intro(3P) Sun Performance Library intro(3P)NAME
intro: sunperf - Introduction to Sun Performance Library functions and
subroutines
DESCRIPTION
Sun Performance Library (Sunperf) is a set of optimized, high-speed
mathematical subroutines for solving linear algebra and other numeri‐
cally intensive problems. Sun Performance Library is based on a collec‐
tion of public domain applications available from Netlib at
http://www.netlib.org. Sun has enhanced these public domain applica‐
tions and bundled them as the Sun Performance Library.
More information about Sun Performance Library can be found in the Sun
Performance Library User's Guide and Sun Performance Library Reference
Manual.
LIBRARIES
Sun Performance Library contains enhanced versions of the following
standard libraries:
Library Version Description
LAPACK 3.1.1 solving linear algebra problems
BLAS1 - performing vector-vector operations
BLAS2 - performing matrix-vector operations
BLAS3 - performing matrix-matrix operations
Netlib Sparse-BLAS - performing sparse vector operations
NIST Sparse-BLAS 0.5 performing fundamental sparse matrix operations
SuperLU 3.0 solving sparse linear systems of equations
Sparse Solver - direct sparse solver routines
FFTPACK - performing fast Fourier transform
VFFTPACK - performing vectorized fast Fourier transform
IBLAS - interval BLAS routines
Other Routines - trabspose, Convolution, correlation and sort
A list of the individual subroutines is included at the bottom of this page.
FEATURES
Sun Performance Library routines can increase application performance
on both serial and multiprocessor (MP) platforms, because the serial
speed of many Sun Performance Library routines has been increased, and
many routines have been parallelized. Sun Performance Library routines
also have SPARC, AMD and Intel specific optimizations that are not
present in the base Netlib libraries.
Sun Performance Library provides the following optimizations and exten‐
sions to the base Netlib libraries:
Extensions that support Fortran 95 and C language inter‐
faces
Fortran 95 language features, including type indepen‐
dence, compile time checking, and optional arguments.
Consistent API across the different libraries in Sun Per‐
formance Library
Compatibility with LAPACK 1, 2.0, 3.0, and 3.1.1
libraries
Increased performance, and in some cases, greater accu‐
racy
Optimizations for specific SPARC and x86/x64 instruction
set architectures
Support for 64-bit enabled Solaris and Linux operating
environments
Support for parallel processing compiler options for
SPARC and x86/x64 platforms
Support for multiple processor hardware options
USAGE
To use the Sun Performance Library, type one of the following commands.
% f95 -dalign file.f -xlic_lib=sunperf
or
% cc -dalign file.c -xlic_lib=sunperf
or
% CC -dalign file.c -library=sunperf
SUBROUTINES
Copy_CompCol_Matrix - A utility C function in the serial SuperLU solver
that copies one SuperMatrix into another.
Create_CompCol_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in compressed sparse column
format (also known as the Harwell-Boeing format).
Create_CompRow_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in compressed sparse row
format.
Create_Dense_Matrix - A utility C function in the serial SuperLU solver
that creates a SuperMatrix in dense format.
Create_SuperNode_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in supernodal format.
Destroy_CompCol_Matrix - Precision-independent C function in the serial
SuperLU solver that deallocates a supermatrix in compressed
sparse column format (also known as the Harwell-Boeing for‐
mat).
Destroy_CompCol_Permuted - Precision-independent C function in the
serial SuperLU solver that deallocates a supermatrix in per‐
muted, compressed sparse column format.
Destroy_CompRow_Matrix - Precision-independent C function in the serial
SuperLU solver that deallocates a supermatrix in compressed
sparse row format.
Destroy_Dense_Matrix - Precision-independent C function in the serial
SuperLU solver that deallocates a SuperMatrix in dense for‐
mat.
Destroy_SuperMatrix_Store - Precision-independent C function in the
serial SuperLU solver that deallocates the actual storage
used to store the matrix in a SuperMatrix.
Destroy_SuperNode_Matrix - Precision-independent C function in the
serial SuperLU solver that deallocates a SuperMatrix in
supernodal format.
LUFactFlops - A query function that returns the floating point opera‐
tion count of the factorization step of the SuperLU solver.
LUFactTime - A query function that returns the time spent in the fac‐
torization step by the SuperLU solver.
LUSolveFlops - A query function that returns the floating point opera‐
tion count of the solve step of the SuperLU solver.
LUSolveTime - A query function that returns the time spent in the solve
stage by the SuperLU solver.
PrintPerf - A utility function of the SuperLU solver that prints sta‐
tistics collected by the computational routines.
QuerySpace - A inquiry function that provides information on the memory
statistics of the SuperLU solver.
StatFree - frees storage that was previously allocated to hold perfor‐
mance statistics of the SuperLU solver.
StatInit - A utility C function that allocates and initializes vari‐
ables in structure that stores performance statistics col‐
lected during the computation of the SuperLU solver.
SuperMatrix - C data structure in the SuperLU software that represents
a sparse or dense general matrix.
available_threads - returns information about current thread usage
blas_dpermute - permutes a real (double precision) array in terms of
the permutation vector P, output by dsortv
blas_dsort - sorts a real (double precision) vector X in increasing or
decreasing order using quick sort algorithm
blas_dsortv - sorts a real (double precision) vector X in increasing or
decreasing order using quick sort algorithm and overwrite P
with the permutation vector
blas_ipermute - permutes an integer array in terms of the permutation
vector P, output by dsortv
blas_isort - sorts an integer vector X in increasing or decreasing
order using quick sort algorithm
blas_isortv - sorts a real vector X in increasing or decreasing order
using quick sort algorithm and overwrite P with the permuta‐
tion vector
blas_spermute - permutes a real array in terms of the permutation vec‐
tor P, output by dsortv
blas_ssort - sorts a real vector X in increasing or decreasing order
using quick sort algorithm
blas_ssortv - sorts a real vector X in increasing or decreasing order
using quick sort algorithm and overwrite P with the permuta‐
tion vector
cCopy_CompCol_Matrix - A utility C function in the serial SuperLU
solver that copies one SuperMatrix into another.
cCreate_CompCol_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in compressed sparse column
format (also known as the Harwell-Boeing format).
cCreate_CompRow_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in compressed sparse row
format.
cCreate_Dense_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in dense format.
cCreate_SuperNode_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in supernodal format.
cPrintPerf - A utility function of the SuperLU solver that prints sta‐
tistics collected by the computational routines.
cQuerySpace - A inquiry function that provides information on the mem‐
ory statistics of the SuperLU solver.
caxpy - compute y := alpha * x + y
caxpyi - Compute y := alpha * x + y
cbcomm - block coordinate matrix-matrix multiply
cbdimm - block diagonal format matrix-matrix multiply
cbdism - block diagonal format triangular solve
cbdsqr - compute the singular value decomposition (SVD) of a real N-by-
N (upper or lower) bidiagonal matrix B.
cbelmm - block Ellpack format matrix-matrix multiply
cbelsm - block Ellpack format triangular solve
cbscmm - block sparse column matrix-matrix multiply
cbscsm - block sparse column format triangular solve
cbsrmm - block sparse row format matrix-matrix multiply
cbsrsm - block sparse row format triangular solve
ccnvcor - compute the convolution or correlation of complex vectors
ccnvcor2 - compute the convolution or correlation of complex matrices
ccoomm - coordinate matrix-matrix multiply
ccopy - Copy x to y
ccscmm - compressed sparse column format matrix-matrix multiply
ccscsm - compressed sparse column format triangular solve
ccsrmm - compressed sparse row format matrix-matrix multiply
ccsrsm - compressed sparse row format triangular solve
cdiamm - diagonal format matrix-matrix multiply
cdiasm - diagonal format triangular solve
cdotc - compute the dot product of two vectors conjg(x) and y.
cdotci - Compute the complex conjugated indexed dot product.
cdotu - compute the dot product of two vectors x and y.
cdotui - Compute the complex unconjugated indexed dot product.
cellmm - Ellpack format matrix-matrix multiply
cellsm - Ellpack format triangular solve
cfft2b - compute a periodic sequence from its Fourier coefficients.
The xFFT operations are unnormalized, so a call of xFFT2F
followed by a call of xFFT2B will multiply the input sequence
by M*N.
cfft2f - compute the Fourier coefficients of a periodic sequence. The
xFFT operations are unnormalized, so a call of xFFT2F fol‐
lowed by a call of xFFT2B will multiply the input sequence by
M*N.
cfft2i - initialize the array WSAVE, which is used in both the forward
and backward transforms.
cfft3b - compute a periodic sequence from its Fourier coefficients.
The FFT operations are unnormalized, so a call of CFFT3F fol‐
lowed by a call of CFFT3B will multiply the input sequence by
M*N*K.
cfft3f - compute the Fourier coefficients of a periodic sequence. The
FFT operations are unnormalized, so a call of CFFT3F followed
by a call of CFFT3B will multiply the input sequence by
M*N*K.
cfft3i - initialize the array WSAVE, which is used in both CFFT3F and
CFFT3B.
cfftb - compute a periodic sequence from its Fourier coefficients. The
FFT operations are unnormalized, so a call of CFFTF followed
by a call of CFFTB will multiply the input sequence by N.
cfftc - initialize the trigonometric weight and factor tables or com‐
pute the Fast Fourier transform (forward or inverse) of a
complex sequence.
cfftc2 - initialize the trigonometric weight and factor tables or com‐
pute the two-dimensional Fast Fourier Transform (forward or
inverse) of a two-dimensional complex array.
cfftc3 - initialize the trigonometric weight and factor tables or com‐
pute the three-dimensional Fast Fourier Transform (forward or
inverse) of a three-dimensional complex array.
cfftcm - initialize the trigonometric weight and factor tables or com‐
pute the one-dimensional Fast Fourier Transform (forward or
inverse) of a set of data sequences stored in a two-dimen‐
sional complex array.
cfftf - compute the Fourier coefficients of a periodic sequence. The
FFT operations are unnormalized, so a call of CFFTF followed
by a call of CFFTB will multiply the input sequence by N.
cffti - initialize the array WSAVE, which is used in both CFFTF and
CFFTB.
cfftopt - compute the length of the closest fast FFT
cffts - initialize the trigonometric weight and factor tables or com‐
pute the inverse Fast Fourier Transform of a complex sequence
as follows.
cffts2 - initialize the trigonometric weight and factor tables or com‐
pute the two-dimensional inverse Fast Fourier Transform of a
two-dimensional complex array.
cffts3 - initialize the trigonometric weight and factor tables or com‐
pute the three-dimensional inverse Fast Fourier Transform of
a three-dimensional complex array.
cfftsm - initialize the trigonometric weight and factor tables or com‐
pute the one-dimensional inverse Fast Fourier Transform of a
set of complex data sequences stored in a two-dimensional
array.
cgbbrd - reduce a complex general m-by-n band matrix A to real upper
bidiagonal form B by a unitary transformation
cgbcon - estimate the reciprocal of the condition number of a complex
general band matrix A, in either the 1-norm or the infinity-
norm,
cgbequ - compute row and column scalings intended to equilibrate an M-
by-N band matrix A and reduce its condition number
cgbmv - perform one of the matrix-vector operationsy := alpha*A*x +
beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg(
A' )*x + beta*y
cgbrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is banded, and provides error
bounds and backward error estimates for the solution
cgbsv - compute the solution to a complex system of linear equations A
* X = B, where A is a band matrix of order N with KL subdiag‐
onals and KU superdiagonals, and X and B are N-by-NRHS matri‐
ces
cgbsvx - use the LU factorization to compute the solution to a complex
system of linear equations A * X = B, A**T * X = B, or A**H *
X = B,
cgbtf2 - compute an LU factorization of a complex m-by-n band matrix A
using partial pivoting with row interchanges
cgbtrf - compute an LU factorization of a complex m-by-n band matrix A
using partial pivoting with row interchanges
cgbtrs - solve a system of linear equations A * X = B, A**T * X = B,
or A**H * X = B with a general band matrix A using the LU
factorization computed by CGBTRF
cgebak - form the right or left eigenvectors of a complex general
matrix by backward transformation on the computed eigenvec‐
tors of the balanced matrix output by CGEBAL
cgebal - balance a general complex matrix A
cgebrd - reduce a general complex M-by-N matrix A to upper or lower
bidiagonal form B by a unitary transformation
cgecon - estimate the reciprocal of the condition number of a general
complex matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by CGETRF
cgeequ - compute row and column scalings intended to equilibrate an M-
by-N matrix A and reduce its condition number
cgees - compute for an N-by-N complex nonsymmetric matrix A, the eigen‐
values, the Schur form T, and, optionally, the matrix of
Schur vectors Z
cgeesx - compute for an N-by-N complex nonsymmetric matrix A, the ei‐
genvalues, the Schur form T, and, optionally, the matrix of
Schur vectors Z
cgeev - compute for an N-by-N complex nonsymmetric matrix A, the eigen‐
values and, optionally, the left and/or right eigenvectors
cgeevx - compute for an N-by-N complex nonsymmetric matrix A, the ei‐
genvalues and, optionally, the left and/or right eigenvectors
cgegs - routine is deprecated and has been replaced by routine CGGES
cgegv - routine is deprecated and has been replaced by routine CGGEV
cgehrd - reduce a complex general matrix A to upper Hessenberg form H
by a unitary similarity transformation
cgelqf - compute an LQ factorization of a complex M-by-N matrix A
cgels - solve overdetermined or underdetermined complex linear systems
involving an M-by-N matrix A, or its conjugate-transpose,
using a QR or LQ factorization of A
cgelsd - compute the minimum-norm solution to a real linear least
squares problem
cgelss - compute the minimum norm solution to a complex linear least
squares problem
cgelsx - routine is deprecated and has been replaced by routine CGELSY
cgelsy - compute the minimum-norm solution to a complex linear least
squares problem
cgemm - perform one of the matrix-matrix operations C := alpha*op( A
)*op( B ) + beta*C
cgemv - perform one of the matrix-vector operationsy := alpha*A*x +
beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg(
A' )*x + beta*y
cgeqlf - compute a QL factorization of a complex M-by-N matrix A
cgeqp3 - compute a QR factorization with column pivoting of a matrix A
cgeqpf - routine is deprecated and has been replaced by routine CGEQP3
cgeqrf - compute a QR factorization of a complex M-by-N matrix A
cgerc - perform the rank 1 operation A := alpha*x*conjg( y' ) + A
cgerfs - improve the computed solution to a system of linear equations
and provides error bounds and backward error estimates for
the solution
cgerqf - compute an RQ factorization of a complex M-by-N matrix A
cgeru - perform the rank 1 operation A := alpha*x*y' + A
cgesdd - compute the singular value decomposition (SVD) of a complex M-
by-N matrix A, optionally computing the left and/or right
singular vectors, by using divide-and-conquer method
cgesv - compute the solution to a complex system of linear equationsA *
X = B,
cgesvd - compute the singular value decomposition (SVD) of a complex M-
by-N matrix A, optionally computing the left and/or right
singular vectors
cgesvx - use the LU factorization to compute the solution to a complex
system of linear equations A * X = B,
cgetf2 - compute an LU factorization of a general m-by-n matrix A using
partial pivoting with row interchanges
cgetrf - compute an LU factorization of a general M-by-N matrix A using
partial pivoting with row interchanges
cgetri - compute the inverse of a matrix using the LU factorization
computed by CGETRF
cgetrs - solve a system of linear equations A * X = B, A**T * X = B,
or A**H * X = B with a general N-by-N matrix A using the LU
factorization computed by CGETRF
cggbak - form the right or left eigenvectors of a complex generalized
eigenvalue problem A*x = lambda*B*x, by backward transforma‐
tion on the computed eigenvectors of the balanced pair of
matrices output by CGGBAL
cggbal - balance a pair of general complex matrices (A,B)
cgges - compute for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, the generalized complex
Schur form (S, T), and optionally left and/or right Schur
vectors (VSL and VSR)
cggesx - compute for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, the complex Schur form
(S,T),
cggev - compute for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, and optionally, the left
and/or right generalized eigenvectors
cggevx - compute for a pair of N-by-N complex nonsymmetric matrices
(A,B) the generalized eigenvalues, and optionally, the left
and/or right generalized eigenvectors
cggglm - solve a general Gauss-Markov linear model (GLM) problem
cgghrd - reduce a pair of complex matrices (A,B) to generalized upper
Hessenberg form using unitary transformations, where A is a
general matrix and B is upper triangular
cgglse - solve the linear equality-constrained least squares (LSE)
problem
cggqrf - compute a generalized QR factorization of an N-by-M matrix A
and an N-by-P matrix B.
cggrqf - compute a generalized RQ factorization of an M-by-N matrix A
and a P-by-N matrix B
cggsvd - compute the generalized singular value decomposition (GSVD) of
an M-by-N complex matrix A and P-by-N complex matrix B
cggsvp - compute unitary matrices U, V and Q such that N-K-L K L
U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
cgscon - estimates the reciprocal of the condition number of a general
real matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by SuperLU routine
sgstrf.
cgsequ - computes row and column scalings intended to equilibrate an M-
by-N sparse matrix A and reduce its condition number.
cgsrfs - improves the computed solution to a system of linear equations
and provides error bounds and backward error estimates for
the solution. It is a SuperLU routine.
cgssco - General sparse solver condition number estimate.
cgssda - Deallocate working storage for the general sparse solver.
cgssfa - General sparse solver numeric factorization.
cgssfs - General sparse solver one call interface.
cgssin - Initialize the general sparse solver.
cgssor - General sparse solver ordering and symbolic factorization.
cgssps - Print general sparse solver statics.
cgssrp - Return permutation used by the general sparse solver.
cgsssl - Solve routine for the general sparse solver.
cgssuo - Provide general sparse solvers SPSOLVE and SuperLU a user-
supplied permutation for ordering.
cgssv - solves a system of linear equations A*X=B using the LU factor‐
ization from sgstrf.
cgssvx - solves the system of linear equations A*X=B or A'*X=B, using
the LU factorization from sgstrf(). Error bounds on the solu‐
tion and a condition estimate are also provided.
cgstrf - computes an LU factorization of a general sparse m-by-n matrix
A using partial pivoting with row interchanges.
cgstrs - solves a system of linear equations A*X=B or A'*X=B with A
sparse and B dense, using the LU factorization computed by
sgstrf.
cgtcon - estimate the reciprocal of the condition number of a complex
tridiagonal matrix A using the LU factorization as computed
by CGTTRF
cgthr - Gathers specified elements from y into x.
cgthrz - Gather and zero.
cgtrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is tridiagonal, and provides
error bounds and backward error estimates for the solution
cgtsv - solve the equation A*X = B,
cgtsvx - use the LU factorization to compute the solution to a complex
system of linear equations A * X = B, A**T * X = B, or A**H *
X = B,
cgttrf - compute an LU factorization of a complex tridiagonal matrix A
using elimination with partial pivoting and row interchanges
cgttrs - solve one of the systems of equations A * X = B, A**T * X =
B, or A**H * X = B,
chbev - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian band matrix A
chbevd - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian band matrix A
chbevx - compute selected eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A
chbgst - reduce a complex Hermitian-definite banded generalized eigen‐
problem A*x = lambda*B*x to standard form C*y = lambda*y,
chbgv - compute all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenprob‐
lem, of the form A*x=(lambda)*B*x
chbgvd - compute all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenprob‐
lem, of the form A*x=(lambda)*B*x
chbgvx - compute all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenprob‐
lem, of the form A*x=(lambda)*B*x
chbmv - perform the matrix-vector operationy := alpha*A*x + beta*y
chbtrd - reduce a complex Hermitian band matrix A to real symmetric
tridiagonal form T by a unitary similarity transformation
checon - estimate the reciprocal of the condition number of a complex
Hermitian matrix A using the factorization A = U*D*U**H or A
= L*D*L**H computed by CHETRF
cheev - compute all eigenvalues and, optionally, eigenvectors of a com‐
plex Hermitian matrix A
cheevd - compute all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A
cheevr - compute selected eigenvalues and, optionally, eigenvectors of
a complex Hermitian tridiagonal matrix T
cheevx - compute selected eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A
chegs2 - reduce a complex Hermitian-definite generalized eigenproblem
to standard form
chegst - reduce a complex Hermitian-definite generalized eigenproblem
to standard form
chegv - compute all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of
the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x
chegvd - compute all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of
the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x
chegvx - compute selected eigenvalues, and optionally, eigenvectors of
a complex generalized Hermitian-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
chemm - perform one of the matrix-matrix operations C := alpha*A*B +
beta*C or C := alpha*B*A + beta*C
chemv - perform the matrix-vector operationy := alpha*A*x + beta*y
cher - perform the hermitian rank 1 operation A := alpha*x*conjg( x'
) + A
cher2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y'
) + conjg( alpha )*y*conjg( x' ) + A
cher2k - perform one of the Hermitian rank 2k operations C :=
alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C
or C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A +
beta*C
cherfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian indefinite, and pro‐
vides error bounds and backward error estimates for the solu‐
tion
cherk - perform one of the Hermitian rank k operations C :=
alpha*A*conjg( A' ) + beta*C or C := alpha*conjg( A' )*A +
beta*C
chesv - compute the solution to a complex system of linear equationsA *
X = B,
chesvx - use the diagonal pivoting factorization to compute the solu‐
tion to a complex system of linear equations A * X = B,
chetf2 - compute the factorization of a complex Hermitian matrix A
using the Bunch-Kaufman diagonal pivoting method
chetrd - reduce a complex Hermitian matrix A to real symmetric tridiag‐
onal form T by a unitary similarity transformation
chetrf - compute the factorization of a complex Hermitian matrix A
using the Bunch-Kaufman diagonal pivoting method
chetri - compute the inverse of a complex Hermitian indefinite matrix A
using the factorization A = U*D*U**H or A = L*D*L**H computed
by CHETRF
chetrs - solve a system of linear equations A*X = B with a complex Her‐
mitian matrix A using the factorization A = U*D*U**H or A =
L*D*L**H computed by CHETRF
chgeqz - implement a single-shift version of the QZ method for finding
the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the
equation det( A-w(i) B ) = 0 If JOB='S', then the pair
(A,B) is simultaneously reduced to Schur form (i.e., A and B
are both upper triangular) by applying one unitary tranforma‐
tion (usually called Q) on the left and another (usually
called Z) on the right
chpcon - estimate the reciprocal of the condition number of a complex
Hermitian packed matrix A using the factorization A =
U*D*U**H or A = L*D*L**H computed by CHPTRF
chpev - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix in packed storage
chpevd - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A in packed storage
chpevx - compute selected eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A in packed storage
chpgst - reduce a complex Hermitian-definite generalized eigenproblem
to standard form, using packed storage
chpgv - compute all the eigenvalues and, optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of
the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x
chpgvd - compute all the eigenvalues and, optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of
the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x
chpgvx - compute selected eigenvalues and, optionally, eigenvectors of
a complex generalized Hermitian-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
chpmv - perform the matrix-vector operationy := alpha*A*x + beta*y
chpr - perform the hermitian rank 1 operation A := alpha*x*conjg( x'
) + A
chpr2 - perform the Hermitian rank 2 operation A := alpha*x*conjg( y'
) + conjg( alpha )*y*conjg( x' ) + A
chprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian indefinite and
packed, and provides error bounds and backward error esti‐
mates for the solution
chpsv - compute the solution to a complex system of linear equationsA *
X = B,
chpsvx - use the diagonal pivoting factorization A = U*D*U**H or A =
L*D*L**H to compute the solution to a complex system of lin‐
ear equations A * X = B, where A is an N-by-N Hermitian
matrix stored in packed format and X and B are N-by-NRHS
matrices
chptrd - reduce a complex Hermitian matrix A stored in packed form to
real symmetric tridiagonal form T by a unitary similarity
transformation
chptrf - compute the factorization of a complex Hermitian packed matrix
A using the Bunch-Kaufman diagonal pivoting method
chptri - compute the inverse of a complex Hermitian indefinite matrix A
in packed storage using the factorization A = U*D*U**H or A =
L*D*L**H computed by CHPTRF
chptrs - solve a system of linear equations A*X = B with a complex Her‐
mitian matrix A stored in packed format using the factoriza‐
tion A = U*D*U**H or A = L*D*L**H computed by CHPTRF
chsein - use inverse iteration to find specified right and/or left
eigenvectors of a complex upper Hessenberg matrix H
chseqr - compute the eigenvalues of a complex upper Hessenberg matrix
H, and, optionally, the matrices T and Z from the Schur
decomposition H = Z T Z**H, where T is an upper triangular
matrix (the Schur form), and Z is the unitary matrix of Schur
vectors
cinfinite_norm_error - A utility function of the SuperLU solver that
computes the infinity-norm of an array of vectors that are
approximations to the exact solution vector.
cjadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack)
cjadrp - right permutation of a jagged diagonal matrix
cjadsm - Jagged-diagonal format triangular solve
clangs - returns the value of the one-norm, or the Frobenius-norm, or
the infinity-norm, or the element with largest absolute value
of a general real matrix A in sparse format.
claqgs - a SuperLU function that equilibrates a general sparse M by N
matrix A.
clarz - applie a complex elementary reflector H to a complex M-by-N
matrix C, from either the left or the right
clarzb - applie a complex block reflector H or its transpose H**H to a
complex distributed M-by-N C from the left or the right
clarzt - form the triangular factor T of a complex block reflector H of
order > n, which is defined as a product of k elementary
reflectors
clatzm - routine is deprecated and has been replaced by routine CUNMRZ
cosqb - synthesize a Fourier sequence from its representation in terms
of a cosine series with odd wave numbers. The COSQ operations
are unnormalized inverses of themselves, so a call to COSQF
followed by a call to COSQB will multiply the input sequence
by 4 * N.
cosqf - compute the Fourier coefficients in a cosine series representa‐
tion with only odd wave numbers. The COSQ operations are
unnormalized inverses of themselves, so a call to COSQF fol‐
lowed by a call to COSQB will multiply the input sequence by
4 * N.
cosqi - initialize the array WSAVE, which is used in both COSQF and
COSQB.
cost - compute the discrete Fourier cosine transform of an even
sequence. The COST transforms are unnormalized inverses of
themselves, so a call of COST followed by another call of
COST will multiply the input sequence by 2 * (N-1).
costi - initialize the array WSAVE, which is used in COST.
cpbcon - estimate the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite band matrix
using the Cholesky factorization A = U**H*U or A = L*L**H
computed by CPBTRF
cpbequ - compute row and column scalings intended to equilibrate a Her‐
mitian positive definite band matrix A and reduce its condi‐
tion number (with respect to the two-norm)
cpbrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite
and banded, and provides error bounds and backward error
estimates for the solution
cpbstf - compute a split Cholesky factorization of a complex Hermitian
positive definite band matrix A
cpbsv - compute the solution to a complex system of linear equationsA *
X = B,
cpbsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
cpbtf2 - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite band matrix A
cpbtrf - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite band matrix A
cpbtrs - solve a system of linear equations A*X = B with a Hermitian
positive definite band matrix A using the Cholesky factoriza‐
tion A = U**H*U or A = L*L**H computed by CPBTRF
cpocon - estimate the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite matrix using
the Cholesky factorization A = U**H*U or A = L*L**H computed
by CPOTRF
cpoequ - compute row and column scalings intended to equilibrate a Her‐
mitian positive definite matrix A and reduce its condition
number (with respect to the two-norm)
cporfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite,
cposv - compute the solution to a complex system of linear equationsA *
X = B,
cposvx - use the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
cpotf2 - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite matrix A
cpotrf - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite matrix A
cpotri - compute the inverse of a complex Hermitian positive definite
matrix A using the Cholesky factorization A = U**H*U or A =
L*L**H computed by CPOTRF
cpotrs - solve a system of linear equations A*X = B with a Hermitian
positive definite matrix A using the Cholesky factorization A
= U**H*U or A = L*L**H computed by CPOTRF
cppcon - estimate the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite packed
matrix using the Cholesky factorization A = U**H*U or A =
L*L**H computed by CPPTRF
cppequ - compute row and column scalings intended to equilibrate a Her‐
mitian positive definite matrix A in packed storage and
reduce its condition number (with respect to the two-norm)
cpprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite
and packed, and provides error bounds and backward error
estimates for the solution
cppsv - compute the solution to a complex system of linear equationsA *
X = B,
cppsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
cpptrf - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite matrix A stored in packed format
cpptri - compute the inverse of a complex Hermitian positive definite
matrix A using the Cholesky factorization A = U**H*U or A =
L*L**H computed by CPPTRF
cpptrs - solve a system of linear equations A*X = B with a Hermitian
positive definite matrix A in packed storage using the
Cholesky factorization A = U**H*U or A = L*L**H computed by
CPPTRF
cptcon - compute the reciprocal of the condition number (in the 1-norm)
of a complex Hermitian positive definite tridiagonal matrix
using the factorization A = L*D*L**H or A = U**H*D*U computed
by CPTTRF
cpteqr - compute all eigenvalues and, optionally, eigenvectors of a
symmetric positive definite tridiagonal matrix by first fac‐
toring the matrix using SPTTRF and then calling CBDSQR to
compute the singular values of the bidiagonal factor
cptrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite
and tridiagonal, and provides error bounds and backward error
estimates for the solution
cptsv - compute the solution to a complex system of linear equations
A*X = B, where A is an N-by-N Hermitian positive definite
tridiagonal matrix, and X and B are N-by-NRHS matrices.
cptsvx - use the factorization A = L*D*L**H to compute the solution to
a complex system of linear equations A*X = B, where A is an
N-by-N Hermitian positive definite tridiagonal matrix and X
and B are N-by-NRHS matrices
cpttrf - compute the L*D*L' factorization of a complex Hermitian posi‐
tive definite tridiagonal matrix A
cpttrs - solve a tridiagonal system of the form A * X = B using the
factorization A = U'*D*U or A = L*D*L' computed by CPTTRF
cptts2 - solve a tridiagonal system of the form A * X = B using the
factorization A = U'*D*U or A = L*D*L' computed by CPTTRF
crot - apply a plane rotation, where the cos (C) is real and the sin
(S) is complex, and the vectors X and Y are complex
crotg - Construct a Given's plane rotation
cscal - Compute y := alpha * y
csctr - Scatters elements from x into y.
cskymm - Skyline format matrix-matrix multiply
cskysm - Skyline format triangular solve
cspcon - estimate the reciprocal of the condition number (in the
1-norm) of a complex symmetric packed matrix A using the fac‐
torization A = U*D*U**T or A = L*D*L**T computed by CSPTRF
csprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite and
packed, and provides error bounds and backward error esti‐
mates for the solution
cspsv - compute the solution to a complex system of linear equationsA *
X = B,
cspsvx - use the diagonal pivoting factorization A = U*D*U**T or A =
L*D*L**T to compute the solution to a complex system of lin‐
ear equations A * X = B, where A is an N-by-N symmetric
matrix stored in packed format and X and B are N-by-NRHS
matrices
csptrf - compute the factorization of a complex symmetric matrix A
stored in packed format using the Bunch-Kaufman diagonal piv‐
oting method
csptri - compute the inverse of a complex symmetric indefinite matrix A
in packed storage using the factorization A = U*D*U**T or A =
L*D*L**T computed by CSPTRF
csptrs - solve a system of linear equations A*X = B with a complex sym‐
metric matrix A stored in packed format using the factoriza‐
tion A = U*D*U**T or A = L*D*L**T computed by CSPTRF
csrot - Apply a plane rotation.
csscal - Compute y := alpha * y
cstedc - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer
method
cstegr - Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is
a relatively robust representation
cstein - compute the eigenvectors of a real symmetric tridiagonal
matrix T corresponding to specified eigenvalues, using
inverse iteration
cstemr - computes selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix T.
csteqr - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR
method
cstsv - compute the solution to a complex system of linear equations A
* X = B where A is a symmetric tridiagonal matrix
csttrf - compute the factorization of a complex symmetric tridiagonal
matrix A using the Bunch-Kaufman diagonal pivoting method
csttrs - computes the solution to a complex system of linear equations
A * X = B
cswap - Exchange vectors x and y.
csycon - estimate the reciprocal of the condition number (in the
1-norm) of a complex symmetric matrix A using the factoriza‐
tion A = U*D*U**T or A = L*D*L**T computed by CSYTRF
csymm - perform one of the matrix-matrix operationsC := alpha*A*B +
beta*C or C := alpha*B*A + beta*C
csyr2k - perform one of the symmetric rank 2k operations C :=
alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B +
alpha*B'*A + beta*C
csyrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite, and pro‐
vides error bounds and backward error estimates for the solu‐
tion
csyrk - perform one of the symmetric rank k operations C :=
alpha*A*A' + beta*C or C := alpha*A'*A + beta*C
csysv - compute the solution to a complex system of linear equationsA *
X = B,
csysvx - use the diagonal pivoting factorization to compute the solu‐
tion to a complex system of linear equations A * X = B,
csytf2 - compute the factorization of a complex symmetric matrix A
using the Bunch-Kaufman diagonal pivoting method
csytrf - compute the factorization of a complex symmetric matrix A
using the Bunch-Kaufman diagonal pivoting method
csytri - compute the inverse of a complex symmetric indefinite matrix A
using the factorization A = U*D*U**T or A = L*D*L**T computed
by CSYTRF
csytrs - solve a system of linear equations A*X = B with a complex sym‐
metric matrix A using the factorization A = U*D*U**T or A =
L*D*L**T computed by CSYTRF
ctbcon - estimate the reciprocal of the condition number of a triangu‐
lar band matrix A, in either the 1-norm or the infinity-norm
ctbmv - perform one of the matrix-vector operationsx := A*x, or x :=
A'*x, or x := conjg( A' )*x
ctbrfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
band coefficient matrix
ctbsv - solve one of the systems of equations A*x = b, or A'*x = b,
or conjg( A' )*x = b
ctbtrs - solve a triangular system of the form A * X = B, A**T * X =
B, or A**H * X = B,
ctgevc - compute some or all of the right and/or left generalized
eigenvectors of a pair of complex upper triangular matrices
(A,B) that was obtained from from the generalized Schur fac‐
torization of an original pair of complex nonsymmetric matri‐
ces. A and B are upper triangular matrices and B must have
real diagonal elements.
ctgexc - reorder the generalized Schur decomposition of a complex
matrix pair (A,B), using an unitary equivalence transforma‐
tion (A, B) := Q * (A, B) * Z', so that the diagonal block of
(A, B) with row index IFST is moved to row ILST
ctgsen - reorder the generalized Schur decomposition of a complex
matrix pair (A, B) (in terms of an unitary equivalence trans-
formation Q' * (A, B) * Z), so that a selected cluster of ei‐
genvalues appears in the leading diagonal blocks of the pair
(A,B)
ctgsja - compute the generalized singular value decomposition (GSVD) of
two complex upper triangular (or trapezoidal) matrices A and
B
ctgsna - estimate reciprocal condition numbers for specified eigenval‐
ues and/or eigenvectors of a matrix pair (A, B)
ctgsyl - solve the generalized Sylvester equation
ctpcon - estimate the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-
norm
ctpmv - perform one of the matrix-vector operationsx := A*x, or x :=
A'*x, or x := conjg( A' )*x
ctprfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
packed coefficient matrix
ctpsv - solve one of the systems of equations A*x = b, or A'*x = b,
or conjg( A' )*x = b
ctptri - compute the inverse of a complex upper or lower triangular
matrix A stored in packed format
ctptrs - solve a triangular system of the form A * X = B, A**T * X =
B, or A**H * X = B,
ctrans - transpose and scale source matrix
ctrcon - estimate the reciprocal of the condition number of a triangu‐
lar matrix A, in either the 1-norm or the infinity-norm
ctrevc - compute some or all of the right and/or left eigenvectors of a
complex upper triangular matrix T
ctrexc - reorder the Schur factorization of a complex matrix A =
Q*T*Q**H, so that the diagonal element of T with row index
IFST is moved to row ILST
ctrmm - perform one of the matrix-matrix operationsB := alpha*op( A
)*B, or B := alpha*B*op( A ) where alpha is a scalar, B is
an m by n matrix, A is a unit, or non-unit, upper or lower
triangular matrix and op( A ) is one of op( A ) = A or op(
A ) = A' or op( A ) = conjg( A' )
ctrmv - perform one of the matrix-vector operationsx := A*x, or x :=
A'*x, or x := conjg( A' )*x
ctrrfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
coefficient matrix
ctrsen - reorder the Schur factorization of a complex matrix A =
Q*T*Q**H, so that a selected cluster of eigenvalues appears
in the leading positions on the diagonal of the upper trian‐
gular matrix T, and the leading columns of Q form an
orthonormal basis of the corresponding right invariant sub‐
space
ctrsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op(
A ) = alpha*B
ctrsna - estimate reciprocal condition numbers for specified eigenval‐
ues and/or right eigenvectors of a complex upper triangular
matrix T (or of any matrix Q*T*Q**H with Q unitary)
ctrsv - solve one of the systems of equations A*x = b, or A'*x = b,
or conjg( A' )*x = b
ctrsyl - solve the complex Sylvester matrix equation
ctrti2 - compute the inverse of a complex upper or lower triangular
matrix
ctrtri - compute the inverse of a complex upper or lower triangular
matrix A
ctrtrs - solve a triangular system of the form A * X = B, A**T * X =
B, or A**H * X = B,
ctzrqf - routine is deprecated and has been replaced by routine CTZRZF
ctzrzf - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A
to upper triangular form by means of unitary transformations
cung2l - generate an m by n complex matrix Q with orthonormal columns,
cung2r - generate an m by n complex matrix Q with orthonormal columns,
cungbr - generate one of the complex unitary matrices Q or P**H deter‐
mined by CGEBRD when reducing a complex matrix A to bidiago‐
nal form
cunghr - generate a complex unitary matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as
returned by CGEHRD
cungl2 - generate an m-by-n complex matrix Q with orthonormal rows,
cunglq - generate an M-by-N complex matrix Q with orthonormal rows,
cungql - generate an M-by-N complex matrix Q with orthonormal columns,
cungqr - generate an M-by-N complex matrix Q with orthonormal columns,
cungr2 - generate an m by n complex matrix Q with orthonormal rows,
cungrq - generate an M-by-N complex matrix Q with orthonormal rows,
cungtr - generate a complex unitary matrix Q which is defined as the
product of n-1 elementary reflectors of order N, as returned
by CHETRD
cunmbr - overwrites the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q or P*C or P**H*C or C*P or C*P**H.
cunmhr - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
cunml2 - overwrite the general complex m-by-n matrix C with Q * C if
SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS
= 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q'
if SIDE = 'R' and TRANS = 'C',
cunmlq - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
cunmql - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
cunmqr - overwrite the general complex M-by-N matrix C with SIDE =
'L' SIDE = 'R' TRANS = 'N'
cunmr2 - overwrite the general complex m-by-n matrix C with Q * C if
SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS
= 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q'
if SIDE = 'R' and TRANS = 'C',
cunmrq - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
cunmrz - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
cunmtr - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
cupgtr - generate a complex unitary matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as
returned by CHPTRD using packed storage
cupmtr - overwrite the general complex M-by-N matrix C with SIDE =
'L' SIDE = 'R' TRANS = 'N'
cvbrmm - variable block sparse row format matrix-matrix multiply
cvbrsm - variable block sparse row format triangular solve
cvmul - compute the scaled product of complex vectors
dCopy_CompCol_Matrix - A utility C function in the serial SuperLU
solver that copies one SuperMatrix into another.
dCreate_CompCol_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in compressed sparse column
format (also known as the Harwell-Boeing format).
dCreate_CompRow_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in compressed sparse row
format.
dCreate_Dense_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in dense format.
dCreate_SuperNode_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in supernodal format.
dPrintPerf - A utility function of the SuperLU solver that prints sta‐
tistics collected by the computational routines.
dQuerySpace - A inquiry function that provides information on the mem‐
ory statistics of the SuperLU solver.
dasum - Return the sum of the absolute values of a vector x.
daxpy - compute y := alpha * x + y
daxpyi - Compute y := alpha * x + y
dbcomm - block coordinate matrix-matrix multiply
dbdimm - block diagonal format matrix-matrix multiply
dbdism - block diagonal format triangular solve
dbdsdc - compute the singular value decomposition (SVD) of a real N-by-
N (upper or lower) bidiagonal matrix B
dbdsqr - compute the singular value decomposition (SVD) of a real N-by-
N (upper or lower) bidiagonal matrix B.
dbelmm - block Ellpack format matrix-matrix multiply
dbelsm - block Ellpack format triangular solve
dbscmm - block sparse column matrix-matrix multiply
dbscsm - block sparse column format triangular solve
dbsrmm - block sparse row format matrix-matrix multiply
dbsrsm - block sparse row format triangular solve
dcnvcor - compute the convolution or correlation of real vectors
dcnvcor2 - compute the convolution or correlation of real matrices
dcoomm - coordinate matrix-matrix multiply
dcopy - Copy x to y
dcosqb - synthesize a Fourier sequence from its representation in terms
of a cosine series with odd wave numbers. The COSQ operations
are unnormalized inverses of themselves, so a call to COSQF
followed by a call to COSQB will multiply the input sequence
by 4 * N.
dcosqf - compute the Fourier coefficients in a cosine series represen‐
tation with only odd wave numbers. The COSQ operations are
unnormalized inverses of themselves, so a call to COSQF fol‐
lowed by a call to COSQB will multiply the input sequence by
4 * N.
dcosqi - initialize the array WSAVE, which is used in both COSQF and
COSQB.
dcost - compute the discrete Fourier cosine transform of an even
sequence. The COST transforms are unnormalized inverses of
themselves, so a call of COST followed by another call of
COST will multiply the input sequence by 2 * (N-1).
dcosti - initialize the array WSAVE, which is used in COST.
dcscmm - compressed sparse column format matrix-matrix multiply
dcscsm - compressed sparse column format triangular solve
dcsrmm - compressed sparse row format matrix-matrix multiply
dcsrsm - compressed sparse row format triangular solve
ddiamm - diagonal format matrix-matrix multiply
ddiasm - diagonal format triangular solve
ddisna - compute 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 m-by-n matrix
ddot - compute the dot product of two vectors x and y.
ddoti - Compute the indexed dot product.
dellmm - Ellpack format matrix-matrix multiply
dellsm - Ellpack format triangular solve
dezftb - computes a periodic sequence from its Fourier coefficients.
DEZFTB is a simplified but slower version of DFFTB.
dezftf - computes the Fourier coefficients of a periodic sequence.
DEZFTF is a simplified but slower version of DFFTF.
dezfti - initializes the array WSAVE, which is used in both DEZFTF and
DEZFTB.
dfft2b - compute a periodic sequence from its Fourier coefficients.
The DFFT operations are unnormalized, so a call of DFFT2F
followed by a call of DFFT2B will multiply the input sequence
by M*N.
dfft2f - compute the Fourier coefficients of a periodic sequence. The
DFFT operations are unnormalized, so a call of DFFT2F fol‐
lowed by a call of DFFT2B will multiply the input sequence by
M*N.
dfft2i - initialize the array WSAVE, which is used in both the forward
and backward transforms.
dfft3b - compute a periodic sequence from its Fourier coefficients. The
DFFT operations are unnormalized, so a call of DFFT3F fol‐
lowed by a call of DFFT3B will multiply the input sequence by
M*N*K.
dfft3f - compute the Fourier coefficients of a real periodic sequence.
The DFFT operations are unnormalized, so a call of DFFT3F
followed by a call of DFFT3B will multiply the input sequence
by M*N*K.
dfft3i - initialize the array WSAVE, which is used in both DFFT3F and
DFFT3B.
dfftb - compute a periodic sequence from its Fourier coefficients. The
DFFT operations are unnormalized, so a call of DFFTF followed
by a call of DFFTB will multiply the input sequence by N.
dfftf - compute the Fourier coefficients of a periodic sequence. The
FFT operations are unnormalized, so a call of DFFTF followed
by a call of DFFTB will multiply the input sequence by N.
dffti - initialize the array WSAVE, which is used in both DFFTF and
DFFTB.
dfftopt - compute the length of the closest fast FFT
dfftz - initialize the trigonometric weight and factor tables or com‐
pute the forward Fast Fourier Transform of a double precision
sequence.
dfftz2 - initialize the trigonometric weight and factor tables or com‐
pute the two-dimensional forward Fast Fourier Transform of a
two-dimensional double precision array.
dfftz3 - initialize the trigonometric weight and factor tables or com‐
pute the three-dimensional forward Fast Fourier Transform of
a three-dimensional double complex array.
dfftzm - initialize the trigonometric weight and factor tables or com‐
pute the one-dimensional forward Fast Fourier Transform of a
set of double precision data sequences stored in a two-dimen‐
sional array.
dgbbrd - reduce a real general m-by-n band matrix A to upper bidiagonal
form B by an orthogonal transformation
dgbcon - estimate the reciprocal of the condition number of a real gen‐
eral band matrix A, in either the 1-norm or the infinity-
norm,
dgbequ - compute row and column scalings intended to equilibrate an M-
by-N band matrix A and reduce its condition number
dgbmv - perform one of the matrix-vector operationsy := alpha*A*x +
beta*y or y := alpha*A'*x + beta*y
dgbrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is banded, and provides error
bounds and backward error estimates for the solution
dgbsv - compute the solution to a real system of linear equations A * X
= B, where A is a band matrix of order N with KL subdiagonals
and KU superdiagonals, and X and B are N-by-NRHS matrices
dgbsvx - use the LU factorization to compute the solution to a real
system of linear equations A * X = B, A**T * X = B, or A**H *
X = B,
dgbtf2 - compute an LU factorization of a real m-by-n band matrix A
using partial pivoting with row interchanges
dgbtrf - compute an LU factorization of a real m-by-n band matrix A
using partial pivoting with row interchanges
dgbtrs - solve a system of linear equations A * X = B or A' * X = B
with a general band matrix A using the LU factorization com‐
puted by DGBTRF
dgebak - form the right or left eigenvectors of a real general matrix
by backward transformation on the computed eigenvectors of
the balanced matrix output by DGEBAL
dgebal - balance a general real matrix A
dgebrd - reduce a general real M-by-N matrix A to upper or lower bidi‐
agonal form B by an orthogonal transformation
dgecon - estimate the reciprocal of the condition number of a general
real matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by DGETRF
dgeequ - compute row and column scalings intended to equilibrate an M-
by-N matrix A and reduce its condition number
dgees - compute for an N-by-N real nonsymmetric matrix A, the eigenval‐
ues, the real Schur form T, and, optionally, the matrix of
Schur vectors Z
dgeesx - compute for an N-by-N real nonsymmetric matrix A, the eigen‐
values, the real Schur form T, and, optionally, the matrix of
Schur vectors Z
dgeev - compute for an N-by-N real nonsymmetric matrix A, the eigenval‐
ues and, optionally, the left and/or right eigenvectors
dgeevx - compute for an N-by-N real nonsymmetric matrix A, the eigen‐
values and, optionally, the left and/or right eigenvectors
dgegs - routine is deprecated and has been replaced by routine DGGES
dgegv - routine is deprecated and has been replaced by routine DGGEV
dgehrd - reduce a real general matrix A to upper Hessenberg form H by
an orthogonal similarity transformation
dgelqf - compute an LQ factorization of a real M-by-N matrix A
dgels - solve overdetermined or underdetermined real linear systems
involving an M-by-N matrix A, or its transpose, using a QR or
LQ factorization of A
dgelsd - compute the minimum-norm solution to a real linear least
squares problem
dgelss - compute the minimum norm solution to a real linear least
squares problem
dgelsx - routine is deprecated and has been replaced by routine DGELSY
dgelsy - compute the minimum-norm solution to a real linear least
squares problem
dgemm - perform one of the matrix-matrix operationsC := alpha*op( A
)*op( B ) + beta*C
dgemv - perform one of the matrix-vector operationsy := alpha*A*x +
beta*y or y := alpha*A'*x + beta*y
dgeqlf - compute a QL factorization of a real M-by-N matrix A
dgeqp3 - compute a QR factorization with column pivoting of a matrix A
dgeqpf - routine is deprecated and has been replaced by routine DGEQP3
dgeqrf - compute a QR factorization of a real M-by-N matrix A
dger - perform the rank 1 operation A := alpha*x*y' + A
dgerfs - improve the computed solution to a system of linear equations
and provides error bounds and backward error estimates for
the solution
dgerqf - compute an RQ factorization of a real M-by-N matrix A
dgesdd - compute the singular value decomposition (SVD) of a real M-by-
N matrix A, optionally computing the left and right singular
vectors
dgesv - compute the solution to a real system of linear equations A *
X = B,
dgesvd - compute the singular value decomposition (SVD) of a real M-by-
N matrix A, optionally computing the left and/or right singu‐
lar vectors
dgesvx - use the LU factorization to compute the solution to a real
system of linear equations A * X = B,
dgetf2 - compute an LU factorization of a general m-by-n matrix A using
partial pivoting with row interchanges
dgetrf - compute an LU factorization of a general M-by-N matrix A using
partial pivoting with row interchanges
dgetri - compute the inverse of a matrix using the LU factorization
computed by DGETRF
dgetrs - solve a system of linear equations A * X = B or A' * X = B
with a general N-by-N matrix A using the LU factorization
computed by DGETRF
dggbak - form the right or left eigenvectors of a real generalized ei‐
genvalue problem A*x = lambda*B*x, by backward transformation
on the computed eigenvectors of the balanced pair of matrices
output by DGGBAL
dggbal - balance a pair of general real matrices (A,B)
dgges - compute for a pair of N-by-N real nonsymmetric matrices (A,B),
dggesx - compute for a pair of N-by-N real nonsymmetric matrices (A,B),
the generalized eigenvalues, the real Schur form (S,T), and,
dggev - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
dggevx - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
dggglm - solve a general Gauss-Markov linear model (GLM) problem
dgghrd - reduce a pair of real matrices (A,B) to generalized upper Hes‐
senberg form using orthogonal transformations, where A is a
general matrix and B is upper triangular
dgglse - solve the linear equality-constrained least squares (LSE)
problem
dggqrf - compute a generalized QR factorization of an N-by-M matrix A
and an N-by-P matrix B.
dggrqf - compute a generalized RQ factorization of an M-by-N matrix A
and a P-by-N matrix B
dggsvd - compute the generalized singular value decomposition (GSVD) of
an M-by-N real matrix A and P-by-N real matrix B
dggsvp - compute orthogonal matrices U, V and Q such that N-K-L K
LU'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
dgscon - estimates the reciprocal of the condition number of a general
real matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by SuperLU routine
sgstrf.
dgsequ - computes row and column scalings intended to equilibrate an M-
by-N sparse matrix A and reduce its condition number.
dgsrfs - improves the computed solution to a system of linear equations
and provides error bounds and backward error estimates for
the solution. It is a SuperLU routine.
dgssco - General sparse solver condition number estimate.
dgssda - Deallocate working storage for the general sparse solver.
dgssfa - General sparse solver numeric factorization.
dgssfs - General sparse solver one call interface.
dgssin - Initialize the general sparse solver.
dgssor - General sparse solver ordering and symbolic factorization.
dgssps - Print general sparse solver statics.
dgssrp - Return permutation used by the general sparse solver.
dgsssl - Solve routine for the general sparse solver.
dgssuo - Provide general sparse solvers SPSOLVE and SuperLU a user-sup‐
plied permutation for ordering.
dgssv - solves a system of linear equations A*X=B using the LU factor‐
ization from sgstrf.
dgssvx - solves the system of linear equations A*X=B or A'*X=B, using
the LU factorization from sgstrf(). Error bounds on the solu‐
tion and a condition estimate are also provided.
dgstrf - computes an LU factorization of a general sparse m-by-n matrix
A using partial pivoting with row interchanges.
dgstrs - solves a system of linear equations A*X=B or A'*X=B with A
sparse and B dense, using the LU factorization computed by
sgstrf.
dgtcon - estimate the reciprocal of the condition number of a real
tridiagonal matrix A using the LU factorization as computed
by DGTTRF
dgthr - Gathers specified elements from y into x.
dgthrz - Gather and zero.
dgtrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is tridiagonal, and provides
error bounds and backward error estimates for the solution
dgtsv - solve the equation A*X = B,
dgtsvx - use the LU factorization to compute the solution to a real
system of linear equations A * X = B or A**T * X = B,
dgttrf - compute an LU factorization of a real tridiagonal matrix A
using elimination with partial pivoting and row interchanges
dgttrs - solve one of the systems of equations A*X = B or A'*X = B,
dhgeqz - implement a single-/double-shift version of the QZ method for
finding the generalized eigenvalues w(j)=(ALPHAR(j) +
i*ALPHAI(j))/BETAR(j) of the equation det( A-w(i) B ) = 0
In addition, the pair A,B may be reduced to generalized Schur
form
dhsein - use inverse iteration to find specified right and/or left
eigenvectors of a real upper Hessenberg matrix H
dhseqr - compute the eigenvalues of a real upper Hessenberg matrix H
and, optionally, the matrices T and Z from the Schur decompo‐
sition H = Z T Z**T, where T is an upper quasi-triangular
matrix (the Schur form), and Z is the orthogonal matrix of
Schur vectors
dinfinite_norm_error - A utility function of the SuperLU solver that
computes the infinity-norm of an array of vectors that are
approximations to the exact solution vector.
djadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack)
djadrp - right permutation of a jagged diagonal matrix
djadsm - Jagged-diagonal format triangular solve
dlagtf - factorize the matrix (T-lambda*I), where T is an n by n tridi‐
agonal matrix and lambda is a scalar, as T-lambda*I = PLU
dlamch - Determines double precision machine parameters.
dlamrg - will create a permutation list which will merge the elements
of A (which is composed of two independently sorted sets)
into a single set which is sorted in ascending order
dlangs - returns the value of the one-norm, or the Frobenius-norm, or
the infinity-norm, or the element with largest absolute value
of a general real matrix A in sparse format.
dlaqgs - a SuperLU function that equilibrates a general sparse M by N
matrix A.
dlarz - applies a real elementary reflector H to a real M-by-N matrix
C, from either the left or the right
dlarzb - applies a real block reflector H or its transpose H**T to a
real distributed M-by-N C from the left or the right
dlarzt - form the triangular factor T of a real block reflector H of
order > n, which is defined as a product of k elementary
reflectors
dlasrt - the numbers in D in increasing order (if ID = 'I') or in
decreasing order (if ID = 'D' )
dlatzm - routine is deprecated and has been replaced by routine DORMRZ
dnrm2 - Return the Euclidian norm of a vector.
dopgtr - generate a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as
returned by DSPTRD using packed storage
dopmtr - overwrite the general real M-by-N matrix C with SIDE = 'L'
SIDE = 'R' TRANS = 'N'
dorg2l - generate an m by n real matrix Q with orthonormal columns,
dorg2r - generate an m by n real matrix Q with orthonormal columns,
dorgbr - generate one of the real orthogonal matrices Q or P**T deter‐
mined by DGEBRD when reducing a real matrix A to bidiagonal
form
dorghr - generate a real orthogonal matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as
returned by DGEHRD
dorgl2 - generate an m by n real matrix Q with orthonormal rows,
dorglq - generate an M-by-N real matrix Q with orthonormal rows,
dorgql - generate an M-by-N real matrix Q with orthonormal columns,
dorgqr - generate an M-by-N real matrix Q with orthonormal columns,
dorgr2 - generate an m by n real matrix Q with orthonormal rows,
dorgrq - generate an M-by-N real matrix Q with orthonormal rows,
dorgtr - generate a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors of order N, as returned
by DSYTRD
dormbr - overwrites the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q or P*C or P**T*C or C*P or C*P**T.
dormhr - overwrite the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q.
dormlq - overwrite the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q.
dormql - overwrite the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q.
dormqr - overwrite the general real M-by-N matrix C with SIDE = 'L'
SIDE = 'R' TRANS = 'N'
dormrq - overwrite the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q.
dormrz - overwrite the general real M-by-N matrix C with Q*C or Q**H*C
or C*Q**H or C*Q.
dormtr - overwrite the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q.
dpbcon - estimate the reciprocal of the condition number (in the
1-norm) of a real symmetric positive definite band matrix
using the Cholesky factorization A = U**T*U or A = L*L**T
computed by DPBTRF
dpbequ - compute row and column scalings intended to equilibrate a sym‐
metric positive definite band matrix A and reduce its condi‐
tion number (with respect to the two-norm)
dpbrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite
and banded, and provides error bounds and backward error
estimates for the solution
dpbstf - compute a split Cholesky factorization of a real symmetric
positive definite band matrix A
dpbsv - compute the solution to a real system of linear equations A *
X = B,
dpbsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equationsA *
X = B,
dpbtf2 - compute the Cholesky factorization of a real symmetric posi‐
tive definite band matrix A
dpbtrf - compute the Cholesky factorization of a real symmetric posi‐
tive definite band matrix A
dpbtrs - solve a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factoriza‐
tion A = U**T*U or A = L*L**T computed by DPBTRF
dpocon - estimate the reciprocal of the condition number (in the
1-norm) of a real symmetric positive definite matrix using
the Cholesky factorization A = U**T*U or A = L*L**T computed
by DPOTRF
dpoequ - compute row and column scalings intended to equilibrate a sym‐
metric positive definite matrix A and reduce its condition
number (with respect to the two-norm)
dporfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite,
dposv - compute the solution to a real system of linear equations A *
X = B,
dposvx - use the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equationsA *
X = B,
dpotf2 - compute the Cholesky factorization of a real symmetric posi‐
tive definite matrix A
dpotrf - compute the Cholesky factorization of a real symmetric posi‐
tive definite matrix A
dpotri - compute the inverse of a real symmetric positive definite
matrix A using the Cholesky factorization A = U**T*U or A =
L*L**T computed by DPOTRF
dpotrs - solve a system of linear equations A*X = B with a symmetric
positive definite matrix A using the Cholesky factorization A
= U**T*U or A = L*L**T computed by DPOTRF
dppcon - estimate the reciprocal of the condition number (in the
1-norm) of a real symmetric positive definite packed matrix
using the Cholesky factorization A = U**T*U or A = L*L**T
computed by DPPTRF
dppequ - compute row and column scalings intended to equilibrate a sym‐
metric positive definite matrix A in packed storage and
reduce its condition number (with respect to the two-norm)
dpprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite
and packed, and provides error bounds and backward error
estimates for the solution
dppsv - compute the solution to a real system of linear equations A *
X = B,
dppsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equationsA *
X = B,
dpptrf - compute the Cholesky factorization of a real symmetric posi‐
tive definite matrix A stored in packed format
dpptri - compute the inverse of a real symmetric positive definite
matrix A using the Cholesky factorization A = U**T*U or A =
L*L**T computed by DPPTRF
dpptrs - solve a system of linear equations A*X = B with a symmetric
positive definite matrix A in packed storage using the
Cholesky factorization A = U**T*U or A = L*L**T computed by
DPPTRF
dptcon - compute the reciprocal of the condition number (in the 1-norm)
of a real symmetric positive definite tridiagonal matrix
using the factorization A = L*D*L**T or A = U**T*D*U computed
by DPTTRF
dpteqr - compute all eigenvalues and, optionally, eigenvectors of a
symmetric positive definite tridiagonal matrix by first fac‐
toring the matrix using DPTTRF, and then calling DBDSQR to
compute the singular values of the bidiagonal factor
dptrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite
and tridiagonal, and provides error bounds and backward error
estimates for the solution
dptsv - compute the solution to a real system of linear equations A*X =
B, where A is an N-by-N symmetric positive definite tridiago‐
nal matrix, and X and B are N-by-NRHS matrices.
dptsvx - use the factorization A = L*D*L**T to compute the solution to
a real system of linear equations A*X = B, where A is an N-
by-N symmetric positive definite tridiagonal matrix and X and
B are N-by-NRHS matrices
dpttrf - compute the L*D*L' factorization of a real symmetric positive
definite tridiagonal matrix A
dpttrs - solve a tridiagonal system of the form A * X = B using the
L*D*L' factorization of A computed by DPTTRF
dptts2 - solve a tridiagonal system of the form A * X = B using the
L*D*L' factorization of A computed by DPTTRF
dqdota - compute a double precision constant plus an extended precision
constant plus the extended precision dot product of two dou‐
ble precision vectors x and y.
dqdoti - compute a constant plus the extended precision dot product of
two double precision vectors x and y.
drot - Apply a Given's rotation constructed by SROTG.
drotg - Construct a Given's plane rotation
droti - Apply an indexed Givens rotation.
drotm - Apply a Gentleman's modified Given's rotation constructed by
SROTMG.
drotmg - Construct a Gentleman's modified Given's plane rotation
dsbev - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric band matrix A
dsbevd - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric band matrix A
dsbevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A
dsbgst - reduce a real symmetric-definite banded generalized eigenprob‐
lem A*x = lambda*B*x to standard form C*y = lambda*y,
dsbgv - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem,
of the form A*x=(lambda)*B*x
dsbgvd - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem,
of the form A*x=(lambda)*B*x
dsbgvx - compute selected eigenvalues, and optionally, eigenvectors of
a real generalized symmetric-definite banded eigenproblem, of
the form A*x=(lambda)*B*x
dsbmv - perform the matrix-vector operationy := alpha*A*x + beta*y
dsbtrd - reduce a real symmetric band matrix A to symmetric tridiagonal
form T by an orthogonal similarity transformation
dscal - Compute y := alpha * y
dsctr - Scatters elements from x into y.
dsdot - compute the double precision dot product of two single preci‐
sion vectors x and y.
dsecnd - return the user time for a process in seconds
dsgesv - computes the solution to a real system of linear equations A *
X = B
dsinqb - synthesize a Fourier sequence from its representation in terms
of a sine series with odd wave numbers. The SINQ operations
are unnormalized inverses of themselves, so a call to SINQF
followed by a call to SINQB will multiply the input sequence
by 4 * N.
dsinqf - compute the Fourier coefficients in a sine series representa‐
tion with only odd wave numbers.The SINQ operations are
unnormalized inverses of themselves, so a call to SINQF fol‐
lowed by a call to SINQB will multiply the input sequence by
4 * N.
dsinqi - initialize the array xWSAVE, which is used in both SINQF and
SINQB.
dsint - compute the discrete Fourier sine transform of an odd sequence.
The SINT transforms are unnormalized inverses of themselves,
so a call of SINT followed by another call of SINT will mul‐
tiply the input sequence by 2 * (N+1).
dsinti - initialize the array WSAVE, which is used in subroutine SINT.
dskymm - Skyline format matrix-matrix multiply
dskysm - Skyline format triangular solve
dspcon - estimate the reciprocal of the condition number (in the
1-norm) of a real symmetric packed matrix A using the factor‐
ization A = U*D*U**T or A = L*D*L**T computed by DSPTRF
dspev - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage
dspevd - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage
dspevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric matrix A in packed storage
dspgst - reduce a real symmetric-definite generalized eigenproblem to
standard form, using packed storage
dspgv - compute all the eigenvalues and, optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dspgvd - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dspgvx - compute selected eigenvalues, and optionally, eigenvectors of
a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dspmv - perform the matrix-vector operationy := alpha*A*x + beta*y
dspr - perform the symmetric rank 1 operation A := alpha*x*x' + A
dspr2 - perform the symmetric rank 2 operation A := alpha*x*y' +
alpha*y*x' + A
dsprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite and
packed, and provides error bounds and backward error esti‐
mates for the solution
dspsv - compute the solution to a real system of linear equations A *
X = B,
dspsvx - use the diagonal pivoting factorization A = U*D*U**T or A =
L*D*L**T to compute the solution to a real system of linear
equations A * X = B, where A is an N-by-N symmetric matrix
stored in packed format and X and B are N-by-NRHS matrices
dsptrd - reduce a real symmetric matrix A stored in packed form to sym‐
metric tridiagonal form T by an orthogonal similarity trans‐
formation
dsptrf - compute the factorization of a real symmetric matrix A stored
in packed format using the Bunch-Kaufman diagonal pivoting
method
dsptri - compute the inverse of a real symmetric indefinite matrix A in
packed storage using the factorization A = U*D*U**T or A =
L*D*L**T computed by DSPTRF
dsptrs - solve a system of linear equations A*X = B with a real symmet‐
ric matrix A stored in packed format using the factorization
A = U*D*U**T or A = L*D*L**T computed by DSPTRF
dstebz - compute the eigenvalues of a symmetric tridiagonal matrix T
dstedc - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer
method
dstegr - (a) Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T
is a relatively robust representation
dstein - compute the eigenvectors of a real symmetric tridiagonal
matrix T corresponding to specified eigenvalues, using
inverse iteration
dstemr - computes selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix T.
dsteqr - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR
method
dsterf - compute all eigenvalues of a symmetric tridiagonal matrix
using the Pal-Walker-Kahan variant of the QL or QR algorithm
dstev - compute all eigenvalues and, optionally, eigenvectors of a real
symmetric tridiagonal matrix A
dstevd - compute all eigenvalues and, optionally, eigenvectors of a
real symmetric tridiagonal matrix
dstevr - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix T
dstevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix A
dstsv - compute the solution to a system of linear equations A * X = B
where A is a symmetric tridiagonal matrix
dsttrf - compute the factorization of a symmetric tridiagonal matrix A
using the Bunch-Kaufman diagonal pivoting method
dsttrs - computes the solution to a real system of linear equations A *
X = B
dswap - Exchange vectors x and y.
dsycon - estimate the reciprocal of the condition number (in the
1-norm) of a real symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by DSYTRF
dsyev - compute all eigenvalues and, optionally, eigenvectors of a real
symmetric matrix A
dsyevd - compute all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A
dsyevr - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix T
dsyevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric matrix A
dsygs2 - reduce a real symmetric-definite generalized eigenproblem to
standard form
dsygst - reduce a real symmetric-definite generalized eigenproblem to
standard form
dsygv - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dsygvd - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dsygvx - compute selected eigenvalues, and optionally, eigenvectors of
a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dsymm - perform one of the matrix-matrix operationsC := alpha*A*B +
beta*C or C := alpha*B*A + beta*C
dsymv - perform the matrix-vector operationy := alpha*A*x + beta*y
dsyr - perform the symmetric rank 1 operation A := alpha*x*x' + A
dsyr2 - perform the symmetric rank 2 operation A := alpha*x*y' +
alpha*y*x' + A
dsyr2k - perform one of the symmetric rank 2k operations C :=
alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B +
alpha*B'*A + beta*C
dsyrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite, and pro‐
vides error bounds and backward error estimates for the solu‐
tion
dsyrk - perform one of the symmetric rank k operations C :=
alpha*A*A' + beta*C or C := alpha*A'*A + beta*C
dsysv - compute the solution to a real system of linear equations A *
X = B,
dsysvx - use the diagonal pivoting factorization to compute the solu‐
tion to a real system of linear equations A * X = B,
dsytd2 - reduce a real symmetric matrix A to symmetric tridiagonal form
T by an orthogonal similarity transformation
dsytf2 - compute the factorization of a real symmetric matrix A using
the Bunch-Kaufman diagonal pivoting method
dsytrd - reduce a real symmetric matrix A to real symmetric tridiagonal
form T by an orthogonal similarity transformation
dsytrf - compute the factorization of a real symmetric matrix A using
the Bunch-Kaufman diagonal pivoting method
dsytri - compute the inverse of a real symmetric indefinite matrix A
using the factorization A = U*D*U**T or A = L*D*L**T computed
by DSYTRF
dsytrs - solve a system of linear equations A*X = B with a real symmet‐
ric matrix A using the factorization A = U*D*U**T or A =
L*D*L**T computed by DSYTRF
dtbcon - estimate the reciprocal of the condition number of a triangu‐
lar band matrix A, in either the 1-norm or the infinity-norm
dtbmv - perform one of the matrix-vector operationsx := A*x, or x :=
A'*x
dtbrfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
band coefficient matrix
dtbsv - solve one of the systems of equations A*x = b, or A'*x = b
dtbtrs - solve a triangular system of the form A * X = B or A**T * X
= B,
dtgevc - compute some or all of the right and/or left generalized
eigenvectors of a pair of real upper triangular matrices
(A,B) that was obtained from the generalized Schur factoriza‐
tion of an original pair of real nonsymmetric matrices. B is
upper triangular and A is a block upper triangular, where the
diagonal blocks are either 1-by-1 or 2-by-2.
dtgexc - reorder the generalized real Schur decomposition of a real
matrix pair (A,B) using an orthogonal equivalence transforma‐
tion(A, B) = Q * (A, B) * Z', so that the diagonal block of
(A, B) with row index IFST is moved to row ILST.
dtgsen - reorder the generalized real Schur decomposition of a real
matrix pair (A, B) (in terms of an orthonormal equivalence
trans- formation Q' * (A, B) * Z), so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the
upper quasi-triangular matrix A and the upper triangular B
dtgsja - compute the generalized singular value decomposition (GSVD) of
two real upper triangular (or trapezoidal) matrices A and B
dtgsna - estimate reciprocal condition numbers for specified eigenval‐
ues and/or eigenvectors of a matrix pair (A, B) in general‐
ized real Schur canonical form (or of any matrix pair
(Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where Z'
denotes the transpose of Z
dtgsyl - solve the generalized Sylvester equation
dtpcon - estimate the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-
norm
dtpmv - perform one of the matrix-vector operations x := A*x, or x :=
A'*x
dtprfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
packed coefficient matrix
dtpsv - solve one of the systems of equations A*x = b, or A'*x = b
dtptri - compute the inverse of a real upper or lower triangular matrix
A stored in packed format
dtptrs - solve a triangular system of the form A * X = B or A**T * X
= B,
dtrans - transpose and scale source matrix
dtrcon - estimate the reciprocal of the condition number of a triangu‐
lar matrix A, in either the 1-norm or the infinity-norm
dtrevc - compute some or all of the right and/or left eigenvectors of a
real upper quasi-triangular matrix T
dtrexc - reorder the real Schur factorization of a real matrix A =
Q*T*Q**T, so that the diagonal block of T with row index IFST
is moved to row ILST
dtrmm - perform one of the matrix-matrix operationsB := alpha*op( A
)*B, or B := alpha*B*op( A )
dtrmv - perform one of the matrix-vector operations x := A*x, or x :=
A'*x
dtrrfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
coefficient matrix
dtrsen - reorder the real Schur factorization of a real matrix A =
Q*T*Q**T, so that a selected cluster of eigenvalues appears
in the leading diagonal blocks of the upper quasi-triangular
matrix T,
dtrsm - solve one of the matrix equations op( A )*X = alpha*B, or
X*op( A ) = alpha*B
dtrsna - estimate reciprocal condition numbers for specified eigenval‐
ues and/or right eigenvectors of a real upper quasi-triangu‐
lar matrix T (or of any matrix Q*T*Q**T with Q orthogonal)
dtrsv - solve one of the systems of equations A*x = b, or A'*x = b
dtrsyl - solve the real Sylvester matrix equation
dtrti2 - compute the inverse of a real upper or lower triangular matrix
dtrtri - compute the inverse of a real upper or lower triangular matrix
A
dtrtrs - solve a triangular system of the form A * X = B or A**T * X
= B,
dtzrqf - routine is deprecated and has been replaced by routine DTZRZF
dtzrzf - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to
upper triangular form by means of orthogonal transformations
dvbrmm - variable block sparse row format matrix-matrix multiply
dvbrsm - variable block sparse row format triangular solve
dwiener - perform Wiener deconvolution of two signals
dzasum - Return the sum of the absolute values of a vector x.
dznrm2 - Return the Euclidian norm of a vector.
ezfftb - computes a periodic sequence from its Fourier coefficients.
EZFFTB is a simplified but slower version of RFFTB.
ezfftf - computes the Fourier coefficients of a periodic sequence.
EZFFTF is a simplified but slower version of RFFTF.
ezffti - initializes the array WSAVE, which is used in both EZFFTF and
EZFFTB.
fft - Fast Fourier transform subroutines
gen_custom - extract necessary routines from an archive library to cre‐
ate a purpose-built library.
gscon - estimates the reciprocal of the condition number of a general
real matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by SuperLU routine
sgstrf.
gsequ - computes row and column scalings intended to equilibrate an M-
by-N sparse matrix A and reduce its condition number.
gsrfs - improves the computed solution to a system of linear equations
and provides error bounds and backward error estimates for
the solution. It is a SuperLU routine.
gssv - solves a system of linear equations A*X=B using the LU factor‐
ization from sgstrf.
gssvx - solves the system of linear equations A*X=B or A'*X=B, using
the LU factorization from sgstrf(). Error bounds on the solu‐
tion and a condition estimate are also provided.
gstrf - computes an LU factorization of a general sparse m-by-n matrix
A using partial pivoting with row interchanges.
gstrs - solves a system of linear equations A*X=B or A'*X=B with A
sparse and B dense, using the LU factorization computed by
sgstrf.
icamax - return the index of the element with largest absolute value.
idamax - return the index of the element with largest absolute value.
ilaenv - The name of the calling subroutine, in either upper case or
lower case.
ilaver - return the Lapack version Arguments
infinite_norm_error - A utility function of the SuperLU solver that
computes the infinity-norm of an array of vectors that are
approximations to the exact solution vector.
isamax - return the index of the element with largest absolute value.
izamax - return the index of the element with largest absolute value.
langs - returns the value of the one-norm, or the Frobenius-norm, or
the infinity-norm, or the element with largest absolute value
of a general real matrix A in sparse format.
laqgs - a SuperLU function that equilibrates a general sparse M by N
matrix A.
lsame - returns .TRUE. if CA is the same letter as CB regardless of
case
rfft2b - compute a periodic sequence from its Fourier coefficients.
The RFFT operations are unnormalized, so a call of RFFT2F
followed by a call of RFFT2B will multiply the input sequence
by M*N.
rfft2f - compute the Fourier coefficients of a periodic sequence. The
RFFT operations are unnormalized, so a call of RFFT2F fol‐
lowed by a call of RFFT2B will multiply the input sequence by
M*N.
rfft2i - initialize the array WSAVE, which is used in both the forward
and backward transforms.
rfft3b - compute a periodic sequence from its Fourier coefficients. The
RFFT operations are unnormalized, so a call of RFFT3F fol‐
lowed by a call of RFFT3B will multiply the input sequence by
M*N*K.
rfft3f - compute the Fourier coefficients of a real periodic sequence.
The RFFT operations are unnormalized, so a call of RFFT3F
followed by a call of RFFT3B will multiply the input sequence
by M*N*K.
rfft3i - initialize the array WSAVE, which is used in both RFFT3F and
RFFT3B.
rfftb - compute a periodic sequence from its Fourier coefficients. The
RFFT operations are unnormalized, so a call of RFFTF followed
by a call of RFFTB will multiply the input sequence by N.
rfftf - compute the Fourier coefficients of a periodic sequence. The
FFT operations are unnormalized, so a call of RFFTF followed
by a call of RFFTB will multiply the input sequence by N.
rffti - initialize the array WSAVE, which is used in both RFFTF and
RFFTB.
rfftopt - compute the length of the closest fast FFT
sCopy_CompCol_Matrix - A utility C function in the serial SuperLU
solver that copies one SuperMatrix into another.
sCreate_CompCol_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in compressed sparse column
format (also known as the Harwell-Boeing format).
sCreate_CompRow_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in compressed sparse row
format.
sCreate_Dense_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in dense format.
sCreate_SuperNode_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in supernodal format.
sPrintPerf - A utility function of the SuperLU solver that prints sta‐
tistics collected by the computational routines.
sQuerySpace - A inquiry function that provides information on the mem‐
ory statistics of the SuperLU solver.
sasum - Return the sum of the absolute values of a vector x.
saxpy - compute y := alpha * x + y
saxpyi - Compute y := alpha * x + y
sbcomm - block coordinate matrix-matrix multiply
sbdimm - block diagonal format matrix-matrix multiply
sbdism - block diagonal format triangular solve
sbdsdc - compute the singular value decomposition (SVD) of a real N-by-
N (upper or lower) bidiagonal matrix B
sbdsqr - compute the singular value decomposition (SVD) of a real N-by-
N (upper or lower) bidiagonal matrix B.
sbelmm - block Ellpack format matrix-matrix multiply
sbelsm - block Ellpack format triangular solve
sbscmm - block sparse column matrix-matrix multiply
sbscsm - block sparse column format triangular solve
sbsrmm - block sparse row format matrix-matrix multiply
sbsrsm - block sparse row format triangular solve
scasum - Return the sum of the absolute values of a vector x.
scnrm2 - Return the Euclidian norm of a vector.
scnvcor - compute the convolution or correlation of real vectors
scnvcor2 - compute the convolution or correlation of real matrices
scoomm - coordinate matrix-matrix multiply
scopy - Copy x to y
scscmm - compressed sparse column format matrix-matrix multiply
scscsm - compressed sparse column format triangular solve
scsrmm - compressed sparse row format matrix-matrix multiply
scsrsm - compressed sparse row format triangular solve
sdiamm - diagonal format matrix-matrix multiply
sdiasm - diagonal format triangular solve
sdisna - compute 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 m-by-n matrix
sdot - compute the dot product of two vectors x and y.
sdoti - Compute the indexed dot product.
sdsdot - compute a constant plus the double precision dot product of
two single precision vectors x and y
second - return the user time for a process in seconds
sellmm - Ellpack format matrix-matrix multiply
sellsm - Ellpack format triangular solve
set_default_options - C function that sets to default parameters the
options that control the behavior of the serial SuperLU
solver.
sfftc - initialize the trigonometric weight and factor tables or com‐
pute the forward Fast Fourier Transform of a real sequence.
sfftc2 - initialize the trigonometric weight and factor tables or com‐
pute the two-dimensional forward Fast Fourier Transform of a
two-dimensional real array.
sfftc3 - initialize the trigonometric weight and factor tables or com‐
pute the three-dimensional forward Fast Fourier Transform of
a three-dimensional complex array.
sfftcm - initialize the trigonometric weight and factor tables or com‐
pute the one-dimensional forward Fast Fourier Transform of a
set of real data sequences stored in a two-dimensional array.
sgbbrd - reduce a real general m-by-n band matrix A to upper bidiagonal
form B by an orthogonal transformation
sgbcon - estimate the reciprocal of the condition number of a real gen‐
eral band matrix A, in either the 1-norm or the infinity-
norm,
sgbequ - compute row and column scalings intended to equilibrate an M-
by-N band matrix A and reduce its condition number
sgbmv - perform one of the matrix-vector operationsy := alpha*A*x +
beta*y or y := alpha*A'*x + beta*y
sgbrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is banded, and provides error
bounds and backward error estimates for the solution
sgbsv - compute the solution to a real system of linear equations A * X
= B, where A is a band matrix of order N with KL subdiagonals
and KU superdiagonals, and X and B are N-by-NRHS matrices
sgbsvx - use the LU factorization to compute the solution to a real
system of linear equations A * X = B, A**T * X = B, or A**H *
X = B,
sgbtf2 - compute an LU factorization of a real m-by-n band matrix A
using partial pivoting with row interchanges
sgbtrf - compute an LU factorization of a real m-by-n band matrix A
using partial pivoting with row interchanges
sgbtrs - solve a system of linear equations A * X = B or A' * X = B
with a general band matrix A using the LU factorization com‐
puted by SGBTRF
sgebak - form the right or left eigenvectors of a real general matrix
by backward transformation on the computed eigenvectors of
the balanced matrix output by SGEBAL
sgebal - balance a general real matrix A
sgebrd - reduce a general real M-by-N matrix A to upper or lower bidi‐
agonal form B by an orthogonal transformation
sgecon - estimate the reciprocal of the condition number of a general
real matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by SGETRF
sgeequ - compute row and column scalings intended to equilibrate an M-
by-N matrix A and reduce its condition number
sgees - compute for an N-by-N real nonsymmetric matrix A, the eigenval‐
ues, the real Schur form T, and, optionally, the matrix of
Schur vectors Z
sgeesx - compute for an N-by-N real nonsymmetric matrix A, the eigen‐
values, the real Schur form T, and, optionally, the matrix of
Schur vectors Z
sgeev - compute for an N-by-N real nonsymmetric matrix A, the eigenval‐
ues and, optionally, the left and/or right eigenvectors
sgeevx - compute for an N-by-N real nonsymmetric matrix A, the eigen‐
values and, optionally, the left and/or right eigenvectors
sgegs - routine is deprecated and has been replaced by routine SGGES
sgegv - routine is deprecated and has been replaced by routine SGGEV
sgehrd - reduce a real general matrix A to upper Hessenberg form H by
an orthogonal similarity transformation
sgelqf - compute an LQ factorization of a real M-by-N matrix A
sgels - solve overdetermined or underdetermined real linear systems
involving an M-by-N matrix A, or its transpose, using a QR or
LQ factorization of A
sgelsd - compute the minimum-norm solution to a real linear least
squares problem
sgelss - compute the minimum norm solution to a real linear least
squares problem
sgelsx - routine is deprecated and has been replaced by routine SGELSY
sgelsy - compute the minimum-norm solution to a real linear least
squares problem
sgemm - perform one of the matrix-matrix operationsC := alpha*op( A
)*op( B ) + beta*C
sgemv - perform one of the matrix-vector operationsy := alpha*A*x +
beta*y or y := alpha*A'*x + beta*y
sgeqlf - compute a QL factorization of a real M-by-N matrix A
sgeqp3 - compute a QR factorization with column pivoting of a matrix A
sgeqpf - routine is deprecated and has been replaced by routine SGEQP3
sgeqrf - compute a QR factorization of a real M-by-N matrix A
sger - perform the rank 1 operation A := alpha*x*y' + A
sgerfs - improve the computed solution to a system of linear equations
and provides error bounds and backward error estimates for
the solution
sgerqf - compute an RQ factorization of a real M-by-N matrix A
sgesdd - compute the singular value decomposition (SVD) of a real M-by-
N matrix A, optionally computing the left and right singular
vectors
sgesv - compute the solution to a real system of linear equations A *
X = B,
sgesvd - compute the singular value decomposition (SVD) of a real M-by-
N matrix A, optionally computing the left and/or right singu‐
lar vectors
sgesvx - use the LU factorization to compute the solution to a real
system of linear equations A * X = B,
sgetf2 - compute an LU factorization of a general m-by-n matrix A using
partial pivoting with row interchanges
sgetrf - compute an LU factorization of a general M-by-N matrix A using
partial pivoting with row interchanges
sgetri - compute the inverse of a matrix using the LU factorization
computed by SGETRF
sgetrs - solve a system of linear equations A * X = B or A' * X = B
with a general N-by-N matrix A using the LU factorization
computed by SGETRF
sggbak - form the right or left eigenvectors of a real generalized ei‐
genvalue problem A*x = lambda*B*x, by backward transformation
on the computed eigenvectors of the balanced pair of matrices
output by SGGBAL
sggbal - balance a pair of general real matrices (A,B)
sgges - compute for a pair of N-by-N real nonsymmetric matrices (A,B),
sggesx - compute for a pair of N-by-N real nonsymmetric matrices (A,B),
the generalized eigenvalues, the real Schur form (S,T), and,
sggev - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
sggevx - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
sggglm - solve a general Gauss-Markov linear model (GLM) problem
sgghrd - reduce a pair of real matrices (A,B) to generalized upper Hes‐
senberg form using orthogonal transformations, where A is a
general matrix and B is upper triangular
sgglse - solve the linear equality-constrained least squares (LSE)
problem
sggqrf - compute a generalized QR factorization of an N-by-M matrix A
and an N-by-P matrix B.
sggrqf - compute a generalized RQ factorization of an M-by-N matrix A
and a P-by-N matrix B
sggsvd - compute the generalized singular value decomposition (GSVD) of
an M-by-N real matrix A and P-by-N real matrix B
sggsvp - compute orthogonal matrices U, V and Q such that N-K-L K
LU'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
sgscon - estimates the reciprocal of the condition number of a general
real matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by SuperLU routine
sgstrf.
sgsequ - computes row and column scalings intended to equilibrate an M-
by-N sparse matrix A and reduce its condition number.
sgsrfs - improves the computed solution to a system of linear equations
and provides error bounds and backward error estimates for
the solution. It is a SuperLU routine.
sgssco - General sparse solver condition number estimate.
sgssda - Deallocate working storage for the general sparse solver.
sgssfa - General sparse solver numeric factorization.
sgssfs - General sparse solver one call interface.
sgssin - Initialize the general sparse solver.
sgssor - General sparse solver ordering and symbolic factorization.
sgssps - Print general sparse solver statics.
sgssrp - Return permutation used by the general sparse solver.
sgsssl - Solve routine for the general sparse solver.
sgssuo - Provide general sparse solvers SPSOLVE and SuperLU a user-
supplied permutation for ordering.
sgssv - solves a system of linear equations A*X=B using the LU factor‐
ization from sgstrf.
sgssvx - solves the system of linear equations A*X=B or A'*X=B, using
the LU factorization from sgstrf(). Error bounds on the solu‐
tion and a condition estimate are also provided.
sgstrf - computes an LU factorization of a general sparse m-by-n matrix
A using partial pivoting with row interchanges.
sgstrs - solves a system of linear equations A*X=B or A'*X=B with A
sparse and B dense, using the LU factorization computed by
sgstrf.
sgtcon - estimate the reciprocal of the condition number of a real
tridiagonal matrix A using the LU factorization as computed
by SGTTRF
sgthr - Gathers specified elements from y into x.
sgthrz - Gather and zero.
sgtrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is tridiagonal, and provides
error bounds and backward error estimates for the solution
sgtsv - solve the equation A*X = B,
sgtsvx - use the LU factorization to compute the solution to a real
system of linear equations A * X = B or A**T * X = B,
sgttrf - compute an LU factorization of a real tridiagonal matrix A
using elimination with partial pivoting and row interchanges
sgttrs - solve one of the systems of equations A*X = B or A'*X = B,
shgeqz - implement a single-/double-shift version of the QZ method for
finding the generalized eigenvalues w(j)=(ALPHAR(j) +
i*ALPHAI(j))/BETAR(j) of the equation det( A-w(i) B ) = 0
In addition, the pair A,B may be reduced to generalized Schur
form
shsein - use inverse iteration to find specified right and/or left
eigenvectors of a real upper Hessenberg matrix H
shseqr - compute the eigenvalues of a real upper Hessenberg matrix H
and, optionally, the matrices T and Z from the Schur decompo‐
sition H = Z T Z**T, where T is an upper quasi-triangular
matrix (the Schur form), and Z is the orthogonal matrix of
Schur vectors
sinfinite_norm_error - A utility function of the SuperLU solver that
computes the infinity-norm of an array of vectors that are
approximations to the exact solution vector.
sinqb - synthesize a Fourier sequence from its representation in terms
of a sine series with odd wave numbers. The SINQ operations
are unnormalized inverses of themselves, so a call to SINQF
followed by a call to SINQB will multiply the input sequence
by 4 * N.
sinqf - compute the Fourier coefficients in a sine series representa‐
tion with only odd wave numbers.The SINQ operations are
unnormalized inverses of themselves, so a call to SINQF fol‐
lowed by a call to SINQB will multiply the input sequence by
4 * N.
sinqi - initialize the array xWSAVE, which is used in both SINQF and
SINQB.
sint - compute the discrete Fourier sine transform of an odd sequence.
The SINT transforms are unnormalized inverses of themselves,
so a call of SINT followed by another call of SINT will mul‐
tiply the input sequence by 2 * (N+1).
sinti - initialize the array WSAVE, which is used in subroutine SINT.
sjadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack)
sjadrp - right permutation of a jagged diagonal matrix
sjadsm - Jagged-diagonal format triangular solve
slagtf - factorize the matrix (T-lambda*I), where T is an n by n tridi‐
agonal matrix and lambda is a scalar, as T-lambda*I = PLU
slamch - Determines single precision machine parameters.
slamrg - will create a permutation list which will merge the elements
of A (which is composed of two independently sorted sets)
into a single set which is sorted in ascending order
slangs - returns the value of the one-norm, or the Frobenius-norm, or
the infinity-norm, or the element with largest absolute value
of a general real matrix A in sparse format.
slaqgs - a SuperLU function that equilibrates a general sparse M by N
matrix A.
slarz - applies a real elementary reflector H to a real M-by-N matrix
C, from either the left or the right
slarzb - applies a real block reflector H or its transpose H**T to a
real distributed M-by-N C from the left or the right
slarzt - form the triangular factor T of a real block reflector H of
order > n, which is defined as a product of k elementary
reflectors
slasrt - the numbers in D in increasing order (if ID = 'I') or in
decreasing order (if ID = 'D' )
slatzm - routine is deprecated and has been replaced by routine SORMRZ
snrm2 - Return the Euclidian norm of a vector.
sopgtr - generate a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as
returned by SSPTRD using packed storage
sopmtr - overwrite the general real M-by-N matrix C with SIDE = 'L'
SIDE = 'R' TRANS = 'N'
sorg2l - generate an m by n real matrix Q with orthonormal columns,
sorg2r - generate an m by n real matrix Q with orthonormal columns,
sorgbr - generate one of the real orthogonal matrices Q or P**T deter‐
mined by SGEBRD when reducing a real matrix A to bidiagonal
form
sorghr - generate a real orthogonal matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as
returned by SGEHRD
sorgl2 - generate an m by n real matrix Q with orthonormal rows,
sorglq - generate an M-by-N real matrix Q with orthonormal rows,
sorgql - generate an M-by-N real matrix Q with orthonormal columns,
sorgqr - generate an M-by-N real matrix Q with orthonormal columns,
sorgr2 - generate an m by n real matrix Q with orthonormal rows,
sorgrq - generate an M-by-N real matrix Q with orthonormal rows,
sorgtr - generate a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors of order N, as returned
by SSYTRD
sormbr - overwrites the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q or P*C or P**T*C or C*P or C*P**T.
sormhr - overwrite the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q.
sormlq - overwrite the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q.
sormql - overwrite the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q.
sormqr - overwrite the general real M-by-N matrix C with SIDE = 'L'
SIDE = 'R' TRANS = 'N'
sormrq - overwrite the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q.
sormrz - overwrite the general real M-by-N matrix C with Q*C or Q**H*C
or C*Q**H or C*Q.
sormtr - overwrite the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q.
sp_cgemm - a SuperLU routine that performs one of the matrix-matrix
operations C := alpha*op( A )*op( B ) + beta*C where op(X)
is one of op(X) = X or op(X) = X' or op(X) = conjg(X'),
alpha and beta are scalars, A is a sparse matrix of type
SuperMatrix, and B and C are dense matrices, with op( A ) an
m by k matrix,op( B ) a k by n matrix and C an m by n
matrix.
sp_dgemm - a SuperLU routine that performs one of the matrix-matrix
operations C := alpha*op( A )*op( B ) + beta*C where op(X)
is one of op(X) = X or op(X) = X' or op(X) = conjg(X'),
alpha and beta are scalars, A is a sparse matrix of type
SuperMatrix, and B and C are dense matrices, with op( A ) an
m by k matrix,op( B ) a k by n matrix and C an m by n
matrix.
sp_gemm - a SuperLU routine that performs one of the matrix-matrix
operations C := alpha*op( A )*op( B ) + beta*C where op(X)
is one of op(X) = X or op(X) = X' or op(X) = conjg(X'),
alpha and beta are scalars, A is a sparse matrix of type
SuperMatrix, and B and C are dense matrices, with op( A ) an
m by k matrix,op( B ) a k by n matrix and C an m by n
matrix.
sp_ienv - called by SuperLU routines to choose machine dependent param‐
eters for the local environment. See ISPEC for a description
of the parameters.
sp_preorder - permutes the columns of the original sparse matrix.
sp_sgemm - a SuperLU routine that performs one of the matrix-matrix
operations C := alpha*op( A )*op( B ) + beta*C where op(X)
is one of op(X) = X or op(X) = X' or op(X) = conjg(X'),
alpha and beta are scalars, A is a sparse matrix of type
SuperMatrix, and B and C are dense matrices, with op( A ) an
m by k matrix,op( B ) a k by n matrix and C an m by n
matrix.
sp_zgemm - a SuperLU routine that performs one of the matrix-matrix
operations C := alpha*op( A )*op( B ) + beta*C where op(X)
is one of op(X) = X or op(X) = X' or op(X) = conjg(X'),
alpha and beta are scalars, A is a sparse matrix of type
SuperMatrix, and B and C are dense matrices, with op( A ) an
m by k matrix,op( B ) a k by n matrix and C an m by n
matrix.
spbcon - estimate the reciprocal of the condition number (in the
1-norm) of a real symmetric positive definite band matrix
using the Cholesky factorization A = U**T*U or A = L*L**T
computed by SPBTRF
spbequ - compute row and column scalings intended to equilibrate a sym‐
metric positive definite band matrix A and reduce its condi‐
tion number (with respect to the two-norm)
spbrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite
and banded, and provides error bounds and backward error
estimates for the solution
spbstf - compute a split Cholesky factorization of a real symmetric
positive definite band matrix A
spbsv - compute the solution to a real system of linear equations A *
X = B,
spbsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equationsA *
X = B,
spbtf2 - compute the Cholesky factorization of a real symmetric posi‐
tive definite band matrix A
spbtrf - compute the Cholesky factorization of a real symmetric posi‐
tive definite band matrix A
spbtrs - solve a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factoriza‐
tion A = U**T*U or A = L*L**T computed by SPBTRF
spocon - estimate the reciprocal of the condition number (in the
1-norm) of a real symmetric positive definite matrix using
the Cholesky factorization A = U**T*U or A = L*L**T computed
by SPOTRF
spoequ - compute row and column scalings intended to equilibrate a sym‐
metric positive definite matrix A and reduce its condition
number (with respect to the two-norm)
sporfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite,
sposv - compute the solution to a real system of linear equations A *
X = B,
sposvx - use the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equationsA *
X = B,
spotf2 - compute the Cholesky factorization of a real symmetric posi‐
tive definite matrix A
spotrf - compute the Cholesky factorization of a real symmetric posi‐
tive definite matrix A
spotri - compute the inverse of a real symmetric positive definite
matrix A using the Cholesky factorization A = U**T*U or A =
L*L**T computed by SPOTRF
spotrs - solve a system of linear equations A*X = B with a symmetric
positive definite matrix A using the Cholesky factorization A
= U**T*U or A = L*L**T computed by SPOTRF
sppcon - estimate the reciprocal of the condition number (in the
1-norm) of a real symmetric positive definite packed matrix
using the Cholesky factorization A = U**T*U or A = L*L**T
computed by SPPTRF
sppequ - compute row and column scalings intended to equilibrate a sym‐
metric positive definite matrix A in packed storage and
reduce its condition number (with respect to the two-norm)
spprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite
and packed, and provides error bounds and backward error
estimates for the solution
sppsv - compute the solution to a real system of linear equations A *
X = B,
sppsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equationsA *
X = B,
spptrf - compute the Cholesky factorization of a real symmetric posi‐
tive definite matrix A stored in packed format
spptri - compute the inverse of a real symmetric positive definite
matrix A using the Cholesky factorization A = U**T*U or A =
L*L**T computed by SPPTRF
spptrs - solve a system of linear equations A*X = B with a symmetric
positive definite matrix A in packed storage using the
Cholesky factorization A = U**T*U or A = L*L**T computed by
SPPTRF
sptcon - compute the reciprocal of the condition number (in the 1-norm)
of a real symmetric positive definite tridiagonal matrix
using the factorization A = L*D*L**T or A = U**T*D*U computed
by SPTTRF
spteqr - compute all eigenvalues and, optionally, eigenvectors of a
symmetric positive definite tridiagonal matrix by first fac‐
toring the matrix using SPTTRF, and then calling SBDSQR to
compute the singular values of the bidiagonal factor
sptrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite
and tridiagonal, and provides error bounds and backward error
estimates for the solution
sptsv - compute the solution to a real system of linear equations A*X =
B, where A is an N-by-N symmetric positive definite tridiago‐
nal matrix, and X and B are N-by-NRHS matrices.
sptsvx - use the factorization A = L*D*L**T to compute the solution to
a real system of linear equations A*X = B, where A is an N-
by-N symmetric positive definite tridiagonal matrix and X and
B are N-by-NRHS matrices
spttrf - compute the L*D*L' factorization of a real symmetric positive
definite tridiagonal matrix A
spttrs - solve a tridiagonal system of the form A * X = B using the
L*D*L' factorization of A computed by SPTTRF
sptts2 - solve a tridiagonal system of the form A * X = B using the
L*D*L' factorization of A computed by SPTTRF
srot - Apply a Given's rotation constructed by SROTG.
srotg - Construct a Given's plane rotation
sroti - Apply an indexed Givens rotation.
srotm - Apply a Gentleman's modified Given's rotation constructed by
SROTMG.
srotmg - Construct a Gentleman's modified Given's plane rotation
ssbev - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric band matrix A
ssbevd - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric band matrix A
ssbevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A
ssbgst - reduce a real symmetric-definite banded generalized eigenprob‐
lem A*x = lambda*B*x to standard form C*y = lambda*y,
ssbgv - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem,
of the form A*x=(lambda)*B*x
ssbgvd - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem,
of the form A*x=(lambda)*B*x
ssbgvx - compute selected eigenvalues, and optionally, eigenvectors of
a real generalized symmetric-definite banded eigenproblem, of
the form A*x=(lambda)*B*x
ssbmv - perform the matrix-vector operationy := alpha*A*x + beta*y
ssbtrd - reduce a real symmetric band matrix A to symmetric tridiagonal
form T by an orthogonal similarity transformation
sscal - Compute y := alpha * y
ssctr - Scatters elements from x into y.
sskymm - Skyline format matrix-matrix multiply
sskysm - Skyline format triangular solve
sspcon - estimate the reciprocal of the condition number (in the
1-norm) of a real symmetric packed matrix A using the factor‐
ization A = U*D*U**T or A = L*D*L**T computed by SSPTRF
sspev - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage
sspevd - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage
sspevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric matrix A in packed storage
sspgst - reduce a real symmetric-definite generalized eigenproblem to
standard form, using packed storage
sspgv - compute all the eigenvalues and, optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
sspgvd - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
sspgvx - compute selected eigenvalues, and optionally, eigenvectors of
a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
sspmv - perform the matrix-vector operationy := alpha*A*x + beta*y
sspr - perform the symmetric rank 1 operation A := alpha*x*x' + A
sspr2 - perform the symmetric rank 2 operation A := alpha*x*y' +
alpha*y*x' + A
ssprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite and
packed, and provides error bounds and backward error esti‐
mates for the solution
sspsv - compute the solution to a real system of linear equations A *
X = B,
sspsvx - use the diagonal pivoting factorization A = U*D*U**T or A =
L*D*L**T to compute the solution to a real system of linear
equations A * X = B, where A is an N-by-N symmetric matrix
stored in packed format and X and B are N-by-NRHS matrices
ssptrd - reduce a real symmetric matrix A stored in packed form to sym‐
metric tridiagonal form T by an orthogonal similarity trans‐
formation
ssptrf - compute the factorization of a real symmetric matrix A stored
in packed format using the Bunch-Kaufman diagonal pivoting
method
ssptri - compute the inverse of a real symmetric indefinite matrix A in
packed storage using the factorization A = U*D*U**T or A =
L*D*L**T computed by SSPTRF
ssptrs - solve a system of linear equations A*X = B with a real symmet‐
ric matrix A stored in packed format using the factorization
A = U*D*U**T or A = L*D*L**T computed by SSPTRF
sstebz - compute the eigenvalues of a symmetric tridiagonal matrix T
sstedc - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer
method
sstegr - (a) Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T
is a relatively robust representation
sstein - compute the eigenvectors of a real symmetric tridiagonal
matrix T corresponding to specified eigenvalues, using
inverse iteration
sstemr - computes selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix T.
ssteqr - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR
method
ssterf - compute all eigenvalues of a symmetric tridiagonal matrix
using the Pal-Walker-Kahan variant of the QL or QR algorithm
sstev - compute all eigenvalues and, optionally, eigenvectors of a real
symmetric tridiagonal matrix A
sstevd - compute all eigenvalues and, optionally, eigenvectors of a
real symmetric tridiagonal matrix
sstevr - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix T
sstevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix A
sstsv - compute the solution to a system of linear equations A * X = B
where A is a symmetric tridiagonal matrix
ssttrf - compute the factorization of a symmetric tridiagonal matrix A
using the Bunch-Kaufman diagonal pivoting method
ssttrs - computes the solution to a real system of linear equations A *
X = B
sswap - Exchange vectors x and y.
ssycon - estimate the reciprocal of the condition number (in the
1-norm) of a real symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by SSYTRF
ssyev - compute all eigenvalues and, optionally, eigenvectors of a real
symmetric matrix A
ssyevd - compute all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A
ssyevr - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix T
ssyevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric matrix A
ssygs2 - reduce a real symmetric-definite generalized eigenproblem to
standard form
ssygst - reduce a real symmetric-definite generalized eigenproblem to
standard form
ssygv - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
ssygvd - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
ssygvx - compute selected eigenvalues, and optionally, eigenvectors of
a real generalized symmetric-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
ssymm - perform one of the matrix-matrix operationsC := alpha*A*B +
beta*C or C := alpha*B*A + beta*C
ssymv - perform the matrix-vector operationy := alpha*A*x + beta*y
ssyr - perform the symmetric rank 1 operation A := alpha*x*x' + A
ssyr2 - perform the symmetric rank 2 operation A := alpha*x*y' +
alpha*y*x' + A
ssyr2k - perform one of the symmetric rank 2k operations C :=
alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B +
alpha*B'*A + beta*C
ssyrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite, and pro‐
vides error bounds and backward error estimates for the solu‐
tion
ssyrk - perform one of the symmetric rank k operations C :=
alpha*A*A' + beta*C or C := alpha*A'*A + beta*C
ssysv - compute the solution to a real system of linear equations A *
X = B,
ssysvx - use the diagonal pivoting factorization to compute the solu‐
tion to a real system of linear equations A * X = B,
ssytd2 - reduce a real symmetric matrix A to symmetric tridiagonal form
T by an orthogonal similarity transformation
ssytf2 - compute the factorization of a real symmetric matrix A using
the Bunch-Kaufman diagonal pivoting method
ssytrd - reduce a real symmetric matrix A to real symmetric tridiagonal
form T by an orthogonal similarity transformation
ssytrf - compute the factorization of a real symmetric matrix A using
the Bunch-Kaufman diagonal pivoting method
ssytri - compute the inverse of a real symmetric indefinite matrix A
using the factorization A = U*D*U**T or A = L*D*L**T computed
by SSYTRF
ssytrs - solve a system of linear equations A*X = B with a real symmet‐
ric matrix A using the factorization A = U*D*U**T or A =
L*D*L**T computed by SSYTRF
stbcon - estimate the reciprocal of the condition number of a triangu‐
lar band matrix A, in either the 1-norm or the infinity-norm
stbmv - perform one of the matrix-vector operationsx := A*x, or x :=
A'*x
stbrfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
band coefficient matrix
stbsv - solve one of the systems of equations A*x = b, or A'*x = b
stbtrs - solve a triangular system of the form A * X = B or A**T * X
= B,
stgevc - compute some or all of the right and/or left generalized
eigenvectors of a pair of real upper triangular matrices
(A,B) that was obtained from the generalized Schur factoriza‐
tion of an original pair of real nonsymmetric matrices. B is
upper triangular and A is a block upper triangular, where the
diagonal blocks are either 1-by-1 or 2-by-2.
stgexc - reorder the generalized real Schur decomposition of a real
matrix pair (A,B) using an orthogonal equivalence transforma‐
tion(A, B) = Q * (A, B) * Z', so that the diagonal block of
(A, B) with row index IFST is moved to row ILST.
stgsen - reorder the generalized real Schur decomposition of a real
matrix pair (A, B) (in terms of an orthonormal equivalence
trans- formation Q' * (A, B) * Z), so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the
upper quasi-triangular matrix A and the upper triangular B
stgsja - compute the generalized singular value decomposition (GSVD) of
two real upper triangular (or trapezoidal) matrices A and B
stgsna - estimate reciprocal condition numbers for specified eigenval‐
ues and/or eigenvectors of a matrix pair (A, B) in general‐
ized real Schur canonical form (or of any matrix pair
(Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where Z'
denotes the transpose of Z
stgsyl - solve the generalized Sylvester equation
stpcon - estimate the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-
norm
stpmv - perform one of the matrix-vector operations x := A*x, or x :=
A'*x
stprfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
packed coefficient matrix
stpsv - solve one of the systems of equations A*x = b, or A'*x = b
stptri - compute the inverse of a real upper or lower triangular matrix
A stored in packed format
stptrs - solve a triangular system of the form A * X = B or A**T * X
= B,
strans - transpose and scale source matrix
strcon - estimate the reciprocal of the condition number of a triangu‐
lar matrix A, in either the 1-norm or the infinity-norm
strevc - compute some or all of the right and/or left eigenvectors of a
real upper quasi-triangular matrix T
strexc - reorder the real Schur factorization of a real matrix A =
Q*T*Q**T, so that the diagonal block of T with row index IFST
is moved to row ILST
strmm - perform one of the matrix-matrix operationsB := alpha*op( A
)*B, or B := alpha*B*op( A )
strmv - perform one of the matrix-vector operations x := A*x, or x :=
A'*x
strrfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
coefficient matrix
strsen - reorder the real Schur factorization of a real matrix A =
Q*T*Q**T, so that a selected cluster of eigenvalues appears
in the leading diagonal blocks of the upper quasi-triangular
matrix T,
strsm - solve one of the matrix equations op( A )*X = alpha*B, or
X*op( A ) = alpha*B
strsna - estimate reciprocal condition numbers for specified eigenval‐
ues and/or right eigenvectors of a real upper quasi-triangu‐
lar matrix T (or of any matrix Q*T*Q**T with Q orthogonal)
strsv - solve one of the systems of equations A*x = b, or A'*x = b
strsyl - solve the real Sylvester matrix equation
strti2 - compute the inverse of a real upper or lower triangular matrix
strtri - compute the inverse of a real upper or lower triangular matrix
A
strtrs - solve a triangular system of the form A * X = B or A**T * X
= B,
stzrqf - routine is deprecated and has been replaced by routine STZRZF
stzrzf - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to
upper triangular form by means of orthogonal transformations
sunperf_version - gets library information 1i SUBROUTINE SUNPERF_VER‐
SION(VERSION, PATCH, UPDATE) 1i INTEGER VERSION, PATCH,
UPDATE 1i
svbrmm - variable block sparse row format matrix-matrix multiply
svbrsm - variable block sparse row format triangular solve
swiener - perform Wiener deconvolution of two signals
use_threads - Sets the number of threads to use for subsequent parallel
regions
using_threads - In a parallel environment, if called from a serial
region of the master thread it returns the number of threads
available for execution (determined by function
OMP_GET_NUM_THREADS). Else, if it is called from a thread in
the team executing the parallel region it returns a 1.
USING_THREADS subroutine
vcfftb - compute a periodic sequence from its Fourier coefficients.
The VCFFT operations are normalized, so a call of VCFFTF fol‐
lowed by a call of VCFFTB will return the original sequence.
vcfftf - compute the Fourier coefficients of a periodic sequence. The
VCFFT operations are normalized, so a call of VCFFTF followed
by a call of VCFFTB will return the original sequence.
vcffti - initialize the array WSAVE, which is used in both VCFFTF and
VCFFTB.
vcosqb - synthesize a Fourier sequence from its representation in terms
of a cosine series with odd wave numbers. The VCOSQ opera‐
tions are normalized, so a call of VCOSQF followed by a call
of VCOSQB will return the original sequence.
vcosqf - compute the Fourier coefficients in a cosine series represen‐
tation with only odd wave numbers. The VCOSQ operations are
normalized, so a call of VCOSQF followed by a call of VCOSQB
will return the original sequence.
vcosqi - initialize the array WSAVE, which is used in both VCOSQF and
VCOSQB.
vcost - compute the discrete Fourier cosine transform of an even
sequence. The VCOST transform is normalized, so a call of
VCOST followed by a call of VCOST will return the original
sequence.
vcosti - initialize the array WSAVE, which is used in VCOST.
vdcosqb - synthesize a Fourier sequence from its representation in
terms of a cosine series with odd wave numbers. The VCOSQ
operations are normalized, so a call of VCOSQF followed by a
call of VCOSQB will return the original sequence.
vdcosqf - compute the Fourier coefficients in a cosine series represen‐
tation with only odd wave numbers. The VCOSQ operations are
normalized, so a call of VCOSQF followed by a call of VCOSQB
will return the original sequence.
vdcosqi - initialize the array WSAVE, which is used in both VCOSQF and
VCOSQB.
vdcost - compute the discrete Fourier cosine transform of an even
sequence. The VCOST transform is normalized, so a call of
VCOST followed by a call of VCOST will return the original
sequence.
vdcosti - initialize the array WSAVE, which is used in VCOST.
vdfftb - compute a periodic sequence from its Fourier coefficients.
The VDFFT operations are normalized, so a call of VDFFTF fol‐
lowed by a call of VDFFTB will return the original sequence.
vdfftf - compute the Fourier coefficients of a periodic sequence. The
VDFFT operations are normalized, so a call of VDFFTF followed
by a call of VDFFTB will return the original sequence.
vdffti - initialize the array WSAVE, which is used in both VRFFTF and
VRFFTB.
vdsinqb - synthesize a Fourier sequence from its representation in
terms of a sine series with odd wave numbers. The VSINQ
operations are normalized, so a call of VSINQF followed by a
call of VSINQB will return the original sequence.
vdsinqf - compute the Fourier coefficients in a sine series representa‐
tion with only odd wave numbers.The VSINQ operations are nor‐
malized, so a call of VSINQF followed by a call of VSINQB
will return the original sequence.
vdsinqi - initialize the array WSAVE, which is used in both VSINQF and
VSINQB.
vdsint - compute the discrete Fourier sine transform of an odd
sequence. The VSINT transforms are unnormalized inverses of
themselves, so a call of VSINT followed by another call of
VSINT will multiply the input sequence by 2 * (N+1). The
VSINT transforms are normalized, so a call of VSINT followed
by a call of VSINT will return the original sequence.
vdsinti - initialize the array WSAVE, which is used in subroutine
VSINT.
vrfftb - compute a periodic sequence from its Fourier coefficients.
The VRFFT operations are normalized, so a call of VRFFTF fol‐
lowed by a call of VRFFTB will return the original sequence.
vrfftf - compute the Fourier coefficients of a periodic sequence. The
VRFFT operations are normalized, so a call of VRFFTF followed
by a call of VRFFTB will return the original sequence.
vrffti - initialize the array WSAVE, which is used in both VRFFTF and
VRFFTB.
vsinqb - synthesize a Fourier sequence from its representation in terms
of a sine series with odd wave numbers. The VSINQ operations
are normalized, so a call of VSINQF followed by a call of
VSINQB will return the original sequence.
vsinqf - compute the Fourier coefficients in a sine series representa‐
tion with only odd wave numbers.The VSINQ operations are nor‐
malized, so a call of VSINQF followed by a call of VSINQB
will return the original sequence.
vsinqi - initialize the array WSAVE, which is used in both VSINQF and
VSINQB.
vsint - compute the discrete Fourier sine transform of an odd sequence.
The VSINT transforms are unnormalized inverses of themselves,
so a call of VSINT followed by another call of VSINT will
multiply the input sequence by 2 * (N+1). The VSINT trans‐
forms are normalized, so a call of VSINT followed by a call
of VSINT will return the original sequence.
vsinti - initialize the array WSAVE, which is used in subroutine VSINT.
vzfftb - compute a periodic sequence from its Fourier coefficients.
The VZFFT operations are normalized, so a call of VZFFTF fol‐
lowed by a call of VZFFTB will return the original sequence.
vzfftf - compute the Fourier coefficients of a periodic sequence. The
VZFFT operations are normalized, so a call of VZFFTF followed
by a call of VZFFTB will return the original sequence.
vzffti - initialize the array WSAVE, which is used in both VZFFTF and
VZFFTB.
zCopy_CompCol_Matrix - A utility C function in the serial SuperLU
solver that copies one SuperMatrix into another.
zCreate_CompCol_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in compressed sparse column
format (also known as the Harwell-Boeing format).
zCreate_CompRow_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in compressed sparse row
format.
zCreate_Dense_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in dense format.
zCreate_SuperNode_Matrix - A utility C function in the serial SuperLU
solver that creates a SuperMatrix in supernodal format.
zPrintPerf - A utility function of the SuperLU solver that prints sta‐
tistics collected by the computational routines.
zQuerySpace - A inquiry function that provides information on the mem‐
ory statistics of the SuperLU solver.
zaxpy - compute y := alpha * x + y
zaxpyi - Compute y := alpha * x + y
zbcomm - block coordinate matrix-matrix multiply
zbdimm - block diagonal format matrix-matrix multiply
zbdism - block diagonal format triangular solve
zbdsqr - compute the singular value decomposition (SVD) of a real N-by-
N (upper or lower) bidiagonal matrix B.
zbelmm - block Ellpack format matrix-matrix multiply
zbelsm - block Ellpack format triangular solve
zbscmm - block sparse column matrix-matrix multiply
zbscsm - block sparse column format triangular solve
zbsrmm - block sparse row format matrix-matrix multiply
zbsrsm - block sparse row format triangular solve
zcgesv - computes the solution to a complex system of linear equations
A * X = B
zcnvcor - compute the convolution or correlation of complex vectors
zcnvcor2 - compute the convolution or correlation of complex matrices
zcoomm - coordinate matrix-matrix multiply
zcopy - Copy x to y
zcscmm - compressed sparse column format matrix-matrix multiply
zcscsm - compressed sparse column format triangular solve
zcsrmm - compressed sparse row format matrix-matrix multiply
zcsrsm - compressed sparse row format triangular solve
zdiamm - diagonal format matrix-matrix multiply.
zdiasm - diagonal format triangular solve
zdotc - compute the dot product of two vectors conjg(x) and y.
zdotci - Compute the complex conjugated indexed dot product.
zdotu - compute the dot product of two vectors x and y.
zdotui - Compute the complex unconjugated indexed dot product.
zdrot - Apply a plane rotation.
zdscal - Compute y := alpha * y
zellmm - Ellpack format matrix-matrix multiply
zellsm - Ellpack format triangular solve
zfft2b - compute a periodic sequence from its Fourier coefficients.
The FFT operations are unnormalized, so a call of ZFFT2F fol‐
lowed by a call of ZFFT2B will multiply the input sequence by
M*N.
zfft2f - compute the Fourier coefficients of a periodic sequence. The
FFT operations are unnormalized, so a call of ZFFT2F followed
by a call of ZFFT2B will multiply the input sequence by M*N.
zfft2i - initialize the array WSAVE, which is used in both the forward
and backward transforms.
zfft3b - compute a periodic sequence from its Fourier coefficients.
The FFT operations are unnormalized, so a call of ZFFT3F fol‐
lowed by a call of ZFFT3B will multiply the input sequence by
M*N*K.
zfft3f - compute the Fourier coefficients of a periodic sequence. The
FFT operations are unnormalized, so a call of ZFFT3F followed
by a call of ZFFT3B will multiply the input sequence by
M*N*K.
zfft3i - initialize the array WSAVE, which is used in both ZFFT3F and
ZFFT3B.
zfftb - compute a periodic sequence from its Fourier coefficients. The
FFT operations are unnormalized, so a call of ZFFTF followed
by a call of ZFFTB will multiply the input sequence by N.
zfftd - initialize the trigonometric weight and factor tables or com‐
pute the inverse Fast Fourier Transform of a double complex
sequence.
zfftd2 - initialize the trigonometric weight and factor tables or com‐
pute the two-dimensional inverse Fast Fourier Transform of a
two-dimensional double complex array.
zfftd3 - initialize the trigonometric weight and factor tables or com‐
pute the three-dimensional inverse Fast Fourier Transform of
a three-dimensional double complex array.
zfftdm - initialize the trigonometric weight and factor tables or com‐
pute the one-dimensional inverse Fast Fourier Transform of a
set of double complex data sequences stored in a two-dimen‐
sional array.
zfftf - compute the Fourier coefficients of a periodic sequence. The
FFT operations are unnormalized, so a call of ZFFTF followed
by a call of ZFFTB will multiply the input sequence by N.
zffti - initialize the array WSAVE, which is used in both ZFFTF and
ZFFTB.
zfftopt - compute the length of the closest fast FFT
zfftz - initialize the trigonometric weight and factor tables or com‐
pute the Fast Fourier transform (forward or inverse) of a
double complex sequence.
zfftz2 - initialize the trigonometric weight and factor tables or com‐
pute the two-dimensional Fast Fourier Transform (forward or
inverse) of a two-dimensional double complex array.
zfftz3 - initialize the trigonometric weight and factor tables or com‐
pute the three-dimensional Fast Fourier Transform (forward or
inverse) of a three-dimensional double complex array.
zfftzm - initialize the trigonometric weight and factor tables or com‐
pute the one-dimensional Fast Fourier Transform (forward or
inverse) of a set of data sequences stored in a two-dimen‐
sional double complex array.
zgbbrd - reduce a complex general m-by-n band matrix A to real upper
bidiagonal form B by a unitary transformation
zgbcon - estimate the reciprocal of the condition number of a complex
general band matrix A, in either the 1-norm or the infinity-
norm,
zgbequ - compute row and column scalings intended to equilibrate an M-
by-N band matrix A and reduce its condition number
zgbmv - perform one of the matrix-vector operationsy := alpha*A*x +
beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg(
A' )*x + beta*y
zgbrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is banded, and provides error
bounds and backward error estimates for the solution
zgbsv - compute the solution to a complex system of linear equations A
* X = B, where A is a band matrix of order N with KL subdiag‐
onals and KU superdiagonals, and X and B are N-by-NRHS matri‐
ces
zgbsvx - use the LU factorization to compute the solution to a complex
system of linear equations A * X = B, A**T * X = B, or A**H *
X = B,
zgbtf2 - compute an LU factorization of a complex m-by-n band matrix A
using partial pivoting with row interchanges
zgbtrf - compute an LU factorization of a complex m-by-n band matrix A
using partial pivoting with row interchanges
zgbtrs - solve a system of linear equations A * X = B, A**T * X = B,
or A**H * X = B with a general band matrix A using the LU
factorization computed by ZGBTRF
zgebak - form the right or left eigenvectors of a complex general
matrix by backward transformation on the computed eigenvec‐
tors of the balanced matrix output by ZGEBAL
zgebal - balance a general complex matrix A
zgebrd - reduce a general complex M-by-N matrix A to upper or lower
bidiagonal form B by a unitary transformation
zgecon - estimate the reciprocal of the condition number of a general
complex matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by ZGETRF
zgeequ - compute row and column scalings intended to equilibrate an M-
by-N matrix A and reduce its condition number
zgees - compute for an N-by-N complex nonsymmetric matrix A, the eigen‐
values, the Schur form T, and, optionally, the matrix of
Schur vectors Z
zgeesx - compute for an N-by-N complex nonsymmetric matrix A, the ei‐
genvalues, the Schur form T, and, optionally, the matrix of
Schur vectors Z
zgeev - compute for an N-by-N complex nonsymmetric matrix A, the eigen‐
values and, optionally, the left and/or right eigenvectors
zgeevx - compute for an N-by-N complex nonsymmetric matrix A, the ei‐
genvalues and, optionally, the left and/or right eigenvectors
zgegs - routine is deprecated and has been replaced by routine ZGGES
zgegv - routine is deprecated and has been replaced by routine ZGGEV
zgehrd - reduce a complex general matrix A to upper Hessenberg form H
by a unitary similarity transformation
zgelqf - compute an LQ factorization of a complex M-by-N matrix A
zgels - solve overdetermined or underdetermined complex linear systems
involving an M-by-N matrix A, or its conjugate-transpose,
using a QR or LQ factorization of A
zgelsd - compute the minimum-norm solution to a real linear least
squares problem
zgelss - compute the minimum norm solution to a complex linear least
squares problem
zgelsx - routine is deprecated and has been replaced by routine ZGELSY
zgelsy - compute the minimum-norm solution to a complex linear least
squares problem
zgemm - perform one of the matrix-matrix operations C := alpha*op( A
)*op( B ) + beta*C
zgemv - perform one of the matrix-vector operationsy := alpha*A*x +
beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg(
A' )*x + beta*y
zgeqlf - compute a QL factorization of a complex M-by-N matrix A
zgeqp3 - compute a QR factorization with column pivoting of a matrix A
zgeqpf - routine is deprecated and has been replaced by routine ZGEQP3
zgeqrf - compute a QR factorization of a complex M-by-N matrix A
zgerc - perform the rank 1 operation A := alpha*x*conjg( y' ) + A
zgerfs - improve the computed solution to a system of linear equations
and provides error bounds and backward error estimates for
the solution
zgerqf - compute an RQ factorization of a complex M-by-N matrix A
zgeru - perform the rank 1 operation A := alpha*x*y' + A
zgesdd - compute the singular value decomposition (SVD) of a complex M-
by-N matrix A, optionally computing the left and/or right
singular vectors, by using divide-and-conquer method
zgesv - compute the solution to a complex system of linear equationsA *
X = B,
zgesvd - compute the singular value decomposition (SVD) of a complex M-
by-N matrix A, optionally computing the left and/or right
singular vectors
zgesvx - use the LU factorization to compute the solution to a complex
system of linear equations A * X = B,
zgetf2 - compute an LU factorization of a general m-by-n matrix A using
partial pivoting with row interchanges
zgetrf - compute an LU factorization of a general M-by-N matrix A using
partial pivoting with row interchanges
zgetri - compute the inverse of a matrix using the LU factorization
computed by ZGETRF
zgetrs - solve a system of linear equations A * X = B, A**T * X = B,
or A**H * X = B with a general N-by-N matrix A using the LU
factorization computed by ZGETRF
zggbak - form the right or left eigenvectors of a complex generalized
eigenvalue problem A*x = lambda*B*x, by backward transforma‐
tion on the computed eigenvectors of the balanced pair of
matrices output by ZGGBAL
zggbal - balance a pair of general complex matrices (A,B)
zgges - compute for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, the generalized complex
Schur form (S, T), and optionally left and/or right Schur
vectors (VSL and VSR)
zggesx - compute for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, the complex Schur form
(S,T),
zggev - compute for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, and optionally, the left
and/or right generalized eigenvectors
zggevx - compute for a pair of N-by-N complex nonsymmetric matrices
(A,B) the generalized eigenvalues, and optionally, the left
and/or right generalized eigenvectors
zggglm - solve a general Gauss-Markov linear model (GLM) problem
zgghrd - reduce a pair of complex matrices (A,B) to generalized upper
Hessenberg form using unitary transformations, where A is a
general matrix and B is upper triangular
zgglse - solve the linear equality-constrained least squares (LSE)
problem
zggqrf - compute a generalized QR factorization of an N-by-M matrix A
and an N-by-P matrix B.
zggrqf - compute a generalized RQ factorization of an M-by-N matrix A
and a P-by-N matrix B
zggsvd - compute the generalized singular value decomposition (GSVD) of
an M-by-N complex matrix A and P-by-N complex matrix B
zggsvp - compute unitary matrices U, V and Q such that N-K-L K L
U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
zgscon - estimates the reciprocal of the condition number of a general
real matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by SuperLU routine
sgstrf.
zgsequ - computes row and column scalings intended to equilibrate an M-
by-N sparse matrix A and reduce its condition number.
zgsrfs - improves the computed solution to a system of linear equations
and provides error bounds and backward error estimates for
the solution. It is a SuperLU routine.
zgssco - General sparse solver condition number estimate.
zgssda - Deallocate working storage for the general sparse solver.
zgssfa - General sparse solver numeric factorization.
zgssfs - General sparse solver one call interface.
zgssin - Initialize the general sparse solver.
zgssor - General sparse solver ordering and symbolic factorization.
zgssps - Print general sparse solver statics.
zgssrp - Return permutation used by the general sparse solver.
zgsssl - Solve routine for the general sparse solver.
zgssuo - Provide general sparse solvers SPSOLVE and SuperLU a user-
supplied permutation for ordering.
zgssv - solves a system of linear equations A*X=B using the LU factor‐
ization from sgstrf.
zgssvx - solves the system of linear equations A*X=B or A'*X=B, using
the LU factorization from sgstrf(). Error bounds on the solu‐
tion and a condition estimate are also provided.
zgstrf - computes an LU factorization of a general sparse m-by-n matrix
A using partial pivoting with row interchanges.
zgstrs - solves a system of linear equations A*X=B or A'*X=B with A
sparse and B dense, using the LU factorization computed by
sgstrf.
zgtcon - estimate the reciprocal of the condition number of a complex
tridiagonal matrix A using the LU factorization as computed
by ZGTTRF
zgthr - Gathers specified elements from y into x.
zgthrz - Gather and zero.
zgtrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is tridiagonal, and provides
error bounds and backward error estimates for the solution
zgtsv - solve the equation A*X = B,
zgtsvx - use the LU factorization to compute the solution to a complex
system of linear equations A * X = B, A**T * X = B, or A**H *
X = B,
zgttrf - compute an LU factorization of a complex tridiagonal matrix A
using elimination with partial pivoting and row interchanges
zgttrs - solve one of the systems of equations A * X = B, A**T * X =
B, or A**H * X = B,
zhbev - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian band matrix A
zhbevd - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian band matrix A
zhbevx - compute selected eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A
zhbgst - reduce a complex Hermitian-definite banded generalized eigen‐
problem A*x = lambda*B*x to standard form C*y = lambda*y,
zhbgv - compute all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenprob‐
lem, of the form A*x=(lambda)*B*x
zhbgvd - compute all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenprob‐
lem, of the form A*x=(lambda)*B*x
zhbgvx - compute all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenprob‐
lem, of the form A*x=(lambda)*B*x
zhbmv - perform the matrix-vector operationy := alpha*A*x + beta*y
zhbtrd - reduce a complex Hermitian band matrix A to real symmetric
tridiagonal form T by a unitary similarity transformation
zhecon - estimate the reciprocal of the condition number of a complex
Hermitian matrix A using the factorization A = U*D*U**H or A
= L*D*L**H computed by ZHETRF
zheev - compute all eigenvalues and, optionally, eigenvectors of a com‐
plex Hermitian matrix A
zheevd - compute all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A
zheevr - compute selected eigenvalues and, optionally, eigenvectors of
a complex Hermitian tridiagonal matrix T
zheevx - compute selected eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A
zhegs2 - reduce a complex Hermitian-definite generalized eigenproblem
to standard form
zhegst - reduce a complex Hermitian-definite generalized eigenproblem
to standard form
zhegv - compute all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of
the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x
zhegvd - compute all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of
the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x
zhegvx - compute selected eigenvalues, and optionally, eigenvectors of
a complex generalized Hermitian-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
zhemm - perform one of the matrix-matrix operations C := alpha*A*B +
beta*C or C := alpha*B*A + beta*C
zhemv - perform the matrix-vector operationy := alpha*A*x + beta*y
zher - perform the hermitian rank 1 operation A := alpha*x*conjg( x'
) + A
zher2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y'
) + conjg( alpha )*y*conjg( x' ) + A
zher2k - perform one of the Hermitian rank 2k operations C :=
alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C
or C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A +
beta*C
zherfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian indefinite, and pro‐
vides error bounds and backward error estimates for the solu‐
tion
zherk - perform one of the Hermitian rank k operations C :=
alpha*A*conjg( A' ) + beta*C or C := alpha*conjg( A' )*A +
beta*C
zhesv - compute the solution to a complex system of linear equationsA *
X = B,
zhesvx - use the diagonal pivoting factorization to compute the solu‐
tion to a complex system of linear equations A * X = B,
zhetf2 - compute the factorization of a complex Hermitian matrix A
using the Bunch-Kaufman diagonal pivoting method
zhetrd - reduce a complex Hermitian matrix A to real symmetric tridiag‐
onal form T by a unitary similarity transformation
zhetrf - compute the factorization of a complex Hermitian matrix A
using the Bunch-Kaufman diagonal pivoting method
zhetri - compute the inverse of a complex Hermitian indefinite matrix A
using the factorization A = U*D*U**H or A = L*D*L**H computed
by ZHETRF
zhetrs - solve a system of linear equations A*X = B with a complex Her‐
mitian matrix A using the factorization A = U*D*U**H or A =
L*D*L**H computed by ZHETRF
zhgeqz - implement a single-shift version of the QZ method for finding
the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the
equation det( A-w(i) B ) = 0 If JOB='S', then the pair
(A,B) is simultaneously reduced to Schur form (i.e., A and B
are both upper triangular) by applying one unitary tranforma‐
tion (usually called Q) on the left and another (usually
called Z) on the right
zhpcon - estimate the reciprocal of the condition number of a complex
Hermitian packed matrix A using the factorization A =
U*D*U**H or A = L*D*L**H computed by ZHPTRF
zhpev - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix in packed storage
zhpevd - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A in packed storage
zhpevx - compute selected eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A in packed storage
zhpgst - reduce a complex Hermitian-definite generalized eigenproblem
to standard form, using packed storage
zhpgv - compute all the eigenvalues and, optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of
the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x
zhpgvd - compute all the eigenvalues and, optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of
the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x
zhpgvx - compute selected eigenvalues and, optionally, eigenvectors of
a complex generalized Hermitian-definite eigenproblem, of the
form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
zhpmv - perform the matrix-vector operationy := alpha*A*x + beta*y
zhpr - perform the hermitian rank 1 operation A := alpha*x*conjg( x'
) + A
zhpr2 - perform the Hermitian rank 2 operation A := alpha*x*conjg( y'
) + conjg( alpha )*y*conjg( x' ) + A
zhprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian indefinite and
packed, and provides error bounds and backward error esti‐
mates for the solution
zhpsv - compute the solution to a complex system of linear equationsA *
X = B,
zhpsvx - use the diagonal pivoting factorization A = U*D*U**H or A =
L*D*L**H to compute the solution to a complex system of lin‐
ear equations A * X = B, where A is an N-by-N Hermitian
matrix stored in packed format and X and B are N-by-NRHS
matrices
zhptrd - reduce a complex Hermitian matrix A stored in packed form to
real symmetric tridiagonal form T by a unitary similarity
transformation
zhptrf - compute the factorization of a complex Hermitian packed matrix
A using the Bunch-Kaufman diagonal pivoting method
zhptri - compute the inverse of a complex Hermitian indefinite matrix A
in packed storage using the factorization A = U*D*U**H or A =
L*D*L**H computed by ZHPTRF
zhptrs - solve a system of linear equations A*X = B with a complex Her‐
mitian matrix A stored in packed format using the factoriza‐
tion A = U*D*U**H or A = L*D*L**H computed by ZHPTRF
zhsein - use inverse iteration to find specified right and/or left
eigenvectors of a complex upper Hessenberg matrix H
zhseqr - compute the eigenvalues of a complex upper Hessenberg matrix
H, and, optionally, the matrices T and Z from the Schur
decomposition H = Z T Z**H, where T is an upper triangular
matrix (the Schur form), and Z is the unitary matrix of Schur
vectors
zinfinite_norm_error - A utility function of the SuperLU solver that
computes the infinity-norm of an array of vectors that are
approximations to the exact solution vector.
zjadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack)
zjadrp - right permutation of a jagged diagonal matrix
zjadsm - Jagged-diagonal format triangular solve
zlangs - returns the value of the one-norm, or the Frobenius-norm, or
the infinity-norm, or the element with largest absolute value
of a general real matrix A in sparse format.
zlaqgs - a SuperLU function that equilibrates a general sparse M by N
matrix A.
zlarz - applie a complex elementary reflector H to a complex M-by-N
matrix C, from either the left or the right
zlarzb - applie a complex block reflector H or its transpose H**H to a
complex distributed M-by-N C from the left or the right
zlarzt - form the triangular factor T of a complex block reflector H of
order > n, which is defined as a product of k elementary
reflectors
zlatzm - routine is deprecated and has been replaced by routine ZUNMRZ
zpbcon - estimate the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite band matrix
using the Cholesky factorization A = U**H*U or A = L*L**H
computed by ZPBTRF
zpbequ - compute row and column scalings intended to equilibrate a Her‐
mitian positive definite band matrix A and reduce its condi‐
tion number (with respect to the two-norm)
zpbrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite
and banded, and provides error bounds and backward error
estimates for the solution
zpbstf - compute a split Cholesky factorization of a complex Hermitian
positive definite band matrix A
zpbsv - compute the solution to a complex system of linear equationsA *
X = B,
zpbsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
zpbtf2 - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite band matrix A
zpbtrf - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite band matrix A
zpbtrs - solve a system of linear equations A*X = B with a Hermitian
positive definite band matrix A using the Cholesky factoriza‐
tion A = U**H*U or A = L*L**H computed by ZPBTRF
zpocon - estimate the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite matrix using
the Cholesky factorization A = U**H*U or A = L*L**H computed
by ZPOTRF
zpoequ - compute row and column scalings intended to equilibrate a Her‐
mitian positive definite matrix A and reduce its condition
number (with respect to the two-norm)
zporfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite,
zposv - compute the solution to a complex system of linear equationsA *
X = B,
zposvx - use the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
zpotf2 - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite matrix A
zpotrf - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite matrix A
zpotri - compute the inverse of a complex Hermitian positive definite
matrix A using the Cholesky factorization A = U**H*U or A =
L*L**H computed by ZPOTRF
zpotrs - solve a system of linear equations A*X = B with a Hermitian
positive definite matrix A using the Cholesky factorization A
= U**H*U or A = L*L**H computed by ZPOTRF
zppcon - estimate the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite packed
matrix using the Cholesky factorization A = U**H*U or A =
L*L**H computed by ZPPTRF
zppequ - compute row and column scalings intended to equilibrate a Her‐
mitian positive definite matrix A in packed storage and
reduce its condition number (with respect to the two-norm)
zpprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite
and packed, and provides error bounds and backward error
estimates for the solution
zppsv - compute the solution to a complex system of linear equationsA *
X = B,
zppsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
zpptrf - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite matrix A stored in packed format
zpptri - compute the inverse of a complex Hermitian positive definite
matrix A using the Cholesky factorization A = U**H*U or A =
L*L**H computed by ZPPTRF
zpptrs - solve a system of linear equations A*X = B with a Hermitian
positive definite matrix A in packed storage using the
Cholesky factorization A = U**H*U or A = L*L**H computed by
ZPPTRF
zptcon - compute the reciprocal of the condition number (in the 1-norm)
of a complex Hermitian positive definite tridiagonal matrix
using the factorization A = L*D*L**H or A = U**H*D*U computed
by ZPTTRF
zpteqr - compute all eigenvalues and, optionally, eigenvectors of a
symmetric positive definite tridiagonal matrix by first fac‐
toring the matrix using SPTTRF and then calling CBDSQR to
compute the singular values of the bidiagonal factor
zptrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite
and tridiagonal, and provides error bounds and backward error
estimates for the solution
zptsv - compute the solution to a complex system of linear equations
A*X = B, where A is an N-by-N Hermitian positive definite
tridiagonal matrix, and X and B are N-by-NRHS matrices.
zptsvx - use the factorization A = L*D*L**H to compute the solution to
a complex system of linear equations A*X = B, where A is an
N-by-N Hermitian positive definite tridiagonal matrix and X
and B are N-by-NRHS matrices
zpttrf - compute the L*D*L' factorization of a complex Hermitian posi‐
tive definite tridiagonal matrix A
zpttrs - solve a tridiagonal system of the form A * X = B using the
factorization A = U'*D*U or A = L*D*L' computed by ZPTTRF
zptts2 - solve a tridiagonal system of the form A * X = B using the
factorization A = U'*D*U or A = L*D*L' computed by ZPTTRF
zrot - apply a plane rotation, where the cos (C) is real and the sin
(S) is complex, and the vectors X and Y are complex
zrotg - Construct a Given's plane rotation
zscal - Compute y := alpha * y
zsctr - Scatters elements from x into y.
zskymm - Skyline format matrix-matrix multiply
zskysm - Skyline format triangular solve
zspcon - estimate the reciprocal of the condition number (in the
1-norm) of a complex symmetric packed matrix A using the fac‐
torization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
zsprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite and
packed, and provides error bounds and backward error esti‐
mates for the solution
zspsv - compute the solution to a complex system of linear equationsA *
X = B,
zspsvx - use the diagonal pivoting factorization A = U*D*U**T or A =
L*D*L**T to compute the solution to a complex system of lin‐
ear equations A * X = B, where A is an N-by-N symmetric
matrix stored in packed format and X and B are N-by-NRHS
matrices
zsptrf - compute the factorization of a complex symmetric matrix A
stored in packed format using the Bunch-Kaufman diagonal piv‐
oting method
zsptri - compute the inverse of a complex symmetric indefinite matrix A
in packed storage using the factorization A = U*D*U**T or A =
L*D*L**T computed by ZSPTRF
zsptrs - solve a system of linear equations A*X = B with a complex sym‐
metric matrix A stored in packed format using the factoriza‐
tion A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
zstedc - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer
method
zstegr - Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is
a relatively robust representation
zstein - compute the eigenvectors of a real symmetric tridiagonal
matrix T corresponding to specified eigenvalues, using
inverse iteration
zstemr - computes selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix T.
zsteqr - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR
method
zstsv - compute the solution to a complex system of linear equations A
* X = B where A is a symmetric tridiagonal matrix
zsttrf - compute the factorization of a complex symmetric tridiagonal
matrix A using the Bunch-Kaufman diagonal pivoting method
zsttrs - computes the solution to a complex system of linear equations
A * X = B
zswap - Exchange vectors x and y.
zsycon - estimate the reciprocal of the condition number (in the
1-norm) of a complex symmetric matrix A using the factoriza‐
tion A = U*D*U**T or A = L*D*L**T computed by ZSYTRF
zsymm - perform one of the matrix-matrix operationsC := alpha*A*B +
beta*C or C := alpha*B*A + beta*C
zsyr2k - perform one of the symmetric rank 2k operations C :=
alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B +
alpha*B'*A + beta*C
zsyrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite, and pro‐
vides error bounds and backward error estimates for the solu‐
tion
zsyrk - perform one of the symmetric rank k operations C :=
alpha*A*A' + beta*C or C := alpha*A'*A + beta*C
zsysv - compute the solution to a complex system of linear equationsA *
X = B,
zsysvx - use the diagonal pivoting factorization to compute the solu‐
tion to a complex system of linear equations A * X = B,
zsytf2 - compute the factorization of a complex symmetric matrix A
using the Bunch-Kaufman diagonal pivoting method
zsytrf - compute the factorization of a complex symmetric matrix A
using the Bunch-Kaufman diagonal pivoting method
zsytri - compute the inverse of a complex symmetric indefinite matrix A
using the factorization A = U*D*U**T or A = L*D*L**T computed
by ZSYTRF
zsytrs - solve a system of linear equations A*X = B with a complex sym‐
metric matrix A using the factorization A = U*D*U**T or A =
L*D*L**T computed by ZSYTRF
ztbcon - estimate the reciprocal of the condition number of a triangu‐
lar band matrix A, in either the 1-norm or the infinity-norm
ztbmv - perform one of the matrix-vector operationsx := A*x, or x :=
A'*x, or x := conjg( A' )*x
ztbrfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
band coefficient matrix
ztbsv - solve one of the systems of equations A*x = b, or A'*x = b,
or conjg( A' )*x = b
ztbtrs - solve a triangular system of the form A * X = B, A**T * X =
B, or A**H * X = B,
ztgevc - compute some or all of the right and/or left generalized
eigenvectors of a pair of complex upper triangular matrices
(A,B) that was obtained from from the generalized Schur fac‐
torization of an original pair of complex nonsymmetric matri‐
ces. A and B are upper triangular matrices and B must have
real diagonal elements.
ztgexc - reorder the generalized Schur decomposition of a complex
matrix pair (A,B), using an unitary equivalence transforma‐
tion (A, B) := Q * (A, B) * Z', so that the diagonal block of
(A, B) with row index IFST is moved to row ILST
ztgsen - reorder the generalized Schur decomposition of a complex
matrix pair (A, B) (in terms of an unitary equivalence trans-
formation Q' * (A, B) * Z), so that a selected cluster of ei‐
genvalues appears in the leading diagonal blocks of the pair
(A,B)
ztgsja - compute the generalized singular value decomposition (GSVD) of
two complex upper triangular (or trapezoidal) matrices A and
B
ztgsna - estimate reciprocal condition numbers for specified eigenval‐
ues and/or eigenvectors of a matrix pair (A, B)
ztgsyl - solve the generalized Sylvester equation
ztpcon - estimate the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-
norm
ztpmv - perform one of the matrix-vector operationsx := A*x, or x :=
A'*x, or x := conjg( A' )*x
ztprfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
packed coefficient matrix
ztpsv - solve one of the systems of equations A*x = b, or A'*x = b,
or conjg( A' )*x = b
ztptri - compute the inverse of a complex upper or lower triangular
matrix A stored in packed format
ztptrs - solve a triangular system of the form A * X = B, A**T * X =
B, or A**H * X = B,
ztrans - transpose and scale source matrix
ztrcon - estimate the reciprocal of the condition number of a triangu‐
lar matrix A, in either the 1-norm or the infinity-norm
ztrevc - compute some or all of the right and/or left eigenvectors of a
complex upper triangular matrix T
ztrexc - reorder the Schur factorization of a complex matrix A =
Q*T*Q**H, so that the diagonal element of T with row index
IFST is moved to row ILST
ztrmm - perform one of the matrix-matrix operationsB := alpha*op( A
)*B, or B := alpha*B*op( A ) where alpha is a scalar, B is
an m by n matrix, A is a unit, or non-unit, upper or lower
triangular matrix and op( A ) is one of op( A ) = A or op(
A ) = A' or op( A ) = conjg( A' )
ztrmv - perform one of the matrix-vector operationsx := A*x, or x :=
A'*x, or x := conjg( A' )*x
ztrrfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
coefficient matrix
ztrsen - reorder the Schur factorization of a complex matrix A =
Q*T*Q**H, so that a selected cluster of eigenvalues appears
in the leading positions on the diagonal of the upper trian‐
gular matrix T, and the leading columns of Q form an
orthonormal basis of the corresponding right invariant sub‐
space
ztrsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op(
A ) = alpha*B
ztrsna - estimate reciprocal condition numbers for specified eigenval‐
ues and/or right eigenvectors of a complex upper triangular
matrix T (or of any matrix Q*T*Q**H with Q unitary)
ztrsv - solve one of the systems of equations A*x = b, or A'*x = b,
or conjg( A' )*x = b
ztrsyl - solve the complex Sylvester matrix equation
ztrti2 - compute the inverse of a complex upper or lower triangular
matrix
ztrtri - compute the inverse of a complex upper or lower triangular
matrix A
ztrtrs - solve a triangular system of the form A * X = B, A**T * X =
B, or A**H * X = B,
ztzrqf - routine is deprecated and has been replaced by routine ZTZRZF
ztzrzf - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A
to upper triangular form by means of unitary transformations
zung2l - generate an m by n complex matrix Q with orthonormal columns,
zung2r - generate an m by n complex matrix Q with orthonormal columns,
zungbr - generate one of the complex unitary matrices Q or P**H deter‐
mined by ZGEBRD when reducing a complex matrix A to bidiago‐
nal form
zunghr - generate a complex unitary matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as
returned by ZGEHRD
zungl2 - generate an m-by-n complex matrix Q with orthonormal rows,
zunglq - generate an M-by-N complex matrix Q with orthonormal rows,
zungql - generate an M-by-N complex matrix Q with orthonormal columns,
zungqr - generate an M-by-N complex matrix Q with orthonormal columns,
zungr2 - generate an m by n complex matrix Q with orthonormal rows,
zungrq - generate an M-by-N complex matrix Q with orthonormal rows,
zungtr - generate a complex unitary matrix Q which is defined as the
product of n-1 elementary reflectors of order N, as returned
by CHETRD
zunmbr - overwrites the general complex M-by-N matrix C Q*C or Q**H*C
or C*Q**H or C*Q or P*C or P**H*C or C*P or C*P**H.
zunmhr - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
zunml2 - overwrite the general complex m-by-n matrix C with Q * C if
SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS
= 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q'
if SIDE = 'R' and TRANS = 'C',
zunmlq - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
zunmql - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
zunmqr - overwrite the general complex M-by-N matrix C with SIDE =
'L' SIDE = 'R' TRANS = 'N'
zunmr2 - overwrite the general complex m-by-n matrix C with Q * C if
SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS
= 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q'
if SIDE = 'R' and TRANS = 'C',
zunmrq - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
zunmrz - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
zunmtr - overwrite the general complex M-by-N matrix C with Q*C or
Q**H*C or C*Q**H or C*Q.
zupgtr - generate a complex unitary matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as
returned by CHPTRD using packed storage
zupmtr - overwrite the general complex M-by-N matrix C with SIDE =
'L' SIDE = 'R' TRANS = 'N'
zvbrmm - variable block sparse row format matrix-matrix multiply
zvbrsm - variable block sparse row format triangular solve
zvmul - compute the scaled product of complex vectors
6 Mar 2009 intro(3P)
