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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/zgebak(3) -- form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eig ZGEBAK forms the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL. complib/zgebal(3) -- balance a general complex matrix A ZGEBAL balances a general complex 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/zgebd2(3) -- reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation
ZGEBD2 reduces a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation: Q' * A * P = B. If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
complib/zgebrd(3) -- reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
ZGEBRD reduces a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation: Q**H * A * P = B. If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
complib/zgecon(3) -- complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF
ZGECON estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF. 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/zgeequ(3) -- compute row and column scalings intended to equilibrate an Mby-N matrix A and reduce its condition number
ZGEEQU 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/zgees(3) -- compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the m
ZGEES computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**H). Optionally, it also orders the eigenvalues on the diagonal of the 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 complex matrix is in Schur form if it is upper tria...
complib/zgeesx(3) -- compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the m
ZGEESX computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**H). Optionally, it also orders the eigenvalues on the diagonal of the 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 correspon...
complib/zgeev(3) -- compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right ei
ZGEEV computes for an N-by-N complex 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/zgeevx(3) -- compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right ei
ZGEEVX computes for an N-by-N complex 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 it...
complib/zgegs(3) -- compute for a pair of N-by-N complex nonsymmetric matrices A,
DGEGS computes for a pair of N-by-N complex nonsymmetric matrices A, B: the generalized eigenvalues (alpha, beta), the complex 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 ZGEGV 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 there is a r...
complib/zgegv(3) -- B, the generalized eigenvalues (alpha, beta), and optionally,
ZGEGV computes for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR). 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 there is a reasonable interpretation for beta=0, and even for both being zero. A good beginning reference ...
complib/zgehd2(3) -- reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation: Q' * A * Q = H .
complib/zgehrd(3) -- reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation: Q' * A * Q = H .
complib/zgelq2(3) -- compute an LQ factorization of a complex m by n matrix A
ZGELQ2 computes an LQ factorization of a complex m by n matrix A: A = L * Q.
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