, CLARGV, ZLARGV: Generate a vector of real or complex
plane rotations
* SLARNV, DLARNV, CLARNV, ZLARNV: Generates a vector of random
numbers.
* SLARTG, DLARTG, CLARTG, ZLARTG: Generates a plane rotation.
* SLARTV, DLARTV, CLARTV, ZLARTV: Apply a vector of real or complex
plane rotations to two vectors
* SLASR, DLASR, CLASR, ZLASR: Apply a sequence of real plane rotations
to a matrix
Page 15
INTRO_LAPACK(3S)INTRO_LAPACK(3S)
* SOPGTR, DOPGTR, CUPGTR, ZUPGTR: Generates the orthogonal/unitary
matrix Q from SSPTRD/CHPTRD.
* SOPMTR, DOPMTR, CUPMTR, ZUPMTR: Multiplies by the orthogonal/unitary
matrix Q from SSPTRD/CHPTRD.
* SORGBR, DORGBR, CUNGBR, ZUNGBR: Generates one of the
orghogonal/unitary matrices:
H
Q or P
from SGEBRD/CGEBRD.
* SORGHR, DORGHR, CUNGHR, ZUNGHR: Generates the orthogonal/unitary
matrix Q from SGEHRD/CGEHRD.
* SORGLQ, DORGLQ, CUNGLQ, ZUNGLQ: Generates all or part of the
orthogonal or unitary matrix Q from an LQ factorization determined by
SGELQF or CGELQF.
* SORGQL, DORGQL, CUNGQL, ZUNGQL: Generates all or part of the
orthogonal or unitary matrix Q from a QL factorization determined by
SGEQLF or CGEQLF.
* SORGQR, DORGQR, CUNGQR, ZUNGQR: Generates all or part of the
orthogonal or unitary matrix Q from a QR factorization determined by
SGEQRF or CGEQRF.
* SORGRQ, DORGRQ, CUNGRQ, ZUNGRQ: Generates all or part of the
orthogonal or unitary matrix Q from an RQ factorization determined by
SGERQF or CGERQF.
* SORGTR, DORGTR, CUNGTR, ZUNGTR: Generates the orthogonal/unitary
matrix Q from SSYTRD/CHETRD.
* SORMBR, DORMBR, CUNMBR, ZUNMBR: Multiplies by one of the
orthogonal/unitary matrices Q or P from SGEBRD/CGEBRD.
* SORMHR, DORMHR, CUNMHR, ZUNMHR: Multiplies by the orthogonal/unitary
matrix Q from SGEHRD/CGEHRD.
* SORMLQ, DORMLQ, CUNMLQ, ZUNMLQ: Multiplies a general matrix by the
orthogonal or unitary matrix from an LQ factorization determined by
SGELQF or CGELQF.
* SORMQL, DORMQL, CUNMQL, ZUNMQL: Multiplies a general matrix by the
orthogonal or unitary matrix from a QL factorization determined by
SGEQLF or CGEQLF.
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INTRO_LAPACK(3S)INTRO_LAPACK(3S)
* SORMQR, DORMQR, CUNMQR, ZUNMQR: Multiplies a general matrix by the
orthogonal or unitary matrix from a QR factorization determined by
SGEQRF or CGEQRF.
* SORMRQ, DORMRQ, CUNMRQ, ZUNMRQ: Multiplies a general matrix by the
orthogonal or unitary matrix from an RQ factorization determined by
SGERQF or CGERQF.
* SORMRZ, DORMRZ, CUNMRZ, ZUNMRZ: Multiplies a general matrix by the
orthogonal or unitary matrix from an RZ factorization determined by
STZRZF or CTZRZF.
* SORMTR, DORMTR, CUNMTR, ZUNMTR: Multiplies by the orthogonal/unitary
matrix Q from SSYTRD/CHETRD.
* SPBCON, DPBCON, CPBCON, ZPBCON: Estimates the reciprocal of the
condition number of a symmetric or Hermitian positive definite band
matrix, using the Cholesky factorization computed by SPBTRF or
CPBTRF.
* SPBEQU, DPBEQU, CPBEQU, ZPBEQU: Computes row and column scalings to
equilibrate a symmetric or Hermitian positive definite band matrix
and to reduce its condition number.
* SPBRFS, DPBRFS, CPBRFS, ZPBRFS: Improves the computed solution to a
symmetric or Hermitian positive definite banded system of linear
equations AX = B and provides error bounds for the solution.
* SPBSTF, DPBSTF, CPBSTF, ZPBSTF: Compute a split Cholesky
factorization of a symmetric or Hermitian positive definite band
matrix.
* SPBTRF, DPBTRF, CPBTRF, ZPBTRF: Computes the Cholesky factorization
of a symmetric or Hermitian positive definite band matrix.
* SPBTRS, DPBTRS, CPBTRS, ZPBTRS: Solves a symmetric or Hermitian
positive definite banded system of linear equations AX = B, using the
Cholesky factorization computed by SPBTRF or CPBTRF.
* SPOCON, DPOCON, CPOCON, ZPOCON: Estimates the reciprocal of the
condition number of a symmetric or Hermitian positive definite
matrix, using the Cholesky factorization computed by SPOTRF or
CPOTRF.
* SPOEQU, DPOEQU, CPOEQU, ZPOEQU: Computes row and column scalings to
equilibrate a symmetric or Hermitian positive definite matrix and
reduces its condition number.
* SPORFS, DPORFS, CPORFS, ZPORFS: Improves the computed solution to a
symmetric or Hermitian positive definite system of linear equations
AX = B and provides error bounds for the solution.
Page 17
INTRO_LAPACK(3S)INTRO_LAPACK(3S)
* SPOTRF, DPOTRF, CPOTRF, ZPOTRF: Computes the Cholesky factorization
of a symmetric or Hermitian positive definite matrix.
* SPOTRI, DPOTRI, CPOTRI, ZPOTRI: Computes the inverse of a symmetric
or Hermitian positive definite matrix, using the Cholesky
factorization computed by SPOTRF or CPOTRF.
* SPOTRS, DPOTRS, CPOTRS, ZPOTRS: Solves a symmetric or Hermitian
positive definite system of linear equations AX = B, using the
Cholesky factorization computed by SPOTRF or CPOTRF.
* SPPCON, DPPCON, CPPCON, ZPPCON: Estimates the reciprocal of the
condition number of a symmetric or Hermitian positive definite matrix
in packed storage, using the Cholesky factorization computed by
SPPTRF or CPPTRF.
* SPPEQU, DPPEQU, CPPEQU, ZPPEQU: Computes row and column scalings to
equilibrate a symmetric or Hermitian positive definite matrix in
packed storage and reduces its condition number.
* SPPRFS, DPPRFS, CPPRFS, ZPPRFS: Improves the computed solution to a
symmetric or Hermitian positive definite system of linear equations
AX = B (A is held in packed storage) and provides error bounds for
the solution.
* SPPTRF, DPPTRF, CPPTRF, ZPPTRF: Computes the Cholesky factorization
of a symmetric or Hermitian positive definite matrix in packed
storage.
* SPPTRI, DPPTRI, CPPTRI, ZPPTRI: Computes the inverse of a symmetric
or Hermitian positive definite matrix in packed storage, using the
Cholesky factorization computed by SPPTRF or CPPTRF.
* SPPTRS, DPPTRS, CPPTRS, ZPPTRS: Solves a symmetric or Hermitian
positive definite system of linear equations AX = B (A is held in
packed storage) using the Cholesky factorization computed by SPPTRF
or CPPTRF.
* SPTCON, DPTCON, CPTCON, ZPTCON: Uses the LDLH factorization computed
by SPTTRF or CPTTRF to compute the reciprocal of the condition number
of a symmetric or Hermitian positive definite tridiagonal matrix.
* SPTEQR, DPTEQR, CPTEQR, ZPTEQR: Compute eigenvalues and eigenvectors
of a symmetric or Hermitian positive definite tridiagonal matrix.
* SPTRFS, DPTRFS, CPTRFS, ZPTRFS: Improves the computed solution to a
symmetric or Hermitian positive definite tridiagonal system of linear
equations AX = B and provides error bounds for the solution.
* SPTTRF, DPTTRF, CPTTRF, ZPTTRF: Computes the LDLH factorization of a
symmetric or Hermitian positive definite tridiagonal matrix.
Page 18
INTRO_LAPACK(3S)INTRO_LAPACK(3S)
* SPTTRS, DPTTRS, CPTTRS, ZPTTRS: Uses the LDLH factorization computed
by SPTTRF or CPTTRF to solve a symmetric or Hermitian positive
definite tridiagonal system of linear equations.
* SSBGST, DSBGST, CHBGST, ZHBGST: Reduce a symmetric or Hermitian
definite banded generalized eigenproblem to standard form.
* SSBTRD, DSBTRD, CHBTRD, ZHBTRD: Reduce a symmetric or Hermitian band
matrix to real symmetric tridiagonal form by an orthogonal/unitary
transformation.
* SSPCON, DSPCON, CSPCON, ZSPCON: Estimates the reciprocal of the
condition number of a real or complex symmetric indefinite matrix in
packed storage, using the factorization computed by SSPTRF or CSPTRF.
* SSPGST, DSPGST, CHPGST, ZHPGST: Reduce a symmetric or Hermitian
definite generalized eigenproblem to standard form, using packed
storage.
* SSPRFS, DSPRFS, CSPRFS, ZSPRFS: Improves the computed solution to a
real or complex symmetric indefinite system of linear equations AX =
B (A is held in packed storage) and provides error bounds for the
solution.
* SSPTRD, DSPTRD, CHPTRD, ZHPTRD: Reduces a symmetric/Hermitian packed
matrix A to real symmetric tridiagonal form by an orthogonal/unitary
transformation.
* SSPTRF, DSPTRF, CSPTRF, ZSPTRF: Computes the factorization of a real
or complex symmetric indefinite matrix in packed storage, using the
diagonal pivoting method.
* SSPTRI, DSPTRI, CSPTRI, ZSPTRI: Computes the inverse of a real or
complex symmetric indefinite matrix in packed storage, using the
factorization computed by SSPTRF or CSPTRF.
* SSPTRS, DSPTRS, CSPTRS, ZSPTRS: Solves a real or complex symmetric
indefinite system of linear equations AX = B (A is held in packed
storage) using the factorization computed by SSPTRF or CSPTRF.
* SSTEBZ, DSTEBZ: Compute eigenvalues of a symmetric tridiagonal
matrix by bisection.
* SSTEDC, DSTEDC, CSTEDC, ZSTEDC: Computes all eigenvalues and,
optionally, eigenvectors of a symmetric tridiagonal matrix using the
divide and conquer algorithm.
* SSTEGR, DSTEGR, CSTEGR, ZSTEGR: Computes selected eigenvalues and,
optionally, eigenvectors of a real symmetric tridiagonal matrix using
the Relatively Robust Representations.
Page 19
INTRO_LAPACK(3S)INTRO_LAPACK(3S)
* SSTEIN, DSTEIN, CSTEIN, ZSTEIN: Compute eigenvectors of a real
symmetric tridiagonal matrix by inverse iteration.
* SSTEQR, DSTEQR, CSTEQR, ZSTEQR: Compute eigenvalues and eigenvectors
of a real symmetric tridiagonal matrix using the implicit QL or QR
method.
* SSTERF, DSTERF: Compute all eigenvalues of a symmetric tridiagonal
matrix using the root-free variant of the QL or QR algorithm.
* SSYCON, DSYCON, CSYCON, ZSYCON: Estimates the reciprocal of the
condition number of a real or complex symmetric indefinite matrix,
using the factorization computed by SSYTRF or CSYTRF.
* SSYGST, DSYGST, CHEGST, ZHEGST: Reduce a symmetric or Hermitian
definite generalized eigenproblem to standard form.
* SSYRFS, DSYRFS, CSYRFS, ZSYRFS: Improves the computed solution to a
real or complex symmetric indefinite system of linear equations AX =
B and provides error bounds for the solution.
* SSYTRD, DSYTRD, CHETRD, ZHETRD: Reduces a symmetric/Hermitian matrix
A to real symmetric tridiagonal form by an orthogonal/unitary
transformation.
* SSYTRF, DSYTRF, CSYTRF, ZSYTRF: Computes the factorization of a real
complex symmetric indefinite matrix, using the diagonal pivoting
method.
* SSYTRI, DSYTRI, CSYTRI, ZSYTRI: Computes the inverse of a real or
complex symmetric indefinite matrix, using the factorization computed
by SSYTRF or CSYTRF.
* SSYTRS, DSYTRS, CSYTRS, ZSYTRS: Solves a real or complex symmetric
indefinite system of linear equations AX = B, using the factorization
computed by SSYTRF or CSYTRF.
* STBCON, DTBCON, CTBCON, ZTBCON: Estimates the reciprocal of the
condition number of a triangular band matrix, in either the 1-norm or
the infinity-norm.
* STBRFS, DTBRFS, CTBRFS, ZTBRFS: Provides error bounds for the
solution of any of the following triangular banded systems of linear
equations:
A X = B
T
A X = B
H
A X = B
Page 20
INTRO_LAPACK(3S)INTRO_LAPACK(3S)
* STBTRS, DTBTRS, CTBTRS, ZTBTRS: Solves any of the following
triangular banded systems of linear equations:
A X = B
T
A X = B
H
A X = B
* STGEVC, DTGEVC, CTGEVC, ZTGEVC: Compute eigenvectors of a pair of
matrices (A,B) in generalized Schur form.
* STGEXC, DTGEXC, CTGEXC, ZTGEXC: Reorders the generalized real-
Schur/Schur decomposition of a matrix pair (A,B) using an
orthogonal/unitary equivalence transformation so that the diagonal
block of (A,B) with row index IFST is moved to row ILST.
* STGSEN, DTGSEN, CTGSEN, ZTGSEN: Reorders the generalized real-
Schur/Schur decomposition of a matrix pair (A,B), computes the
generalized eigenvalues of the reordered matrix pair, and,
optionally, computes the estimates of reciprocal condition numbers
for eigenvalues and eigenspaces.
* STGSJA, DTGSJA, CTGSJA, ZTGSJA: Computes the generalized singular
value decomposition (GSVD) of a pair of upper triangular (or
trapezoidal) matrices, which may be obtained by the preprocessing
subroutine SGGSVP/CGGSVP.
* STGSNA, DTGSNA, CTGSNA, ZTGSNA: Estimates reciprocal condition
numbers for specified eigenvalues and/or eigenvectors of a matrix
pair (A,B) in generalized real-Schur/Schur canonical form.
* STGSYL, DTGSYL, CTGSYL, ZTGSYL: Solves the generalized Sylvester
equation.
* STPCON, DTPCON, CTPCON, ZTPCON: Estimates the reciprocal of the
condition number of a triangular matrix in packed storage, in either
the 1-norm or the infinity-norm.
* STPRFS, DTPRFS, CTPRFS, ZTPRFS: Provides error bounds for the
solution of any of the following triangular systems of linear
equations where A is held in packed storage.
A X = B
T
A X = B
H
Page 21
INTRO_LAPACK(3S)INTRO_LAPACK(3S)
A X = B
* STPTRI, DTPTRI, CTPTRI, ZTPTRI: Computes the inverse of a triangular
matrix in packed storage.
* STPTRS, DTPTRS, CTPTRS, ZTPTRS: Solves any of the following
triangular systems of linear equations where A is held in packed
storage.
A X = B
T
A X = B
H
A X = B
* STRCON, DTRCON, CTRCON, ZTRCON: Estimates the reciprocal of the
condition number of a triangular matrix, in either the 1-norm or the
infinity-norm.
* STREVC, DTREVC, CTREVC, ZTREVC: Compute eigenvectors of a real upper
quasi-triangular matrix or a complex triangular matrix.
* STREXC, DTREXC, CTREXC, ZTREXC: Exchange diagonal blocks in the real
Schur factorization of a real or complex matrix.
* STRRFS, DTRRFS, CTRRFS, ZTRRFS: Provides error bounds for the
solution of any of the following triangular systems of linear
equations:
A X = B
T
A X = B
H
A X = B
* STRSEN, DTRSEN, CTRSEN, ZTRSEN: Compute condition numbers to measure
the sensitivity of a cluster of eigenvalues and its corresponding
invariant subspace.
* STRSNA, DTRSNA, CTRSNA, ZTRSNA: Compute condition numbers for
specified eigenvalues and eigenvectors of a real upper quasi-
triangular matrix or complex upper triangular matrix.
Page 22
INTRO_LAPACK(3S)INTRO_LAPACK(3S)
* STRSYL, DTRSYL, CTRSYL, ZTRSYL: Solve the Sylvester matrix equation.
* STRTRI, DTRTRI, CTRTRI, ZTRTRI: Computes the inverse of a triangular
matrix.
* STRTRS, DTRTRS, CTRTRS, ZTRTRS: Solves any of the following
triangular systems of linear equations:
A X = B
T
A X = B
H
A X = B
* STZRQF, DTZRQF, CTZRQF, ZTZRQF: Reduces an upper trapezoidal matrix
to upper triangular form by an orthogonal/unitary transformation.
* STZRZF, DTZRZF, CTZRZF, ZTZRZF: Reduces an upper trapezoidal matrix
to upper triangular form by an orthogonal/unitary transformation.
In addition to the driver and computational routines, the following
auxiliary routines are also available. For information about using these
routines, see the individual man pages.
CLACGV ZLACGV CLACRM ZLACRM
CLACRT ZLACRT CLAESY ZLAESY
CROT ZROT CSROT ZDROT CSPMV ZSPMV
CSPR ZSPR CSYMV ZSYMV
CSYR ZSYR ICMAX1 IZMAX1
SCSUM1 DZSUM1 SGBTF2 DGBTF2 CGBTF2 ZGBTF2
SGEBD2 DGEBD2 CGEBD2 ZGEBD2 SGEHD2 DGEHD2 CGEHD2 ZGEHD2
SGELQ2 DGELQ2 CGELQ2 ZGELQ2 SGEQL2 DGEQL2 CGEQL2 ZGEQL2
SGEQR2 DGEQR2 CGEQR2 ZGEQR2 SGETF2 DGETF2 CGETF2 ZGETF2
SLABAD DLABAD SLABRD DLABRD CLABRD ZLABRD
SLACON DLACON CLACON ZLACON SLACPY DLACPY CLACPY ZLACPY
SLADIV DLADIV CLADIV ZLADIV SLAE2 DLAE2
Page 23
INTRO_LAPACK(3S)INTRO_LAPACK(3S)
SLAEBZ DLAEBZ SLAED0 DLAED0 CLAED0 ZLAED0
SLAED1 DLAED1 SLAED2 DLAED2
SLAED3 DLAED3 SLAED4 DLAED4
SLAED5 DLAED5 SLAED6 DLAED6
SLAED7 DLAED7 CLAED7 ZLAED7 SLAED8 DLAED8 CLAED8 ZLAED8
SLAED9 DLAED9 SLAEDA DLAEDA
SLAEIN DLAEIN CLAEIN ZLAEIN SLAEV2 DLAEV2 CLAEV2 ZLAEV2
SLAEXC DLAEXC SLAG2 DLAG2
SLAGTF DLAGTF SLAGTM DLAGTM CLAGTM ZLAGTM
SLAGTS DLAGTS SLAHQR DLAHQR CLAHQR ZLAHQR
SLAHRD DLAHRD CLAHRD ZLAHRD SLAIC1 DLAIC1 CLAIC1 ZLAIC1
SLALN2 DLALN2 SLAMRG DLAMRG
SLANGB DLANGB CLANGB ZLANGB SLANGE DLANGE CLANGE ZLANGE
SLANGT DLANGT CLANGT ZLANGT SLANHS DLANHS CLANHS ZLANHS
SLANSB DLANSB CLANSB ZLANSB CLANHB ZLANHB
SLANSP DLANSP CLANSP ZLANSP CLANHP ZLANHP
SLANST DLANST CLANST ZLANST SLANSY DLANSY CLANSY ZLANSY
CLANHE ZLANHE SLANTB DLANTB CLANTB ZLANTB
SLANTP DLANTP CLANTP ZLANTP SLANTR DLANTR CLANTR ZLANTR
SLANV2 DLANV2 SLAPLL DLAPLL CLAPLL ZLAPLL
SLAPMT DLAPMT CLAPMT ZLAPMT SLAPY2 DLAPY2
SLAPY3 DLAPY3 SLAQGB DLAQGB CLAQGB ZLAQGB
SLAQGE DLAQGE CLAQGE ZLAQGE SLAQSB DLAQSB CLAQSB ZLAQSB
SLAQSP DLAQSP CLAQSP ZLAQSP SLAQSY DLAQSY CLAQSY ZLAQSY
SLAQTR DLAQTR SLAR2V DLAR2V CLAR2V ZLAR2V
Page 24
INTRO_LAPACK(3S)INTRO_LAPACK(3S)
SLARFX DLARFX CLARFX ZLARFX SLARUV DLARUV
SLAS2 DLAS2 SLASCL DLASCL CLASCL ZLASCL
SLASET DLASET CLASET ZLASET SLASQ1 DLASQ1
SLASQ2 DLASQ2 SLASQ3 DLASQ3
SLASQ4 DLASQ4 SLASRT DLASRT
SLASSQ DLASSQ CLASSQ ZLASSQ SLASV2 DLASV2
SLASWP DLASWP CLASWP ZLASWP SLASY2 DLASY2
SLASYF DLASYF CLASYF ZLASYF CLAHEF ZLAHEF
SLATBS DLATBS CLATBS ZLATBS SLATPS DLATPS CLATPS ZLATPS
SLATRD DLATRD CLATRD ZLATRD SLATRS DLATRS CLATRS ZLATRS
SLATZM DLATZM CLATZM ZLATZM SLAUU2 DLAUU2 CLAUU2 ZLAUU2
SLAUUM DLAUUM CLAUUM ZLAUUM SORG2L DORG2L CUNG2L ZUNG2L
SORG2R DORG2R CUNG2R ZUNG2R SORGL2 DORGL2 CUNGL2 ZUNGL2
SORGR2 DORGR2 CUNGR2 ZUNGR2 SORM2L DORM2L CUNM2L ZUNM2L
SORM2R DORM2R CUNM2R ZUNM2R SORML2 DORML2 CUNML2 ZUNML2
SORMR2 DORMR2 CUNMR2 ZUNMR2 SPBTF2 DPBTF2 CPBTF2 ZPBTF2
SPOTF2 DPOTF2 CPOTF2 ZPOTF2 SRSCL DRSCL CSRSCL ZDRSCL
SSYGS2 DSYGS2 CHEGS2 ZHEGS2 SSYTD2 DSYTD2 CHETD2 ZHETD2
SSYTF2 DSYTF2 CSYTF2 ZSYTF2 CHETF2 ZHETF2
STRTI2 DTRTI2 CTRTI2 ZTRTI2
LSNAME LSAMEN XERBLA
NOTES
SCSL does not currently support reshaped arrays.
SEE ALSO
LAPACK User's Guide
INTRO_BLAS1(3S), INTRO_BLAS2(3S), INTRO_BLAS3(3S), INTRO_SCSL(3S),
INTRO_SOLVERS(3S)
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INTRO_LAPACK(3S)INTRO_LAPACK(3S)
Page 26
