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 Section All Sections 1 - General Commands 2 - System Calls 3 - Subroutines 4 - Special Files 5 - File Formats 6 - Games 7 - Macros and Conventions 8 - Maintenance Commands 9 - Kernel Interface n - New Commands
 complib/dgbtrs(3) -- solve a system of linear equations A * X = B or A' * X = B with a general band matrix A using the LU factoriza DGBTRS solves a system of linear equations A * X = B or A' * X = B with a general band matrix A using the LU factorization computed by DGBTRF. complib/dgebak(3) -- form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenv DGEBAK forms the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL.
complib/dgebal(3) -- balance a general real matrix A
DGEBAL balances a general real matrix A. This involves, first, permuting A by a similarity transformation to isolate eigenvalues in the first 1 to ILO-1 and last IHI+1 to N elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional. Balancing may reduce the 1-norm of the matrix, and improve the accuracy of the computed eigenvalues and/or eigenvectors....
complib/dgebd2(3) -- reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
DGEBD2 reduces a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q' * A * P = B. If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
complib/dgebrd(3) -- reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation
DGEBRD reduces a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
complib/DGECO(3) -- DGECO factors a double precision matrix by Gaussian elimination and estimates the condition of the matrix. If
On Entry A DOUBLE PRECISION(LDA, N) the matrix to be factored. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . On Return A an upper triangular matrix and the multipliers which were used to obtain it. The factorization can be written A = L*U where L is a product of permutation and unit lower triangular matrices and U is upper triangular. IPVT INTEGER(N) an INTEGER vector of pivot indices. RCOND DOUBLE PRECISION an estimate of the reciprocal condition of A ...
complib/dgecon(3) -- real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF
DGECON estimates 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. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).
complib/DGEDI(3) -- DGEDI computes the determinant and inverse of a matrix using the factors computed by DGECO or DGEFA.
On Entry A DOUBLE PRECISION(LDA, N) the output from DGECO or DGEFA. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . IPVT INTEGER(N) the pivot vector from DGECO or DGEFA. WORK DOUBLE PRECISION(N) work vector. Contents destroyed. JOB INTEGER = 11 both determinant and inverse. = 01 inverse only. = 10 determinant only. On Return A inverse of original matrix if requested. Otherwise unchanged. DET DOUBLE PRECISION(2) determinant of original matrix if requested....
complib/dgeequ(3) -- compute row and column scalings intended to equilibrate an Mby-N matrix A and reduce its condition number
DGEEQU computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1. R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition ...
complib/dgees(3) -- compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the
DGEES computes for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T). Optionally, it also orders the eigenvalues on the diagonal of the real Schur form so that selected eigenvalues are at the top left. The leading columns of Z then form an orthonormal basis for the invariant subspace corresponding to the selected eigenvalues. A matrix is in real Schur form if it is upper ...
complib/dgeesx(3) -- compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the
DGEESX computes for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T). Optionally, it also orders the eigenvalues on the diagonal of the real Schur form so that selected eigenvalues are at the top left; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right invariant subspace co...
complib/dgeev(3) -- compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigen
DGEEV computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. The right eigenvector v(j) of A satisfies A * v(j) = lambda(j) * v(j) where lambda(j) is its eigenvalue. The left eigenvector u(j) of A satisfies u(j)**H * A = lambda(j) * u(j)**H where u(j)**H denotes the conjugate transpose of u(j). The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real....
complib/dgeevx(3) -- compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigen
DGEEVX computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. Optionally also, it computes a balancing transformation to improve the conditioning of the eigenvalues and eigenvectors (ILO, IHI, SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues (RCONDE), and reciprocal condition numbers for the right eigenvectors (RCONDV). The right eigenvector v(j) of A satisfies A * v(j) = lambda(j) * v(j) where lambda(j) is its e...
complib/DGEFA(3) -- DGEFA factors a double precision matrix by Gaussian elimination. DGEFA is usually called by DGECO, but it can
On Entry A DOUBLE PRECISION(LDA, N) the matrix to be factored. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . On Return A an upper triangular matrix and the multipliers which were used to obtain it. The factorization can be written A = L*U where L is a product of permutation and unit lower triangular matrices and U is upper triangular. IPVT INTEGER(N) an integer vector of pivot indices. INFO INTEGER = 0 normal value. = K if U(K,K) .EQ. 0.0 . This is not ...
complib/dgegs(3) -- compute for a pair of N-by-N real nonsymmetric matrices A, B
DGEGS computes for a pair of N-by-N real nonsymmetric matrices A, B: the generalized eigenvalues (alphar +/- alphai*i, beta), the real Schur form (A, B), and optionally left and/or right Schur vectors (VSL and VSR). (If only the generalized eigenvalues are needed, use the driver DGEGV instead.) A generalized eigenvalue for a pair of matrices (A,B) is, roughly speaking, a scalar w or a ratio alpha/beta = w, such that A - w*B is singular. It is usually represented as the pair (alpha,beta), as ther...
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