Linux man pages (HTML) - manl: Local
A
abort - Aborts the current transaction
alter_group - Add users to a group, remove users from a group
alter_table - Modifies table properties
alter_user - Modifies user account information
B
begin - Begins a transaction in chained mode
C
cbdsqr - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
cgbbrd - reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
cgbcon - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,
cgbequ - compute row and column scalings intended to equi librate an M-by-N band matrix A and reduce its condition number
cgbmv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y,
cgbrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
cgbsv - compute the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
cgbsvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
cgbtf2 - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
cgbtrf - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
cgbtrs - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by CGBTRF
cgebak - form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by CGEBAL
cgebal - balance a general complex matrix A
cgebd2 - reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transforma tion
cgebrd - reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
cgecon - estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF
cgeequ - compute row and column scalings intended to equi librate an M-by-N matrix A and reduce its condition number
cgees - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
cgeesx - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
cgeev - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
cgeevx - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
cgegs - routine is deprecated and has been replaced by routine CGGES
cgegv - routine is deprecated and has been replaced by routine CGGEV
cgehd2 - reduce a complex general matrix A to upper Hes senberg form H by a unitary similarity transformation
cgehrd - reduce a complex general matrix A to upper Hes senberg form H by a unitary similarity transformation
cgelq2 - compute an LQ factorization of a complex m by n matrix A
cgelqf - compute an LQ factorization of a complex M-by-N matrix A
cgelsd - compute the minimum-norm solution to a real lin ear least squares problem
cgels - solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conju gate-transpose, using a QR or LQ factorization of A
cgelss - compute the minimum norm solution to a complex linear least squares problem
cgelsx - routine is deprecated and has been replaced by routine CGELSY
cgelsy - compute the minimum-norm solution to a complex linear least squares problem
cgemm - perform one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C,
cgemv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y,
cgeql2 - compute a QL factorization of a complex m by n matrix A
cgeqlf - compute a QL factorization of a complex M-by-N matrix A
cgeqp3 - compute a QR factorization with column pivoting of a matrix A
cgeqpf - routine is deprecated and has been replaced by routine CGEQP3
cgeqr2 - compute a QR factorization of a complex m by n matrix A
cgeqrf - compute a QR factorization of a complex M-by-N matrix A
cgerc - perform the rank 1 operation A := alpha*x*conjg( y' ) + A,
cgerfs - improve the computed solution to a system of lin ear equations and provides error bounds and backward error estimates for the solution
cgerq2 - compute an RQ factorization of a complex m by n matrix A
cgerqf - compute an RQ factorization of a complex M-by-N matrix A
cgeru - perform the rank 1 operation A := alpha*x*y' + A,
cgesc2 - solve a system of linear equations A * X = scale* RHS with a general N-by-N matrix A using the LU factorization with complete pivoting computed by CGETC2
cgesdd - compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method
cgesvd - compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors
cgesv - compute the solution to a complex system of linear equations A * X = B,
cgesvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B,
cgetc2 - compute an LU factorization, using complete piv oting, of the n-by-n matrix A
cgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
cgetrf - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
cgetri - compute the inverse of a matrix using the LU fac torization computed by CGETRF
cgetrs - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by CGETRF
cggbak - form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by back ward transformation on the computed eigenvectors of the balanced pair of matrices output by CGGBAL
cggbal - balance a pair of general complex matrices (A,B)
cgges - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the general ized complex Schur form (S, T), and optionally left and/or right Schur vectors (VSL and VSR)
cggesx - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T),
cggev - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and option ally, the left and/or right generalized eigenvectors
cggevx - compute for a pair of N-by-N complex nonsymmetric matrices (A,B) the generalized eigenvalues, and option ally, the left and/or right generalized eigenvectors
cggglm - solve a general Gauss-Markov linear model (GLM) problem
cgghrd - reduce a pair of complex matrices (A,B) to gener alized upper Hessenberg form using unitary transforma tions, where A is a general matrix and B is upper triangu lar
cgglse - solve the linear equality-constrained least squares (LSE) problem
cggqrf - compute a generalized QR factorization of an N- by-M matrix A and an N-by-P matrix B
cggrqf - compute a generalized RQ factorization of an M- by-N matrix A and a P-by-N matrix B
cggsvd - compute the generalized singular value decomposi tion (GSVD) of an M-by-N complex matrix A and P-by-N com plex matrix B
cggsvp - compute unitary matrices U, V and Q such that N- K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
cgtcon - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factoriza tion as computed by CGTTRF
cgtrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
cgtsv - solve the equation A*X = B,
cgtsvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
cgttrf - compute an LU factorization of a complex tridiag onal matrix A using elimination with partial pivoting and row interchanges
cgttrs - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
cgtts2 - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
chbevd - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
chbev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
chbevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
chbgst - reduce a complex Hermitian-definite banded gener alized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
chbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x
chbgv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x
chbgvx - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x
chbmv - perform the matrix-vector operation y := alpha*A*x + beta*y,
chbtrd - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
checkpoint - Force transaction log checkpoint
checon - estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF
cheevd - compute all eigenvalues and, optionally, eigen vectors of a complex Hermitian matrix A
cheev - compute all eigenvalues and, optionally, eigenvec tors of a complex Hermitian matrix A
cheevr - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix T
cheevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
chegs2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form
chegst - reduce a complex Hermitian-definite generalized eigenproblem to standard form
chegvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
chegv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
chegvx - compute selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
chemm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C,
chemv - perform the matrix-vector operation y := alpha*A*x + beta*y,
cher2k - perform one of the hermitian rank 2k operations C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,
cher2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
cherfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution
cherk - perform one of the hermitian rank k operations C := alpha*A*conjg( A' ) + beta*C,
cher - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A,
chesv - compute the solution to a complex system of linear equations A * X = B,
chesvx - use the diagonal pivoting factorization to com pute the solution to a complex system of linear equations A * X = B,
chetd2 - reduce a complex Hermitian matrix A to real sym metric tridiagonal form T by a unitary similarity trans formation
chetf2 - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
chetrd - reduce a complex Hermitian matrix A to real sym metric tridiagonal form T by a unitary similarity trans formation
chetrf - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
chetri - compute the inverse of a complex Hermitian indef inite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF
chetrs - solve a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF
chgeqz - implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A - w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper trian
chpcon - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factor ization A = U*D*U**H or A = L*D*L**H computed by CHPTRF
chpevd - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
chpev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed stor age
chpevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
chpgst - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage
chpgvd - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
chpgv - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
chpgvx - compute selected eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
chpmv - perform the matrix-vector operation y := alpha*A*x + beta*y,
chpr2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
chprfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and back ward error estimates for the solution
chpr - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A,
chpsv - compute the solution to a complex system of linear equations A * X = B,
chpsvx - use the diagonal pivoting factorization A = U*D*U**H or A = L*D*L**H to compute the solution to a com plex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices
chptrd - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a uni tary similarity transformation
chptrf - compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method
chptri - compute the inverse of a complex Hermitian indef inite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF
chptrs - solve a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF
chsein - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H
chseqr - compute the eigenvalues of a complex upper Hes senberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors
clabrd - reduce 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 Q' * A * P, and returns the matrices X and Y which are needed to apply the trans formation to the unreduced part of A
clacgv - conjugate a complex vector of length N
clacon - estimate the 1-norm of a square, complex matrix A
clacp2 - copie all or part of a real two-dimensional matrix A to a complex matrix B
clacpy - copie all or part of a two-dimensional matrix A to another matrix B
clacrm - perform a very simple matrix-matrix multiplica tion
clacrt - perform the operation ( c s )( x ) ==> ( x ) ( -s c )( y ) ( y ) where c and s are complex and the vec tors x and y are complex
cladiv - := X / Y, where X and Y are complex
claed0 - the divide and conquer method, CLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix
claed7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
claed8 - merge the two sets of eigenvalues together into a single sorted set
claein - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H
claesy - compute the eigendecomposition of a 2-by-2 sym metric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value
claev2 - compute the eigendecomposition of a 2-by-2 Hermi tian matrix [ A B ] [ CONJG(B) C ]
clags2 - compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0
clagtm - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
clahef - compute a partial factorization of a complex Her mitian matrix A using the Bunch-Kaufman diagonal pivoting method
clahqr - i an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by CHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
clahrd - reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th sub diagonal are zero
claic1 - applie one step of incremental condition estima tion in its simplest version
clals0 - applie 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
clalsa - i an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.)
clalsd - use the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of A*X-B, where A is N- by-N upper bidiagonal, and X and B are N-by-NRHS
clangb - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub- diagonals and ku super-diagonals
clange - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A
clangt - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A
clanhb - return the value of the one norm, or the Frobe nius 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 - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A
clanhp - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form
clanhs - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
clanht - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A
clansb - return the value of the one norm, or the Frobe nius 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 - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form
clansy - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A
clantb - return the value of the one norm, or the Frobe nius 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 - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
clantr - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
clapll - two column vectors X and Y, let A = ( X Y )
clapmt - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
claqgb - equilibrate 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
claqge - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
claqhb - equilibrate a symmetric band matrix A using the scaling factors in the vector S
claqhe - equilibrate a Hermitian matrix A using the scal ing factors in the vector S
claqhp - equilibrate a Hermitian matrix A using the scal ing factors in the vector S
claqp2 - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)
claqps - compute a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3
claqsb - equilibrate a symmetric band matrix A using the scaling factors in the vector S
claqsp - equilibrate a symmetric matrix A using the scal ing factors in the vector S
claqsy - equilibrate a symmetric matrix A using the scal ing factors in the vector S
clar1v - compute the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma I
clar2v - applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 com plex Hermitian matrices,
clarcm - perform a very simple matrix-matrix multiplica tion
clarfb - applie a complex block reflector H or its trans pose H' to a complex M-by-N matrix C, from either the left or the right
clarfg - generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I
clarf - applie a complex elementary reflector H to a com plex M-by-N matrix C, from either the left or the right
clarft - form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors
clarfx - applie a complex elementary reflector H to a com plex m by n matrix C, from either the left or the right
clargv - generate a vector of complex plane rotations with real cosines, determined by elements of the complex vec tors x and y
clarnv - return a vector of n random complex numbers from a uniform or normal distribution
clarrv - compute the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the eigenvalues of L D L^T
clartg - generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]
clartv - applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
clarzb - applie a complex block reflector H or its trans pose H**H to a complex distributed M-by-N C from the left or the right
clarz - applie a complex elementary reflector H to a com plex M-by-N matrix C, from either the left or the right
clarzt - form the triangular factor T of a complex block reflector H of order > n, which is defined as a product of k elementary reflectors
clascl - multiplie the M by N complex matrix A by the real scalar CTO/CFROM
claset - initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
clasr - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix,
classq - return the values scl and ssq such that ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
claswp - perform a series of row interchanges on the matrix A
clasyf - compute a partial factorization of a complex sym metric matrix A using the Bunch-Kaufman diagonal pivoting method
clatbs - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
clatdf - compute the contribution to the reciprocal Dif- estimate by solving for x in Z * x = b, where b is chosen such that the norm of x is as large as possible
clatps - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
clatrd - reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary simi larity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
clatrs - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
clatrz - factor the M-by-(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means of unitary transformations, where Z is an (M+L)-by-(M+L) unitary matrix and, R and A1 are M-by-M upper triangular matrices
clatzm - routine is deprecated and has been replaced by routine CUNMRZ
clauu2 - compute 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
clauum - compute 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
close - Close a cursor
cluster - Gives storage clustering advice to the server
comment - Add comment to an object
commit - Commits the current transaction
copy - Copies data between files and tables
cpbcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF
cpbequ - compute row and column scalings intended to equi librate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)
cpbrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution
cpbstf - compute a split Cholesky factorization of a com plex Hermitian positive definite band matrix A
cpbsv - compute the solution to a complex system of linear equations A * X = B,
cpbsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of lin ear equations A * X = B,
cpbtf2 - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
cpbtrf - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
cpbtrs - solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF
cpocon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF
cpoequ - compute row and column scalings intended to equi librate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm)
cporfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian positive definite,
cposv - compute the solution to a complex system of linear equations A * X = B,
cposvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of lin ear equations A * X = B,
cpotf2 - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
cpotrf - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
cpotri - compute the inverse of a complex Hermitian posi tive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF
cpotrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF
cppcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF
cppequ - compute row and column scalings intended to equi librate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
cpprfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution
cppsv - compute the solution to a complex system of linear equations A * X = B,
cppsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of lin ear equations A * X = B,
cpptrf - compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed for mat
cpptri - compute the inverse of a complex Hermitian posi tive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF
cpptrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF
cptcon - compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF
cpteqr - compute all eigenvalues and, optionally, eigen vectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidi agonal factor
cptrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
cptsv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
cptsvx - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiago nal matrix and X and B are N-by-NRHS matrices
cpttrf - compute the L*D*L' factorization of a complex Hermitian positive definite tridiagonal matrix A
cpttrs - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF
cptts2 - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF
create_aggregate - Defines a new aggregate function
create_constraint_trigger - Create a trigger to support a constraint
create_database - Creates a new database
create_function - Defines a new function
create_group - Creates a new group
create_index - Constructs a secondary index
create_language - Defines a new language for functions
create_operator - Defines a new user operator
create_rule - Defines a new rule
create_sequence - Creates a new sequence number generator
create_table_as - Creates a new table from the results of a SELECT
create_table - Creates a new table
create_trigger - Creates a new trigger
create_type - Defines a new base data type
create_user - Creates a new database user
create_view - Constructs a virtual table
crot - applie a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex
cscal integer i,incx,ix,n if(n.le.0)return if(incx.eq.1)go to 20 c code for increment not equal to 1 ix = 1
cspcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T com puted by CSPTRF
cspmv - perform the matrix-vector operation y := alpha*A*x + beta*y,
csprfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and back ward error estimates for the solution
cspr - perform the symmetric rank 1 operation A := alpha*x*conjg( x' ) + A,
cspsv - compute the solution to a complex system of linear equations A * X = B,
cspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a com plex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
csptrf - compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
csptri - compute the inverse of a complex symmetric indef inite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF
csptrs - solve a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF
csrot IF( N.LE.0 ) RETURN IF( INCX.EQ.1 .AND. INCY.EQ.1 ) GO TO 20 IX = 1 IY = 1 IF( INCX.LT.0 ) IX = ( -N+1 )*INCX + 1
csrscl - multiplie an n-element complex vector x by the real scalar 1/a
cstedc - compute all eigenvalues and, optionally, eigen vectors of a symmetric tridiagonal matrix using the divide and conquer method
cstegr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
cstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenval ues, using inverse iteration
csteqr - compute all eigenvalues and, optionally, eigen vectors of a symmetric tridiagonal matrix using the implicit QL or QR method
csycon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF
csymm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C,
csymv - perform the matrix-vector operation y := alpha*A*x + beta*y,
csyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C,
csyrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
csyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C,
csyr - perform the symmetric rank 1 operation A := alpha*x*( x' ) + A,
csysv - compute the solution to a complex system of linear equations A * X = B,
csysvx - use the diagonal pivoting factorization to com pute the solution to a complex system of linear equations A * X = B,
csytf2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
csytrf - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
csytri - compute the inverse of a complex symmetric indef inite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF
csytrs - solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF
ctbcon - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
ctbmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x,
ctbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
ctbsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b,
ctbtrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
ctgevc - compute some or all of the right and/or left gen eralized eigenvectors of a pair of complex upper triangu lar matrices (A,B)
ctgex2 - swap adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
ctgexc - reorder the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST
ctgsen - reorder the generalized Schur decomposition of a complex matrix pair (A, B) (in terms of an unitary equiva lence trans- formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the pair (A,B)
ctgsja - compute the generalized singular value decomposi tion (GSVD) of two complex upper triangular (or trape zoidal) matrices A and B
ctgsna - estimate reciprocal condition numbers for speci fied eigenvalues and/or eigenvectors of a matrix pair (A, B)
ctgsy2 - solve the generalized Sylvester equation A * R - L * B = scale * C (1) D * R - L * E = scale * F using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices,
ctgsyl - solve the generalized Sylvester equation
ctpcon - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
ctpmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x,
ctprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
ctpsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b,
ctptri - compute the inverse of a complex upper or lower triangular matrix A stored in packed format
ctptrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
ctrcon - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
ctrevc - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
ctrexc - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST
ctrmm - perform one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A' or op( A ) = conjg( A' )
ctrmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x,
ctrrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
ctrsen - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigen values appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right
ctrsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,
ctrsna - estimate reciprocal condition numbers for speci fied eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary)
ctrsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b,
ctrsyl - solve the complex Sylvester matrix equation
ctrti2 - compute the inverse of a complex upper or lower triangular matrix
ctrtri - compute the inverse of a complex upper or lower triangular matrix A
ctrtrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
ctzrqf - routine is deprecated and has been replaced by routine CTZRZF
ctzrzf - reduce the M-by-N ( M<=N ) complex upper trape zoidal matrix A to upper triangular form by means of uni tary transformations
cung2l - generate an m by n complex matrix Q with orthonormal columns,
cung2r - generate an m by n complex matrix Q with orthonormal columns,
cungbr - generate one of the complex unitary matrices Q or P**H determined by CGEBRD when reducing a complex matrix A to bidiagonal form
cunghr - generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD
cungl2 - generate an m-by-n complex matrix Q with orthonormal rows,
cunglq - generate an M-by-N complex matrix Q with orthonormal rows,
cungql - generate an M-by-N complex matrix Q with orthonormal columns,
cungqr - generate an M-by-N complex matrix Q with orthonormal columns,
cungr2 - generate an m by n complex matrix Q with orthonormal rows,
cungrq - generate an M-by-N complex matrix Q with orthonormal rows,
cungtr - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD
cunm2l - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
cunm2r - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
cunmbr - VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmhr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunml2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
cunmlq - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmql - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmqr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmr2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
cunmr3 - overwrite the general complex m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
cunmrq - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmrz - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmtr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cupgtr - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by CHPTRD using packed storage
cupmtr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
D
dbdsdc - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
dbdsqr - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
dcabs1 return end
ddisna - compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a gen eral m-by-n matrix
declare - Defines a cursor for table access
delete - Removes rows from a table
dgbbrd - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation
dgbcon - estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,
dgbequ - compute row and column scalings intended to equi librate an M-by-N band matrix A and reduce its condition number
dgbmv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
dgbrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
dgbsv - compute the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
dgbsvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
dgbtf2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
dgbtrf - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
dgbtrs - solve a system of linear equations A * X = B or A' * X = B with a general band matrix A using the LU fac torization computed by DGBTRF
dgebak - form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL
dgebal - balance a general real matrix A
dgebd2 - reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
dgebrd - reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation
dgecon - estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF
dgeequ - compute row and column scalings intended to equi librate an M-by-N matrix A and reduce its condition number
dgees - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
dgeesx - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
dgeev - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
dgeevx - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
dgegs - routine is deprecated and has been replaced by routine DGGES
dgegv - routine is deprecated and has been replaced by routine DGGEV
dgehd2 - reduce a real general matrix A to upper Hessen berg form H by an orthogonal similarity transformation
dgehrd - reduce a real general matrix A to upper Hessen berg form H by an orthogonal similarity transformation
dgelq2 - compute an LQ factorization of a real m by n matrix A
dgelqf - compute an LQ factorization of a real M-by-N matrix A
dgelsd - compute the minimum-norm solution to a real lin ear least squares problem
dgels - solve overdetermined or underdetermined real lin ear systems involving an M-by-N matrix A, or its trans pose, using a QR or LQ factorization of A
dgelss - compute the minimum norm solution to a real lin ear least squares problem
dgelsx - routine is deprecated and has been replaced by routine DGELSY
dgelsy - compute the minimum-norm solution to a real lin ear least squares problem
dgemm - perform one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C,
dgemv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
dgeql2 - compute a QL factorization of a real m by n matrix A
dgeqlf - compute a QL factorization of a real M-by-N matrix A
dgeqp3 - compute a QR factorization with column pivoting of a matrix A
dgeqpf - routine is deprecated and has been replaced by routine DGEQP3
dgeqr2 - compute a QR factorization of a real m by n matrix A
dgeqrf - compute a QR factorization of a real M-by-N matrix A
dgerfs - improve the computed solution to a system of lin ear equations and provides error bounds and backward error estimates for the solution
dger - perform the rank 1 operation A := alpha*x*y' + A,
dgerq2 - compute an RQ factorization of a real m by n matrix A
dgerqf - compute an RQ factorization of a real M-by-N matrix A
dgesc2 - solve a system of linear equations A * X = scale* RHS with a general N-by-N matrix A using the LU factorization with complete pivoting computed by DGETC2
dgesdd - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors
dgesvd - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors
dgesv - compute the solution to a real system of linear equations A * X = B,
dgesvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B,
dgetc2 - compute an LU factorization with complete pivot ing of the n-by-n matrix A
dgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
dgetrf - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
dgetri - compute the inverse of a matrix using the LU fac torization computed by DGETRF
dgetrs - solve a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU factorization computed by DGETRF
dggbak - form the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by back ward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL
dggbal - balance a pair of general real matrices (A,B)
dgges - compute for a pair of N-by-N real nonsymmetric matrices (A,B),
dggesx - compute for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized eigenvalues, the real Schur form (S,T), and,
dggev - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
dggevx - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
dggglm - solve a general Gauss-Markov linear model (GLM) problem
dgghrd - reduce a pair of real matrices (A,B) to general ized upper Hessenberg form using orthogonal transforma tions, where A is a general matrix and B is upper triangu lar
dgglse - solve the linear equality-constrained least squares (LSE) problem
dggqrf - compute a generalized QR factorization of an N- by-M matrix A and an N-by-P matrix B
dggrqf - compute a generalized RQ factorization of an M- by-N matrix A and a P-by-N matrix B
dggsvd - compute the generalized singular value decomposi tion (GSVD) of an M-by-N real matrix A and P-by-N real matrix B
dggsvp - compute orthogonal matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
dgtcon - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF
dgtrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
dgtsv - solve the equation A*X = B,
dgtsvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B,
dgttrf - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges
dgttrs - solve one of the systems of equations A*X = B or A'*X = B,
dgtts2 - solve one of the systems of equations A*X = B or A'*X = B,
dhgeqz - implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i*ALPHAI(j))/BETAR(j) of the equation det( A - w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form
dhsein - use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H
dhseqr - compute the eigenvalues of a real upper Hessen berg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors
dlabad - take as input the values computed by DLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large
dlabrd - reduce 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 Q' * A * P, and returns the matrices X and Y which are needed to apply the trans formation to the unreduced part of A
dlacon - estimate the 1-norm of a square, real matrix A
dlacpy - copie all or part of a two-dimensional matrix A to another matrix B
dladiv - perform complex division in real arithmetic a + i*b p + i*q = --------- c + i*d The algorithm is due to Robert L
dlae2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
dlaebz - contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
dlaed0 - compute all eigenvalues and corresponding eigen vectors of a symmetric tridiagonal matrix using the divide and conquer method
dlaed1 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
dlaed2 - merge the two sets of eigenvalues together into a single sorted set
dlaed3 - find the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
dlaed4 - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
dlaed5 - subroutine computes the I-th eigenvalue of a sym metric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO * Z * transpose(Z)
dlaed6 - compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true
dlaed7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
dlaed8 - merge the two sets of eigenvalues together into a single sorted set
dlaed9 - find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
dlaeda - compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem
dlaein - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
dlaev2 - compute the eigendecomposition of a 2-by-2 sym metric matrix [ A B ] [ B C ]
dlaexc - swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation
dlag2 - compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow
dlags2 - compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1
dlagtf - factorize the matrix (T - lambda*I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T - lambda*I = PLU,
dlagtm - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
dlagts - may be used to solve one of the systems of equa tions (T - lambda*I)*x = y or (T - lambda*I)'*x = y,
dlagv2 - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangu lar
dlahqr - i an auxiliary routine called by DHSEQR to update the eigenvalues and Schur decomposition already computed by DHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
dlahrd - reduce the first NB columns of a real general n- by-(n-k+1) matrix A so that elements below the k-th subdi agonal are zero
dlaic1 - applie one step of incremental condition estima tion in its simplest version
dlaln2 - solve a system of the form (ca A - w D ) X = s B or (ca A' - w D) X = s B with possible scaling ("s") and perturbation of A
dlals0 - applie 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 - i an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.)
dlalsd - use the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of A*X-B, where A is N- by-N upper bidiagonal, and X and B are N-by-NRHS
dlamch - determine double precision machine parameters
dlamrg - will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascend ing order
dlangb - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub- diagonals and ku super-diagonals
dlange - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
dlangt - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
dlanhs - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
dlansb - return the value of the one norm, or the Frobe nius 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 - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
dlanst - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
dlansy - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A
dlantb - return the value of the one norm, or the Frobe nius 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 - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
dlantr - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
dlanv2 - compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
dlapll - two column vectors X and Y, let A = ( X Y )
dlapmt - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
dlapy2 - return sqrt(x**2+y**2), taking care not to cause unnecessary overflow
dlapy3 - return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow
dlaqgb - equilibrate 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 - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
dlaqp2 - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)
dlaqps - compute a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3
dlaqsb - equilibrate a symmetric band matrix A using the scaling factors in the vector S
dlaqsp - equilibrate a symmetric matrix A using the scal ing factors in the vector S
dlaqsy - equilibrate a symmetric matrix A using the scal ing factors in the vector S
dlaqtr - solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE
dlar1v - compute the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma I
dlar2v - applie 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
dlarfb - applie 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 - generate a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I
dlarf - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
dlarft - form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors
dlarfx - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
dlargv - generate a vector of real plane rotations, deter mined by elements of the real vectors x and y
dlarnv - return a vector of n random real numbers from a uniform or normal distribution
dlarrb - the relatively robust representation(RRR) L D L^T, DLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T,
dlarre - the tridiagonal matrix T, DLARRE sets "small" off-diagonal elements to zero, and for each unreduced block T_i, it finds (i) the numbers sigma_i (ii) the base T_i - sigma_i I = L_i D_i L_i^T representations and (iii) eigenvalues of each L_i D_i L_i^T
dlarrf - the initial representation L D L^T and its clus ter of close eigenvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ),
dlarrv - compute the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the eigenvalues of L D L^T
dlartg - generate a plane rotation so that [ CS SN ]
dlartv - applie a vector of real plane rotations to ele ments of the real vectors x and y
dlaruv - return a vector of n random real numbers from a uniform (0,1)
dlarzb - applie a real block reflector H or its transpose H**T to a real distributed M-by-N C from the left or the right
dlarz - applie a real elementary reflector H to a real M- by-N matrix C, from either the left or the right
dlarzt - form the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors
dlas2 - compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]
dlascl - multiplie the M by N real matrix A by the real scalar CTO/CFROM
dlasd0 - a divide and conquer approach, DLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE
dlasd1 - compute the SVD of an upper bidiagonal N-by-M matrix B,
dlasd2 - merge the two sets of singular values together into a single sorted set
dlasd3 - find all the square roots of the roots of the secular equation, as defined by the values in D and Z
dlasd4 - subroutine computes the square root of the I-th updated eigenvalue of a positive symmetric rank-one modi fication to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i < j and that
dlasd5 - subroutine computes the square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) * diag( D ) + RHO * Z * transpose(Z)
dlasd6 - compute the SVD of an updated upper bidiagonal matrix B obtained by merging two smaller ones by appending a row
dlasd7 - merge the two sets of singular values together into a single sorted set
dlasd8 - find the square roots of the roots of the secular equation,
dlasd9 - find the square roots of the roots of the secular equation,
dlasda - a divide and conquer approach, DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE
dlasdq - compute 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 - create a tree of subproblems for bidiagonal divide and conquer
dlaset - initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals
dlasq1 - compute the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E
dlasq2 - compute all the eigenvalues of the symmetric pos itive definite tridiagonal matrix associated with the qd array Z to high relative accuracy are computed to high relative accuracy, in the absence of denormalization, underflow and overflow
dlasq3 - check for deflation, computes a shift (TAU) and calls dqds
dlasq4 - compute an approximation TAU to the smallest eigenvalue using values of d from the previous transform
dlasq5 - compute one dqds transform in ping-pong form, one version for IEEE machines another for non IEEE machines
dlasq6 - compute one dqd (shift equal to zero) transform in ping-pong form, with protection against underflow and overflow
dlasr - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix,
dlasrt - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' )
dlassq - return the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
dlasv2 - compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]
dlaswp - perform a series of row interchanges on the matrix A
dlasy2 - solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)*X + ISGN*X*op(TR) = SCALE*B,
dlasyf - compute a partial factorization of a real symmet ric matrix A using the Bunch-Kaufman diagonal pivoting method
dlatbs - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular band matrix
dlatdf - use the LU factorization of the n-by-n matrix Z computed by DGETC2 and computes a contribution to the reciprocal Dif-estimate by solving Z * x = b for x, and choosing the r.h.s
dlatps - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form
dlatrd - reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transforma tion to the unreduced part of A
dlatrs - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow
dlatrz - factor the M-by-(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means of orthogonal transformations
dlatzm - routine is deprecated and has been replaced by routine DORMRZ
dlauu2 - compute 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 - compute 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 - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by DSPTRD using packed storage
dopmtr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dorg2l - generate an m by n real matrix Q with orthonormal columns,
dorg2r - generate an m by n real matrix Q with orthonormal columns,
dorgbr - generate one of the real orthogonal matrices Q or P**T determined by DGEBRD when reducing a real matrix A to bidiagonal form
dorghr - generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD
dorgl2 - generate an m by n real matrix Q with orthonormal rows,
dorglq - generate an M-by-N real matrix Q with orthonormal rows,
dorgql - generate an M-by-N real matrix Q with orthonormal columns,
dorgqr - generate an M-by-N real matrix Q with orthonormal columns,
dorgr2 - generate an m by n real matrix Q with orthonormal rows,
dorgrq - generate an M-by-N real matrix Q with orthonormal rows,
dorgtr - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD
dorm2l - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
dorm2r - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
dormbr - VECT = 'Q', DORMBR overwrites the general real M- by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormhr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dorml2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
dormlq - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormql - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormqr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormr2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
dormr3 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
dormrq - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormrz - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormtr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dpbcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF
dpbequ - compute row and column scalings intended to equi librate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm)
dpbrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution
dpbstf - compute a split Cholesky factorization of a real symmetric positive definite band matrix A
dpbsv - compute the solution to a real system of linear equations A * X = B,
dpbsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
dpbtf2 - compute the Cholesky factorization of a real sym metric positive definite band matrix A
dpbtrf - compute the Cholesky factorization of a real sym metric positive definite band matrix A
dpbtrs - solve a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF
dpocon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF
dpoequ - compute row and column scalings intended to equi librate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
dporfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric positive definite,
dposv - compute the solution to a real system of linear equations A * X = B,
dposvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
dpotf2 - compute the Cholesky factorization of a real sym metric positive definite matrix A
dpotrf - compute the Cholesky factorization of a real sym metric positive definite matrix A
dpotri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF
dpotrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF
dppcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF
dppequ - compute row and column scalings intended to equi librate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
dpprfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution
dppsv - compute the solution to a real system of linear equations A * X = B,
dppsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
dpptrf - compute the Cholesky factorization of a real sym metric positive definite matrix A stored in packed format
dpptri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF
dpptrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF
dptcon - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF
dpteqr - compute all eigenvalues and, optionally, eigen vectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF, and then calling DBDSQR to compute the singular values of the bidiagonal factor
dptrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
dptsv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
dptsvx - use the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiago nal matrix and X and B are N-by-NRHS matrices
dpttrf - compute the L*D*L' factorization of a real sym metric positive definite tridiagonal matrix A
dpttrs - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by DPTTRF
dptts2 - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by DPTTRF
drop_aggregate - Removes the definition of an aggregate function
drop_database - Removes an existing database
drop_function - Removes a user-defined C function
drop_group - Removes a group
drop_index - Removes existing indexes from a database
drop_language - Removes a user-defined procedural language
drop_operator - Removes an operator from the database
drop_rule - Removes existing rules from the database
drop_sequence - Removes existing sequences from a database
drop_table - Removes existing tables from a database
drop_trigger - Removes the definition of a trigger
drop_type - Removes user-defined types from the system catalogs
drop_user - Removes a user
drop_view - Removes existing views from a database
drscl - multiplie an n-element real vector x by the real scalar 1/a
dsbevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
dsbev - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
dsbevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
dsbgst - reduce a real symmetric-definite banded general ized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
dsbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
dsbgv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
dsbgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
dsbmv - perform the matrix-vector operation y := alpha*A*x + beta*y,
dsbtrd - reduce a real symmetric band matrix A to symmet ric tridiagonal form T by an orthogonal similarity trans formation
dsecnd - return the user time for a process in seconds
dspcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF
dspevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed stor age
dspev - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed stor age
dspevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed stor age
dspgst - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage
dspgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dspgv - compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dspgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dspmv - perform the matrix-vector operation y := alpha*A*x + beta*y,
dspr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A,
dsprfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and back ward error estimates for the solution
dspr - perform the symmetric rank 1 operation A := alpha*x*x' + A,
dspsv - compute the solution to a real system of linear equations A * X = B,
dspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
dsptrd - reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal sim ilarity transformation
dsptrf - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
dsptri - compute the inverse of a real symmetric indefi nite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF
dsptrs - solve a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF
dstebz - compute the eigenvalues of a symmetric tridiago nal matrix T
dstedc - compute all eigenvalues and, optionally, eigen vectors of a symmetric tridiagonal matrix using the divide and conquer method
dstegr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
dstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenval ues, using inverse iteration
dsteqr - compute all eigenvalues and, optionally, eigen vectors of a symmetric tridiagonal matrix using the implicit QL or QR method
dsterf - compute all eigenvalues of a symmetric tridiago nal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm
dstevd - compute all eigenvalues and, optionally, eigen vectors of a real symmetric tridiagonal matrix
dstev - compute all eigenvalues and, optionally, eigenvec tors of a real symmetric tridiagonal matrix A
dstevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
dstevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
dsycon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF
dsyevd - compute all eigenvalues and, optionally, eigen vectors of a real symmetric matrix A
dsyev - compute all eigenvalues and, optionally, eigenvec tors of a real symmetric matrix A
dsyevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix T
dsyevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
dsygs2 - reduce a real symmetric-definite generalized eigenproblem to standard form
dsygst - reduce a real symmetric-definite generalized eigenproblem to standard form
dsygvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dsygv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dsygvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dsymm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C,
dsymv - perform the matrix-vector operation y := alpha*A*x + beta*y,
dsyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C,
dsyr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A,
dsyrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
dsyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C,
dsyr - perform the symmetric rank 1 operation A := alpha*x*x' + A,
dsysv - compute the solution to a real system of linear equations A * X = B,
dsysvx - use the diagonal pivoting factorization to com pute the solution to a real system of linear equations A * X = B,
dsytd2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transforma tion
dsytf2 - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
dsytrd - reduce a real symmetric matrix A to real symmet ric tridiagonal form T by an orthogonal similarity trans formation
dsytrf - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
dsytri - compute the inverse of a real symmetric indefi nite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF
dsytrs - solve a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF
dtbcon - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
dtbmv - perform one of the matrix-vector operations x := A*x, or x := A'*x,
dtbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
dtbsv - solve one of the systems of equations A*x = b, or A'*x = b,
dtbtrs - solve a triangular system of the form A * X = B or A**T * X = B,
dtgevc - compute some or all of the right and/or left gen eralized eigenvectors of a pair of real upper triangular matrices (A,B)
dtgex2 - swap 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
dtgexc - reorder the generalized real Schur decomposition of a real matrix pair (A,B) using an orthogonal equiva lence transformation (A, B) = Q * (A, B) * Z',
dtgsen - reorder the generalized real Schur decomposition of a real matrix pair (A, B) (in terms of an orthonormal equivalence trans- formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix A and
dtgsja - compute the generalized singular value decomposi tion (GSVD) of two real upper triangular (or trapezoidal) matrices A and B
dtgsna - estimate reciprocal condition numbers for speci fied eigenvalues and/or eigenvectors of a matrix pair (A, B) in generalized real Schur canonical form (or of any matrix pair (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where Z' denotes the transpose of Z
dtgsy2 - solve the generalized Sylvester equation
dtgsyl - solve the generalized Sylvester equation
dtpcon - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
dtpmv - perform one of the matrix-vector operations x := A*x, or x := A'*x,
dtprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
dtpsv - solve one of the systems of equations A*x = b, or A'*x = b,
dtptri - compute the inverse of a real upper or lower tri angular matrix A stored in packed format
dtptrs - solve a triangular system of the form A * X = B or A**T * X = B,
dtrcon - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
dtrevc - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
dtrexc - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST
dtrmm - perform one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ),
dtrmv - perform one of the matrix-vector operations x := A*x, or x := A'*x,
dtrrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
dtrsen - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigen values appears in the leading diagonal blocks of the upper quasi-triangular matrix T,
dtrsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,
dtrsna - estimate reciprocal condition numbers for speci fied eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal)
dtrsv - solve one of the systems of equations A*x = b, or A'*x = b,
dtrsyl - solve the real Sylvester matrix equation
dtrti2 - compute the inverse of a real upper or lower tri angular matrix
dtrtri - compute the inverse of a real upper or lower tri angular matrix A
dtrtrs - solve a triangular system of the form A * X = B or A**T * X = B,
dtzrqf - routine is deprecated and has been replaced by routine DTZRZF
dtzrzf - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations
dzsum1 - take the sum of the absolute values of a complex vector and returns a double precision result
E
end - Commits the current transaction
explain - Shows statement execution plan
F
fetch - Gets rows using a cursor
G
grant - Grants access privilege to a user, a group or all users
I
icmax1 - find the index of the element whose real part has maximum absolute value
ilaenv - i called from the LAPACK routines to choose prob lem-dependent parameters for the local environment
insert - Inserts new rows into a table
izmax1 - find the index of the element whose real part has maximum absolute value
L
lapack LAPACK is a transportable library of Fortran 77 subroutines for solving the most common problems in numerical linear algebra: systems of linear equations, linear least squares problems, eigenvalue problems, and singular value problems. It has been designed to be efficient on a wide range of mod
listen - Listen for a response on a notify condition
load - Dynamically loads an object file
lock - Explicitly lock a table inside a transaction
lsame - return .TRUE
lsamen - test if the first N letters of CA are the same as the first N letters of CB, regardless of case
M
move - Moves cursor position
N
notify - Signals all frontends and backends listening on a notify condition
R
reindex - Recover corrupted system indexes under stand- alone Postgres
reset - Restores run-time parameters to default values
revoke - Revokes access privilege from a user, a group or all users
rollback - Aborts the current transaction
S
sbdsdc - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
sbdsqr - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
scsum1 - take the sum of the absolute values of a complex vector and returns a single precision result
sdisna - compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a gen eral m-by-n matrix
second - return the user time for a process in seconds
select_into - Creates a new table from the results of a SELECT
select - Retrieves rows from a table or view
set_constraints - Set the constraint mode of the current SQL-transaction
set - Set run-time parameters
set_transaction - Set the characteristics of the current SQL-transaction
sgbbrd - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation
sgbcon - estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,
sgbequ - compute row and column scalings intended to equi librate an M-by-N band matrix A and reduce its condition number
sgbmv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
sgbrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
sgbsv - compute the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
sgbsvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
sgbtf2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
sgbtrf - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
sgbtrs - solve a system of linear equations A * X = B or A' * X = B with a general band matrix A using the LU fac torization computed by SGBTRF
sgebak - form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by SGEBAL
sgebal - balance a general real matrix A
sgebd2 - reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
sgebrd - reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation
sgecon - estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF
sgeequ - compute row and column scalings intended to equi librate an M-by-N matrix A and reduce its condition number
sgees - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
sgeesx - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
sgeev - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
sgeevx - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
sgegs - routine is deprecated and has been replaced by routine SGGES
sgegv - routine is deprecated and has been replaced by routine SGGEV
sgehd2 - reduce a real general matrix A to upper Hessen berg form H by an orthogonal similarity transformation
sgehrd - reduce a real general matrix A to upper Hessen berg form H by an orthogonal similarity transformation
sgelq2 - compute an LQ factorization of a real m by n matrix A
sgelqf - compute an LQ factorization of a real M-by-N matrix A
sgelsd - compute the minimum-norm solution to a real lin ear least squares problem
sgels - solve overdetermined or underdetermined real lin ear systems involving an M-by-N matrix A, or its trans pose, using a QR or LQ factorization of A
sgelss - compute the minimum norm solution to a real lin ear least squares problem
sgelsx - routine is deprecated and has been replaced by routine SGELSY
sgelsy - compute the minimum-norm solution to a real lin ear least squares problem
sgemm - perform one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C,
sgemv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
sgeql2 - compute a QL factorization of a real m by n matrix A
sgeqlf - compute a QL factorization of a real M-by-N matrix A
sgeqp3 - compute a QR factorization with column pivoting of a matrix A
sgeqpf - routine is deprecated and has been replaced by routine SGEQP3
sgeqr2 - compute a QR factorization of a real m by n matrix A
sgeqrf - compute a QR factorization of a real M-by-N matrix A
sgerfs - improve the computed solution to a system of lin ear equations and provides error bounds and backward error estimates for the solution
sger - perform the rank 1 operation A := alpha*x*y' + A,
sgerq2 - compute an RQ factorization of a real m by n matrix A
sgerqf - compute an RQ factorization of a real M-by-N matrix A
sgesc2 - solve a system of linear equations A * X = scale* RHS with a general N-by-N matrix A using the LU factorization with complete pivoting computed by SGETC2
sgesdd - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors
sgesvd - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors
sgesv - compute the solution to a real system of linear equations A * X = B,
sgesvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B,
sgetc2 - compute an LU factorization with complete pivot ing of the n-by-n matrix A
sgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
sgetrf - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
sgetri - compute the inverse of a matrix using the LU fac torization computed by SGETRF
sgetrs - solve a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF
sggbak - form the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by back ward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL
sggbal - balance a pair of general real matrices (A,B)
sgges - compute for a pair of N-by-N real nonsymmetric matrices (A,B),
sggesx - compute for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized eigenvalues, the real Schur form (S,T), and,
sggev - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
sggevx - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
sggglm - solve a general Gauss-Markov linear model (GLM) problem
sgghrd - reduce a pair of real matrices (A,B) to general ized upper Hessenberg form using orthogonal transforma tions, where A is a general matrix and B is upper triangu lar
sgglse - solve the linear equality-constrained least squares (LSE) problem
sggqrf - compute a generalized QR factorization of an N- by-M matrix A and an N-by-P matrix B
sggrqf - compute a generalized RQ factorization of an M- by-N matrix A and a P-by-N matrix B
sggsvd - compute the generalized singular value decomposi tion (GSVD) of an M-by-N real matrix A and P-by-N real matrix B
sggsvp - compute orthogonal matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
sgtcon - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF
sgtrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
sgtsv - solve the equation A*X = B,
sgtsvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B,
sgttrf - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges
sgttrs - solve one of the systems of equations A*X = B or A'*X = B,
sgtts2 - solve one of the systems of equations A*X = B or A'*X = B,
shgeqz - implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i*ALPHAI(j))/BETAR(j) of the equation det( A - w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form
show - Shows run-time parameters
shsein - use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H
shseqr - compute the eigenvalues of a real upper Hessen berg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors
slabad - take 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 - reduce 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 Q' * A * P, and returns the matrices X and Y which are needed to apply the trans formation to the unreduced part of A
slacon - estimate the 1-norm of a square, real matrix A
slacpy - copie all or part of a two-dimensional matrix A to another matrix B
sladiv - perform complex division in real arithmetic a + i*b p + i*q = --------- c + i*d The algorithm is due to Robert L
slae2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
slaebz - contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
slaed0 - compute all eigenvalues and corresponding eigen vectors of a symmetric tridiagonal matrix using the divide and conquer method
slaed1 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
slaed2 - merge the two sets of eigenvalues together into a single sorted set
slaed3 - find the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
slaed4 - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
slaed5 - subroutine computes the I-th eigenvalue of a sym metric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO * Z * transpose(Z)
slaed6 - compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true
slaed7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
slaed8 - merge the two sets of eigenvalues together into a single sorted set
slaed9 - find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
slaeda - compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem
slaein - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
slaev2 - compute the eigendecomposition of a 2-by-2 sym metric matrix [ A B ] [ B C ]
slaexc - swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation
slag2 - compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow
slags2 - compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1
slagtf - factorize the matrix (T - lambda*I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T - lambda*I = PLU,
slagtm - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
slagts - may be used to solve one of the systems of equa tions (T - lambda*I)*x = y or (T - lambda*I)'*x = y,
slagv2 - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangu lar
slahqr - i an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
slahrd - reduce the first NB columns of a real general n- by-(n-k+1) matrix A so that elements below the k-th subdi agonal are zero
slaic1 - applie one step of incremental condition estima tion in its simplest version
slaln2 - solve a system of the form (ca A - w D ) X = s B or (ca A' - w D) X = s B with possible scaling ("s") and perturbation of A
slals0 - applie 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
slalsa - i an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.)
slalsd - use the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of A*X-B, where A is N- by-N upper bidiagonal, and X and B are N-by-NRHS
slamch - determine single precision machine parameters
slamrg - will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascend ing order
slangb - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub- diagonals and ku super-diagonals
slange - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
slangt - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
slanhs - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
slansb - return the value of the one norm, or the Frobe nius 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 - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
slanst - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
slansy - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A
slantb - return the value of the one norm, or the Frobe nius 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
slantp - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
slantr - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
slanv2 - compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
slapll - two column vectors X and Y, let A = ( X Y )
slapmt - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
slapy2 - return sqrt(x**2+y**2), taking care not to cause unnecessary overflow
slapy3 - return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow
slaqgb - equilibrate 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
slaqge - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
slaqp2 - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)
slaqps - compute a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3
slaqsb - equilibrate a symmetric band matrix A using the scaling factors in the vector S
slaqsp - equilibrate a symmetric matrix A using the scal ing factors in the vector S
slaqsy - equilibrate a symmetric matrix A using the scal ing factors in the vector S
slaqtr - solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE
slar1v - compute the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma I
slar2v - applie 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
slarfb - applie 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 - generate a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I
slarf - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
slarft - form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors
slarfx - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
slargv - generate a vector of real plane rotations, deter mined by elements of the real vectors x and y
slarnv - return a vector of n random real numbers from a uniform or normal distribution
slarrb - the relatively robust representation(RRR) L D L^T, SLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T,
slarre - the tridiagonal matrix T, SLARRE sets "small" off-diagonal elements to zero, and for each unreduced block T_i, it finds (i) the numbers sigma_i (ii) the base T_i - sigma_i I = L_i D_i L_i^T representations and (iii) eigenvalues of each L_i D_i L_i^T
slarrf - the initial representation L D L^T and its clus ter of close eigenvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ),
slarrv - compute the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the eigenvalues of L D L^T
slartg - generate a plane rotation so that [ CS SN ]
slartv - applie a vector of real plane rotations to ele ments of the real vectors x and y
slaruv - return a vector of n random real numbers from a uniform (0,1)
slarzb - applie a real block reflector H or its transpose H**T to a real distributed M-by-N C from the left or the right
slarz - applie a real elementary reflector H to a real M- by-N matrix C, from either the left or the right
slarzt - form the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors
slas2 - compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]
slascl - multiplie the M by N real matrix A by the real scalar CTO/CFROM
slasd0 - a divide and conquer approach, SLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE
slasd1 - compute the SVD of an upper bidiagonal N-by-M matrix B,
slasd2 - merge the two sets of singular values together into a single sorted set
slasd3 - find all the square roots of the roots of the secular equation, as defined by the values in D and Z
slasd4 - subroutine computes the square root of the I-th updated eigenvalue of a positive symmetric rank-one modi fication to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i < j and that
slasd5 - subroutine computes the square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) * diag( D ) + RHO * Z * transpose(Z)
slasd6 - compute the SVD of an updated upper bidiagonal matrix B obtained by merging two smaller ones by appending a row
slasd7 - merge the two sets of singular values together into a single sorted set
slasd8 - find the square roots of the roots of the secular equation,
slasd9 - find the square roots of the roots of the secular equation,
slasda - a divide and conquer approach, SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE
slasdq - compute 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 - create a tree of subproblems for bidiagonal divide and conquer
slaset - initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals
slasq1 - compute the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E
slasq2 - compute all the eigenvalues of the symmetric pos itive definite tridiagonal matrix associated with the qd array Z to high relative accuracy are computed to high relative accuracy, in the absence of denormalization, underflow and overflow
slasq3 - check for deflation, computes a shift (TAU) and calls dqds
slasq4 - compute an approximation TAU to the smallest eigenvalue using values of d from the previous transform
slasq5 - compute one dqds transform in ping-pong form, one version for IEEE machines another for non IEEE machines
slasq6 - compute one dqd (shift equal to zero) transform in ping-pong form, with protection against underflow and overflow
slasr - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix,
slasrt - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' )
slassq - return the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
slasv2 - compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]
slaswp - perform a series of row interchanges on the matrix A
slasy2 - solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)*X + ISGN*X*op(TR) = SCALE*B,
slasyf - compute a partial factorization of a real symmet ric matrix A using the Bunch-Kaufman diagonal pivoting method
slatbs - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular band matrix
slatdf - use the LU factorization of the n-by-n matrix Z computed by SGETC2 and computes a contribution to the reciprocal Dif-estimate by solving Z * x = b for x, and choosing the r.h.s
slatps - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form
slatrd - reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transforma tion to the unreduced part of A
slatrs - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow
slatrz - factor the M-by-(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means of orthogonal transformations
slatzm - routine is deprecated and has been replaced by routine SORMRZ
slauu2 - compute 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
slauum - compute 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 - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by SSPTRD using packed storage
sopmtr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sorg2l - generate an m by n real matrix Q with orthonormal columns,
sorg2r - generate an m by n real matrix Q with orthonormal columns,
sorgbr - generate one of the real orthogonal matrices Q or P**T determined by SGEBRD when reducing a real matrix A to bidiagonal form
sorghr - generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD
sorgl2 - generate an m by n real matrix Q with orthonormal rows,
sorglq - generate an M-by-N real matrix Q with orthonormal rows,
sorgql - generate an M-by-N real matrix Q with orthonormal columns,
sorgqr - generate an M-by-N real matrix Q with orthonormal columns,
sorgr2 - generate an m by n real matrix Q with orthonormal rows,
sorgrq - generate an M-by-N real matrix Q with orthonormal rows,
sorgtr - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD
sorm2l - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
sorm2r - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
sormbr - VECT = 'Q', SORMBR overwrites the general real M- by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormhr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sorml2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
sormlq - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormql - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormqr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormr2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
sormr3 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
sormrq - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormrz - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormtr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
spbcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF
spbequ - compute row and column scalings intended to equi librate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm)
spbrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution
spbstf - compute a split Cholesky factorization of a real symmetric positive definite band matrix A
spbsv - compute the solution to a real system of linear equations A * X = B,
spbsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
spbtf2 - compute the Cholesky factorization of a real sym metric positive definite band matrix A
spbtrf - compute the Cholesky factorization of a real sym metric positive definite band matrix A
spbtrs - solve a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF
spocon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF
spoequ - compute row and column scalings intended to equi librate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
sporfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric positive definite,
sposv - compute the solution to a real system of linear equations A * X = B,
sposvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
spotf2 - compute the Cholesky factorization of a real sym metric positive definite matrix A
spotrf - compute the Cholesky factorization of a real sym metric positive definite matrix A
spotri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF
spotrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF
sppcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF
sppequ - compute row and column scalings intended to equi librate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
spprfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution
sppsv - compute the solution to a real system of linear equations A * X = B,
sppsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
spptrf - compute the Cholesky factorization of a real sym metric positive definite matrix A stored in packed format
spptri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF
spptrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF
sptcon - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF
spteqr - compute all eigenvalues and, optionally, eigen vectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor
sptrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
sptsv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
sptsvx - use the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiago nal matrix and X and B are N-by-NRHS matrices
spttrf - compute the L*D*L' factorization of a real sym metric positive definite tridiagonal matrix A
spttrs - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by SPTTRF
sptts2 - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by SPTTRF
srscl - multiplie an n-element real vector x by the real scalar 1/a
ssbevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
ssbev - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
ssbevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
ssbgst - reduce a real symmetric-definite banded general ized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
ssbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
ssbgv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
ssbgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
ssbmv - perform the matrix-vector operation y := alpha*A*x + beta*y,
ssbtrd - reduce a real symmetric band matrix A to symmet ric tridiagonal form T by an orthogonal similarity trans formation
sspcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF
sspevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed stor age
sspev - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed stor age
sspevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed stor age
sspgst - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage
sspgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
sspgv - compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
sspgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
sspmv - perform the matrix-vector operation y := alpha*A*x + beta*y,
sspr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A,
ssprfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and back ward error estimates for the solution
sspr - perform the symmetric rank 1 operation A := alpha*x*x' + A,
sspsv - compute the solution to a real system of linear equations A * X = B,
sspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
ssptrd - reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal sim ilarity transformation
ssptrf - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
ssptri - compute the inverse of a real symmetric indefi nite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF
ssptrs - solve a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF
sstebz - compute the eigenvalues of a symmetric tridiago nal matrix T
sstedc - compute all eigenvalues and, optionally, eigen vectors of a symmetric tridiagonal matrix using the divide and conquer method
sstegr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
sstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenval ues, using inverse iteration
ssteqr - compute all eigenvalues and, optionally, eigen vectors of a symmetric tridiagonal matrix using the implicit QL or QR method
ssterf - compute all eigenvalues of a symmetric tridiago nal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm
sstevd - compute all eigenvalues and, optionally, eigen vectors of a real symmetric tridiagonal matrix
sstev - compute all eigenvalues and, optionally, eigenvec tors of a real symmetric tridiagonal matrix A
sstevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
sstevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
ssycon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF
ssyevd - compute all eigenvalues and, optionally, eigen vectors of a real symmetric matrix A
ssyev - compute all eigenvalues and, optionally, eigenvec tors of a real symmetric matrix A
ssyevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix T
ssyevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
ssygs2 - reduce a real symmetric-definite generalized eigenproblem to standard form
ssygst - reduce a real symmetric-definite generalized eigenproblem to standard form
ssygvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
ssygv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
ssygvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
ssymm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C,
ssymv - perform the matrix-vector operation y := alpha*A*x + beta*y,
ssyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C,
ssyr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A,
ssyrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
ssyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C,
ssyr - perform the symmetric rank 1 operation A := alpha*x*x' + A,
ssysv - compute the solution to a real system of linear equations A * X = B,
ssysvx - use the diagonal pivoting factorization to com pute the solution to a real system of linear equations A * X = B,
ssytd2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transforma tion
ssytf2 - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
ssytrd - reduce a real symmetric matrix A to real symmet ric tridiagonal form T by an orthogonal similarity trans formation
ssytrf - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
ssytri - compute the inverse of a real symmetric indefi nite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF
ssytrs - solve a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF
stbcon - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
stbmv - perform one of the matrix-vector operations x := A*x, or x := A'*x,
stbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
stbsv - solve one of the systems of equations A*x = b, or A'*x = b,
stbtrs - solve a triangular system of the form A * X = B or A**T * X = B,
stgevc - compute some or all of the right and/or left gen eralized eigenvectors of a pair of real upper triangular matrices (A,B)
stgex2 - swap 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 - reorder the generalized real Schur decomposition of a real matrix pair (A,B) using an orthogonal equiva lence transformation (A, B) = Q * (A, B) * Z',
stgsen - reorder the generalized real Schur decomposition of a real matrix pair (A, B) (in terms of an orthonormal equivalence trans- formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix A and
stgsja - compute the generalized singular value decomposi tion (GSVD) of two real upper triangular (or trapezoidal) matrices A and B
stgsna - estimate reciprocal condition numbers for speci fied eigenvalues and/or eigenvectors of a matrix pair (A, B) in generalized real Schur canonical form (or of any matrix pair (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where Z' denotes the transpose of Z
stgsy2 - solve the generalized Sylvester equation
stgsyl - solve the generalized Sylvester equation
stpcon - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
stpmv - perform one of the matrix-vector operations x := A*x, or x := A'*x,
stprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
stpsv - solve one of the systems of equations A*x = b, or A'*x = b,
stptri - compute the inverse of a real upper or lower tri angular matrix A stored in packed format
stptrs - solve a triangular system of the form A * X = B or A**T * X = B,
strcon - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
strevc - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
strexc - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST
strmm - perform one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ),
strmv - perform one of the matrix-vector operations x := A*x, or x := A'*x,
strrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
strsen - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigen values appears in the leading diagonal blocks of the upper quasi-triangular matrix T,
strsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,
strsna - estimate reciprocal condition numbers for speci fied eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal)
strsv - solve one of the systems of equations A*x = b, or A'*x = b,
strsyl - solve the real Sylvester matrix equation
strti2 - compute the inverse of a real upper or lower tri angular matrix
strtri - compute the inverse of a real upper or lower tri angular matrix A
strtrs - solve a triangular system of the form A * X = B or A**T * X = B,
stzrqf - routine is deprecated and has been replaced by routine STZRZF
stzrzf - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations
T
truncate - Empty a table
U
unlisten - Stop listening for notification
update - Replaces values of columns in a table
V
vacuum - Clean and analyze a Postgres database
X
xerbla - i an error handler for the LAPACK routines
Z
zbdsqr - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
zdrot IF( N.LE.0 ) RETURN IF( INCX.EQ.1 .AND. INCY.EQ.1 ) GO TO 20 IX = 1 IY = 1 IF( INCX.LT.0 ) IX = ( -N+1 )*INCX + 1
zdrscl - multiplie an n-element complex vector x by the real scalar 1/a
zgbbrd - reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
zgbcon - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,
zgbequ - compute row and column scalings intended to equi librate an M-by-N band matrix A and reduce its condition number
zgbmv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y,
zgbrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
zgbsv - compute the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
zgbsvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
zgbtf2 - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
zgbtrf - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
zgbtrs - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by ZGBTRF
zgebak - form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL
zgebal - balance a general complex matrix A
zgebd2 - reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transforma tion
zgebrd - reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
zgecon - estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF
zgeequ - compute row and column scalings intended to equi librate an M-by-N matrix A and reduce its condition number
zgees - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
zgeesx - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
zgeev - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
zgeevx - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
zgegs - routine is deprecated and has been replaced by routine ZGGES
zgegv - routine is deprecated and has been replaced by routine ZGGEV
zgehd2 - reduce a complex general matrix A to upper Hes senberg form H by a unitary similarity transformation
zgehrd - reduce a complex general matrix A to upper Hes senberg form H by a unitary similarity transformation
zgelq2 - compute an LQ factorization of a complex m by n matrix A
zgelqf - compute an LQ factorization of a complex M-by-N matrix A
zgelsd - compute the minimum-norm solution to a real lin ear least squares problem
zgels - solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conju gate-transpose, using a QR or LQ factorization of A
zgelss - compute the minimum norm solution to a complex linear least squares problem
zgelsx - routine is deprecated and has been replaced by routine ZGELSY
zgelsy - compute the minimum-norm solution to a complex linear least squares problem
zgemm - perform one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C,
zgemv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y,
zgeql2 - compute a QL factorization of a complex m by n matrix A
zgeqlf - compute a QL factorization of a complex M-by-N matrix A
zgeqp3 - compute a QR factorization with column pivoting of a matrix A
zgeqpf - routine is deprecated and has been replaced by routine ZGEQP3
zgeqr2 - compute a QR factorization of a complex m by n matrix A
zgeqrf - compute a QR factorization of a complex M-by-N matrix A
zgerc - perform the rank 1 operation A := alpha*x*conjg( y' ) + A,
zgerfs - improve the computed solution to a system of lin ear equations and provides error bounds and backward error estimates for the solution
zgerq2 - compute an RQ factorization of a complex m by n matrix A
zgerqf - compute an RQ factorization of a complex M-by-N matrix A
zgeru - perform the rank 1 operation A := alpha*x*y' + A,
zgesc2 - solve a system of linear equations A * X = scale* RHS with a general N-by-N matrix A using the LU factorization with complete pivoting computed by ZGETC2
zgesdd - compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method
zgesvd - compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors
zgesv - compute the solution to a complex system of linear equations A * X = B,
zgesvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B,
zgetc2 - compute an LU factorization, using complete piv oting, of the n-by-n matrix A
zgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
zgetrf - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
zgetri - compute the inverse of a matrix using the LU fac torization computed by ZGETRF
zgetrs - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by ZGETRF
zggbak - form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by back ward transformation on the computed eigenvectors of the balanced pair of matrices output by ZGGBAL
zggbal - balance a pair of general complex matrices (A,B)
zgges - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the general ized complex Schur form (S, T), and optionally left and/or right Schur vectors (VSL and VSR)
zggesx - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T),
zggev - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and option ally, the left and/or right generalized eigenvectors
zggevx - compute for a pair of N-by-N complex nonsymmetric matrices (A,B) the generalized eigenvalues, and option ally, the left and/or right generalized eigenvectors
zggglm - solve a general Gauss-Markov linear model (GLM) problem
zgghrd - reduce a pair of complex matrices (A,B) to gener alized upper Hessenberg form using unitary transforma tions, where A is a general matrix and B is upper triangu lar
zgglse - solve the linear equality-constrained least squares (LSE) problem
zggqrf - compute a generalized QR factorization of an N- by-M matrix A and an N-by-P matrix B
zggrqf - compute a generalized RQ factorization of an M- by-N matrix A and a P-by-N matrix B
zggsvd - compute the generalized singular value decomposi tion (GSVD) of an M-by-N complex matrix A and P-by-N com plex matrix B
zggsvp - compute unitary matrices U, V and Q such that N- K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
zgtcon - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factoriza tion as computed by ZGTTRF
zgtrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
zgtsv - solve the equation A*X = B,
zgtsvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
zgttrf - compute an LU factorization of a complex tridiag onal matrix A using elimination with partial pivoting and row interchanges
zgttrs - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
zgtts2 - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
zhbevd - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
zhbev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
zhbevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
zhbgst - reduce a complex Hermitian-definite banded gener alized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
zhbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x
zhbgv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x
zhbgvx - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x
zhbmv - perform the matrix-vector operation y := alpha*A*x + beta*y,
zhbtrd - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
zhecon - estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF
zheevd - compute all eigenvalues and, optionally, eigen vectors of a complex Hermitian matrix A
zheev - compute all eigenvalues and, optionally, eigenvec tors of a complex Hermitian matrix A
zheevr - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix T
zheevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
zhegs2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form
zhegst - reduce a complex Hermitian-definite generalized eigenproblem to standard form
zhegvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
zhegv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
zhegvx - compute selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
zhemm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C,
zhemv - perform the matrix-vector operation y := alpha*A*x + beta*y,
zher2k - perform one of the hermitian rank 2k operations C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,
zher2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
zherfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution
zherk - perform one of the hermitian rank k operations C := alpha*A*conjg( A' ) + beta*C,
zher - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A,
zhesv - compute the solution to a complex system of linear equations A * X = B,
zhesvx - use the diagonal pivoting factorization to com pute the solution to a complex system of linear equations A * X = B,
zhetd2 - reduce a complex Hermitian matrix A to real sym metric tridiagonal form T by a unitary similarity trans formation
zhetf2 - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
zhetrd - reduce a complex Hermitian matrix A to real sym metric tridiagonal form T by a unitary similarity trans formation
zhetrf - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
zhetri - compute the inverse of a complex Hermitian indef inite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF
zhetrs - solve a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF
zhgeqz - implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A - w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper trian
zhpcon - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factor ization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF
zhpevd - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
zhpev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed stor age
zhpevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
zhpgst - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage
zhpgvd - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
zhpgv - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
zhpgvx - compute selected eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
zhpmv - perform the matrix-vector operation y := alpha*A*x + beta*y,
zhpr2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
zhprfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and back ward error estimates for the solution
zhpr - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A,
zhpsv - compute the solution to a complex system of linear equations A * X = B,
zhpsvx - use the diagonal pivoting factorization A = U*D*U**H or A = L*D*L**H to compute the solution to a com plex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices
zhptrd - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a uni tary similarity transformation
zhptrf - compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method
zhptri - compute the inverse of a complex Hermitian indef inite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF
zhptrs - solve a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF
zhsein - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H
zhseqr - compute the eigenvalues of a complex upper Hes senberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors
zlabrd - reduce 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 Q' * A * P, and returns the matrices X and Y which are needed to apply the trans formation to the unreduced part of A
zlacgv - conjugate a complex vector of length N
zlacon - estimate the 1-norm of a square, complex matrix A
zlacp2 - copie all or part of a real two-dimensional matrix A to a complex matrix B
zlacpy - copie all or part of a two-dimensional matrix A to another matrix B
zlacrm - perform a very simple matrix-matrix multiplica tion
zlacrt - perform the operation ( c s )( x ) ==> ( x ) ( -s c )( y ) ( y ) where c and s are complex and the vec tors x and y are complex
zladiv - := X / Y, where X and Y are complex
zlaed0 - the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix
zlaed7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
zlaed8 - merge the two sets of eigenvalues together into a single sorted set
zlaein - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H
zlaesy - compute the eigendecomposition of a 2-by-2 sym metric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value
zlaev2 - compute the eigendecomposition of a 2-by-2 Hermi tian matrix [ A B ] [ CONJG(B) C ]
zlags2 - compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0
zlagtm - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
zlahef - compute a partial factorization of a complex Her mitian matrix A using the Bunch-Kaufman diagonal pivoting method
zlahqr - i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
zlahrd - reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th sub diagonal are zero
zlaic1 - applie one step of incremental condition estima tion in its simplest version
zlals0 - applie 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 - i an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.)
zlalsd - use the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of A*X-B, where A is N- by-N upper bidiagonal, and X and B are N-by-NRHS
zlangb - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub- diagonals and ku super-diagonals
zlange - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A
zlangt - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A
zlanhb - return the value of the one norm, or the Frobe nius 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 - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A
zlanhp - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form
zlanhs - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
zlanht - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A
zlansb - return the value of the one norm, or the Frobe nius 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 - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form
zlansy - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A
zlantb - return the value of the one norm, or the Frobe nius 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 - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
zlantr - return the value of the one norm, or the Frobe nius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
zlapll - two column vectors X and Y, let A = ( X Y )
zlapmt - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
zlaqgb - equilibrate 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 - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
zlaqhb - equilibrate a symmetric band matrix A using the scaling factors in the vector S
zlaqhe - equilibrate a Hermitian matrix A using the scal ing factors in the vector S
zlaqhp - equilibrate a Hermitian matrix A using the scal ing factors in the vector S
zlaqp2 - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)
zlaqps - compute a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3
zlaqsb - equilibrate a symmetric band matrix A using the scaling factors in the vector S
zlaqsp - equilibrate a symmetric matrix A using the scal ing factors in the vector S
zlaqsy - equilibrate a symmetric matrix A using the scal ing factors in the vector S
zlar1v - compute the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma I
zlar2v - applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 com plex Hermitian matrices,
zlarcm - perform a very simple matrix-matrix multiplica tion
zlarfb - applie a complex block reflector H or its trans pose H' to a complex M-by-N matrix C, from either the left or the right
zlarfg - generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I
zlarf - applie a complex elementary reflector H to a com plex M-by-N matrix C, from either the left or the right
zlarft - form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors
zlarfx - applie a complex elementary reflector H to a com plex m by n matrix C, from either the left or the right
zlargv - generate a vector of complex plane rotations with real cosines, determined by elements of the complex vec tors x and y
zlarnv - return a vector of n random complex numbers from a uniform or normal distribution
zlarrv - compute the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the eigenvalues of L D L^T
zlartg - generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]
zlartv - applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
zlarzb - applie a complex block reflector H or its trans pose H**H to a complex distributed M-by-N C from the left or the right
zlarz - applie a complex elementary reflector H to a com plex M-by-N matrix C, from either the left or the right
zlarzt - form the triangular factor T of a complex block reflector H of order > n, which is defined as a product of k elementary reflectors
zlascl - multiplie the M by N complex matrix A by the real scalar CTO/CFROM
zlaset - initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
zlasr - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix,
zlassq - return the values scl and ssq such that ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
zlaswp - perform a series of row interchanges on the matrix A
zlasyf - compute a partial factorization of a complex sym metric matrix A using the Bunch-Kaufman diagonal pivoting method
zlatbs - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
zlatdf - compute the contribution to the reciprocal Dif- estimate by solving for x in Z * x = b, where b is chosen such that the norm of x is as large as possible
zlatps - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
zlatrd - reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary simi larity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
zlatrs - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
zlatrz - factor the M-by-(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means of unitary transformations, where Z is an (M+L)-by-(M+L) unitary matrix and, R and A1 are M-by-M upper triangular matrices
zlatzm - routine is deprecated and has been replaced by routine ZUNMRZ
zlauu2 - compute 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
zlauum - compute 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
zpbcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF
zpbequ - compute row and column scalings intended to equi librate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)
zpbrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution
zpbstf - compute a split Cholesky factorization of a com plex Hermitian positive definite band matrix A
zpbsv - compute the solution to a complex system of linear equations A * X = B,
zpbsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of lin ear equations A * X = B,
zpbtf2 - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
zpbtrf - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
zpbtrs - solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF
zpocon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF
zpoequ - compute row and column scalings intended to equi librate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm)
zporfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian positive definite,
zposv - compute the solution to a complex system of linear equations A * X = B,
zposvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of lin ear equations A * X = B,
zpotf2 - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
zpotrf - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
zpotri - compute the inverse of a complex Hermitian posi tive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF
zpotrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF
zppcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF
zppequ - compute row and column scalings intended to equi librate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
zpprfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution
zppsv - compute the solution to a complex system of linear equations A * X = B,
zppsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of lin ear equations A * X = B,
zpptrf - compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed for mat
zpptri - compute the inverse of a complex Hermitian posi tive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF
zpptrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF
zptcon - compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF
zpteqr - compute all eigenvalues and, optionally, eigen vectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF and then calling ZBDSQR to compute the singular values of the bidi agonal factor
zptrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
zptsv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
zptsvx - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiago nal matrix and X and B are N-by-NRHS matrices
zpttrf - compute the L*D*L' factorization of a complex Hermitian positive definite tridiagonal matrix A
zpttrs - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by ZPTTRF
zptts2 - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by ZPTTRF
zrotg c = 0.0d0 s = (1.0d0,0.0d0) ca = cb go to 20 10 continue
zrot - applie a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex
zscal integer i,incx,ix,n if(n.le.0)return if(incx.eq.1)go to 20 c code for increment not equal to 1 ix = 1
zspcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T com puted by ZSPTRF
zspmv - perform the matrix-vector operation y := alpha*A*x + beta*y,
zsprfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and back ward error estimates for the solution
zspr - perform the symmetric rank 1 operation A := alpha*x*conjg( x' ) + A,
zspsv - compute the solution to a complex system of linear equations A * X = B,
zspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a com plex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
zsptrf - compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
zsptri - compute the inverse of a complex symmetric indef inite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
zsptrs - solve a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
zstedc - compute all eigenvalues and, optionally, eigen vectors of a symmetric tridiagonal matrix using the divide and conquer method
zstegr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
zstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenval ues, using inverse iteration
zsteqr - compute all eigenvalues and, optionally, eigen vectors of a symmetric tridiagonal matrix using the implicit QL or QR method
zsycon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF
zsymm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C,
zsymv - perform the matrix-vector operation y := alpha*A*x + beta*y,
zsyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C,
zsyrfs - improve the computed solution to a system of lin ear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
zsyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C,
zsyr - perform the symmetric rank 1 operation A := alpha*x*( x' ) + A,
zsysv - compute the solution to a complex system of linear equations A * X = B,
zsysvx - use the diagonal pivoting factorization to com pute the solution to a complex system of linear equations A * X = B,
zsytf2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
zsytrf - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
zsytri - compute the inverse of a complex symmetric indef inite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF
zsytrs - solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF
ztbcon - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
ztbmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x,
ztbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
ztbsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b,
ztbtrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
ztgevc - compute some or all of the right and/or left gen eralized eigenvectors of a pair of complex upper triangu lar matrices (A,B)
ztgex2 - swap adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
ztgexc - reorder the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST
ztgsen - reorder the generalized Schur decomposition of a complex matrix pair (A, B) (in terms of an unitary equiva lence trans- formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the pair (A,B)
ztgsja - compute the generalized singular value decomposi tion (GSVD) of two complex upper triangular (or trape zoidal) matrices A and B
ztgsna - estimate reciprocal condition numbers for speci fied eigenvalues and/or eigenvectors of a matrix pair (A, B)
ztgsy2 - solve the generalized Sylvester equation A * R - L * B = scale * C (1) D * R - L * E = scale * F using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices,
ztgsyl - solve the generalized Sylvester equation
ztpcon - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
ztpmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x,
ztprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
ztpsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b,
ztptri - compute the inverse of a complex upper or lower triangular matrix A stored in packed format
ztptrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
ztrcon - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
ztrevc - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
ztrexc - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST
ztrmm - perform one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A' or op( A ) = conjg( A' )
ztrmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x,
ztrrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
ztrsen - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigen values appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right
ztrsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,
ztrsna - estimate reciprocal condition numbers for speci fied eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary)
ztrsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b,
ztrsyl - solve the complex Sylvester matrix equation
ztrti2 - compute the inverse of a complex upper or lower triangular matrix
ztrtri - compute the inverse of a complex upper or lower triangular matrix A
ztrtrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
ztzrqf - routine is deprecated and has been replaced by routine ZTZRZF
ztzrzf - reduce the M-by-N ( M<=N ) complex upper trape zoidal matrix A to upper triangular form by means of uni tary transformations
zung2l - generate an m by n complex matrix Q with orthonormal columns,
zung2r - generate an m by n complex matrix Q with orthonormal columns,
zungbr - generate one of the complex unitary matrices Q or P**H determined by ZGEBRD when reducing a complex matrix A to bidiagonal form
zunghr - generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD
zungl2 - generate an m-by-n complex matrix Q with orthonormal rows,
zunglq - generate an M-by-N complex matrix Q with orthonormal rows,
zungql - generate an M-by-N complex matrix Q with orthonormal columns,
zungqr - generate an M-by-N complex matrix Q with orthonormal columns,
zungr2 - generate an m by n complex matrix Q with orthonormal rows,
zungrq - generate an M-by-N complex matrix Q with orthonormal rows,
zungtr - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD
zunm2l - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
zunm2r - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
zunmbr - VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmhr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunml2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
zunmlq - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmql - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmqr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmr2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
zunmr3 - overwrite the general complex m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
zunmrq - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmrz - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmtr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zupgtr - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by ZHPTRD using packed storage
zupmtr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'