cdotc - compute the dot product of two vectors
x and conjg(y).
cdotci - compute the dot product of two vectors
x and y
cdotu - compute the dot product of two vectors
x and y.
cdotui - compute the dot product of two vectors
x and y
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 followed 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 xFFT operations are unnormalized, so a call of
xFFT3F followed by a call of xFFT3B will multiply the input sequence by
M*N*K.
cfft3f - compute the Fourier coefficients of
a periodic sequence. The xFFT operations are unnormalized, so a call of
xFFT3F followed by a call of xFFT3B will multiply the input sequence by
M*N*K.
cfft3i - initialize the array WSAVE, which is
used in both xFFT3F and xFFT3B.
cfftb - compute a periodic sequence from its Fourier
coefficients. The xFFT operations are unnormalized, so a call of xFFTF
followed by a call of xFFTB will multiply the input sequence by N.
cfftf - compute the Fourier coefficients of a
periodic sequence. The xFFT operations are unnormalized, so a call of xFFTF
followed by a call of xFFTB will multiply the input sequence by N.
cffti - initialize the array WSAVE, which is used
in both xFFTF and xFFTB.
cfftopt - compute the length of the closest
fast FFT
cgbbrd - reduce a complex general m-by-n band
matrix A to real upper bidiagonal form B by a unitary transformation
cgbco - compute the LU factorization and condition
number of a general matrix A in banded storage. If the condition number
is not needed then xGBFA is slightly faster. It is typical to follow a
call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute
the determinant of A.
cgbcon - estimate the reciprocal of the condition
number of a complex general band matrix A, in either the 1-norm or the
infinity-norm,
cgbdi - compute the determinant of a general matrix
A in banded storage, which has been LU-factored by CGBCO or CGBFA.
cgbequ - compute row and column scalings intended
to equilibrate an M-by-N band matrix A and reduce its condition number
cgbfa - compute the LU factorization of a matrix
A in banded storage. It is typical to follow a call to CGBFA with a call
to CGBSL to solve Ax = b or to CGBDI to compute the determinant of A.
cgbmv - perform one of the matrix-vector operations
y := 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
cgbsl - solve the linear system Ax = b for a matrix
A in banded storage, which has been LU-factored by CGBCO or CGBFA, and
vectors b and x.
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 subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
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
eigenvectors of the balanced matrix output by CGEBAL
cgebrd - reduce a general complex M-by-N matrix
A to upper or lower bidiagonal form B by a unitary transformation
cgeco - compute the LU factorization and estimate
the condition number of a general matrix A. If the condition number is
not needed then CGEFA is slightly faster. It is typical to follow a call
to CGECO with a call to CGESL to solve Ax = b or to CGEDI to compute the
determinant and inverse of A.
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
cgedi - compute the determinant and inverse of
a general matrix A, which has been LU-factored by CGECO or CGEFA.
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 eigenvalues, the Schur form T, and, optionally, the matrix
of Schur vectors Z
cgeesx - compute for an N-by-N complex nonsymmetric
matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix
of Schur vectors Z
cgeev - compute for an N-by-N complex nonsymmetric
matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
cgeevx - compute for an N-by-N complex nonsymmetric
matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
cgefa - compute the LU factorization of a general
matrix A. It is typical to follow a call to CGEFA with a call to CGESL
to solve Ax = b or to CGEDI to compute the determinant of A.
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 operations
y := 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
cgesl - solve the linear system Ax = b for a general
matrix A, which has been LU- factored by CGECO or CGEFA, and vectors b
and x.
cgesv - compute the solution to a complex system
of linear equations A * 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
transformation 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
cgtcon - estimate the reciprocal of the condition
number of a complex tridiagonal matrix A using the LU factorization as
computed by CGTTRF
cgthrz - gathers specified elements from y into
x and sets gathered elements in y to 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
cgtsl - solve the linear system Ax = b for a tridiagonal
matrix A and vectors b and x.
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 eigenproblem 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 eigenproblem,
of the form A*x=(lambda)*B*x
chbgvd - compute all the eigenvalues, and optionally,
the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem,
of the form A*x=(lambda)*B*x
chbgvx - compute all the eigenvalues, and optionally,
the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem,
of the form A*x=(lambda)*B*x
chbmv - perform the matrix-vector operation y
:= 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 complex 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 operation y
:= 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 provides error bounds and backward error estimates for the solution
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 equations A * X = B,
chesvx - use the diagonal pivoting factorization
to compute the solution 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 tridiagonal 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 Hermitian 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 tranformation (usually called Q) on the left and
another (usually called Z) on the right
chico - compute the UDU factorization and condition
number of a Hermitian matrix A. If the condition number is not needed then
xHIFA is slightly faster. It is typical to follow a call to xHICO with
a call to xHISL to solve Ax = b or to xHIDI to compute the determinant,
inverse, and inertia of A.
chidi - compute the determinant, inertia, and
inverse of a Hermitian matrix A, which has been UDU-factored by CHICO or
CHIFA.
chifa - compute the UDU factorization of a Hermitian
matrix A. It is typical to follow a call to CHIFA with a call to CHISL
to solve Ax = b or to CHIDI to compute the determinant, inverse, and inertia
of A.
chisl - solve the linear system Ax = b for a Hermitian
matrix A, which has been UDU-factored by CHICO or CHIFA, and vectors b
and x.
chpco - compute the UDU factorization and condition
number of a Hermitian matrix A in packed storage. If the condition number
is not needed then xHPFA is slightly faster. It is typical to follow a
call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute
the determinant, inverse, and inertia of A.
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
chpdi - compute the determinant, inertia, and
inverse of a Hermitian matrix A in packed storage, which has been UDU-factored
by CHPCO or CHPFA.
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
chpfa - compute the UDU factorization of a Hermitian
matrix A in packed storage. It is typical to follow a call to CHPFA with
a call to CHPSL to solve Ax = b or to CHPDI to compute the determinant,
inverse, and inertia of A.
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 operation y
:= 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 estimates for
the solution
chpsl - solve the linear system Ax = b for a Hermitian
matrix A in packed storage, which has been UDU-factored by CHPCO or CHPFA,
and vectors b and x.
chpsv - compute the solution to a complex system
of linear equations A * 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 linear 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 Hermitian matrix A stored in packed format using the
factorization 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
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 representation with only 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.
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.
cpbco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A in banded storage. If
the condition number is not needed then xPBFA is slightly faster. It is
typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b
or to xPBDI to compute the determinant of A.
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
cpbdi - compute the determinant of a symmetric
positive definite matrix A in banded storage, which has been Cholesky-factored
by CPBCO or CPBFA.
cpbequ - compute row and column scalings intended
to equilibrate a Hermitian positive definite band matrix A and reduce its
condition number (with respect to the two-norm)
cpbfa - compute a Cholesky factorization of a
symmetric positive definite matrix A in banded storage. It is typical to
follow a call to CPBFA with a call to CPBSL to solve Ax = b or to CPBDI
to compute the determinant of A.
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
cpbsl - section solve the linear system Ax = b
for a symmetric positive definite matrix A in banded storage, which has
been Cholesky-factored by CPBCO or CPBFA, and vectors b and x.
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 equations A * 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 positive definite band matrix A
cpbtrf - compute the Cholesky factorization of
a complex Hermitian positive 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
factorization A = U**H*U or A = L*L**H computed by CPBTRF
cpoco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A. If the condition number
is not needed then xPOFA is slightly faster. It is typical to follow a
call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute
the determinant and inverse of A.
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
cpodi - compute the determinant and inverse of
a symmetric positive definite matrix A, which has been Cholesky-factored
by CPOCO, CPOFA, or CQRDC.
cpoequ - compute row and column scalings intended
to equilibrate a Hermitian positive definite matrix A and reduce its condition
number (with respect to the two-norm)
cpofa - compute a Cholesky factorization of a
symmetric positive definite matrix A. It is typical to follow a call to
CPOFA with a call to CPOSL to solve Ax = b or to CPODI to compute the determinant
and inverse of A.
cporfs - improve the computed solution to a system
of linear equations when the coefficient matrix is Hermitian positive definite,
cposl - solve the linear system Ax = b for a symmetric
positive definite matrix A, which has been Cholesky-factored by CPOCO or
CPOFA, and vectors b and x.
cposv - compute the solution to a complex system
of linear equations A * 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 positive definite matrix A
cpotrf - compute the Cholesky factorization of
a complex Hermitian positive 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
cppco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A in packed storage. If
the condition number is not needed then CPPFA is slightly faster. It is
typical to follow a call to CPPCO with a call to CPPSL to solve Ax = b
or to CPPDI to compute the determinant and inverse of A.
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
cppdi - compute the determinant and inverse of
a symmetric positive definite matrix A in packed storage, which has been
Cholesky-factored by CPPCO or CPPFA.
cppequ - compute row and column scalings intended
to equilibrate a Hermitian positive definite matrix A in packed storage
and reduce its condition number (with respect to the two-norm)
cppfa - compute a Cholesky factorization of a
symmetric positive definite matrix A in packed storage. It is typical to
follow a call to CPPFA with a call to CPPSL to solve Ax = b or to CPPDI
to compute the determinant and inverse of A.
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
cppsl - solve the linear system Ax = b for a symmetric
positive definite matrix A in packed storage, which has been Cholesky-factored
by CPPCO or CPPFA, and vectors b and x.
cppsv - compute the solution to a complex system
of linear equations A * 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 positive 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
factoring 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
cptsl - solve the linear system Ax = b for a symmetric
positive definite tridiagonal matrix A and vectors b and x.
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 positive 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
cqrdc - compute the QR factorization of a general
matrix A. It is typical to follow a call to CQRDC with a call to CQRSL
to solve Ax = b or to CPODI to compute the determinant of A.
cqrsl - solve the linear system Ax = b for a general
matrix A, which has been QR- factored by CQRDC, and vectors b and x.
crot - CROT - apply a plane rotation, where the
cos (C) is real and the sin (S) is complex, and the vectors CX and CY are
complex
csico - compute the UDU factorization and condition
number of a symmetric matrix A. If the condition number is not needed then
CSIFA is slightly faster. It is typical to follow a call to CSICO with
a call to CSISL to solve Ax = b or to CSIDI to compute the determinant,
inverse, and inertia of A.
csidi - compute the determinant, inertia, and
inverse of a symmetric matrix A, which has been UDU-factored by CSICO or
CSIFA.
csifa - compute the UDU factorization of a symmetric
matrix A. It is typical to follow a call to CSIFA with a call to CSISL
to solve Ax = b or to CSIDI to compute the determinant, inverse, and inertia
of A.
csisl - solve the linear system Ax = b for a symmetric
matrix A, which has been UDU-factored by CSICO or CSIFA, and vectors b
and x.
cspco - compute the UDU factorization and condition
number of a symmetric matrix A in packed storage. If the condition number
is not needed then CSPFA is slightly faster. It is typical to follow a
call to CSPCO with a call to CSPSL to solve Ax = b or to CSPDI to compute
the determinant, inverse, and inertia of A.
cspcon - estimate the reciprocal of the condition
number (in the 1-norm) of a complex symmetric packed matrix A using the
factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF
cspdi - compute the determinant, inertia, and
inverse of a symmetric matrix A in packed storage, which has been UDU-factored
by CSPCO or CSPFA.
cspfa - compute the UDU factorization of a symmetric
matrix A in packed storage. It is typical to follow a call to CSPFA with
a call to CSPSL to solve Ax = b or to CSPDI to compute the determinant,
inverse, and inertia of A.
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 estimates for
the solution
cspsl - solve the linear system Ax = b for a symmetric
matrix A in packed storage, which has been UDU-factored by CSPCO or CSPFA,
and vectors b and x.
cspsv - compute the solution to a complex system
of linear equations A * 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 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
csptrf - compute the factorization of a complex
symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal
pivoting 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 symmetric matrix A stored in packed format using the
factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF
csycon - estimate the reciprocal of the condition
number (in the 1-norm) of a complex symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by CSYTRF
csymm - perform one of the matrix-matrix operations
C := 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 provides error bounds and backward error estimates for the solution
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 equations A * X = B,
csysvx - use the diagonal pivoting factorization
to compute the solution 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 symmetric 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 triangular band matrix A, in either the 1-norm or the infinity-norm
ctbmv - perform one of the matrix-vector operations
x := 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)
ctgexc - reorder the generalized Schur decomposition
of a complex matrix pair (A,B), using an unitary equivalence transformation
(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 eigenvalues 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 eigenvalues and/or eigenvectors of a matrix pair (A, B)
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 operations
x := 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,
ctrco - estimate the condition number of a triangular
matrix A. It is typical to follow a call to xTRCO with a call to xTRSL
to solve Ax = b or to xTRDI to compute the determinant and inverse of A.
ctrcon - estimate the reciprocal of the condition
number of a triangular matrix A, in either the 1-norm or the infinity-norm
ctrdi - compute the determinant and inverse of
a triangular matrix A.
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 operations
B := 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 operations
x := 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 triangular
matrix T, and the leading columns of Q form an orthonormal basis of the
corresponding right invariant subspace
ctrsl - solve the linear system Ax = b for a triangular
matrix A and vectors b and x.
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 eigenvalues 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 determined by CGEBRD when reducing a complex matrix
A to bidiagonal 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
cunm2r - 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',
cunmbr - VECT = 'Q', CUNMBR overwrites the general
complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmhr - overwrite the general complex M-by-N
matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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 SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmql - overwrite the general complex M-by-N
matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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 SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmrz - overwrite the general complex M-by-N
matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmtr - overwrite the general complex M-by-N
matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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'
cvmul - compute the scaled product of complex
vectors
dasum - Return the sum of the absolute values
of a vector x.
dcosqb - synthesize a Fourier sequence from its
representation in terms of a cosine series with odd wave numbers. The DCOSQ
operations are unnormalized inverses of themselves, so a call to DCOSQF
followed by a call to DCOSQB will multiply the input sequence by 4 * N.
dcosqf - compute the Fourier coefficients in
a cosine series representation with only odd wave numbers. The DCOSQ operations
are unnormalized inverses of themselves, so a call to DCOSQF followed by
a call to DCOSQB will multiply the input sequence by 4 * N.
dcosqi - initialize the array WSAVE, which is
used in both DCOSQF and DCOSQB.
dcost - compute the discrete Fourier cosine transform
of an even sequence. The DDDCOST 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 DCOST.
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
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 dot product of two vectors
x and y
ddoti - compute the dot product of two vectors
x and y
dfft2b - 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.
dfft2f - compute the Fourier coefficients of
a periodic sequence. The RFFT operations are unnormalized, so a call of
RFFT2F followed by a call of RFFT2B 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 RFFT operations are unnormalized, so a call of
RFFT3F followed by a call of RFFT3B will multiply the input sequence by
M*N*K.
dfft3f - 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.
dfft3i - initialize the array WSAVE, which is
used in both RFFT3F and RFFT3B.
dfftb - compute a periodic sequence from its Fourier
coefficients. The RFFT 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 RFFT 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
dgbbrd - reduce a real general m-by-n band matrix
A to upper bidiagonal form B by an orthogonal transformation
dgbco - compute the LU factorization and condition
number of a general matrix A in banded storage. If the condition number
is not needed then DGBFA is slightly faster. It is typical to follow a
call to DGBCO with a call to DGBSL to solve Ax = b or to DGBDI to compute
the determinant of A.
dgbcon - estimate the reciprocal of the condition
number of a real general band matrix A, in either the 1-norm or the infinity-norm,
dgbdi - compute the determinant of a general matrix
A in banded storage, which has been LU-factored by DGBCO or DGBFA.
dgbequ - compute row and column scalings intended
to equilibrate an M-by-N band matrix A and reduce its condition number
dgbfa - compute the LU factorization of a matrix
A in banded storage. It is typical to follow a call to DGBFA with a call
to DGBSL to solve Ax = b or to DGBDI to compute the determinant of A.
dgbmv - perform one of the matrix-vector operations
y := 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
dgbsl - solve the linear system Ax = b for a matrix
A in banded storage, which has been LU-factored by DGBCO or DGBFA, and
vectors b and x.
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
computed 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
dgebrd - reduce a general real M-by-N matrix
A to upper or lower bidiagonal form B by an orthogonal transformation
dgeco - compute the LU factorization and estimate
the condition number of a general matrix A. If the condition number is
not needed then DGEFA is slightly faster. It is typical to follow a call
to DGECO with a call to DGESL to solve Ax = b or to DGEDI to compute the
determinant and inverse of A.
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
dgedi - compute the determinant and inverse of
a general matrix A, which has been LU-factored by DGECO or DGEFA.
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 eigenvalues, 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 eigenvalues, 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 eigenvalues and, optionally, the left and/or right eigenvectors
dgeevx - compute for an N-by-N real nonsymmetric
matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
dgefa - compute the LU factorization of a general
matrix A. It is typical to follow a call to DGEFA with a call to DGESL
to solve Ax = b or to DGEDI to compute the determinant of A.
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 operations
C := alpha*op( A )*op( B ) + beta*C
dgemv - perform one of the matrix-vector operations
y := 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 SGEQP3
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
dgesl - solve the linear system Ax = b for a general
matrix A, which has been LU- factored by DGECO or DGEFA, and vectors b
and x.
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
singular 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 eigenvalue 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 Hessenberg 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 L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
dgthrz - gathers specified elements from y into
x and sets gathered elements in y to zero
dgthrz - gathers specified elements from y into
x and sets gathered elements in y to 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
dgtsl - solve the linear system Ax = b for a tridiagonal
matrix A and vectors b and x.
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
decomposition 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
dlagtf - factorize the matrix (T - lambda*I),
where T is an n by n tridiagonal matrix and lambda is a scalar, as T -
lambda*I = PLU,
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
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
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 determined 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 - VECT = 'Q', DORMBR overwrites the general
real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormhr - overwrite the general real M-by-N matrix
C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormlq - overwrite the general real M-by-N matrix
C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormql - overwrite the general real M-by-N matrix
C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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 SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormrz - overwrite the general real M-by-N matrix
C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormtr - overwrite the general real M-by-N matrix
C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dpbco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A in banded storage. If
the condition number is not needed then DPBFA is slightly faster. It is
typical to follow a call to DPBCO with a call to DPBSL to solve Ax = b
or to DPBDI to compute the determinant of A.
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
dpbdi - compute the determinant of a symmetric
positive definite matrix A in banded storage, which has been Cholesky-factored
by DPBCO or DPBFA.
dpbequ - compute row and column scalings intended
to equilibrate a symmetric positive definite band matrix A and reduce its
condition number (with respect to the two-norm)
dpbfa - compute a Cholesky factorization of a
symmetric positive definite matrix A in banded storage. It is typical to
follow a call to DPBFA with a call to DPBSL to solve Ax = b or to DPBDI
to compute the determinant of A.
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
dpbsl - section solve the linear system Ax = b
for a symmetric positive definite matrix A in banded storage, which has
been Cholesky-factored by DPBCO or DPBFA, and vectors b and x.
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 equations
A * X = B,
dpbtf2 - compute the Cholesky factorization of
a real symmetric positive definite band matrix A
dpbtrf - compute the Cholesky factorization of
a real symmetric positive 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
factorization A = U**T*U or A = L*L**T computed by DPBTRF
dpoco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A. If the condition number
is not needed then DPOFA is slightly faster. It is typical to follow a
call to DPOCO with a call to DPOSL to solve Ax = b or to DPODI to compute
the determinant and inverse of A.
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
dpodi - compute the determinant and inverse of
a symmetric positive definite matrix A, which has been Cholesky-factored
by DPOCO, DPOFA, or DQRDC.
dpoequ - compute row and column scalings intended
to equilibrate a symmetric positive definite matrix A and reduce its condition
number (with respect to the two-norm)
dpofa - compute a Cholesky factorization of a
symmetric positive definite matrix A. It is typical to follow a call to
DPOFA with a call to DPOSL to solve Ax = b or to DPODI to compute the determinant
and inverse of A.
dporfs - improve the computed solution to a system
of linear equations when the coefficient matrix is symmetric positive definite,
dposl - solve the linear system Ax = b for a symmetric
positive definite matrix A, which has been Cholesky-factored by DPOCO or
DPOFA, and vectors b and x.
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 equations
A * X = B,
dpotf2 - compute the Cholesky factorization of
a real symmetric positive definite matrix A
dpotrf - compute the Cholesky factorization of
a real symmetric positive 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
dppco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A in packed storage. If
the condition number is not needed then DPPFA is slightly faster. It is
typical to follow a call to DPPCO with a call to DPPSL to solve Ax = b
or to DPPDI to compute the determinant and inverse of A.
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
dppdi - compute the determinant and inverse of
a symmetric positive definite matrix A in packed storage, which has been
Cholesky-factored by DPPCO or DPPFA.
dppequ - compute row and column scalings intended
to equilibrate a symmetric positive definite matrix A in packed storage
and reduce its condition number (with respect to the two-norm)
dppfa - compute a Cholesky factorization of a
symmetric positive definite matrix A in packed storage. It is typical to
follow a call to DPPFA with a call to DPPSL to solve Ax = b or to DPPDI
to compute the determinant and inverse of A.
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
dppsl - solve the linear system Ax = b for a symmetric
positive definite matrix A in packed storage, which has been Cholesky-factored
by DPPCO or DPPFA, and vectors b and x.
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 equations
A * X = B,
dpptrf - compute the Cholesky factorization of
a real symmetric positive 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
factoring 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
dptsl - solve the linear system Ax = b for a symmetric
positive definite tridiagonal matrix A and vectors b and x.
dptsv - 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.
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 double precision vectors x and y.
dqdoti - compute a constant plus the extended
precision dot product of two double precision vectors x and y.
dqrdc - compute the QR factorization of a general
matrix A. It is typical to follow a call to DQRDC with a call to DQRSL
to solve Ax = b or to DPODI to compute the determinant of A.
dqrsl - solve the linear system Ax = b for a general
matrix A, which has been QR- factored by DQRDC, and vectors b and x.
drot - Apply a Given's rotation constructed by
DROTG.
drotm - Apply a Gentleman's modified Given's rotation
constructed by DROTMG.
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 eigenproblem 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 operation y
:= alpha*A*x + beta*y
dsbtrd - reduce a real symmetric band matrix
A to symmetric tridiagonal form T by an orthogonal similarity transformation
dsdot - compute the double precision dot product
of two single precision vectors x and y.
dsecnd - returns the user time for a process
in seconds
dsico - compute the UDU factorization and condition
number of a symmetric matrix A. If the condition number is not needed then
DSIFA is slightly faster. It is typical to follow a call to DSICO with
a call to DSISL to solve Ax = b or to DSIDI to compute the determinant,
inverse, and inertia of A.
dsidi - compute the determinant, inertia, and
inverse of a symmetric matrix A, which has been UDU-factored by DSICO or
DSIFA.
dsifa - compute the UDU factorization of a symmetric
matrix A. It is typical to follow a call to DSIFA with a call to DSISL
to solve Ax = b or to DSIDI to compute the determinant, inverse, and inertia
of A.
dsinqb - synthesize a Fourier sequence from its
representation in terms of a sine series with odd wave numbers. The DSINQ
operations are unnormalized inverses of themselves, so a call to DSINQF
followed by a call to DSINQB will multiply the input sequence by 4 * N.
dsinqf - compute the Fourier coefficients in
a sine series representation with only odd wave numbers. The DSINQ operations
are unnormalized inverses of themselves, so a call to DSINQF followed by
a call to DSINQB will multiply the input sequence by 4 * N.
dsinqi - initialize the array xWSAVE, which is
used in both DSINQF and DSINQB.
dsint - compute the discrete Fourier sine transform
of an odd sequence. The DDDSINT transforms are unnormalized inverses of
themselves, so a call of SINT followed by another call of SINT will multiply
the input sequence by 2 * (N+1).
dsinti - initialize the array WSAVE, which is
used in subroutine DSINT.
dsisl - solve the linear system Ax = b for a symmetric
matrix A, which has been UDU-factored by DSICO or DSIFA, and vectors b
and x.
dspco - compute the UDU factorization and condition
number of a symmetric matrix A in packed storage. If the condition number
is not needed then DSPFA is slightly faster. It is typical to follow a
call to DSPCO with a call to DSPSL to solve Ax = b or to DSPDI to compute
the determinant, inverse, and inertia of A.
dspcon - estimate the reciprocal of the condition
number (in the 1-norm) of a real symmetric packed matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by DSPTRF
dspdi - compute the determinant, inertia, and
inverse of a symmetric matrix A in packed storage, which has been UDU-factored
by DSPCO or DSPFA.
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
dspfa - compute the UDU factorization of a symmetric
matrix A in packed storage. It is typical to follow a call to DSPFA with
a call to DSPSL to solve Ax = b or to DSPDI to compute the determinant,
inverse, and inertia of A.
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 operation y
:= 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 estimates for
the solution
dspsl - solve the linear system Ax = b for a symmetric
matrix A in packed storage, which has been UDU-factored by DSPCO or DSPFA,
and vectors b and x.
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 symmetric tridiagonal form T by an orthogonal similarity
transformation
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 symmetric 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
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
dsttrs - computes the solution to a real system
of linear equations A * X = B
dsvdc - compute the singular value decomposition
of a general matrix A.
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 operations
C := alpha*A*B + beta*C or C := alpha*B*A + beta*C
dsymv - perform the matrix-vector operation y
:= 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 provides error bounds and backward error estimates for the solution
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 solution 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 symmetric 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 triangular band matrix A, in either the 1-norm or the infinity-norm
dtbmv - perform one of the matrix-vector operations
x := 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)
dtgexc - reorder the generalized real Schur decomposition
of a real matrix pair (A,B) using an orthogonal equivalence transformation
(A, B) = Q * (A, B) * Z',
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 eigenvalues and/or eigenvectors of a matrix pair (A, B) in
generalized 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
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,
dtrco - estimate the condition number of a triangular
matrix A. It is typical to follow a call to DTRCO with a call to DTRSL
to solve Ax = b or to DTRDI to compute the determinant and inverse of A.
dtrcon - estimate the reciprocal of the condition
number of a triangular matrix A, in either the 1-norm or the infinity-norm
dtrdi - compute the determinant and inverse of
a triangular matrix A.
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 operations
B := 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,
dtrsl - solve the linear system Ax = b for a triangular
matrix A and vectors b and x.
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 eigenvalues and/or right eigenvectors of a real upper quasi-triangular
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
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 followed 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 followed 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 RFFT 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
sasum - Return the sum of the absolute values
of a vector x.
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 dot product of two vectors
x and y
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
sgbbrd - reduce a real general m-by-n band matrix
A to upper bidiagonal form B by an orthogonal transformation
sgbco - compute the LU factorization and condition
number of a general matrix A in banded storage. If the condition number
is not needed then SGBFA is slightly faster. It is typical to follow a
call to SGBCO with a call to SGBSL to solve Ax = b or to SGBDI to compute
the determinant of A.
sgbcon - estimate the reciprocal of the condition
number of a real general band matrix A, in either the 1-norm or the infinity-norm,
sgbdi - compute the determinant of a general matrix
A in banded storage, which has been LU-factored by SGBCO or SGBFA.
sgbequ - compute row and column scalings intended
to equilibrate an M-by-N band matrix A and reduce its condition number
sgbfa - compute the LU factorization of a matrix
A in banded storage. It is typical to follow a call to SGBFA with a call
to SGBSL to solve Ax = b or to SGBDI to compute the determinant of A.
sgbmv - perform one of the matrix-vector operations
y := 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
sgbsl - solve the linear system Ax = b for a matrix
A in banded storage, which has been LU-factored by SGBCO or SGBFA, and
vectors b and x.
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
computed 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
sgebrd - reduce a general real M-by-N matrix
A to upper or lower bidiagonal form B by an orthogonal transformation
sgeco - compute the LU factorization and estimate
the condition number of a general matrix A. If the condition number is
not needed then SGEFA is slightly faster. It is typical to follow a call
to SGECO with a call to SGESL to solve Ax = b or to SGEDI to compute the
determinant and inverse of A.
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
sgedi - compute the determinant and inverse of
a general matrix A, which has been LU-factored by SGECO or SGEFA.
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 eigenvalues, 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 eigenvalues, 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 eigenvalues and, optionally, the left and/or right eigenvectors
sgeevx - compute for an N-by-N real nonsymmetric
matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
sgefa - compute the LU factorization of a general
matrix A. It is typical to follow a call to SGEFA with a call to SGESL
to solve Ax = b or to SGEDI to compute the determinant of A.
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 operations
C := alpha*op( A )*op( B ) + beta*C
sgemv - perform one of the matrix-vector operations
y := 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
sgesl - solve the linear system Ax = b for a general
matrix A, which has been LU- factored by SGECO or SGEFA, and vectors b
and x.
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
singular 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 eigenvalue 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 Hessenberg 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 L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
sgtcon - estimate the reciprocal of the condition
number of a real tridiagonal matrix A using the LU factorization as computed
by SGTTRF
sgthrz - gathers specified elements from y into
x and sets gathered elements in y to 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
sgtsl - solve the linear system Ax = b for a tridiagonal
matrix A and vectors b and x.
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
decomposition 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
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 representation with only 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.
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 multiply the input
sequence by 2 * (N+1).
sinti - initialize the array WSAVE, which is used
in subroutine SINT.
slagtf - factorize the matrix (T - lambda*I),
where T is an n by n tridiagonal matrix and lambda is a scalar, as T -
lambda*I = PLU,
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
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
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 determined 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 - VECT = 'Q', SORMBR overwrites the general
real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormhr - overwrite the general real M-by-N matrix
C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormlq - overwrite the general real M-by-N matrix
C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormql - overwrite the general real M-by-N matrix
C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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 SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormrz - overwrite the general real M-by-N matrix
C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormtr - overwrite the general real M-by-N matrix
C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
spbco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A in banded storage. If
the condition number is not needed then SPBFA is slightly faster. It is
typical to follow a call to SPBCO with a call to SPBSL to solve Ax = b
or to SPBDI to compute the determinant of A.
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
spbdi - compute the determinant of a symmetric
positive definite matrix A in banded storage, which has been Cholesky-factored
by SPBCO or SPBFA.
spbequ - compute row and column scalings intended
to equilibrate a symmetric positive definite band matrix A and reduce its
condition number (with respect to the two-norm)
spbfa - compute a Cholesky factorization of a
symmetric positive definite matrix A in banded storage. It is typical to
follow a call to SPBFA with a call to SPBSL to solve Ax = b or to SPBDI
to compute the determinant of A.
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
spbsl - section solve the linear system Ax = b
for a symmetric positive definite matrix A in banded storage, which has
been Cholesky-factored by SPBCO or SPBFA, and vectors b and x.
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 equations
A * X = B,
spbtf2 - compute the Cholesky factorization of
a real symmetric positive definite band matrix A
spbtrf - compute the Cholesky factorization of
a real symmetric positive 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
factorization A = U**T*U or A = L*L**T computed by SPBTRF
spoco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A. If the condition number
is not needed then SPOFA is slightly faster. It is typical to follow a
call to SPOCO with a call to SPOSL to solve Ax = b or to SPODI to compute
the determinant and inverse of A.
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
spodi - compute the determinant and inverse of
a symmetric positive definite matrix A, which has been Cholesky-factored
by SPOCO, SPOFA, or SQRDC.
spoequ - compute row and column scalings intended
to equilibrate a symmetric positive definite matrix A and reduce its condition
number (with respect to the two-norm)
spofa - compute a Cholesky factorization of a
symmetric positive definite matrix A. It is typical to follow a call to
SPOFA with a call to SPOSL to solve Ax = b or to SPODI to compute the determinant
and inverse of A.
sporfs - improve the computed solution to a system
of linear equations when the coefficient matrix is symmetric positive definite,
sposl - solve the linear system Ax = b for a symmetric
positive definite matrix A, which has been Cholesky-factored by SPOCO or
SPOFA, and vectors b and x.
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 equations
A * X = B,
spotf2 - compute the Cholesky factorization of
a real symmetric positive definite matrix A
spotrf - compute the Cholesky factorization of
a real symmetric positive 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
sppco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A in packed storage. If
the condition number is not needed then SPPFA is slightly faster. It is
typical to follow a call to SPPCO with a call to SPPSL to solve Ax = b
or to SPPDI to compute the determinant and inverse of A.
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
sppdi - compute the determinant and inverse of
a symmetric positive definite matrix A in packed storage, which has been
Cholesky-factored by SPPCO or SPPFA.
sppequ - compute row and column scalings intended
to equilibrate a symmetric positive definite matrix A in packed storage
and reduce its condition number (with respect to the two-norm)
sppfa - compute a Cholesky factorization of a
symmetric positive definite matrix A in packed storage. It is typical to
follow a call to SPPFA with a call to SPPSL to solve Ax = b or to SPPDI
to compute the determinant and inverse of A.
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
sppsl - solve the linear system Ax = b for a symmetric
positive definite matrix A in packed storage, which has been Cholesky-factored
by SPPCO or SPPFA, and vectors b and x.
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 equations
A * X = B,
spptrf - compute the Cholesky factorization of
a real symmetric positive 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
factoring 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
sptsl - solve the linear system Ax = b for a symmetric
positive definite tridiagonal matrix A and vectors b and x.
sptsv - 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.
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
sqrdc - compute the QR factorization of a general
matrix A. It is typical to follow a call to SQRDC with a call to SQRSL
to solve Ax = b or to SPODI to compute the determinant of A.
sqrsl - solve the linear system Ax = b for a general
matrix A, which has been QR- factored by SQRDC, and vectors b and x.
srot - Apply a Given's rotation constructed by
SROTG.
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 eigenproblem 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 operation y
:= alpha*A*x + beta*y
ssbtrd - reduce a real symmetric band matrix
A to symmetric tridiagonal form T by an orthogonal similarity transformation
ssico - compute the UDU factorization and condition
number of a symmetric matrix A. If the condition number is not needed then
SSIFA is slightly faster. It is typical to follow a call to SSICO with
a call to SSISL to solve Ax = b or to SSIDI to compute the determinant,
inverse, and inertia of A.
ssidi - compute the determinant, inertia, and
inverse of a symmetric matrix A, which has been UDU-factored by SSICO or
SSIFA.
ssifa - compute the UDU factorization of a symmetric
matrix A. It is typical to follow a call to SSIFA with a call to SSISL
to solve Ax = b or to SSIDI to compute the determinant, inverse, and inertia
of A.
ssisl - solve the linear system Ax = b for a symmetric
matrix A, which has been UDU-factored by SSICO or SSIFA, and vectors b
and x.
sspco - compute the UDU factorization and condition
number of a symmetric matrix A in packed storage. If the condition number
is not needed then SSPFA is slightly faster. It is typical to follow a
call to SSPCO with a call to SSPSL to solve Ax = b or to SSPDI to compute
the determinant, inverse, and inertia of A.
sspcon - estimate the reciprocal of the condition
number (in the 1-norm) of a real symmetric packed matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by SSPTRF
sspdi - compute the determinant, inertia, and
inverse of a symmetric matrix A in packed storage, which has been UDU-factored
by SSPCO or SSPFA.
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
sspfa - compute the UDU factorization of a symmetric
matrix A in packed storage. It is typical to follow a call to SSPFA with
a call to SSPSL to solve Ax = b or to SSPDI to compute the determinant,
inverse, and inertia of A.
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 operation y
:= 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 estimates for
the solution
sspsl - solve the linear system Ax = b for a symmetric
matrix A in packed storage, which has been UDU-factored by SSPCO or SSPFA,
and vectors b and x.
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 symmetric tridiagonal form T by an orthogonal similarity
transformation
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 symmetric 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
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
ssttrs - computes the solution to a real system
of linear equations A * X = B
ssvdc - compute the singular value decomposition
of a general matrix A.
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 operations
C := alpha*A*B + beta*C or C := alpha*B*A + beta*C
ssymv - perform the matrix-vector operation y
:= 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 provides error bounds and backward error estimates for the solution
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 solution 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 symmetric 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 triangular band matrix A, in either the 1-norm or the infinity-norm
stbmv - perform one of the matrix-vector operations
x := 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)
stgexc - reorder the generalized real Schur decomposition
of a real matrix pair (A,B) using an orthogonal equivalence transformation
(A, B) = Q * (A, B) * Z',
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 eigenvalues and/or eigenvectors of a matrix pair (A, B) in
generalized 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
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,
strco - estimate the condition number of a triangular
matrix A. It is typical to follow a call to STRCO with a call to STRSL
to solve Ax = b or to STRDI to compute the determinant and inverse of A.
strcon - estimate the reciprocal of the condition
number of a triangular matrix A, in either the 1-norm or the infinity-norm
strdi - compute the determinant and inverse of
a triangular matrix A.
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 operations
B := 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,
strsl - solve the linear system Ax = b for a triangular
matrix A and vectors b and x.
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 eigenvalues and/or right eigenvectors of a real upper quasi-triangular
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
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 - set the upper bound on the
number of threads that the calling thread wants used
using_threads - returns the current Use
number set by the USE_THREADS subroutine
vcfftb - compute a periodic sequence from its
Fourier coefficients. The VCFFT operations are normalized, so a call of
VCFFTF followed 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
operations 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 representation 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 VDCOSQF followed by a call
of VDCOSQB will return the original sequence.
vdcosqf - compute the Fourier coefficients in
a cosine series representation with only odd wave numbers. The VCOSQ operations
are normalized, so a call of VDCOSQF followed by a call of VDCOSQB will
return the original sequence.
vdcosqi - initialize the array WSAVE, which
is used in both VDCOSQF and VDCOSQB.
vdcost - compute the discrete Fourier cosine
transform of an even sequence. The VDCOST transform is normalized, so a
call of VDCOST followed by a call of VDCOST will return the original sequence.
vdcosti - initialize the array WSAVE, which
is used in VDCOST.
vdfftb - compute a periodic sequence from its
Fourier coefficients. The VRFFT operations are normalized, so a call of
VDFFTF followed by a call of VDFFTB will return the original sequence.
vdfftf - compute the Fourier coefficients of
a periodic sequence. The VRFFT 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 VDFFTF and VDFFTB.
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 VDSINQF followed by a call
of VDSINQB will return the original sequence.
vdsinqf - compute the Fourier coefficients in
a sine series representation with only odd wave numbers. The VSINQ operations
are normalized, so a call of VDSINQF followed by a call of VDSINQB will
return the original sequence.
vdsinqi - initialize the array WSAVE, which
is used in both VDSINQF and VDSINQB.
vdsint - compute the discrete Fourier sine transform
of an odd sequence. The VDSINT transforms are unnormalized inverses of
themselves, so a call of VDSINT followed by another call of VDSINT will
multiply the input sequence by 2 * (N+1). The VDSINT transforms are normalized,
so a call of VDSINT followed by a call of VDSINT will return the original
sequence.
vdsinti - initialize the array WSAVE, which
is used in subroutine VDSINT.
vrfftb - compute a periodic sequence from its
Fourier coefficients. The VRFFT operations are normalized, so a call of
VRFFTF followed 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 representation with only odd wave numbers. The VSINQ operations
are normalized, 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 transforms 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 VCFFT operations are normalized, so a call of
VZFFTF followed by a call of VZFFTB will return the original sequence.
vzfftf - compute the Fourier coefficients of
a periodic sequence. The VCFFT 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.
xerbla - i an error handler for the LAPACK routines
zfft2b - 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.
zfft2f - compute the Fourier coefficients of
a periodic sequence. The xFFT operations are unnormalized, so a call of
xFFT2F followed by a call of xFFT2B 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 xFFT operations are unnormalized, so a call of
xFFT3F followed by a call of xFFT3B will multiply the input sequence by
M*N*K.
zfft3f - compute the Fourier coefficients of
a periodic sequence. The xFFT operations are unnormalized, so a call of
xFFT3F followed by a call of xFFT3B will multiply the input sequence by
M*N*K.
zfft3i - initialize the array WSAVE, which is
used in both xFFT3F and xFFT3B.
zfftb - compute a periodic sequence from its Fourier
coefficients. The xFFT operations are unnormalized, so a call of xFFTF
followed by a call of xFFTB will multiply the input sequence by N.
zfftf - compute the Fourier coefficients of a
periodic sequence. The xFFT operations are unnormalized, so a call of xFFTF
followed by a call of xFFTB will multiply the input sequence by N.
zffti - initialize the array WSAVE, which is used
in both xFFTF and xFFTB.
zfftopt - compute the length of the closest
fast FFT
zgbbrd - reduce a complex general m-by-n band
matrix A to real upper bidiagonal form B by a unitary transformation
zgbco - compute the LU factorization and condition
number of a general matrix A in banded storage. If the condition number
is not needed then xGBFA is slightly faster. It is typical to follow a
call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute
the determinant of A.
zgbcon - estimate the reciprocal of the condition
number of a complex general band matrix A, in either the 1-norm or the
infinity-norm,
zgbdi - compute the determinant of a general matrix
A in banded storage, which has been LU-factored by ZGBCO or ZGBFA.
zgbequ - compute row and column scalings intended
to equilibrate an M-by-N band matrix A and reduce its condition number
zgbfa - compute the LU factorization of a matrix
A in banded storage. It is typical to follow a call to ZGBFA with a call
to ZGBSL to solve Ax = b or to ZGBDI to compute the determinant of A.
zgbmv - perform one of the matrix-vector operations
y := 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
zgbsl - solve the linear system Ax = b for a matrix
A in banded storage, which has been LU-factored by ZGBCO or ZGBFA, and
vectors b and x.
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 subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
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
eigenvectors of the balanced matrix output by ZGEBAL
zgebrd - reduce a general complex M-by-N matrix
A to upper or lower bidiagonal form B by a unitary transformation
zgeco - compute the LU factorization and estimate
the condition number of a general matrix A. If the condition number is
not needed then ZGEFA is slightly faster. It is typical to follow a call
to ZGECO with a call to ZGESL to solve Ax = b or to ZGEDI to compute the
determinant and inverse of A.
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
zgedi - compute the determinant and inverse of
a general matrix A, which has been LU-factored by ZGECO or ZGEFA.
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 eigenvalues, the Schur form T, and, optionally, the matrix
of Schur vectors Z
zgeesx - compute for an N-by-N complex nonsymmetric
matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix
of Schur vectors Z
zgeev - compute for an N-by-N complex nonsymmetric
matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
zgeevx - compute for an N-by-N complex nonsymmetric
matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
zgefa - compute the LU factorization of a general
matrix A. It is typical to follow a call to ZGEFA with a call to ZGESL
to solve Ax = b or to ZGEDI to compute the determinant of A.
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 operations
y := 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 CGEQP3
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
zgesl - solve the linear system Ax = b for a general
matrix A, which has been LU- factored by ZGECO or ZGEFA, and vectors b
and x.
zgesv - compute the solution to a complex system
of linear equations A * 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
transformation 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
zgtcon - estimate the reciprocal of the condition
number of a complex tridiagonal matrix A using the LU factorization as
computed by ZGTTRF
zgthrz - gathers specified elements from y into
x and sets gathered elements in y to zero
zgthrz - gathers specified elements from y into
x and sets gathered elements in y to 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
zgtsl - solve the linear system Ax = b for a tridiagonal
matrix A and vectors b and x.
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 eigenproblem 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 eigenproblem,
of the form A*x=(lambda)*B*x
zhbgvd - compute all the eigenvalues, and optionally,
the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem,
of the form A*x=(lambda)*B*x
zhbgvx - compute all the eigenvalues, and optionally,
the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem,
of the form A*x=(lambda)*B*x
zhbmv - perform the matrix-vector operation y
:= 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 complex 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 operation y
:= 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 provides error bounds and backward error estimates for the solution
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 equations A * X = B,
zhesvx - use the diagonal pivoting factorization
to compute the solution 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 tridiagonal 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 Hermitian 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 tranformation (usually called Q) on the left and
another (usually called Z) on the right
zhico - compute the UDU factorization and condition
number of a Hermitian matrix A. If the condition number is not needed then
xHIFA is slightly faster. It is typical to follow a call to xHICO with
a call to xHISL to solve Ax = b or to xHIDI to compute the determinant,
inverse, and inertia of A.
zhidi - compute the determinant, inertia, and
inverse of a Hermitian matrix A, which has been UDU-factored by ZHICO or
ZHIFA.
zhifa - compute the UDU factorization of a Hermitian
matrix A. It is typical to follow a call to ZHIFA with a call to ZHISL
to solve Ax = b or to ZHIDI to compute the determinant, inverse, and inertia
of A.
zhisl - solve the linear system Ax = b for a Hermitian
matrix A, which has been UDU-factored by ZHICO or ZHIFA, and vectors b
and x.
zhpco - compute the UDU factorization and condition
number of a Hermitian matrix A in packed storage. If the condition number
is not needed then xHPFA is slightly faster. It is typical to follow a
call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute
the determinant, inverse, and inertia of A.
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
zhpdi - compute the determinant, inertia, and
inverse of a Hermitian matrix A in packed storage, which has been UDU-factored
by ZHPCO or ZHPFA.
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
zhpfa - compute the UDU factorization of a Hermitian
matrix A in packed storage. It is typical to follow a call to ZHPFA with
a call to ZHPSL to solve Ax = b or to ZHPDI to compute the determinant,
inverse, and inertia of A.
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 operation y
:= 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 estimates for
the solution
zhpsl - solve the linear system Ax = b for a Hermitian
matrix A in packed storage, which has been UDU-factored by ZHPCO or ZHPFA,
and vectors b and x.
zhpsv - compute the solution to a complex system
of linear equations A * 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 linear 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 Hermitian matrix A stored in packed format using the
factorization 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
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
zpbco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A in banded storage. If
the condition number is not needed then xPBFA is slightly faster. It is
typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b
or to xPBDI to compute the determinant of A.
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
zpbdi - compute the determinant of a symmetric
positive definite matrix A in banded storage, which has been Cholesky-factored
by ZPBCO or ZPBFA.
zpbequ - compute row and column scalings intended
to equilibrate a Hermitian positive definite band matrix A and reduce its
condition number (with respect to the two-norm)
zpbfa - compute a Cholesky factorization of a
symmetric positive definite matrix A in banded storage. It is typical to
follow a call to ZPBFA with a call to ZPBSL to solve Ax = b or to ZPBDI
to compute the determinant of A.
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
zpbsl - section solve the linear system Ax = b
for a symmetric positive definite matrix A in banded storage, which has
been Cholesky-factored by ZPBCO or ZPBFA, and vectors b and x.
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 equations A * 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 positive definite band matrix A
zpbtrf - compute the Cholesky factorization of
a complex Hermitian positive 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
factorization A = U**H*U or A = L*L**H computed by ZPBTRF
zpoco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A. If the condition number
is not needed then xPOFA is slightly faster. It is typical to follow a
call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute
the determinant and inverse of A.
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
zpodi - compute the determinant and inverse of
a symmetric positive definite matrix A, which has been Cholesky-factored
by ZPOCO, ZPOFA, or ZQRDC.
zpoequ - compute row and column scalings intended
to equilibrate a Hermitian positive definite matrix A and reduce its condition
number (with respect to the two-norm)
zpofa - compute a Cholesky factorization of a
symmetric positive definite matrix A. It is typical to follow a call to
ZPOFA with a call to ZPOSL to solve Ax = b or to ZPODI to compute the determinant
and inverse of A.
zporfs - improve the computed solution to a system
of linear equations when the coefficient matrix is Hermitian positive definite,
zposl - solve the linear system Ax = b for a symmetric
positive definite matrix A, which has been Cholesky-factored by ZPOCO or
ZPOFA, and vectors b and x.
zposv - compute the solution to a complex system
of linear equations A * 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 positive definite matrix A
zpotrf - compute the Cholesky factorization of
a complex Hermitian positive 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
zppco - compute a Cholesky factorization and condition
number of a symmetric positive definite matrix A in packed storage. If
the condition number is not needed then ZPPFA is slightly faster. It is
typical to follow a call to ZPPCO with a call to ZPPSL to solve Ax = b
or to ZPPDI to compute the determinant and inverse of A.
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
zppdi - compute the determinant and inverse of
a symmetric positive definite matrix A in packed storage, which has been
Cholesky-factored by ZPPCO or ZPPFA.
zppequ - compute row and column scalings intended
to equilibrate a Hermitian positive definite matrix A in packed storage
and reduce its condition number (with respect to the two-norm)
zppfa - compute a Cholesky factorization of a
symmetric positive definite matrix A in packed storage. It is typical to
follow a call to ZPPFA with a call to ZPPSL to solve Ax = b or to ZPPDI
to compute the determinant and inverse of A.
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
zppsl - solve the linear system Ax = b for a symmetric
positive definite matrix A in packed storage, which has been Cholesky-factored
by ZPPCO or ZPPFA, and vectors b and x.
zppsv - compute the solution to a complex system
of linear equations A * 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 positive 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
factoring the matrix using DPTTRF and then calling ZBDSQR 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
zptsl - solve the linear system Ax = b for a symmetric
positive definite tridiagonal matrix A and vectors b and x.
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 positive 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
zqrdc - compute the QR factorization of a general
matrix A. It is typical to follow a call to ZQRDC with a call to ZQRSL
to solve Ax = b or to ZPODI to compute the determinant of A.
zqrsl - solve the linear system Ax = b for a general
matrix A, which has been QR- factored by ZQRDC, and vectors b and x.
zrot - ZROT - apply a plane rotation, where the
cos (C) is real and the sin (S) is complex, and the vectors CX and CY are
complex
zsico - compute the UDU factorization and condition
number of a symmetric matrix A. If the condition number is not needed then
ZSIFA is slightly faster. It is typical to follow a call to ZSICO with
a call to ZSISL to solve Ax = b or to ZSIDI to compute the determinant,
inverse, and inertia of A.
zsidi - compute the determinant, inertia, and
inverse of a symmetric matrix A, which has been UDU-factored by ZSICO or
ZSIFA.
zsifa - compute the UDU factorization of a symmetric
matrix A. It is typical to follow a call to ZSIFA with a call to ZSISL
to solve Ax = b or to ZSIDI to compute the determinant, inverse, and inertia
of A.
zsisl - solve the linear system Ax = b for a symmetric
matrix A, which has been UDU-factored by ZSICO or ZSIFA, and vectors b
and x.
zspco - compute the UDU factorization and condition
number of a symmetric matrix A in packed storage. If the condition number
is not needed then ZSPFA is slightly faster. It is typical to follow a
call to ZSPCO with a call to ZSPSL to solve Ax = b or to ZSPDI to compute
the determinant, inverse, and inertia of A.
zspcon - estimate the reciprocal of the condition
number (in the 1-norm) of a complex symmetric packed matrix A using the
factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
zspdi - compute the determinant, inertia, and
inverse of a symmetric matrix A in packed storage, which has been UDU-factored
by ZSPCO or ZSPFA.
zspfa - compute the UDU factorization of a symmetric
matrix A in packed storage. It is typical to follow a call to ZSPFA with
a call to ZSPSL to solve Ax = b or to ZSPDI to compute the determinant,
inverse, and inertia of A.
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 estimates for
the solution
zspsl - solve the linear system Ax = b for a symmetric
matrix A in packed storage, which has been UDU-factored by ZSPCO or ZSPFA,
and vectors b and x.
zspsv - compute the solution to a complex system
of linear equations A * 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 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
zsptrf - compute the factorization of a complex
symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal
pivoting 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 symmetric matrix A stored in packed format using the
factorization 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 - (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,
zstein - compute the eigenvectors of a real symmetric
tridiagonal matrix T corresponding to specified eigenvalues, using inverse
iteration
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 Hermitian tridiagonal matrix
zsttrf - compute the factorization of a complex
Hermitian tridiagonal matrix A
zsttrs - computes the solution to a complex system
of linear equations A * X = B
zsvdc - compute the singular value decomposition
of a general matrix A.
zsycon - estimate the reciprocal of the condition
number (in the 1-norm) of a complex symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by ZSYTRF
zsymm - perform one of the matrix-matrix operations
C := 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 provides error bounds and backward error estimates for the solution
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 equations A * X = B,
zsysvx - use the diagonal pivoting factorization
to compute the solution 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 symmetric 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 triangular band matrix A, in either the 1-norm or the infinity-norm
ztbmv - perform one of the matrix-vector operations
x := 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)
ztgexc - reorder the generalized Schur decomposition
of a complex matrix pair (A,B), using an unitary equivalence transformation
(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 eigenvalues 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 eigenvalues and/or eigenvectors of a matrix pair (A, B)
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 operations
x := 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,
ztrco - estimate the condition number of a triangular
matrix A. It is typical to follow a call to xTRCO with a call to xTRSL
to solve Ax = b or to xTRDI to compute the determinant and inverse of A.
ztrcon - estimate the reciprocal of the condition
number of a triangular matrix A, in either the 1-norm or the infinity-norm
ztrdi - compute the determinant and inverse of
a triangular matrix A.
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 operations
B := 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 operations
x := 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 triangular
matrix T, and the leading columns of Q form an orthonormal basis of the
corresponding right invariant subspace
ztrsl - solve the linear system Ax = b for a triangular
matrix A and vectors b and x.
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 eigenvalues 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 determined by ZGEBRD when reducing a complex matrix
A to bidiagonal 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 ZHETRD
zunm2r - 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',
zunmbr - VECT = 'Q', ZUNMBR overwrites the general
complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmhr - overwrite the general complex M-by-N
matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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 SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmql - overwrite the general complex M-by-N
matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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 SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmrz - overwrite the general complex M-by-N
matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmtr - overwrite the general complex M-by-N
matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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 ZHPTRD using packed storage
zupmtr - overwrite the general complex M-by-N
matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zvmul - compute the scaled product of complex
vectors