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complib/ztrrfs(3) -- provide error bounds and backward error estimates for the solution to a system of linear equations with a tria
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ZTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by ZTRTRS or some other means before entering this routine. ZTRRFS does not do iterative refinement because doing so cannot improve the backward error. |
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complib/ztrsen(3) -- reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues ap
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ZTRSEN reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace. Optionally the routine computes the reciprocal condition numbers of the cluster of eigenvalues and/or the invariant subspace.... |
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complib/ztrsna(3) -- estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper t
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ZTRSNA estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary). |
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complib/ztrsyl(3) -- solve the complex Sylvester matrix equation
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ZTRSYL solves the complex Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**H, and A and B are both upper triangular. A is Mby-M and B is N-by-N; the right hand side C and the solution X are M-byN; and scale is an output scale factor, set <= 1 to avoid overflow in X. |
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complib/ztrti2(3) -- compute the inverse of a complex upper or lower triangular matrix
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ZTRTI2 computes the inverse of a complex upper or lower triangular matrix. This is the Level 2 BLAS version of the algorithm. |
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complib/ztrtri(3) -- compute the inverse of a complex upper or lower triangular matrix A
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ZTRTRI computes the inverse of a complex upper or lower triangular matrix A. This is the Level 3 BLAS version of the algorithm. |
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complib/ztrtrs(3) -- or A**H * X = B,
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ZTRTRS solves a triangular system of the form where A is a triangular matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular. |
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complib/ztzrqf(3) -- reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary tra
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ZTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix. |
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complib/zung2l(3) -- generate an m by n complex matrix Q with orthonormal columns,
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ZUNG2L generates an m by n complex matrix Q with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order m Q = H(k) . . . H(2) H(1) as returned by ZGEQLF. |
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complib/zung2r(3) -- generate an m by n complex matrix Q with orthonormal columns,
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ZUNG2R generates an m by n complex matrix Q with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of order m Q = H(1) H(2) . . . H(k) as returned by ZGEQRF. |
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complib/zungbr(3) -- generate one of the complex unitary matrices Q or P**H determined by ZGEBRD when reducing a complex matrix A t
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ZUNGBR generates one of the complex unitary matrices Q or P**H determined by ZGEBRD when reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q and P**H are defined as products of elementary reflectors H(i) or G(i) respectively. If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q is of order M: if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n columns of Q, where m >= n >= k; if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an M-by-M matri... |
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complib/zunghr(3) -- product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD
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ZUNGHR generates a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD: Q = H(ilo) H(ilo+1) . . . H(ihi-1). |
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complib/zungl2(3) -- generate an m-by-n complex matrix Q with orthonormal rows,
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ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order n Q = H(k)' . . . H(2)' H(1)' as returned by ZGELQF. |
