- dlahqr
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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
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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
- dlaic1
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applie one step of incremental condition estimation in its simplest version
- dlaln2
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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
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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
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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
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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
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determine double precision machine parameters
- dlamrg
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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
- dlamsh
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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
- dlangb
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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
- dlange
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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
- dlangt
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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
- dlanhs
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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
- dlansb
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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
- dlansp
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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
- dlanst
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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
- dlansy
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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
- dlantb
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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
- dlantp
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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
- dlantr
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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
- dlanv2
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compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
- dlapll
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two column vectors X and Y, let A = ( X Y )
- dlapmt
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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
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return sqrt(x**2+y**2), taking care not to cause unnecessary overflow
- dlapy3
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return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow
- dlaqgb
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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
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equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
- dlaqp2
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compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)
- dlaqps
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compute a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3
- dlaqsb
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equilibrate a symmetric band matrix A using the scaling factors in the vector S
- dlaqsp
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equilibrate a symmetric matrix A using the scaling factors in the vector S
- dlaqsy
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equilibrate a symmetric matrix A using the scaling factors in the vector S
- dlaqtr
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solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE
- dlar1v
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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
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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
- dlaref
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applie one or several Householder reflectors of size 3 to one or two matrices (if column is specified) on either their rows or columns
- dlarf
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applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
- dlarfb
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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
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generate a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I
- dlarft
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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
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applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
- dlargv
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generate a vector of real plane rotations, determined by elements of the real vectors x and y
- dlarnv
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return a vector of n random real numbers from a uniform or normal distribution
- dlarrb
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the relatively robust representation(RRR) L D L^T, DLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T,
- dlarre
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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
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the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ), ..
- dlarrv
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compute the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the eigenvalues of L D L^T
- dlartg
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generate a plane rotation so that [ CS SN ]
- dlartv
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applie a vector of real plane rotations to elements of the real vectors x and y