# Pages du manuel Linux : Fonctions des bibliothèques

slaed0
compute all eigenvalues and corresponding eigenvectors 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 symmetric 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 symmetric 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 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Z' denotes the transpose of Z
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 equations (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 triangular
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 subdiagonal are zero
slaic1
applie one step of incremental condition estimation 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 ascending order
slamsh
send multiple shifts through a small (single node) matrix to see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulges that can be sent through
slangb
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
slange
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
slangt
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
slanhs
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
slansb
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
slansp
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
slanst
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
slansy
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A
slantb
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
slantp
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
slantr
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
slanv2
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