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div(3c) -- perform integer division
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div and ldiv compute the quotient and remainder resulting from the division of the integer dividend numer by the integer divisor denom. If the division is inexact, the quotient will be the nearest integer with less magnitude than the algebraic quotient (e.g., div(5/2) yields 2, and div(-5/2) yields -2). div operates on and returns int quantities. ldiv operates on and returns long int quantities. Unless the result cannot be represented, div and ldiv return the result in a structure (div_t for div... |
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complib/dlabad(3) -- take as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of
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DLABAD takes as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large. This subroutine is intended to identify machines with a large exponent range, such as the Crays, and redefine the underflow and overflow limits to be the square roots of the values computed by DLAMCH. This subroutine is needed because DLAMCH does not compensate for poor arithmetic in the upper half of the exponent range, as... |
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complib/dlabrd(3) -- reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an
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DLABRD reduces the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A. If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower bidiagonal form. This is an auxiliary routine called by DGEBRD |
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complib/dlacon(3) -- estimate the 1-norm of a square, real matrix A
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DLACON estimates the 1-norm of a square, real matrix A. Reverse communication is used for evaluating matrix-vector products. |
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complib/dlacpy(3) -- copie all or part of a two-dimensional matrix A to another matrix B
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DLACPY copies all or part of a two-dimensional matrix A to another matrix B. |
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complib/dladiv(3) -- --------- c + i*d The algorithm is due to Robert L
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DLADIV performs complex division in real arithmetic in D. Knuth, The art of Computer Programming, Vol.2, p.195 |
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complib/dlae2(3) -- compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
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DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]. On return, RT1 is the eigenvalue of larger absolute value, and RT2 is the eigenvalue of smaller absolute value. |
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complib/dlaebz(3) -- contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a sy
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DLAEBZ contains 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. It performs a choice of two types of loops: IJOB=1, followed by IJOB=2: It takes as input a list of intervals and returns a list of sufficiently small intervals whose union contains the same eigenvalues as the union of the original intervals. The input intervals are (AB(j,1),AB(j,2)], j=1,...,MINP. The output inte... |
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complib/dlaed0(3) -- compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and
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DLAED0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. |
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complib/dlaed1(3) -- modification by a rank-one symmetric matrix
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DLAED1 computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. This routine is used only for the eigenproblem which requires all eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles the case in which eigenvalues only or eigenvalues and eigenvectors of a full symmetric matrix (which was reduced to tridiagonal form) are desired. T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) where Z = Q'u, u is a vector of le... |
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complib/dlaed2(3) -- merge the two sets of eigenvalues together into a single sorted set
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DLAED2 merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny entry in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one. |
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complib/dlaed3(3) -- find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP
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DLAED3 finds the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP. It makes the appropriate calls to DLAED4 and then updates the eigenvectors by multiplying the matrix of eigenvectors of the pair of eigensystems being combined by the matrix of eigenvectors of the K-by-K system which is solved here. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary... |
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complib/dlaed4(3) -- rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i
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This 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 no loss in generality. The rank-one modified system is thus diag( D ) + RHO * Z * Z_transpose. where we assume the Euclidean norm of Z is 1. The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.... |
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complib/dlaed5(3) -- modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to s
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This subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix We also assume RHO > 0 and that the Euclidean norm of the vector Z is one. |
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complib/dlaed6(3) -- d(2)-x d(3)-x It is assumed that if ORGATI = .true
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DLAED6 computes 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 otherwise it is between d(1) and d(2) This routine will be called by DLAED4 when necessary. In most cases, the root sought is the smallest in magnitude, though it might not be in some extremely rare situations. |
