CBDSQR - computes the singular value
decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix
B
CGBBRD - reduces a complex general
m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
CGBCON - estimates the reciprocal of
the condition number of a complex general band matrix A
CGBEQU - computes row and column scalings
intended to equilibrate an M-by-N band matrix A and reduce its condition
number
CGBRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is banded
CGBSV - computes the solution to a
complex system of linear equations
CGBSVX - uses the LU factorization
to compute the solution to a complex system of linear equations
CGBTF2 - computes an LU factorization
of a complex m-by-n band matrix A using partial pivoting with row interchanges
CGBTRF - computes an LU factorization
of a complex m-by-n band matrix A using partial pivoting with row interchanges
CGBTRS - solves a system of linear
equations with a general band matrix A using the LU factorization computed
by CGBTRF
CGEBAK - forms the right or left eigenvectors
of a complex general matrix by backward transformation on the computed
eigenvectors of the balanced matrix output by CGEBAL
CGEBAL - balances a general complex
matrix A
CGEBD2 - reduces a complex general
m by n matrix A to upper or lower real bidiagonal form B by a unitary
transformation
CGEBRD - reduces a general complex
M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
CGECON - estimates the reciprocal of
the condition number of a general complex matrix A using the LU factorization
computed by CGETRF
CGEEQU - computes row and column scalings
intended to equilibrate an M-by-N matrix A and reduce its condition number
CGEES - computes the eigenvalues, the
Schur form T, and, optionally, the matrix of Schur vectors Z
CGEESX - computes the eigenvalues,
the Schur form T, and, optionally, the matrix of Schur vectors Z
CGEEV - computes the eigenvalues and,
optionally, the left and/or right eigenvectors
CGEEVX - computes the eigenvalues and,
optionally, the left and/or right eigenvectors
CGEGS - routine is deprecated and has
been replaced by routine CGGES
CGEGV - routine is deprecated and has
been replaced by routine CGGEV
CGEHD2 - reduces a complex general
matrix A to upper Hessenberg form H by a unitary similarity transformation
CGEHRD - reduces a complex general
matrix A to upper Hessenberg form H by a unitary similarity transformation
CGELQ2 - computes an LQ factorization
of a complex m by n matrix A
CGELQF - computes an LQ factorization
of a complex M-by-N matrix A
CGELS - solves overdetermined or underdetermined
complex linear systems
CGELSD - computes the minimum-norm
solution to a real linear least squares problem
CGELSS - computes the minimum norm
solution to a complex linear least squares problem
CGELSX - routine is deprecated and
has been replaced by routine CGELSY
CGELSY - computes the minimum-norm
solution to a complex linear least squares problem
CGEQL2 - computes a QL factorization
of a complex m by n matrix A
CGEQLF - computes a QL factorization
of a complex M-by-N matrix A
CGEQP3 - computes a QR factorization
with column pivoting of a matrix A
CGEQPF - routine is deprecated and
has been replaced by routine CGEQP3
CGEQR2 - computes a QR factorization
of a complex m by n matrix A
CGEQRF - computes a QR factorization
of a complex M-by-N matrix A
CGERFS - improves the computed solution
to a system of linear equations
CGERQ2 - computes an RQ factorization
of a complex m by n matrix A
CGERQF - computes an RQ factorization
of a complex M-by-N matrix A
CGESC2 - solves a system of linear
equations with a general N-by-N matrix A using the LU factorization with
complete pivoting computed by CGETC2
CGESDD - computes the singular value
decomposition (SVD) of a complex M-by-N matrix A
CGESV - computes the solution to a
complex system of linear equations
CGESVD - computes the singular value
decomposition (SVD) of a complex M-by-N matrix A, optionally computing
the left and/or right singular vectors
CGESVX - uses the LU factorization
to compute the solution to a complex system of linear equations
CGETC2 - computes an LU factorization,
using complete pivoting, of the n-by-n matrix A
CGETF2 - computes an LU factorization
of a general m-by-n matrix A using partial pivoting with row interchanges
CGETRF - computes an LU factorization
of a general M-by-N matrix A using partial pivoting with row interchanges
CGETRI - computes the inverse of a
matrix using the LU factorization computed by CGETRF
CGETRS - solves a system of linear
equations with a general N-by-N matrix A using the LU factorization computed
by CGETRF
CGGBAK - forms the right or left eigenvectors
of a complex generalized eigenvalue problem by backward transformation
on the computed eigenvectors of the balanced pair of matrices output by
CGGBAL
CGGBAL - balances a pair of general
complex matrices (A,B)
CGGES - computes the generalized eigenvalues,
the generalized complex Schur form (S, T), and optionally left and/or
right Schur vectors (VSL and VSR)
CGGESX - computes the generalized eigenvalues,
the complex Schur form (S,T),
CGGEV - computes the generalized eigenvalues,
and optionally, the left and/or right generalized eigenvectors
CGGEVX - computes the generalized eigenvalues,
and optionally, the left and/or right generalized eigenvectors
CGGGLM - solves a general Gauss-Markov
linear model (GLM) problem
CGGHRD - reduces 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 - solves the linear equality-constrained
least squares (LSE) problem
CGGQRF - computes a generalized QR
factorization of an N-by-M matrix A and an N-by-P matrix B
CGGRQF - computes a generalized RQ
factorization of an M-by-N matrix A and a P-by-N matrix B
CGGSVD - computes the generalized singular
value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex
matrix B
CGGSVP - computes unitary matrices
CGTCON - estimates the reciprocal of
the condition number of a complex tridiagonal matrix A using the LU factorization
as computed by CGTTRF
CGTRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is tridiagonal
CGTSV - solves the equation AX = B,
CGTSVX - uses the LU factorization
to compute the solution to a complex system of linear equations
CGTTRF - computes an LU factorization
of a complex tridiagonal matrix A using elimination with partial pivoting
and row interchanges
CGTTRS - solves systems of equations
CGTTS2 - solves systems of equations
CHBEV - computes all the eigenvalues
and, optionally, eigenvectors of a complex Hermitian band matrix A
CHBEVD - computes all the eigenvalues
and, optionally, eigenvectors of a complex Hermitian band matrix A
CHBEVX - computes selected eigenvalues
and, optionally, eigenvectors of a complex Hermitian band matrix A
CHBGST - reduces a complex Hermitian-definite
banded generalized eigenproblem
CHBGV - computes all the eigenvalues
and optionally, the eigenvectors of a complex generalized Hermitian-definite
banded eigenproblem
CHBGVD - computes all the eigenvalues,
and optionally, the eigenvectors of a complex generalized Hermitian-definite
banded eigenproblem
CHBGVX - computes all the eigenvalues,
and optionally, the eigenvectors of a complex generalized Hermitian-definite
banded eigenproblem
CHBTRD - reduces a complex Hermitian
band matrix A to real symmetric tridiagonal form T by a unitary similarity
transformation
CHECON - estimates the reciprocal of
the condition number of a complex Hermitian matrix A
CHEEV - computes all eigenvalues and,
optionally, eigenvectors of a complex Hermitian matrix A
CHEEVD - computes all eigenvalues and,
optionally, eigenvectors of a complex Hermitian matrix A
CHEEVR - computes selected eigenvalues
and, optionally, eigenvectors of a complex Hermitian matrix T
CHEEVX - computes selected eigenvalues
and, optionally, eigenvectors of a complex Hermitian matrix A
CHEGS2 - reduces a complex Hermitian-definite
generalized eigenproblem to standard form
CHEGST - reduces a complex Hermitian-definite
generalized eigenproblem to standard form
CHEGV - computes all the eigenvalues,
and optionally, the eigenvectors of a complex generalized Hermitian-definite
eigenproblem
CHEGVD - computes all the eigenvalues,
and optionally, the eigenvectors of a complex generalized Hermitian-definite
eigenproblem
CHEGVX - computes selected eigenvalues,
and optionally, eigenvectors of a complex generalized Hermitian-definite
eigenproblem
CHERFS - improves the computed solution
to a system of linear equations when the coefficient matrix is Hermitian
indefinite
CHESV - computes the solution to a
complex system of linear equations
CHESVX - uses the diagonal pivoting
factorization to compute the solution to a complex system of linear equations
CHETD2 - reduces a complex Hermitian
matrix A to real symmetric tridiagonal form T by a unitary similarity
transformation
CHETF2 - computes the factorization
of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting
method
CHETRD - reduces a complex Hermitian
matrix A to real symmetric tridiagonal form T by a unitary similarity
transformation
CHETRF - computes the factorization
of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting
method
CHETRI - computes the inverse of a
complex Hermitian indefinite matrix A using the factorization computed
by CHETRF
CHETRS - solves a system of linear
equations with a complex Hermitian matrix A using the factorization computed
by CHETRF
CHGEQZ - implements a single-shift
version of the QZ method for finding the generalized eigenvalues
CHPCON - estimates the reciprocal of
the condition number of a complex Hermitian packed matrix A using the
factorization computed by CHPTRF
CHPEV - computes all the eigenvalues
and, optionally, eigenvectors of a complex Hermitian matrix in packed
storage
CHPEVD - computes all the eigenvalues
and, optionally, eigenvectors of a complex Hermitian matrix A in packed
storage
CHPEVX - computes selected eigenvalues
and, optionally, eigenvectors of a complex Hermitian matrix A in packed
storage
CHPGST - reduces a complex Hermitian-definite
generalized eigenproblem to standard form, using packed storage
CHPGV - computes all the eigenvalues
and, optionally, the eigenvectors of a complex generalized Hermitian-definite
eigenproblem
CHPGVD - computes all the eigenvalues
and, optionally, the eigenvectors of a complex generalized Hermitian-definite
eigenproblem
CHPGVX - computes selected eigenvalues
and, optionally, eigenvectors of a complex generalized Hermitian-definite
eigenproblem
CHPRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is Hermitian
indefinite and packed
CHPSV - computes the solution to a
complex system of linear equations
CHPSVX - uses diagonal pivoting factorization
to compute the solution to a complex system of linear equations
CHPTRD - reduces a complex Hermitian
matrix A stored in packed form to real symmetric tridiagonal form T by
a unitary similarity transformation
CHPTRF - computes the factorization
of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal
pivoting method
CHPTRI - computes the inverse of a
complex Hermitian indefinite matrix A in packed storage using the factorization
computed by CHPTRF
CHPTRS - solves a system of linear
equations with a complex Hermitian matrix A stored in packed format using
the factorization computed by CHPTRF
CHSEIN - uses inverse iteration to
find specified right and/or left eigenvectors of a complex upper Hessenberg
matrix H
CHSEQR - computes the eigenvalues of
a complex upper Hessenberg matrix H, and, optionally, the matrices T and
Z from the Schur decomposition
CLABRD - reduces the first NB rows
and columns of a complex general m by n matrix A to upper or lower real
bidiagonal form
CLACGV - conjugates a complex vector
of length N
CLACON - estimates the 1-norm of a
square, complex matrix A
CLACP2 - copies all or part of a real
two-dimensional matrix A to a complex matrix B
CLACPY - copies all or part of a two-dimensional
matrix A to another matrix B
CLACRM - performs a very simple matrix-matrix
multiplication
CLACRT - perform the operation ( c
s )( x ) >= ( x ) ( -s c )( y ) ( y ) where c and s
are complex and the vectors x and y are complex
CLADIV - := X / Y, where X and Y are
complex
CLAED0 - computes all eigenvalues of
a symmetric tridiagonal matrix which is one diagonal block
CLAED7 - computes the updated eigensystem
of a diagonal matrix after modification by a rank-one symmetric matrix
CLAED8 - merges the two sets of eigenvalues
together into a single sorted set
CLAEIN - uses inverse iteration to
find a right or left eigenvector corresponding to the eigenvalue W of
a complex upper Hessenberg matrix H
CLAESY - computes the eigendecomposition
of a 2-by-2 symmetric matrix
CLAEV2 - computes the eigendecomposition
of a 2-by-2 Hermitian matrix
CLAGS2 - computes 2-by-2 unitary matrices
U, V and Q
CLAGTM - performs a matrix-vector product
CLAHEF - computes a partial factorization
of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting
method
CLAHQR - an auxiliary routine called
by CHSEQR to update the eigenvalues and Schur decomposition already computed
by CHSEQR
CLAHRD - reduces the first NB columns
of a complex general matrix so that elements below the k-th subdiagonal
are zero
CLAIC1 - applies one step of incremental
condition estimation in its simplest version
CLALS0 - applies back the multiplying
factors of either the left or the right singular vector matrix of a diagonal
matrix
CLALSA - an itermediate step in solving
the least squares problem by computing the SVD of the coefficient matrix
in compact form
CLALSD - uses the singular value decomposition
of A to solve the least squares problem of finding X to minimize the Euclidean
norm of each column of AX-B
CLANGB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n band matrix A
CLANGE - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex matrix A
CLANGT - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex tridiagonal matrix A
CLANHB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n hermitian band matrix A, with k super-diagonals
CLANHE - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex hermitian matrix A
CLANHP - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex hermitian matrix A, supplied in packed form
CLANHS - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a Hessenberg matrix A
CLANHT - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex Hermitian tridiagonal matrix A
CLANSB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n symmetric band matrix A, with k super-diagonals
CLANSP - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex symmetric matrix A, supplied in packed form
CLANSY - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex symmetric matrix A
CLANTB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
CLANTP - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a triangular matrix A, supplied in packed form
CLANTR - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a trapezoidal or triangular matrix A
CLAPLL - computes the QR factorization
of A=QR
CLAPMT - rearranges the columns of
the M by N matrix X
CLAQGB - equilibrates a general M by
N band matrix A
CLAQGE - equilibrates a general M by
N matrix A using the row and scaling factors in the vectors R and C
CLAQHB - equilibrates a symmetric band
matrix A using the scaling factors in the vector S
CLAQHE - equilibrates a Hermitian matrix
A using the scaling factors in the vector S
CLAQHP - equilibrates a Hermitian matrix
A using the scaling factors in the vector S
CLAQP2 - computes a QR factorization
with column pivoting
CLAQPS - computes a step of QR factorization
with column pivoting of a complex M-by-N matrix A
CLAQSB - equilibrates a symmetric band
matrix A using the scaling factors in the vector S
CLAQSP - equilibrates a symmetric matrix
A using the scaling factors in the vector S
CLAQSY - equilibrates a symmetric matrix
A using the scaling factors in the vector S
CLAR1V - computes the (scaled) r
th column of the inverse of the sumbmatrix in rows B1 through
BN of a tridiagonal matrix
CLAR2V - applies a vector of complex
plane rotations with real cosines from both sides to a sequence of 2-by-2
complex Hermitian matrices,
CLARCM - performs a very simple matrix-matrix
multiplication
CLARF - applies a complex elementary
reflector H to a complex M-by-N matrix C, from either the left or the
right
CLARFB - applies a complex block reflector
H or its transpose H' to a complex M-by-N matrix C, from either the left
or the right
CLARFG - generates a complex elementary
reflector H of order n
CLARFT - forms the triangular factor
T of a complex block reflector H of order n, which is defined as a product
of k elementary reflectors
CLARFX - applies a complex elementary
reflector H to a complex m by n matrix C, from either the left or the
right
CLARGV - generates a vector of complex
plane rotations with real cosines, determined by elements of the complex
vectors x and y
CLARNV - returns a vector of n random
complex numbers from a uniform or normal distribution
CLARRV - computes the eigenvectors
of a tridiagonal matrix
CLARTG - generates a plane rotation
CLARTV - applies a vector of complex
plane rotations with real cosines to elements of the complex vectors x
and y
CLARZ - applies a complex elementary
reflector H to a complex M-by-N matrix C, from either the left or the
right
CLARZB - applies a complex block reflector
H or its transpose to a complex distributed M-by-N C from the left or
the right
CLARZT - forms the triangular factor
T of a complex block reflector H
CLASCL - multiplies the M by N complex
matrix A by the real scalar CTO/CFROM
CLASET - initializes a 2-D array A
to BETA on the diagonal and ALPHA on the offdiagonals
CLASR - performs a transformation A
:= PA
CLASSQ - returns the values scl and
ssq
CLASWP - performs a series of row interchanges
on the matrix A
CLASYF - computes a partial factorization
of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
CLATBS - solves a triangular system
CLATDF - computes the contribution
to the reciprocal Dif-estimate
CLATPS - solves a triangular system
CLATRD - reduces NB rows and columns
of a complex Hermitian matrix A
CLATRS - solves a triangular system
CLATRZ - factors a M-by-(M+L) complex
upper trapezoidal matrix
CLATZM - routine is deprecated and
has been replaced by routine CUNMRZ
CLAUU2 - computes the product U ×
U' or L' × L
CLAUUM - computes the product U ×
U' or L' × L, where the triangular factor U or L is stored in the
upper or lower triangular part of the array A
CPBCON - estimates the reciprocal of
the condition number (in the 1-norm) of a complex Hermitian positive definite
band matrix using the Cholesky factorization computed by CPBTRF
CPBEQU - computes 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)
CPBRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is Hermitian
positive definite and banded
CPBSTF - computes a split Cholesky
factorization of a complex Hermitian positive definite band matrix A
CPBSV - computes the solution to a
complex system of linear equations
CPBSVX - uses the Cholesky factorization
to compute the solution to a complex system of linear equations
CPBTF2 - computes the Cholesky factorization
of a complex Hermitian positive definite band matrix A
CPBTRF - computes the Cholesky factorization
of a complex Hermitian positive definite band matrix A
CPBTRS - solves a system of linear
equations with a Hermitian positive definite band matrix A
CPOCON - estimates the reciprocal of
the condition number (in the 1-norm) of a complex Hermitian positive definite
matrix
CPOEQU - computes row and column scalings
intended to equilibrate a Hermitian positive definite matrix A and reduce
its condition number (with respect to the two-norm)
CPORFS - improves the computed solution
to a system of linear equations when the coefficient matrix is Hermitian
positive definite
CPOSV - computes the solution to a
complex system of linear equations
CPOSVX - uses the Cholesky factorization
to compute the solution to a complex system of linear equations
CPOTF2 - computes the Cholesky factorization
of a complex Hermitian positive definite matrix A
CPOTRF - computes the Cholesky factorization
of a complex Hermitian positive definite matrix A
CPOTRI - computes the inverse of a
complex Hermitian positive definite matrix A
CPOTRS - solves a system of linear
equations with a Hermitian positive definite matrix A
CPPCON - estimates the reciprocal of
the condition number (in the 1-norm) of a complex Hermitian positive definite
packed matrix
CPPEQU - computes 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)
CPPRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is Hermitian
positive definite and packed, and provides error bounds and backward error
estimates for the solution
CPPSV - computes the solution to a
complex system of linear equations
CPPSVX - uses the Cholesky factorization
to compute the solution to a complex system of linear equations
CPPTRF - computes the Cholesky factorization
of a complex Hermitian positive definite matrix A stored in packed format
CPPTRI - computes the inverse of a
complex Hermitian positive definite matrix A using the Cholesky factorization
computed by CPPTRF
CPPTRS - solves a system of linear
equations with a Hermitian positive definite matrix A in packed storage
using the Cholesky factorization computed by CPPTRF
CPTCON - computes the reciprocal of
the condition number (in the 1-norm) of a complex Hermitian positive definite
tridiagonal matrix using the factorization computed by CPTTRF
CPTEQR - computes all eigenvalues and,
optionally, eigenvectors of a symmetric positive definite tridiagonal
matrix
CPTRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is Hermitian
positive definite and tridiagonal
CPTSV - computes the solution to a
complex system of linear equations
CPTSVX - computes the solution to a
complex system of linear equations
CPTTRF - computes the factorization
of a complex Hermitian positive definite tridiagonal matrix A
CPTTRS - solves a tridiagonal system
using the factorization computed by CPTTRF
CPTTS2 - solves a tridiagonal system
using the factorization computed by CPTTRF
CSPCON - estimates the reciprocal of
the condition number (in the 1-norm) of a complex symmetric packed matrix
A
CSPRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
indefinite and packed
CSPSV - computes the solution to a
complex system of linear equations
CSPSVX - uses diagonal pivoting factorization
to compute the solution to a complex system of linear equations
CSPTRF - computes the factorization
of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman
diagonal pivoting method
CSPTRI - computes the inverse of a
complex symmetric indefinite matrix A in packed storage using the factorization
computed by CSPTRF
CSPTRS - solves a system of linear
equations with a complex symmetric matrix A stored in packed format using
the factorization computed by CSPTRF
CSRSCL - multiplies an n-element complex
vector x by the real scalar 1/a
CSTEDC - computes all eigenvalues and,
optionally, eigenvectors of a symmetric tridiagonal matrix using the divide
and conquer method
CSTEGR - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
CSTEIN - computes the eigenvectors
of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues,
using inverse iteration
CSTEQR - computes all eigenvalues and,
optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit
QL or QR method
CSYCON - estimates the reciprocal of
the condition number (in the 1-norm) of a complex symmetric matrix A using
the factorization computed by CSYTRF
CSYRFS - improves 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
CSYSV - computes the solution to a
complex system of linear equations
CSYSVX - uses the diagonal pivoting
factorization to compute the solution to a complex system of linear equations
CSYTF2 - computes the factorization
of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
CSYTRF - computes the factorization
of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
CSYTRI - computes the inverse of a
complex symmetric indefinite matrix A using the factorization computed
by CSYTRF
CSYTRS - solves a system of linear
equations with a complex symmetric matrix A using the factorization computed
by CSYTRF
CTBCON - estimates the reciprocal of
the condition number of a triangular band matrix A, in either the 1-norm
or the infinity-norm
CTBRFS - provides error bounds and
backward error estimates for the solution to a system of linear equations
with a triangular band coefficient matrix
CTBTRS - solves a triangular system
CTGEVC - computes some or all of the
right and/or left generalized eigenvectors of a pair of complex upper
triangular matrices (A,B)
CTGEX2 - swaps adjacent diagonal 1
by 1 blocks (A11,B11) and (A22,B22)
CTGEXC - reorders the generalized Schur
decomposition of a complex matrix pair (A,B), using a unitary equivalence
transformation
CTGSEN - reorders the generalized Schur
decomposition of a complex matrix pair (A, B)
CTGSJA - computes the generalized singular
value decomposition (GSVD) of two complex upper triangular (or trapezoidal)
matrices A and B
CTGSNA - estimates reciprocal condition
numbers for specified eigenvalues and/or eigenvectors of a matrix pair
(A, B)
CTGSY2 - solves the generalized Sylvester
equation using Level 1 and 2 BLAS
CTGSYL - solves the generalized Sylvester
equation
CTPCON - estimates the reciprocal of
the condition number of a packed triangular matrix A, in either the 1-norm
or the infinity-norm
CTPRFS - provides error bounds and
backward error estimates for the solution to a system of linear equations
with a triangular packed coefficient matrix
CTPTRI - computes the inverse of a
complex upper or lower triangular matrix A stored in packed format
CTPTRS - solves a triangular system
CTRCON - estimates the reciprocal of
the condition number of a triangular matrix A, in either the 1-norm or
the infinity-norm
CTREVC - computes some or all of the
right and/or left eigenvectors of a complex upper triangular matrix T
CTREXC - reorders the Schur factorization
of a complex matrix so that the diagonal element of T with row index IFST
is moved to row ILST
CTRID - computes the solution to a
complex system of linear equations
CTRRFS - provides error bounds and
backward error estimates for the solution to a system of linear equations
with a triangular coefficient matrix
CTRSEN - reorders the Schur factorization
of a complex matrix
CTRSNA - estimates reciprocal condition
numbers for specified eigenvalues and/or right eigenvectors of a complex
upper triangular matrix T
CTRSYL - solves the complex Sylvester
matrix equation
CTRTI2 - computes the inverse of a
complex upper or lower triangular matrix
CTRTRI - computes the inverse of a
complex upper or lower triangular matrix A
CTRTRS - solves a triangular system
CTZRQF - routine is deprecated and
has been replaced by routine CTZRZF
CTZRZF - reduces the M-by-N ( M<=N
) complex upper trapezoidal matrix A to upper triangular form by means
of unitary transformations
CUNG2L - generates an m by n complex
matrix Q with orthonormal columns,
CUNG2R - generates an m by n complex
matrix Q with orthonormal columns,
CUNGBR - generates one of the complex
unitary matrices Q or PH determined by CGEBRD
when reducing a complex matrix A to bidiagonal form
CUNGHR - generates a complex unitary
matrix Q which is defined as the product of IHI-ILO elementary reflectors
of order N, as returned by CGEHRD
CUNGL2 - generates an m-by-n complex
matrix Q with orthonormal rows,
CUNGLQ - generates an M-by-N complex
matrix Q with orthonormal rows,
CUNGQL - generates an M-by-N complex
matrix Q with orthonormal columns,
CUNGQR - generates an M-by-N complex
matrix Q with orthonormal columns,
CUNGR2 - generates an m by n complex
matrix Q with orthonormal rows,
CUNGRQ - generates an M-by-N complex
matrix Q with orthonormal rows,
CUNGTR - generates a complex unitary
matrix Q which is defined as the product of n-1 elementary reflectors
of order N, as returned by CHETRD
CUNM2L - overwrites the general complex
m-by-n matrix C
CUNM2R - overwrites the general complex
m-by-n matrix C
CUNMBR - overwrites the general complex
M-by-N matrix C
CUNMHR - overwrites the general complex
M-by-N matrix C
CUNML2 - overwrites the general complex
m-by-n matrix C
CUNMLQ - overwrites the general complex
M-by-N matrix C
CUNMQL - overwrites the general complex
M-by-N matrix C
CUNMQR - overwrites the general complex
M-by-N matrix C
CUNMR2 - overwrites the general complex
m-by-n matrix C
CUNMR3 - overwrites the general complex
m by n matrix C
CUNMRQ - overwrites the general complex
M-by-N matrix C
CUNMRZ - overwrites the general complex
M-by-N matrix C
CUNMTR - overwrites the general complex
M-by-N matrix C
CUPGTR - generates a complex unitary
matrix Q
CUPMTR - overwrites the general complex
M-by-N matrix C
DBDSDC - computes the singular value
decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix
B
DBDSQR - computes the singular value
decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix
B
DDISNA - computes the reciprocal condition
numbers for the eigenvectors of a real symmetric or complex Hermitian
matrix or for the left or right singular vectors of a general m-by-n matrix
DGBBRD - reduces a real general m-by-n
band matrix A to upper bidiagonal form B by an orthogonal transformation
DGBCON - estimates the reciprocal of
the condition number of a real general band matrix A
DGBEQU - computes row and column scalings
intended to equilibrate an M-by-N band matrix A and reduce its condition
number
DGBRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is banded
DGBSV - computes the solution to a
real system of linear equations
DGBSVX - uses the LU factorization
to compute the solution to a real system of linear equations
DGBTF2 - computes an LU factorization
of a real m-by-n band matrix A using partial pivoting with row interchanges
DGBTRF - computes an LU factorization
of a real m-by-n band matrix A using partial pivoting with row interchanges
DGBTRS - solves a system of linear
equations with a general band matrix A using the LU factorization computed
by DGBTRF
DGEBAK - forms the right or left eigenvectors
of a real general matrix by backward transformation on the computed eigenvectors
of the balanced matrix output by DGEBAL
DGEBAL - balances a general real matrix
A
DGEBD2 - reduces a real general m by
n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
DGEBRD - reduces a general real M-by-N
matrix A to upper or lower bidiagonal form B by an orthogonal transformation
DGECON - estimates the reciprocal of
the condition number of a general real matrix A, in either the 1-norm
or the infinity-norm, using the LU factorization computed by DGETRF
DGEEQU - computes row and column scalings
intended to equilibrate an M-by-N matrix A and reduce its condition number
DGEES - computes 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 - computes 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 - computes for an N-by-N real
nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or
right eigenvectors
DGEEVX - computes for an N-by-N real
nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or
right eigenvectors
DGEGS - routine is deprecated and has
been replaced by routine DGGES
DGEGV - routine is deprecated and has
been replaced by routine DGGEV
DGEHD2 - reduces a real general matrix
A to upper Hessenberg form H by an orthogonal similarity transformation
DGEHRD - reduces a real general matrix
A to upper Hessenberg form H by an orthogonal similarity transformation
DGELQ2 - computes an LQ factorization
of a real m by n matrix A
DGELQF - computes an LQ factorization
of a real M-by-N matrix A
DGELS - solves 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 - computes the minimum-norm
solution to a real linear least squares problem
DGELSS - computes the minimum norm
solution to a real linear least squares problem
DGELSX - routine is deprecated and
has been replaced by routine DGELSY
DGELSY - computes the minimum-norm
solution to a real linear least squares problem
DGEQL2 - computes a QL factorization
of a real m by n matrix A
DGEQLF - computes a QL factorization
of a real M-by-N matrix A
DGEQP3 - computes a QR factorization
with column pivoting of a matrix A
DGEQPF - routine is deprecated and
has been replaced by routine DGEQP3
DGEQR2 - computes a QR factorization
of a real m by n matrix A
DGEQRF - computes a QR factorization
of a real M-by-N matrix A
DGERFS - improves the computed solution
to a system of linear equations and provides error bounds and backward
error estimates for the solution
DGERQ2 - computes an RQ factorization
of a real m by n matrix A
DGERQF - computes an RQ factorization
of a real M-by-N matrix A
DGESC2 - solves a system of linear
equations with a general N-by-N matrix A using the LU factorization with
complete pivoting computed by DGETC2
DGESDD - computes the singular value
decomposition (SVD) of a real M-by-N matrix A
DGESV - computes the solution to a
real system of linear equations
DGESVD - computes the singular value
decomposition (SVD) of a real M-by-N matrix A
DGESVX - uses the LU factorization
to compute the solution to a real system of linear equations
DGETC2 - computes an LU factorization
with complete pivoting of the n-by-n matrix A
DGETF2 - computes an LU factorization
of a general m-by-n matrix A using partial pivoting with row interchanges
DGETRF - computes an LU factorization
of a general M-by-N matrix A using partial pivoting with row interchanges
DGETRI - computes the inverse of a
matrix using the LU factorization computed by DGETRF
DGETRS - solves a system of linear
equations with a general N-by-N matrix A using the LU factorization computed
by DGETRF
DGGBAK - forms the right or left eigenvectors
of a real generalized eigenvalue problem by backward transformation on
the computed eigenvectors of the balanced pair of matrices output by DGGBAL
DGGBAL - balances a pair of general
real matrices (A,B)
DGGES - computes for a pair of N-by-N
real nonsymmetric matrices (A,B),
DGGESX - computes for a pair of N-by-N
real nonsymmetric matrices (A,B), the generalized eigenvalues and the
real Schur form (S,T)
DGGEV - computes for a pair of N-by-N
real nonsymmetric matrices (A,B) the generalized eigenvalues
DGGEVX - computes for a pair of N-by-N
real nonsymmetric matrices (A,B) the generalized eigenvalues
DGGGLM - solves a general Gauss-Markov
linear model (GLM) problem
DGGHRD - reduces 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 - solves the linear equality-constrained
least squares (LSE) problem
DGGQRF - computes a generalized QR
factorization of an N-by-M matrix A and an N-by-P matrix B
DGGRQF - computes a generalized RQ
factorization of an M-by-N matrix A and a P-by-N matrix B
DGGSVD - computes the generalized singular
value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real
matrix B
DGGSVP - computes orthogonal matrices
U, V and Q
DGTCON - estimates the reciprocal of
the condition number of a real tridiagonal matrix A using the LU factorization
as computed by DGTTRF
DGTRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is tridiagonal
DGTSV - solves the equation AX = B
DGTSVX - uses the LU factorization
to compute the solution to a real system of linear equations
DGTTRF - computes an LU factorization
of a real tridiagonal matrix A using elimination with partial pivoting
and row interchanges
DGTTRS - solves one of the systems
of equations AX = B or A'X = B
DGTTS2 - solves one of the systems
of equations AX = B or A'X = B
DHGEQZ - implements a single-/double-shift
version of the QZ method for finding generalized eigenvalues
DHSEIN - uses inverse iteration to
find specified right and/or left eigenvectors of a real upper Hessenberg
matrix H
DHSEQR - computes the eigenvalues of
a real upper Hessenberg matrix H
DLABAD - returns the square root of
values
DLABRD - reduces the first NB rows
and columns of a real general m by n matrix A to upper or lower bidiagonal
form by an orthogonal transformation
DLACON - estimates the 1-norm of a
square, real matrix A
DLACPY - copies all or part of a two-dimensional
matrix A to another matrix B
DLADIV - performs complex division
in real arithmetic
DLAE2 - computes the eigenvalues of
a 2-by-2 symmetric matrix
DLAEBZ - contains the iteration loops
which compute and use the function N(w)
DLAED0 - computes all eigenvalues and
corresponding eigenvectors of a symmetric tridiagonal matrix using the
divide and conquer method
DLAED1 - computes the updated eigensystem
of a diagonal matrix after modification by a rank-one symmetric matrix
DLAED2 - merges the two sets of eigenvalues
together into a single sorted set
DLAED3 - finds the roots of the secular
equation, as defined by the values in D, W, and RHO, between 1 and K
DLAED4 - computes the I-th updated
eigenvalue of a symmetric rank-one modification to a diagonal matrix
DLAED5 - computes the I-th eigenvalue
of a symmetric rank-one modification of a 2-by-2 diagonal matrix
DLAED6 - computes the positive or negative
root (closest to the origin)
DLAED7 - computes the updated eigensystem
of a diagonal matrix after modification by a rank-one symmetric matrix
DLAED8 - merges the two sets of eigenvalues
together into a single sorted set
DLAED9 - finds the roots of the secular
equation, as defined by the values in D, Z, and RHO, between KSTART and
KSTOP
DLAEDA - computes the Z vector corresponding
to the merge step in the CURLVLth step of the
merge process with TLVLS steps for the CURPBMth problem
DLAEIN - uses inverse iteration to
find a right or left eigenvector corresponding to the eigenvalue (WR,WI)
of a real upper Hessenberg matrix H
DLAEV2 - computes the eigendecomposition
of a 2-by-2 symmetric matrix
DLAEXC - swaps adjacent diagonal blocks
T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an
orthogonal similarity transformation
DLAG2 - computes the eigenvalues of
a 2 x 2 generalized eigenvalue problem with scaling as necessary to avoid
over-/underflow
DLAGS2 - computes 2-by-2 orthogonal
matrices U, V and Q
DLAGTF - factorizes a matrix
DLAGTM - performs a matrix-vector product
DLAGTS - solves one of two systems
of equations
DLAGV2 - computes the Generalized Schur
factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular
DLAHQR - updates the eigenvalues and
Schur decomposition already computed by DHSEQR
DLAHRD - reduces the first NB columns
of a real general n-by-(n-k+1) matrix A so that elements below the k
th subdiagonal are zero
DLAIC1 - applies one step of incremental
condition estimation in its simplest version
DLALN2 - solves a system with possible
scaling and perturbation of A
DLALS0 - applies back the multiplying
factors of either the left or the right singular vector matrix of a diagonal
matrix appended by a row to the right hand side matrix B in solving the
least squares problem using the divide-and-conquer SVD approach
DLALSA - an itermediate step in solving
the least squares problem by computing the SVD of the coefficient matrix
in compact form
DLALSD - uses the singular value decomposition
of A to solve the least squares problem
DLAMCH - determines double precision
machine parameters
DLAMRG - creates a permutation list
which merges the elements of A
DLANGB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n band matrix A
DLANGE - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a real matrix A
DLANGT - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a real tridiagonal matrix A
DLANHS - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a Hessenberg matrix A
DLANSB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n symmetric band matrix A, with k super-diagonals
DLANSP - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a real symmetric matrix A, supplied in packed form
DLANST - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a real symmetric tridiagonal matrix A
DLANSY - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a real symmetric matrix A
DLANTB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
DLANTP - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a triangular matrix A, supplied in packed form
DLANTR - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a trapezoidal or triangular matrix A
DLANV2 - computes the Schur factorization
of a real 2-by-2 nonsymmetric matrix in standard form
DLAPLL - computers the QR factorization
of A=QR
DLAPMT - rearranges the columns of
the M by N matrix X
DLAPY2 - returns sqrt(x
22+y2) without causing unnecessary
overflow
DLAPY3 - returns sqrt(x
2+y2+z2)
without causing unnecessary overflow
DLAQGB - equilibrates a general M by
N band matrix A with KL subdiagonals and KU superdiagonals using the row
and scaling factors in the vectors R and C
DLAQGE - equilibrates a general M by
N matrix A using the row and scaling factors in the vectors R and C
DLAQP2 - computes a QR factorization
with column pivoting of the block A(OFFSET+1:M,1:N)
DLAQPS - computes a step of QR factorization
with column pivoting of a real M-by-N matrix A by using Blas-3
DLAQSB - equilibrates a symmetric band
matrix A using the scaling factors in the vector S
DLAQSP - equilibrates a symmetric matrix
A using the scaling factors in the vector S
DLAQSY - equilibrates a symmetric matrix
A using the scaling factors in the vector S
DLAQTR - solves a real quasi-triangular
system
DLAR1V - computes the (scaled) r
th column of the inverse of a sumbmatrix
DLAR2V - applies a vector of real plane
rotations from both sides to a sequence of 2-by-2 real symmetric matrices,
defined by the elements of the vectors x, y and z
DLARF - applies a real elementary reflector
H to a real m by n matrix C, from either the left or the right
DLARFB - applies a real block reflector
H or its transpose H' to a real m by n matrix C, from either the left
or the right
DLARFG - generates a real elementary
reflector H of order n
DLARFT - forms the triangular factor
T of a real block reflector H of order n, which is defined as a product
of k elementary reflectors
DLARFX - applies a real elementary
reflector H to a real m by n matrix C, from either the left or the right
DLARGV - generates a vector of real
plane rotations, determined by elements of the real vectors x and y
DLARNV - returns a vector of n random
real numbers from a uniform or normal distribution
DLARRB - does limited bisection to
locate eigenvalues
DLARRE - sets "small" off-diagonal
elements to zero
DLARRF - finds a robust representation
of input values
DLARRV - computes the eigenvectors
of the tridiagonal matrix
DLARTG - generates a plane rotation
DLARTV - applies a vector of real plane
rotations to elements of the real vectors x and y
DLARUV - returns a vector of n random
real numbers from a uniform (0,1)
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 to a real distributed M-by-N C from the left or the
right
DLARZT - forms the triangular factor
T of a real block reflector H of order > n, which is defined as a product
of k elementary reflectors
DLAS2 - computes the singular values
of the 2-by-2 matrix
DLASCL - multiplies the M by N real
matrix A by the real scalar CTO/CFROM
DLASD0 - computes the singular value
decomposition (SVD) of a real upper bidiagonal N-by-M matrix B
DLASD1 - computes the SVD of an upper
bidiagonal N-by-M matrix B
DLASD2 - merges the two sets of singular
values together into a single sorted set
DLASD3 - finds all the square roots
of the roots of the secular equation, as defined by the values in D and
Z
DLASD4 - computes the square root of
the Ith updated eigenvalue of a positive symmetric
rank-one modification to a positive diagonal matrix
DLASD5 - computes the square root of
the Ith eigenvalue of a positive symmetric
rank-one modification of a 2-by-2 diagonal matrix
DLASD6 - computes the SVD of an updated
upper bidiagonal matrix B obtained by merging two smaller ones by appending
a row
DLASD7 - merges the two sets of singular
values together into a single sorted set
DLASD8 - finds the square roots of
the roots of the secular equation,
DLASD9 - finds the square roots of
the roots of the secular equation,
DLASDA - computes the singular value
decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal
D and offdiagonal E
DLASDQ - computes the singular value
decomposition (SVD) of a real (upper or lower) bidiagonal matrix with
diagonal D and offdiagonal E, accumulating the transformations if desired
DLASDT - creates a tree of subproblems
for bidiagonal divide and conquer
DLASET - initializes an m-by-n matrix
A to BETA on the diagonal and ALPHA on the offdiagonals
DLASQ1 - computes the singular values
of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E
DLASQ2 - computes all the eigenvalues
of the symmetric positive definite tridiagonal matrix
DLASQ3 - computes a shift (TAU)
DLASQ4 - computes an approximation
TAU to the smallest eigenvalue using values of d from the previous transform
DLASQ5 - computes one dqds transform
in ping-pong form, one version for IEEE machines another for non IEEE
machines
DLASQ6 - computes one dqd (shift equal
to zero) transform in ping-pong form, with protection against underflow
and overflow
DLASR - perform a transformation where
A is an m by n real matrix and P is an orthogonal matrix,
DLASRT - sorts numbers
DLASSQ - returns the values scl and
smsq
DLASV2 - computes the singular value
decomposition of a 2-by-2 triangular matrix
DLASWP - performs a series of row interchanges
on the matrix A
DLASY2 - solves for the N1 by N2 matrix
X
DLASYF - computes a partial factorization
of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
DLATBS - solves one of two triangular
systems with scaling to prevent overflow, where A is an upper or lower
triangular band matrix
DLATDF - uses the LU factorization
of the n-by-n matrix Z computed by DGETC2
DLATPS - solves a triangular system
with scaling to prevent overflow
DLATRD - reduces NB rows and columns
of a real symmetric matrix A to symmetric tridiagonal form
DLATRS - solves a triangular system
with scaling to prevent overflow
DLATRZ - factors the M-by-(M+L) real
upper trapezoidal matrix by means of orthogonal transformations
DLATZM - routine is deprecated and
has been replaced by routine DORMRZ
DLAUU2 - computes the product U ×
U' or L' × L, where the triangular factor U or L is stored in the
upper or lower triangular part of the array A
DLAUUM - computes the product U ×
U' or L' × L, where the triangular factor U or L is stored in the
upper or lower triangular part of the array A
DOPGTR - generates 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 - overwrites the general real
M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
DORG2L - generates an m by n real matrix
Q with orthonormal columns
DORG2R - generates an m by n real matrix
Q with orthonormal columns
DORGBR - generates one of the real
orthogonal matrices Q or PT determined by DGEBRD
when reducing a real matrix A to bidiagonal form
DORGHR - generates a real orthogonal
matrix Q which is defined as the product of IHI-ILO elementary reflectors
of order N, as returned by DGEHRD
DORGL2 - generates an m by n real matrix
Q with orthonormal rows
DORGLQ - generates an M-by-N real matrix
Q with orthonormal rows
DORGQL - generates an M-by-N real matrix
Q with orthonormal columns
DORGQR - generates an M-by-N real matrix
Q with orthonormal columns
DORGR2 - generates an m by n real matrix
Q with orthonormal rows
DORGRQ - generates an M-by-N real matrix
Q with orthonormal rows
DORGTR - generates a real orthogonal
matrix Q as returned by DSYTRD
DORM2L - overwrites the general real
m by n matrix C
DORM2R - overwrites the general real
m by n matrix C
DORMBR - overwrites the general real
M-by-N matrix C
DORMHR - overwrites the general real
M-by-N matrix C
DORML2 - overwrites the general real
m by n matrix C
DORMLQ - overwrites the general real
M-by-N matrix C
DORMQL - overwrites the general real
M-by-N matrix C
DORMQR - overwrites the general real
M-by-N matrix C
DORMR2 - overwrites the general real
m by n matrix C
DORMR3 - overwrites the general real
m by n matrix C
DORMRQ - overwrites the general real
M-by-N matrix C
DORMRZ - overwrites the general real
M-by-N matrix C
DORMTR - overwrites the general real
M-by-N matrix C
DPBCON - estimates the reciprocal of
the condition number (in the 1-norm) of a real symmetric positive definite
band matrix using the Cholesky factorization computed by DPBTRF
DPBEQU - computes 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)
DPBRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
positive definite and banded, and provides error bounds and backward error
estimates for the solution
DPBSTF - computes a split Cholesky
factorization of a real symmetric positive definite band matrix A
DPBSV - computes the solution to a
real system of linear equations
DPBSVX - uses the Cholesky factorization
to compute the solution to a real system of linear equations
DPBTF2 - computes the Cholesky factorization
of a real symmetric positive definite band matrix A
DPBTRF - computes the Cholesky factorization
of a real symmetric positive definite band matrix A
DPBTRS - solves a system of linear
equations with a symmetric positive definite band matrix A using the Cholesky
factorization computed by DPBTRF
DPOCON - estimates the reciprocal of
the condition number (in the 1-norm) of a real symmetric positive definite
matrix using the Cholesky factorization computed by DPOTRF
DPOEQU - computes row and column scalings
intended to equilibrate a symmetric positive definite matrix A and reduce
its condition number (with respect to the two-norm)
DPORFS - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
positive definite
DPOSV - computes the solution to a
real system of linear equations
DPOSVX - uses the Cholesky factorization
to compute the solution to a real system of linear equations
DPOTF2 - computes the Cholesky factorization
of a real symmetric positive definite matrix A
DPOTRF - computes the Cholesky factorization
of a real symmetric positive definite matrix A
DPOTRI - computes the inverse of a
real symmetric positive definite matrix A using the Cholesky factorization
computed by DPOTRF
DPOTRS - solves a system of linear
equations with a symmetric positive definite matrix A using the Cholesky
factorization computed by DPOTRF
DPPCON - estimates the reciprocal of
the condition number (in the 1-norm) of a real symmetric positive definite
packed matrix using the Cholesky factorization computed by DPPTRF
DPPEQU - computes 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)
DPPRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
positive definite and packed
DPPSV - computes the solution to a
real system of linear equations
DPPSVX - uses the Cholesky factorization
to compute the solution to a real system of linear equations
DPPTRF - computes the Cholesky factorization
of a real symmetric positive definite matrix A stored in packed format
DPPTRI - computes the inverse of a
real symmetric positive definite matrix A using the Cholesky factorization
computed by DPPTRF
DPPTRS - solves a system of linear
equations with a symmetric positive definite matrix A in packed storage
using the Cholesky factorization computed by DPPTRF
DPTCON - computes the reciprocal of
the condition number (in the 1-norm) of a real symmetric positive definite
tridiagonal matrix using the factorization computed by DPTTRF
DPTEQR - computes all eigenvalues and,
optionally, eigenvectors of a symmetric positive definite tridiagonal
matrix
DPTRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
positive definite and tridiagonal
DPTSV - computes the solution to a
real system of linear equations
DPTSVX - computes the solution to a
real system of linear equations where A is an N-by-N symmetric positive
definite tridiagonal matrix and X and B are N-by-NRHS matrices
DPTTRF - computes the factorization
of a real symmetric positive definite tridiagonal matrix A
DPTTRS - solves a tridiagonal system
using the factorization of A computed by DPTTRF
DPTTS2 - solves a tridiagonal system
using the factorization of A computed by DPTTRF
DRSCL - multiplies an n-element real
vector x by the real scalar 1/a
DSBEV - computes all the eigenvalues
and, optionally, eigenvectors of a real symmetric band matrix A
DSBEVD - computes all the eigenvalues
and, optionally, eigenvectors of a real symmetric band matrix A
DSBEVX - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric band matrix A
DSBGST - reduces a real symmetric-definite
banded generalized eigenproblem
DSBGV - computes all the eigenvalues,
and optionally, the eigenvectors of a real generalized symmetric-definite
banded eigenproblem
DSBGVD - computes all the eigenvalues,
and optionally, the eigenvectors of a real generalized symmetric-definite
banded eigenproblem
DSBGVX - computes selected eigenvalues,
and optionally, eigenvectors of a real generalized symmetric-definite
banded eigenproblem
DSBTRD - reduces a real symmetric band
matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
DSECND - returns the user time for
a process in seconds
DSPCON - estimates the reciprocal of
the condition number (in the 1-norm) of a real symmetric packed matrix
A
DSPEV - computes all the eigenvalues
and, optionally, eigenvectors of a real symmetric matrix A in packed storage
DSPEVD - computes all the eigenvalues
and, optionally, eigenvectors of a real symmetric matrix A in packed storage
DSPEVX - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric matrix A in packed storage
DSPGST - reduces a real symmetric-definite
generalized eigenproblem to standard form, using packed storage
DSPGV - computes all the eigenvalues
and, optionally, the eigenvectors of a real generalized symmetric-definite
eigenproblem
DSPGVD - computes all the eigenvalues,
and optionally, the eigenvectors of a real generalized symmetric-definite
eigenproblem
DSPGVX - computes selected eigenvalues,
and optionally, eigenvectors of a real generalized symmetric-definite
eigenproblem
DSPRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
indefinite and packed
DSPSV - computes the solution to a
real system of linear equations
DSPSVX - uses the diagonal pivoting
factorization to compute the solution to a real system of linear equations
where A is an N-by-N symmetric matrix stored in packed format and X and
B are N-by-NRHS matrices
DSPTRD - reduces a real symmetric matrix
A stored in packed form to symmetric tridiagonal form T by an orthogonal
similarity transformation
DSPTRF - computes the factorization
of a real symmetric matrix A stored in packed format using the Bunch-Kaufman
diagonal pivoting method
DSPTRI - computes the inverse of a
real symmetric indefinite matrix A in packed storage using a factorization
computed by DSPTRF
DSPTRS - solves a system of linear
equations with a real symmetric matrix A stored in packed format using
a factorization computed by DSPTRF
DSTEBZ - computes the eigenvalues of
a symmetric tridiagonal matrix T
DSTEDC - computes all eigenvalues and,
optionally, eigenvectors of a symmetric tridiagonal matrix using the divide
and conquer method
DSTEGR - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
DSTEIN - computes the eigenvectors
of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues,
using inverse iteration
DSTEQR - computes all eigenvalues and,
optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit
QL or QR method
DSTERF - computes all eigenvalues of
a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the
QL or QR algorithm
DSTEV - computes all eigenvalues and,
optionally, eigenvectors of a real symmetric tridiagonal matrix A
DSTEVD - computes all eigenvalues and,
optionally, eigenvectors of a real symmetric tridiagonal matrix
DSTEVR - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
DSTEVX - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
DSYCON - estimates the reciprocal of
the condition number (in the 1-norm) of a real symmetric matrix A using
a factorization computed by DSYTRF
DSYEV - computes all eigenvalues and,
optionally, eigenvectors of a real symmetric matrix A
DSYEVD - computes all eigenvalues and,
optionally, eigenvectors of a real symmetric matrix A
DSYEVR - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric matrix T
DSYEVX - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric matrix A
DSYGS2 - reduces a real symmetric-definite
generalized eigenproblem to standard form
DSYGST - reduces a real symmetric-definite
generalized eigenproblem to standard form
DSYGV - computes all the eigenvalues,
and optionally, the eigenvectors of a real generalized symmetric-definite
eigenproblem
DSYGVD - computes all the eigenvalues,
and optionally, the eigenvectors of a real generalized symmetric-definite
eigenproblem
DSYGVX - computes selected eigenvalues,
and optionally, eigenvectors of a real generalized symmetric-definite
eigenproblem
DSYRFS - improves 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
DSYSV - computes the solution to a
real system of linear equations
DSYSVX - uses the diagonal pivoting
factorization to compute the solution to a real system of linear equations
DSYTD2 - reduces a real symmetric matrix
A to symmetric tridiagonal form T by an orthogonal similarity transformation
DSYTF2 - computes the factorization
of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
DSYTRD - reduces a real symmetric matrix
A to real symmetric tridiagonal form T by an orthogonal similarity transformation
DSYTRF - computes the factorization
of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
DSYTRI - computes the inverse of a
real symmetric indefinite matrix A using a factorizationcomputed by DSYTRF
DSYTRS - solves a system of linear
equations with a real symmetric matrix A using a factorization computed
by DSYTRF
DTBCON - estimates the reciprocal of
the condition number of a triangular band matrix A, in either the 1-norm
or the infinity-norm
DTBRFS - provides error bounds and
backward error estimates for the solution to a system of linear equations
with a triangular band coefficient matrix
DTBTRS - solves a triangular system
DTGEVC - computes some or all of the
right and/or left generalized eigenvectors of a pair of real upper triangular
matrices (A,B)
DTGEX2 - swaps adjacent diagonal blocks
(A11, B11) and (A22, B22)
DTGEXC - reorders the generalized real
Schur decomposition of a real matrix pair (A,B)
DTGSEN - reorders the generalized real
Schur decomposition of a real matrix pair (A, B)
DTGSJA - computes the generalized singular
value decomposition (GSVD) of two real upper triangular (or trapezoidal)
matrices A and B
DTGSNA - estimates reciprocal condition
numbers for specified eigenvalues and/or eigenvectors of a matrix pair
(A, B) in generalized real Schur canonical form
DTGSY2 - solves the generalized Sylvester
equation
DTGSYL - solves the generalized Sylvester
equation
DTPCON - estimates the reciprocal of
the condition number of a packed triangular matrix A, in either the 1-norm
or the infinity-norm
DTPRFS - provides error bounds and
backward error estimates for the solution to a system of linear equations
with a triangular packed coefficient matrix
DTPTRI - computes the inverse of a
real upper or lower triangular matrix A stored in packed format
DTPTRS - solves a triangular system
DTRCON - estimates the reciprocal of
the condition number of a triangular matrix A, in either the 1-norm or
the infinity-norm
DTREVC - computes some or all of the
right and/or left eigenvectors of a real upper quasi-triangular matrix
T
DTREXC - reorders the real Schur factorization
of a real matrix so that the diagonal block of T with row index IFST is
moved to row ILST
DTRID - computes the solution to a
real system of linear equations where A is an N-by-N tridiagonal matrix,
and x and b are vectors of length N
DTRRFS - provide serror bounds and
backward error estimates for the solution to a system of linear equations
with a triangular coefficient matrix
DTRSEN - reorders the real Schur factorization
of a real matrix so that a selected cluster of eigenvalues appears in
the leading diagonal blocks of the upper quasi-triangular matrix T
DTRSNA - estimates reciprocal condition
numbers for specified eigenvalues and/or right eigenvectors of a real
upper quasi-triangular matrix T
DTRSYL - solves the real Sylvester
matrix equation
DTRTI2 - computes the inverse of a
real upper or lower triangular matrix
DTRTRI - computes the inverse of a
real upper or lower triangular matrix A
DTRTRS - solves a triangular system
DTZRQF - routine is deprecated and
has been replaced by routine DTZRZF
DTZRZF - reduces the M-by-N real upper
trapezoidal matrix A to upper triangular form by means of orthogonal transformations
DZSUM1 - takes the sum of the absolute
values of a complex vector and returns a double precision result
ICMAX1 - finds the index of the element
whose real part has maximum absolute value
ILAENV - called from the LAPACK routines
to choose problem-dependent parameters for the local environment
IZMAX1 - finds the index of the element
whose real part has maximum absolute value
LSAME - return .TRUE
LSAMEN - tests if the first N letters
of CA are the same as the first N letters of CB, regardless of case
SBDSDC - computes the singular value
decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix
B
SBDSQR - computes the singular value
decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix
B
SCSUM1 - take the sum of the absolute
values of a complex vector and returns a single precision result
SDISNA - computes the reciprocal condition
numbers for the eigenvectors of a real symmetric or complex Hermitian
matrix or for the left or right singular vectors of a general m-by-n matrix
SECOND - returns the user time for
a process in seconds
SGBBRD - reduces a real general m-by-n
band matrix A to upper bidiagonal form B by an orthogonal transformation
SGBCON - estimates the reciprocal of
the condition number of a real general band matrix A, in either the 1-norm
or the infinity-norm,
SGBEQU - computes row and column scalings
intended to equilibrate an M-by-N band matrix A and reduce its condition
number
SGBRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is banded
SGBSV - computes the solution to a
real system of linear equations 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 - uses the LU factorization
to compute the solution to a real system of linear equations
SGBTF2 - computes an LU factorization
of a real m-by-n band matrix A using partial pivoting with row interchanges
SGBTRF - computes an LU factorization
of a real m-by-n band matrix A using partial pivoting with row interchanges
SGBTRS - solves a system of linear
equations with a general band matrix A using the LU factorization computed
by SGBTRF
SGEBAK - forms the right or left eigenvectors
of a real general matrix by backward transformation on the computed eigenvectors
of the balanced matrix output by SGEBAL
SGEBAL - balances a general real matrix
A
SGEBD2 - reduces a real general m by
n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
SGEBRD - reduces a general real M-by-N
matrix A to upper or lower bidiagonal form B by an orthogonal transformation
SGECON - estimates the reciprocal of
the condition number of a general real matrix A, in either the 1-norm
or the infinity-norm, using the LU factorization computed by SGETRF
SGEEQU - computes row and column scalings
intended to equilibrate an M-by-N matrix A and reduce its condition number
SGEES - computes 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 - computes 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 - computes for an N-by-N real
nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or
right eigenvectors
SGEEVX - computes for an N-by-N real
nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or
right eigenvectors
SGEGS - routine is deprecated and has
been replaced by routine SGGES
SGEGV - routine is deprecated and has
been replaced by routine SGGEV
SGEHD2 - reduces a real general matrix
A to upper Hessenberg form H by an orthogonal similarity transformation
SGEHRD - reduces a real general matrix
A to upper Hessenberg form H by an orthogonal similarity transformation
SGELQ2 - computes an LQ factorization
of a real m by n matrix A
SGELQF - computes an LQ factorization
of a real M-by-N matrix A
SGELS - solves 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 - computes the minimum-norm
solution to a real linear least squares problem
SGELSS - computes the minimum norm
solution to a real linear least squares problem
SGELSX - routine is deprecated and
has been replaced by routine SGELSY
SGELSY - computes the minimum-norm
solution to a real linear least squares problem
SGEQL2 - computes a QL factorization
of a real m by n matrix A
SGEQLF - computes a QL factorization
of a real M-by-N matrix A
SGEQP3 - computes a QR factorization
with column pivoting of a matrix A
SGEQPF - routine is deprecated and
has been replaced by routine SGEQP3
SGEQR2 - computes a QR factorization
of a real m by n matrix A
SGEQRF - computes a QR factorization
of a real M-by-N matrix A
SGERFS - improves the computed solution
to a system of linear equations and provides error bounds and backward
error estimates for the solution
SGERQ2 - computes an RQ factorization
of a real m by n matrix A
SGERQF - computes an RQ factorization
of a real M-by-N matrix A
SGESC2 - solves a system of linear
equations with a general N-by-N matrix A using the LU factorization with
complete pivoting computed by SGETC2
SGESDD - computes the singular value
decomposition (SVD) of a real M-by-N matrix A
SGESV - computes the solution to a
real system of linear equations
SGESVD - computes the singular value
decomposition (SVD) of a real M-by-N matrix A
SGESVX - uses the LU factorization
to compute the solution to a real system of linear equations
SGETC2 - computes an LU factorization
with complete pivoting of the n-by-n matrix A
SGETF2 - computes an LU factorization
of a general m-by-n matrix A using partial pivoting with row interchanges
SGETRF - computes an LU factorization
of a general M-by-N matrix A using partial pivoting with row interchanges
SGETRI - computes the inverse of a
matrix using the LU factorization computed by SGETRF
SGETRS - solves a system of linear
equations with a general N-by-N matrix A using the LU factorization computed
by SGETRF
SGGBAK - forms the right or left eigenvectors
of a real generalized eigenvalue problem by backward transformation on
the computed eigenvectors of the balanced pair of matrices output by SGGBAL
SGGBAL - balances a pair of general
real matrices (A,B)
SGGES - computes for a pair of N-by-N
real nonsymmetric matrices (A,B),
SGGESX - computes for a pair of N-by-N
real nonsymmetric matrices (A,B), the generalized eigenvalues, the real
Schur form (S,T), and,
SGGEV - computes for a pair of N-by-N
real nonsymmetric matrices (A,B)
SGGEVX - computes for a pair of N-by-N
real nonsymmetric matrices (A,B)
SGGGLM - solves a general Gauss-Markov
linear model (GLM) problem
SGGHRD - reduces 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 - solves the linear equality-constrained
least squares (LSE) problem
SGGQRF - computes a generalized QR
factorization of an N-by-M matrix A and an N-by-P matrix B
SGGRQF - computes a generalized RQ
factorization of an M-by-N matrix A and a P-by-N matrix B
SGGSVD - computes the generalized singular
value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real
matrix B
SGGSVP - computes orthogonal matrices
U, V and Q
SGTCON - estimates the reciprocal of
the condition number of a real tridiagonal matrix A using the LU factorization
as computed by SGTTRF
SGTRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is tridiagonal
SGTSV - solves the equation AX = B,
SGTSVX - uses the LU factorization
to compute the solution to a real system of linear equations
SGTTRF - computes an LU factorization
of a real tridiagonal matrix A using elimination with partial pivoting
and row interchanges
SGTTRS - solves one of two systems
of equations
SGTTS2 - solves one of two systems
of equations
SHGEQZ - implements a single-/double-shift
version of the QZ method for finding generalized eigenvalues
SHSEIN - uses inverse iteration to
find specified right and/or left eigenvectors of a real upper Hessenberg
matrix H
SHSEQR - computes the eigenvalues of
a real upper Hessenberg matrix H and, optionally, the matrices T and Z
from the Schur decomposition
SLABAD - takes as input the values
computed by SLAMCH for underflow and overflow, and returns the square
root of each of these values if the log of LARGE is sufficiently large
SLABRD - reduces the first NB rows
and columns of a real general m by n matrix A to upper or lower bidiagonal
form by an orthogonal transformation
SLACON - estimates the 1-norm of a
square, real matrix A
SLACPY - copies all or part of a two-dimensional
matrix A to another matrix B
SLADIV - performs complex division
in real arithmetic
SLAE2 - computes the eigenvalues of
a 2-by-2 symmetric matrix
SLAEBZ - contains the iteration loops
which compute and use the function N(w)
SLAED0 - computes all eigenvalues and
corresponding eigenvectors of a symmetric tridiagonal matrix using the
divide and conquer method
SLAED1 - computes the updated eigensystem
of a diagonal matrix after modification by a rank-one symmetric matrix
SLAED2 - merges the two sets of eigenvalues
together into a single sorted set
SLAED3 - finds the roots of the secular
equation, as defined by the values in D, W, and RHO, between 1 and K
SLAED4 - computes the I
th updated eigenvalue of a symmetric rank-one modification
to a diagonal matrix
SLAED5 - computes the I
th eigenvalue of a symmetric rank-one modification of a
2-by-2 diagonal matrix
SLAED6 - computes the positive or negative
root (closest to the origin)
SLAED7 - computes the updated eigensystem
of a diagonal matrix after modification by a rank-one symmetric matrix
SLAED8 - merges the two sets of eigenvalues
together into a single sorted set
SLAED9 - finds the roots of the secular
equation, as defined by the values in D, Z, and RHO, between KSTART and
KSTOP
SLAEDA - computes the Z vector corresponding
to the merge step in the CURLVLth step of the
merge process with TLVLS steps for the CURPBMth problem
SLAEIN - uses inverse iteration to
find a right or left eigenvector corresponding to the eigenvalue (WR,WI)
of a real upper Hessenberg matrix H
SLAEV2 - computes the eigendecomposition
of a 2-by-2 symmetric matrix
SLAEXC - swaps adjacent diagonal blocks
T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an
orthogonal similarity transformation
SLAG2 - computes the eigenvalues of
a 2 x 2 generalized eigenvalue problem with scaling as necessary
SLAGS2 - computes 2-by-2 orthogonal
matrices
SLAGTF - factorizes the matrix where
T is an n by n tridiagonal matrix and lambda is a scalar
SLAGTM - performs a matrix-vector product
SLAGTS - solves one of twi systems
of equations
SLAGV2 - computes the Generalized Schur
factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular
SLAHQR - an auxiliary routine called
by SHSEQR to update the eigenvalues and Schur decomposition already computed
by SHSEQR
SLAHRD - reduces the first NB columns
of a real general n-by-(n-k+1) matrix A so that elements below the k
th subdiagonal are zero
SLAIC1 - applies one step of incremental
condition estimation in its simplest version
SLALN2 - solves a system with possible
scaling ("s") and perturbation of A
SLALS0 - applies back the multiplying
factors of either the left or the right singular vector matrix of a diagonal
matrix
SLALSA - an itermediate step in solving
the least squares problem by computing the SVD of the coefficient matrix
in compact form
SLALSD - uses the singular value decomposition
of A to solve the least squares problem
SLAMCH - determines single precision
machine parameters
SLAMRG - creates a permutation list
that merges the elements of A (which is composed of two independently
sorted sets) into a single set which is sorted in ascending order
SLANGB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n band matrix A
SLANGE - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a real matrix A
SLANGT - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a real tridiagonal matrix A
SLANHS - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a Hessenberg matrix A
SLANSB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n symmetric band matrix A, with k super-diagonals
SLANSP - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a real symmetric matrix A, supplied in packed form
SLANST - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a real symmetric tridiagonal matrix A
SLANSY - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a real symmetric matrix A
SLANTB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n triangular band matrix A
SLANTP - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a triangular matrix A
SLANTR - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a trapezoidal or triangular matrix A
SLANV2 - computes the Schur factorization
of a real 2-by-2 nonsymmetric matrix in standard form
SLAPLL - computes the QR factorization
of A=QR
SLAPMT - rearranges the columns of
the M by N matrix X
SLAPY2 - returns sqrt(x
2+y2) without causing unnecessary
overflow
SLAPY3 - returns sqrt(x
2+y2+z2)
without causing unnecessary overflow
SLAQGB - equilibrates a general M by
N band matrix A with KL subdiagonals and KU superdiagonals
SLAQGE - equilibrates a general M by
N matrix A using the row and scaling factors in the vectors R and C
SLAQP2 - computes a QR factorization
with column pivoting of the block A(OFFSET+1:M,1:N)
SLAQPS - computes a step of QR factorization
with column pivoting of a real M-by-N matrix A by using Blas3
SLAQSB - equilibrates a symmetric band
matrix A using the scaling factors in the vector S
SLAQSP - equilibrates a symmetric matrix
A using the scaling factors in the vector S
SLAQSY - equilibrates a symmetric matrix
A using the scaling factors in the vector S
SLAQTR - solves a real quasi-triangular
system
SLAR1V - computes the (scaled) r
th column of the inverse of the sumbmatrix of a tridiagonal
matrix
SLAR2V - applies a vector of real plane
rotations from both sides to a sequence of 2-by-2 real symmetric matrices,
defined by the elements of the vectors x, y and z
SLARF - applies a real elementary reflector
H to a real m by n matrix C, from either the left or the right
SLARFB - applies a real block reflector
H or its transpose H' to a real m by n matrix C, from either the left
or the right
SLARFG - generates a real elementary
reflector H of order n
SLARFT - forms the triangular factor
T of a real block reflector H of order n, which is defined as a product
of k elementary reflectors
SLARFX - applies a real elementary
reflector H to a real m by n matrix C, from either the left or the right
SLARGV - generates a vector of real
plane rotations, determined by elements of the real vectors x and y
SLARNV - returns a vector of n random
real numbers from a uniform or normal distribution
SLARRB - does limited bisection to
locate eigenvalues
SLARRE - sets "small" off-diagonal
elements to zero
SLARRF - finds a robust representation
of input values.
SLARRV - computes the eigenvectors
of the tridiagonal matrix
SLARTG - generates a plane rotation
SLARTV - applies a vector of real plane
rotations to elements of the real vectors x and y
SLARUV - returns a vector of n random
real numbers from a uniform (0,1)
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 to a real distributed M-by-N C from the left or the
right
SLARZT - forms the triangular factor
T of a real block reflector H
SLAS2 - computes the singular values
of the 2-by-2 matrix
SLASCL - multiplie the M by N real
matrix A by the real scalar CTO/CFROM
SLASD0 - computes the singular value
decomposition (SVD) of a real upper bidiagonal N-by-M matrix B
SLASD1 - computes the SVD of an upper
bidiagonal N-by-M matrix B,
SLASD2 - merges the two sets of singular
values together into a single sorted set
SLASD3 - finds all the square roots
of the roots of the secular equation, as defined by the values in D and
Z
SLASD4 - computes the square root of
the Ith updated eigenvalue of a positive symmetric
rank-one modification to a positive diagonal matrix
SLASD5 -computes the square root of
the Ith eigenvalue of a positive symmetric
rank-one modification of a 2-by-2 diagonal matrix
SLASD6 - computes the SVD of an updated
upper bidiagonal matrix B obtained by merging two smaller ones by appending
a row
SLASD7 - merges the two sets of singular
values together into a single sorted set
SLASD8 - finds the square roots of
the roots of the secular equation,
SLASD9 - finds the square roots of
the roots of the secular equation,
SLASDA - computes the singular value
decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal
D and offdiagonal E
SLASDQ - computes the singular value
decomposition (SVD) of a real (upper or lower) bidiagonal matrix with
diagonal D and offdiagonal E, accumulating the transformations if desired
SLASDT - creates a tree of subproblems
for bidiagonal divide and conquer
SLASET - initializes an m-by-n matrix
A to BETA on the diagonal and ALPHA on the offdiagonals
SLASQ1 - computes the singular values
of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E
SLASQ2 - computes all the eigenvalues
of the symmetric positive definite tridiagonal matrix associated with
the qd array Z
SLASQ3 - checks for deflation, computes
a shift (TAU) and calls dqds
SLASQ4 - computes an approximation
TAU to the smallest eigenvalue using values of d from the previous transform
SLASQ5 - computes sone dqds transform
in ping-pong form, one version for IEEE machines another for non IEEE
machines
SLASQ6 - computes one dqd (shift equal
to zero) transform in ping-pong form, with protection against underflow
and overflow
SLASR - performs a transformation
SLASRT - sorts numbers
SLASSQ - returns the values scl and
smsq
SLASV2 - computes the singular value
decomposition of a 2-by-2 triangular matrix
SLASWP - performs a series of row interchanges
on the matrix A
SLASY2 - solves for the N1 by N2 matrix
X
SLASYF - computes a partial factorization
of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
SLATBS - solves one of two triangular
systems with scaling to prevent overflow
SLATDF - computes a contribution to
the reciprocal Dif-estimate
SLATPS - solves one of two triangular
systems with scaling to prevent overflow
SLATRD - reduces NB rows and columns
of a real symmetric matrix A to symmetric tridiagonal form
SLATRS - solves one of two triangular
systems with scaling to prevent overflow
SLATRZ - factors the M-by-(M+L) real
upper trapezoidal matrix by means of orthogonal transformations
SLATZM - routine is deprecated and
has been replaced by routine SORMRZ
SLAUU2 - computes the product U ×
U' or L' × L
SLAUUM - computes the product U ×
U' or L' × L, where the triangular factor U or L is stored in the
upper or lower triangular part of the array A
SOPGTR - generates a real orthogonal
matrix Q as returned by SSPTRD using packed storage
SOPMTR - overwrites the general real
M-by-N matrix C
SORG2L - generates an m by n real matrix
Q with orthonormal columns,
SORG2R - generates an m by n real matrix
Q with orthonormal columns,
SORGBR - generates one of the real
orthogonal matrices determined by SGEBRD when reducing a real matrix A
to bidiagonal form
SORGHR - generates a real orthogonal
matrix Q as returned by SGEHRD
SORGL2 - generates an m by n real matrix
Q with orthonormal rows
SORGLQ - generates an M-by-N real matrix
Q with orthonormal rows
SORGQL - generates an M-by-N real matrix
Q with orthonormal columns
SORGQR - generates an M-by-N real matrix
Q with orthonormal columns
SORGR2 - generates an m by n real matrix
Q with orthonormal rows
SORGRQ - generates an M-by-N real matrix
Q with orthonormal rows
SORGTR - generates a real orthogonal
matrix Q as returned by SSYTRD
SORM2L - overwrites the general real
m by n matrix C
SORM2R - overwrites the general real
m by n matrix C with Q
SORMBR - VECT = 'Q', SORMBR overwrites
the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
SORMHR - overwrites the general real
M-by-N matrix C
SORML2 - overwrites the general real
m by n matrix C
SORMLQ - overwrites the general real
M-by-N matrix C
SORMQL - overwrites the general real
M-by-N matrix C
SORMQR - overwrites the general real
M-by-N matrix C
SORMR2 - overwrites the general real
m by n matrix C
SORMR3 - overwrites the general real
m by n matrix C
SORMRQ - overwrites the general real
M-by-N matrix C
SORMRZ - overwrites the general real
M-by-N matrix C
SORMTR - overwrites the general real
M-by-N matrix C
SPBCON - estimates the reciprocal of
the condition number (in the 1-norm) of a real symmetric positive definite
band matrix using the Cholesky factorization computed by SPBTRF
SPBEQU - computes 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)
SPBRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
positive definite and banded
SPBSTF - computes a split Cholesky
factorization of a real symmetric positive definite band matrix A
SPBSV - computes the solution to a
real system of linear equations
SPBSVX - uses the Cholesky factorization
to compute the solution to a real system of linear equations
SPBTF2 - computes the Cholesky factorization
of a real symmetric positive definite band matrix A
SPBTRF - computes the Cholesky factorization
of a real symmetric positive definite band matrix A
SPBTRS - solves a system of linear
equations with a symmetric positive definite band matrix A using the Cholesky
factorization computed by SPBTRF
SPOCON - estimates the reciprocal of
the condition number (in the 1-norm) of a real symmetric positive definite
matrix using the Cholesky factorization computed by SPOTRF
SPOEQU - computes row and column scalings
intended to equilibrate a symmetric positive definite matrix A and reduce
its condition number (with respect to the two-norm)
SPORFS - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
positive definite
SPOSV - computes the solution to a
real system of linear equations
SPOSVX - uses the Cholesky factorization
to compute the solution to a real system of linear equations
SPOTF2 - computes the Cholesky factorization
of a real symmetric positive definite matrix A
SPOTRF - computes the Cholesky factorization
of a real symmetric positive definite matrix A
SPOTRI - computes the inverse of a
real symmetric positive definite matrix A using the Cholesky factorization
computed by SPOTRF
SPOTRS - solves a system of linear
equations with a symmetric positive definite matrix A using the Cholesky
factorization computed by SPOTRF
SPPCON - estimates the reciprocal of
the condition number (in the 1-norm) of a real symmetric positive definite
packed matrix using the Cholesky factorization computed by SPPTRF
SPPEQU - computes 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)
SPPRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
positive definite and packed, and provides error bounds and backward error
estimates for the solution
SPPSV - computes the solution to a
real system of linear equations
SPPSVX - uses the Cholesky factorization
to compute the solution to a real system of linear equations
SPPTRF - computes the Cholesky factorization
of a real symmetric positive definite matrix A stored in packed format
SPPTRI - computes the inverse of a
real symmetric positive definite matrix A using the Cholesky factorization
computed by SPPTRF
SPPTRS - solves a system of linear
equations with a symmetric positive definite matrix A in packed storage
using the Cholesky factorization computed by SPPTRF
SPTCON - computes the reciprocal of
the condition number (in the 1-norm) of a real symmetric positive definite
tridiagonal matrix using the factorization computed by SPTTRF
SPTEQR - computes 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 - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
positive definite and tridiagonal, and provides error bounds and backward
error estimates for the solution
SPTSV - computes the solution to a
real system of linear equations
SPTSVX - uses a factorization to compute
the solution to a real system of linear equations
SPTTRF - computes the factorization
of a real symmetric positive definite tridiagonal matrix A
SPTTRS - solves a tridiagonal system
SPTTS2 - solves a tridiagonal system
using the factorization of A computed by SPTTRF
SRSCL - multiplies an n-element real
vector x by the real scalar 1/a
SSBEV - computes all the eigenvalues
and, optionally, eigenvectors of a real symmetric band matrix A
SSBEVD - computes all the eigenvalues
and, optionally, eigenvectors of a real symmetric band matrix A
SSBEVX - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric band matrix A
SSBGST - reduces a real symmetric-definite
banded generalized eigenproblem
SSBGV - computes all the eigenvalues,
and optionally, the eigenvectors of a real generalized symmetric-definite
banded eigenproblem
SSBGVD - computes all the eigenvalues,
and optionally, the eigenvectors of a real generalized symmetric-definite
banded eigenproblem
SSBGVX - computes selected eigenvalues,
and optionally, eigenvectors of a real generalized symmetric-definite
banded eigenproblem
SSBTRD - reduces a real symmetric band
matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
SSPCON - estimates the reciprocal of
the condition number (in the 1-norm) of a real symmetric packed matrix
A
SSPEV - computes all the eigenvalues
and, optionally, eigenvectors of a real symmetric matrix A in packed storage
SSPEVD - computes all the eigenvalues
and, optionally, eigenvectors of a real symmetric matrix A in packed storage
SSPEVX - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric matrix A in packed storage
SSPGST - reduces a real symmetric-definite
generalized eigenproblem to standard form, using packed storage
SSPGV - computes all the eigenvalues
and, optionally, the eigenvectors of a real generalized symmetric-definite
eigenproblem
SSPGVD - computes all the eigenvalues,
and optionally, the eigenvectors of a real generalized symmetric-definite
eigenproblem
SSPGVX - computes selected eigenvalues,
and optionally, eigenvectors of a real generalized symmetric-definite
eigenproblem
SSPRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
indefinite and packed
SSPSV - computes the solution to a
real system of linear equations
SSPSVX - uses the diagonal pivoting
factorization to compute the solution to a real system of linear equations
SSPTRD - reduces a real symmetric matrix
A stored in packed form to symmetric tridiagonal form T by an orthogonal
similarity transformation
SSPTRF - computes the factorization
of a real symmetric matrix A stored in packed format using the Bunch-Kaufman
diagonal pivoting method
SSPTRI - computes the inverse of a
real symmetric indefinite matrix A in packed storage using the factorization
computed by SSPTRF
SSPTRS - solves a system of linear
equations with a real symmetric matrix A stored in packed format using
the factorization computed by SSPTRF
SSTEBZ - computes the eigenvalues of
a symmetric tridiagonal matrix T
SSTEDC - computes all eigenvalues and,
optionally, eigenvectors of a symmetric tridiagonal matrix using the divide
and conquer method
SSTEGR - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
SSTEIN - computes the eigenvectors
of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues,
using inverse iteration
SSTEQR - computes all eigenvalues and,
optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit
QL or QR method
SSTERF - computes all eigenvalues of
a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the
QL or QR algorithm
SSTEV - computes all eigenvalues and,
optionally, eigenvectors of a real symmetric tridiagonal matrix A
SSTEVD - computes all eigenvalues and,
optionally, eigenvectors of a real symmetric tridiagonal matrix
SSTEVR - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
SSTEVX - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
SSYCON - estimates the reciprocal of
the condition number (in the 1-norm) of a real symmetric matrix A using
the factorization computed by SSYTRF
SSYEV - computes all eigenvalues and,
optionally, eigenvectors of a real symmetric matrix A
SSYEVD - computes all eigenvalues and,
optionally, eigenvectors of a real symmetric matrix A
SSYEVR - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric matrix T
SSYEVX - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric matrix A
SSYGS2 - reduces a real symmetric-definite
generalized eigenproblem to standard form
SSYGST - reduces a real symmetric-definite
generalized eigenproblem to standard form
SSYGV - computes all the eigenvalues,
and optionally, the eigenvectors of a real generalized symmetric-definite
eigenproblem
SSYGVD - computes all the eigenvalues,
and optionally, the eigenvectors of a real generalized symmetric-definite
eigenproblem
SSYGVX - computes selected eigenvalues,
and optionally, eigenvectors of a real generalized symmetric-definite
eigenproblem
SSYRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is symmetric
indefinite
SSYSV - computes the solution to a
real system of linear equations
SSYSVX - uses the diagonal pivoting
factorization to compute the solution to a real system of linear equations
SSYTD2 - reduces a real symmetric matrix
A to symmetric tridiagonal form T by an orthogonal similarity transformation
SSYTF2 - computes the factorization
of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
SSYTRD - reduces a real symmetric matrix
A to real symmetric tridiagonal form T by an orthogonal similarity transformation
SSYTRF - computes the factorization
of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
SSYTRI - computes the inverse of a
real symmetric indefinite matrix A using the factorization computed by
SSYTRF
SSYTRS - solves a system of linear
equations with a real symmetric matrix A using the factorization computed
by SSYTRF
STBCON - estimates the reciprocal of
the condition number of a triangular band matrix A, in either the 1-norm
or the infinity-norm
STBRFS - provides error bounds and
backward error estimates for the solution to a system of linear equations
with a triangular band coefficient matrix
STBTRS - solves a triangular system
of the form
STGEVC - computes some or all of the
right and/or left generalized eigenvectors of a pair of real upper triangular
matrices (A,B)
STGEX2 - swaps adjacent diagonal blocks
(A11, B11) and (A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi)
triangular matrix pair (A, B) by an orthogonal equivalence transformation
STGEXC - reorders the generalized real
Schur decomposition of a real matrix pair (A,B) using an orthogonal equivalence
transformation
STGSEN - reorders the generalized real
Schur decomposition of a real matrix pair (A, B)
STGSJA - computes the generalized singular
value decomposition (GSVD) of two real upper triangular (or trapezoidal)
matrices A and B
STGSNA - estimates reciprocal condition
numbers for specified eigenvalues and/or eigenvectors of a matrix pair
STGSY2 - solves the generalized Sylvester
equation
STGSYL - solves the generalized Sylvester
equation
STPCON - estimates the reciprocal of
the condition number of a packed triangular matrix A, in either the 1-norm
or the infinity-norm
STPRFS - provides error bounds and
backward error estimates for the solution to a system of linear equations
with a triangular packed coefficient matrix
STPTRI - computes the inverse of a
real upper or lower triangular matrix A stored in packed format
STPTRS - solves a triangular system
STRCON - estimates the reciprocal of
the condition number of a triangular matrix A, in either the 1-norm or
the infinity-norm
STREVC - computes some or all of the
right and/or left eigenvectors of a real upper quasi-triangular matrix
T
STREXC - reorders the real Schur factorization
of a real matrix
STRID - computes the solution to a
real system of linear equations
STRRFS - provides error bounds and
backward error estimates for the solution to a system of linear equations
with a triangular coefficient matrix
STRSEN - reorders the real Schur factorization
of a real matrix
STRSNA - estimates reciprocal condition
numbers for specified eigenvalues and/or right eigenvectors of a real
upper quasi-triangular matrix T
STRSYL - solves the real Sylvester
matrix equation
STRTI2 - computes the inverse of a
real upper or lower triangular matrix
STRTRI - computes the inverse of a
real upper or lower triangular matrix A
STRTRS - solves a triangular system
STZRQF - routine is deprecated and
has been replaced by routine STZRZF
STZRZF - reduces the M-by-N real upper
trapezoidal matrix A to upper triangular form by means of orthogonal transformations
XERBLA - error handler for the LAPACK
routines
ZBDSQR - computes the singular value
decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix
B
ZDRSCL - multiplies an n-element complex
vector x by the real scalar 1/a
ZGBBRD - reduces a complex general
m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
ZGBCON - estimates the reciprocal of
the condition number of a complex general band matrix A, in either the
1-norm or the infinity-norm,
ZGBEQU - computes row and column scalings
intended to equilibrate an M-by-N band matrix A and reduce its condition
number
ZGBRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is banded,
and provides error bounds and backward error estimates for the solution
ZGBSV - computes the solution to a
complex system of linear equations 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 - uses the LU factorization
to compute the solution to a complex system of linear equations
ZGBTF2 - computes an LU factorization
of a complex m-by-n band matrix A using partial pivoting with row interchanges
ZGBTRF - computes an LU factorization
of a complex m-by-n band matrix A using partial pivoting with row interchanges
ZGBTRS - solves a system of linear
equations with a general band matrix A using the LU factorization computed
by ZGBTRF
ZGEBAK - forms the right or left eigenvectors
of a complex general matrix by backward transformation on the computed
eigenvectors of the balanced matrix output by ZGEBAL
ZGEBAL - balances a general complex
matrix A
ZGEBD2 - reduces a complex general
m by n matrix A to upper or lower real bidiagonal form B by a unitary
transformation
ZGEBRD - reduces a general complex
M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
ZGECON - estimates the reciprocal of
the condition number of a general complex matrix A, in either the 1-norm
or the infinity-norm, using the LU factorization computed by ZGETRF
ZGEEQU - computes row and column scalings
intended to equilibrate an M-by-N matrix A and reduce its condition number
ZGEES - computes for an N-by-N complex
nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally,
the matrix of Schur vectors Z
ZGEESX - computes for an N-by-N complex
nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally,
the matrix of Schur vectors Z
ZGEEV - computes for an N-by-N complex
nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or
right eigenvectors
ZGEEVX - computes for an N-by-N complex
nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or
right eigenvectors
ZGEGS - routine is deprecated and has
been replaced by routine ZGGES
ZGEGV - routine is deprecated and has
been replaced by routine ZGGEV
ZGEHD2 - reduces a complex general
matrix A to upper Hessenberg form H by a unitary similarity transformation
ZGEHRD - reduces a complex general
matrix A to upper Hessenberg form H by a unitary similarity transformation
ZGELQ2 - computes an LQ factorization
of a complex m by n matrix A
ZGELQF - computes an LQ factorization
of a complex M-by-N matrix A
ZGELS - solves 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 - computes the minimum-norm
solution to a real linear least squares problem
ZGELSS - computes the minimum norm
solution to a complex linear least squares problem
ZGELSX - routine is deprecated and
has been replaced by routine ZGELSY
ZGELSY - computes the minimum-norm
solution to a complex linear least squares problem
ZGEQL2 - computes a QL factorization
of a complex m by n matrix A
ZGEQLF - computes a QL factorization
of a complex M-by-N matrix A
ZGEQP3 - computes a QR factorization
with column pivoting of a matrix A
ZGEQPF - routine is deprecated and
has been replaced by routine ZGEQP3
ZGEQR2 - computes a QR factorization
of a complex m by n matrix A
ZGEQRF - computes a QR factorization
of a complex M-by-N matrix A
ZGERFS - improves the computed solution
to a system of linear equations and provides error bounds and backward
error estimates for the solution
ZGERQ2 - computes an RQ factorization
of a complex m by n matrix A
ZGERQF - computes an RQ factorization
of a complex M-by-N matrix A
ZGESC2 - solves a system of linear
equations with a general N-by-N matrix A using the LU factorization with
complete pivoting computed by ZGETC2
ZGESDD - computes the singular value
decomposition (SVD) of a complex M-by-N matrix A
ZGESV - computes the solution to a
complex system of linear equations
ZGESVD - computes the singular value
decomposition (SVD) of a complex M-by-N matrix A
ZGESVX - uses the LU factorization
to compute the solution to a complex system of linear equations
ZGETC2 - computes an LU factorization,
using complete pivoting, of the n-by-n matrix A
ZGETF2 - computes an LU factorization
of a general m-by-n matrix A using partial pivoting with row interchanges
ZGETRF - computes an LU factorization
of a general M-by-N matrix A using partial pivoting with row interchanges
ZGETRI - computes the inverse of a
matrix using the LU factorization computed by ZGETRF
ZGETRS - solves a system of linear
equations with a general N-by-N matrix A using the LU factorization computed
by ZGETRF
ZGGBAK - forms the right or left eigenvectors
of a complex generalized eigenvalue problem by backward transformation
on the computed eigenvectors of the balanced pair of matrices output by
ZGGBAL
ZGGBAL - balances a pair of general
complex matrices (A,B)
ZGGES - computes 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 - computes for a pair of N-by-N
complex nonsymmetric matrices (A,B), the generalized eigenvalues, the
complex Schur form (S,T),
ZGGEV - computes 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 - computes 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 - solves a general Gauss-Markov
linear model (GLM) problem
ZGGHRD - reduces 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 - solves the linear equality-constrained
least squares (LSE) problem
ZGGQRF - computes a generalized QR
factorization of an N-by-M matrix A and an N-by-P matrix B
ZGGRQF - computes a generalized RQ
factorization of an M-by-N matrix A and a P-by-N matrix B
ZGGSVD - computes the generalized singular
value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex
matrix B
ZGGSVP - computes unitary matrices
U, V and Q
ZGTCON - estimates the reciprocal of
the condition number of a complex tridiagonal matrix A using the LU factorization
as computed by ZGTTRF
ZGTRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is tridiagonal,
and provides error bounds and backward error estimates for the solution
ZGTSV - solves the equation AX = B
ZGTSVX - uses the LU factorization
to compute the solution to a complex system of linear equations
ZGTTRF - computes an LU factorization
of a complex tridiagonal matrix A using elimination with partial pivoting
and row interchanges
ZGTTRS - solves one of the systems
of equations
ZGTTS2 - solves one of the systems
of equations
ZHBEV - computes all the eigenvalues
and, optionally, eigenvectors of a complex Hermitian band matrix A
ZHBEVD - computes all the eigenvalues
and, optionally, eigenvectors of a complex Hermitian band matrix A
ZHBEVX - computes selected eigenvalues
and, optionally, eigenvectors of a complex Hermitian band matrix A
ZHBGST - reduces a complex Hermitian-definite
banded generalized eigenproblem to standard form
ZHBGV - computes all the eigenvalues,
and optionally, the eigenvectors of a complex generalized Hermitian-definite
banded eigenproblem
ZHBGVD - computes all the eigenvalues,
and optionally, the eigenvectors of a complex generalized Hermitian-definite
banded eigenproblem
ZHBGVX - computes all the eigenvalues,
and optionally, the eigenvectors of a complex generalized Hermitian-definite
banded eigenproblem
ZHBTRD - reduces a complex Hermitian
band matrix A to real symmetric tridiagonal form T by a unitary similarity
transformation
ZHECON - estimates the reciprocal of
the condition number of a complex Hermitian matrix A using the factorization
computed by ZHETRF
ZHEEV - computes all eigenvalues and,
optionally, eigenvectors of a complex Hermitian matrix A
ZHEEVD - computes all eigenvalues and,
optionally, eigenvectors of a complex Hermitian matrix A
ZHEEVR - computes selected eigenvalues
and, optionally, eigenvectors of a complex Hermitian matrix T
ZHEEVX - computes selected eigenvalues
and, optionally, eigenvectors of a complex Hermitian matrix A
ZHEGS2 - reduces a complex Hermitian-definite
generalized eigenproblem to standard form
ZHEGST - reduces a complex Hermitian-definite
generalized eigenproblem to standard form
ZHEGV - computes all the eigenvalues,
and optionally, the eigenvectors of a complex generalized Hermitian-definite
eigenproblem
ZHEGVD - computes all the eigenvalues,
and optionally, the eigenvectors of a complex generalized Hermitian-definite
eigenproblem
ZHEGVX - computes selected eigenvalues,
and optionally, eigenvectors of a complex generalized Hermitian-definite
eigenproblem
ZHERFS - improves 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
ZHESV - computes the solution to a
complex system of linear equations
ZHESVX - uses the diagonal pivoting
factorization to compute the solution to a complex system of linear equations
ZHETD2 - reduces a complex Hermitian
matrix A to real symmetric tridiagonal form T by a unitary similarity
transformation
ZHETF2 - computes the factorization
of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting
method
ZHETRD - reduces a complex Hermitian
matrix A to real symmetric tridiagonal form T by a unitary similarity
transformation
ZHETRF - computes the factorization
of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting
method
ZHETRI - computes the inverse of a
complex Hermitian indefinite matrix A using the factorization computed
by ZHETRF
ZHETRS - solves a system of linear
equations with a complex Hermitian matrix A using the factorization computed
by ZHETRF
ZHGEQZ - implements a single-shift
version of the QZ method for finding generalized eigenvalues
ZHPCON - estimates the reciprocal of
the condition number of a complex Hermitian packed matrix A using the
factorization computed by ZHPTRF
ZHPEV - computes all the eigenvalues
and, optionally, eigenvectors of a complex Hermitian matrix in packed
storage
ZHPEVD - computes all the eigenvalues
and, optionally, eigenvectors of a complex Hermitian matrix A in packed
storage
ZHPEVX - computes selected eigenvalues
and, optionally, eigenvectors of a complex Hermitian matrix A in packed
storage
ZHPGST - reduces a complex Hermitian-definite
generalized eigenproblem to standard form, using packed storage
ZHPGV - computes all the eigenvalues
and, optionally, the eigenvectors of a complex generalized Hermitian-definite
eigenproblem
ZHPGVD - computes all the eigenvalues
and, optionally, the eigenvectors of a complex generalized Hermitian-definite
eigenproblem
ZHPGVX - computes selected eigenvalues
and, optionally, eigenvectors of a complex generalized Hermitian-definite
eigenproblem
ZHPRFS - improves 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
ZHPSV - computes the solution to a
complex system of linear equations
ZHPSVX - uses the diagonal pivoting
factorization to compute the solution to a complex system of linear equations
ZHPTRD - reduces a complex Hermitian
matrix A stored in packed form to real symmetric tridiagonal form T by
a unitary similarity transformation
ZHPTRF - computes the factorization
of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal
pivoting method
ZHPTRI - computes the inverse of a
complex Hermitian indefinite matrix A in packed storage using the factorization
computed by ZHPTRF
ZHPTRS - solves a system of linear
equations with a complex Hermitian matrix A stored in packed format using
the factorization computed by ZHPTRF
ZHSEIN - uses inverse iteration to
find specified right and/or left eigenvectors of a complex upper Hessenberg
matrix H
ZHSEQR - computes the eigenvalues of
a complex upper Hessenberg matrix H, and, optionally, the matrices T and
Z from the Schur decomposition
ZLABRD - reduces the first NB rows
and columns of a complex general m by n matrix A to upper or lower real
bidiagonal form by a unitary transformation
ZLACGV - conjugates a complex vector
of length N
ZLACON - estimatse the 1-norm of a
square, complex matrix A
ZLACP2 - copies all or part of a real
two-dimensional matrix A to a complex matrix B
ZLACPY - copies all or part of a two-dimensional
matrix A to another matrix B
ZLACRM - performs a very simple matrix-matrix
multiplication
ZLACRT - performs the operation ( c
s )( x ) ==> ( x ) ( -s c )( y ) ( y ) where c and
s are complex and the vectors x and y are complex
ZLADIV - := X / Y, where X and Y are
complex
ZLAED0 - computes all eigenvalues of
a symmetric tridiagonal matrix
ZLAED7 - computes the updated eigensystem
of a diagonal matrix after modification by a rank-one symmetric matrix
ZLAED8 - merges the two sets of eigenvalues
together into a single sorted set
ZLAEIN - uses inverse iteration to
find a right or left eigenvector corresponding to the eigenvalue W of
a complex upper Hessenberg matrix H
ZLAESY - computes the eigendecomposition
of a 2-by-2 symmetric matrix
ZLAEV2 - computes the eigendecomposition
of a 2-by-2 Hermitian matrix
ZLAGS2 - computes 2-by-2 unitary matrices
U, V and Q
ZLAGTM - performs a matrix-vector product
ZLAHEF - computes a partial factorization
of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting
method
ZLAHQR - called by ZHSEQR to update
the eigenvalues and Schur decomposition already computed by ZHSEQR
ZLAHRD - reduces the first NB columns
of a complex general n-by-(n-k+1) matrix A so that elements below the
kth subdiagonal are zero
ZLAIC1 - applies one step of incremental
condition estimation in its simplest version
ZLALS0 - applies back the multiplying
factors of either the left or the right singular vector matrix of a diagonal
matrix appended by a row to the right hand side matrix B in solving the
least squares problem using the divide-and-conquer SVD approach
ZLALSA - an itermediate step in solving
the least squares problem by computing the SVD of the coefficient matrix
in compact form
ZLALSD - uses the singular value decomposition
of A to solve the least squares problem of finding X to minimize the Euclidean
norm
ZLANGB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n band matrix A,
ZLANGE - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex matrix A
ZLANGT - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex tridiagonal matrix A
ZLANHB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n hermitian band matrix A, with k super-diagonals
ZLANHE - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex hermitian matrix A
ZLANHP - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex hermitian matrix A, supplied in packed form
ZLANHS - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a Hessenberg matrix A
ZLANHT - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex Hermitian tridiagonal matrix A
ZLANSB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n symmetric band matrix A, with k super-diagonals
ZLANSP - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex symmetric matrix A, supplied in packed form
ZLANSY - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a complex symmetric matrix A
ZLANTB - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
ZLANTP - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a triangular matrix A, supplied in packed form
ZLANTR - returns the value of the one
norm, or the Frobenius norm, or the infinity norm, or the element of largest
absolute value of a trapezoidal or triangular matrix A
ZLAPLL - computes the QR factorization
of A=QR
ZLAPMT - rearranges the columns of
the M by N matrix X
ZLAQGB - equilibrates a general M by
N band matrix A with KL subdiagonals and KU superdiagonals using the row
and scaling factors in the vectors R and C
ZLAQGE - equilibrates a general M by
N matrix A using the row and scaling factors in the vectors R and C
ZLAQHB - equilibrates a symmetric band
matrix A using the scaling factors in the vector S
ZLAQHE - equilibrates a Hermitian matrix
A using the scaling factors in the vector S
ZLAQHP - equilibrates a Hermitian matrix
A using the scaling factors in the vector S
ZLAQP2 - computes a QR factorization
with column pivoting
ZLAQPS - computes a step of QR factorization
with column pivoting of a complex M-by-N matrix A by using Blas-3
ZLAQSB - equilibrates a symmetric band
matrix A using the scaling factors in the vector S
ZLAQSP - equilibrates a symmetric matrix
A using the scaling factors in the vector S
ZLAQSY - equilibrates a symmetric matrix
A using the scaling factors in the vector S
ZLAR1V - computes the (scaled) r
th column of the inverse of the sumbmatrix
ZLAR2V - applies a vector of complex
plane rotations with real cosines from both sides to a sequence of 2-by-2
complex Hermitian matrices,
ZLARCM - performs a very simple matrix-matrix
multiplication
ZLARF - applies a complex elementary
reflector H to a complex M-by-N matrix C, from either the left or the
right
ZLARFB - applies a complex block reflector
H or its transpose H' to a complex M-by-N matrix C, from either the left
or the right
ZLARFG - generates a complex elementary
reflector H o
ZLARFT - forms the triangular factor
T of a complex block reflector H of order n, which is defined as a product
of k elementary reflectors
ZLARFX - applies a complex elementary
reflector H to a complex m by n matrix C, from either the left or the
right
ZLARGV - generates a vector of complex
plane rotations with real cosines, determined by elements of the complex
vectors x and y
ZLARNV - returns a vector of n random
complex numbers from a uniform or normal distribution
ZLARRV - computes the eigenvectors
of a tridiagonal matrix
ZLARTG - generates a plane rotation
ZLARTV - applies a vector of complex
plane rotations with real cosines to elements of the complex vectors x
and y
ZLARZ - applies a complex elementary
reflector H to a complex M-by-N matrix C, from either the left or the
right
ZLARZB - applies a complex block reflector
H or its transpose to a complex distributed M-by-N C from the left or
the right
ZLARZT - forms the triangular factor
T of a complex block reflector which is defined as a product of k elementary
reflectors
ZLASCL - multiplies the M by N complex
matrix A by the real scalar CTO/CFROM
ZLASET - initializes a 2-D array A
to BETA on the diagonal and ALPHA on the offdiagonals
ZLASR - performs a transformation where
A is an m by n complex matrix and P is an orthogonal matrix
ZLASSQ - returns the values scl and
ssq
ZLASWP - performs a series of row interchanges
on the matrix A
ZLASYF - computes a partial factorization
of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
ZLATBS - solves triangular systems
ZLATDF - computes the contribution
to the reciprocal Dif-estimate
ZLATPS - solves triangular systems
ZLATRD - reduces NB rows and columns
of a complex Hermitian matrix A to Hermitian tridiagonal form
ZLATRS - solves triangular systems
ZLATRZ - factors the M-by-(M+L) complex
upper trapezoidal matrix
ZLATZM - routine is deprecated and
has been replaced by routine ZUNMRZ
ZLAUU2 - computes the product U ×
U' or L' × L
ZLAUUM - computes the product U ×
U' or L' × L
ZPBCON - estimates the reciprocal of
the condition number (in the 1-norm) of a complex Hermitian positive definite
band matrix
ZPBEQU - computes row and column scalings
intended to equilibrate a Hermitian positive definite band matrix A
ZPBRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is Hermitian
positive definite and banded
ZPBSTF - computes a split Cholesky
factorization of a complex Hermitian positive definite band matrix A
ZPBSV - computes the solution to a
complex system of linear equations
ZPBSVX - uses the Cholesky factorization
to compute the solution to a complex system of linear equations
ZPBTF2 - computes the Cholesky factorization
of a complex Hermitian positive definite band matrix A
ZPBTRF - computes the Cholesky factorization
of a complex Hermitian positive definite band matrix A
ZPBTRS - solves a system of linear
equations with a Hermitian positive definite band matrix A using the Cholesky
factorization computed by ZPBTRF
ZPOCON - estimates the reciprocal of
the condition number (in the 1-norm) of a complex Hermitian positive definite
matrix using the Cholesky factorization computed by ZPOTRF
ZPOEQU - computes row and column scalings
intended to equilibrate a Hermitian positive definite matrix A and reduce
its condition number (with respect to the two-norm)
ZPORFS - improves the computed solution
to a system of linear equations when the coefficient matrix is Hermitian
positive definite,
ZPOSV - computes the solution to a
complex system of linear equations
ZPOSVX - uses the Cholesky factorization
to compute the solution to a complex system of linear equations
ZPOTF2 - computes the Cholesky factorization
of a complex Hermitian positive definite matrix A
ZPOTRF - computes the Cholesky factorization
of a complex Hermitian positive definite matrix A
ZPOTRI - computes the inverse of a
complex Hermitian positive definite matrix A using the Cholesky factorization
computed by ZPOTRF
ZPOTRS - solves a system of linear
equations with a Hermitian positive definite matrix A using the Cholesky
factorization computed by ZPOTRF
ZPPCON - estimates the reciprocal of
the condition number (in the 1-norm) of a complex Hermitian positive definite
packed matrix using the Cholesky factorization computed by ZPPTRF
ZPPEQU - computes 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)
ZPPRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is Hermitian
positive definite and packed, and provides error bounds and backward error
estimates for the solution
ZPPSV - computes the solution to a
complex system of linear equations
ZPPSVX - use the Cholesky factorization
to compute the solution to a complex system of linear equations
ZPPTRF - computes the Cholesky factorization
of a complex Hermitian positive definite matrix A stored in packed format
ZPPTRI - computes the inverse of a
complex Hermitian positive definite matrix A using the Cholesky factorization
computed by ZPPTRF
ZPPTRS - solves a system of linear
equations with a Hermitian positive definite matrix A in packed storage
using the Cholesky factorization computed by ZPPTRF
ZPTCON - computes the reciprocal of
the condition number (in the 1-norm) of a complex Hermitian positive definite
tridiagonal matrix using the factorization computed by ZPTTRF
ZPTEQR - computes all eigenvalues and,
optionally, eigenvectors of a symmetric positive definite tridiagonal
matrix
ZPTRFS - improves the computed solution
to a system of linear equations when the coefficient matrix is Hermitian
positive definite and tridiagonal, and provides error bounds and backward
error estimates for the solution
ZPTSV - computes the solution to a
complex system of linear equations where A is an N-by-N Hermitian positive
definite tridiagonal matrix, and X and B are N-by-NRHS matrices
ZPTSVX - uses the factorization to
compute the solution to a complex system of linear equations where A is
an N-by-N Hermitian positive definite tridiagonal matrix and X and B are
N-by-NRHS matrices
ZPTTRF - computes the factorization
of a complex Hermitian positive definite tridiagonal matrix A
ZPTTRS - solves a tridiagonal system
of the form using the factorization computed by ZPTTRF
ZPTTS2 - solves a tridiagonal system
of the form using the factorization computed by ZPTTRF
ZSPCON - estimates the reciprocal of
the condition number (in the 1-norm) of a complex symmetric packed matrix
A using the factorization computed by ZSPTRF
ZSPRFS - improves 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
ZSPSV - computes the solution to a
complex system of linear equations
ZSPSVX - uses the diagonal pivoting
factorization to compute the solution to a complex system of linear equations
ZSPTRF - computes the factorization
of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman
diagonal pivoting method
ZSPTRI - computes the inverse of a
complex symmetric indefinite matrix A in packed storage using the factorization
computed by ZSPTRF
ZSPTRS - solves a system of linear
equations with a complex symmetric matrix A stored in packed format using
the factorization computed by ZSPTRF
ZSTEDC - computes all eigenvalues and,
optionally, eigenvectors of a symmetric tridiagonal matrix using the divide
and conquer method
ZSTEGR - computes selected eigenvalues
and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
ZSTEIN - computes the eigenvectors
of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues,
using inverse iteration
ZSTEQR - computes all eigenvalues and,
optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit
QL or QR method
ZSYCON - estimates the reciprocal of
the condition number (in the 1-norm) of a complex symmetric matrix A using
the factorization computed by ZSYTRF
ZSYRFS - improves 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
ZSYSV - computes the solution to a
complex system of linear equations
ZSYSVX - uses the diagonal pivoting
factorization to compute the solution to a complex system of linear equations
ZSYTF2 - computes the factorization
of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
ZSYTRF - computes the factorization
of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting
method
ZSYTRI - computes the inverse of a
complex symmetric indefinite matrix A using the factorization computed
by ZSYTRF
ZSYTRS - solves a system of linear
equations with a complex symmetric matrix A using the factorization computed
by ZSYTRF
ZTBCON - estimates the reciprocal of
the condition number of a triangular band matrix A, in either the 1-norm
or the infinity-norm
ZTBRFS - provides error bounds and
backward error estimates for the solution to a system of linear equations
with a triangular band coefficient matrix
ZTBTRS - solves a triangular system
ZTGEVC - computes some or all of the
right and/or left generalized eigenvectors of a pair of complex upper
triangular matrices (A,B)
ZTGEX2 - swaps adjacent diagonal 1
by 1 blocks (A11,B11) and (A22,B22)
ZTGEXC - reorders the generalized Schur
decomposition of a complex matrix pair (A,B)
ZTGSEN - reorders the generalized Schur
decomposition of a complex matrix pair (A, B)
ZTGSJA - computes the generalized singular
value decomposition (GSVD) of two complex upper triangular (or trapezoidal)
matrices A and B
ZTGSNA - estimates reciprocal condition
numbers for specified eigenvalues and/or eigenvectors of a matrix pair
(A, B)
ZTGSY2 - solves the generalized Sylvester
equation
ZTGSYL - solves the generalized Sylvester
equation
ZTPCON - estimates the reciprocal of
the condition number of a packed triangular matrix A, in either the 1-norm
or the infinity-norm
ZTPRFS - provides error bounds and
backward error estimates for the solution to a system of linear equations
with a triangular packed coefficient matrix
ZTPTRI - computes the inverse of a
complex upper or lower triangular matrix A stored in packed format
ZTPTRS - solves a triangular system
ZTRCON - estimates the reciprocal of
the condition number of a triangular matrix A, in either the 1-norm or
the infinity-norm
ZTREVC - computes some or all of the
right and/or left eigenvectors of a complex upper triangular matrix T
ZTREXC - reorders the Schur factorization
of a complex matrix so that the diagonal element of T with row index IFST
is moved to row ILST
ZTRID - computes the solution to a
complex system of linear equations where A is an N-by-N tridiagonal matrix,
and x and b are vectors of length N
ZTRRFS - provides error bounds and
backward error estimates for the solution to a system of linear equations
with a triangular coefficient matrix
ZTRSEN - reorders the Schur factorization
of a complex matrix
ZTRSNA - estimates reciprocal condition
numbers for specified eigenvalues and/or right eigenvectors of a complex
upper triangular matrix T
ZTRSYL - solves the complex Sylvester
matrix equation
ZTRTI2 - computes the inverse of a
complex upper or lower triangular matrix
ZTRTRI - computes the inverse of a
complex upper or lower triangular matrix A
ZTRTRS - solves a triangular system
ZTZRQF - routine is deprecated and
has been replaced by routine ZTZRZF
ZTZRZF - reduces the M-by-N complex
upper trapezoidal matrix A to upper triangular form by means of unitary
transformations
ZUNG2L - generates an m by n complex
matrix Q with orthonormal columns,
ZUNG2R - generates an m by n complex
matrix Q with orthonormal columns,
ZUNGBR - generates one of the complex
unitary matrices determined by ZGEBRD when reducing a complex matrix A
to bidiagonal form
ZUNGHR - generates a complex unitary
matrix Q
ZUNGL2 - generates an m-by-n complex
matrix Q with orthonormal rows,
ZUNGLQ - generates an M-by-N complex
matrix Q with orthonormal rows,
ZUNGQL - generates an M-by-N complex
matrix Q with orthonormal columns,
ZUNGQR - generates an M-by-N complex
matrix Q with orthonormal columns,
ZUNGR2 - generates an m by n complex
matrix Q with orthonormal rows,
ZUNGRQ - generates an M-by-N complex
matrix Q with orthonormal rows,
ZUNGTR - generates a complex unitary
matrix Q which is defined as the product of n-1 elementary reflectors
of order N, as returned by ZHETRD
ZUNM2L - overwrites the general complex
m-by-n matrix C
ZUNM2R - overwrites the general complex
m-by-n matrix C
ZUNMBR - overwrites the general complex
M-by-N matrix C
ZUNMHR - overwrites the general complex
M-by-N matrix C
ZUNML2 - overwrites the general complex
m-by-n matrix C
ZUNMLQ - overwrites the general complex
M-by-N matrix C
ZUNMQL - overwrites the general complex
M-by-N matrix C
ZUNMQR - overwrites the general complex
M-by-N matrix C
ZUNMR2 - overwrites the general complex
m-by-n matrix C
ZUNMR3 - overwrites the general complex
m by n matrix C
ZUNMRQ - overwrites the general complex
M-by-N matrix C
ZUNMRZ - overwrites the general complex
M-by-N matrix C
ZUPGTR - generates a complex unitary
matrix Q
ZUPMTR - overwrites the general complex
M-by-N matrix C
