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complib/zgbsv(3) -- compute the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N wi
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ZGBSV computes the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L * U, where L is a product of permutation and unit lower triangular matrices with KL subdiagonals, and U is upper triangular with KL+KU superdiagonals. The factored form of A is then used to solve the system of eq... |
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complib/zgbsvx(3) -- system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
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ZGBSVX uses the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices. Error bounds on the solution and a condition estimate are also provided. |
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complib/zgbtf2(3) -- compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
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ZGBTF2 computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges. This is the unblocked version of the algorithm, calling Level 2 BLAS. |
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complib/zgbtrf(3) -- compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
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ZGBTRF computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges. This is the blocked version of the algorithm, calling Level 3 BLAS. |
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complib/zgbtrs(3) -- solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using
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ZGBTRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by ZGBTRF. |
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complib/zgebak(3) -- form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eig
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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. |
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complib/zgebal(3) -- balance a general complex matrix A
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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.... |
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complib/zgebd2(3) -- reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation
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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. |
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complib/zgebrd(3) -- reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
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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. |
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complib/zgecon(3) -- complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF
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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)) ). |
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complib/zgeequ(3) -- compute row and column scalings intended to equilibrate an Mby-N matrix A and reduce its condition number
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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 ... |
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complib/zgees(3) -- compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the m
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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... |
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complib/zgeesx(3) -- compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the m
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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... |
