# Pages du manuel Linux : Fonctions des bibliothèques

slaqsb
equilibrate a symmetric band matrix A using the scaling factors in the vector S
slaqsp
equilibrate a symmetric matrix A using the scaling factors in the vector S
slaqsy
equilibrate a symmetric matrix A using the scaling 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
slaref
applie one or several Householder reflectors of size 3 to one or two matrices (if column is specified) on either their rows or columns
slarf
applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
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
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, determined 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 cluster 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 elements of the real vectors x and y
slaruv
return a vector of n random real numbers from a uniform (0,1)
slarz
applie a real elementary reflector H to a real M-by-N matrix C, from either the left or the right
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
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 modification 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 RHO > 0
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
slasorte
sort eigenpairs so that real eigenpairs are together and complex are together
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 positive 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' )
slasrt2
the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' )