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complib/cgbtrs(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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CGBTRS 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 CGBTRF. |
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complib/cgebak(3) -- form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eig
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CGEBAK forms the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by CGEBAL. |
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complib/cgebal(3) -- balance a general complex matrix A
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CGEBAL 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/cgebd2(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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CGEBD2 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/cgebrd(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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CGEBRD 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/CGECO(3) -- CGECO factors a complex matrix by Gaussian elimination and estimates the condition of the matrix. If RCOND is
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On Entry A COMPLEX(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 REAL an estimate of the reciprocal condition of A . For the system A*X ... |
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complib/cgecon(3) -- complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF
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CGECON 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 CGETRF. 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/CGEDI(3) -- CGEDI computes the determinant and inverse of a matrix using the factors computed by CGECO or CGEFA.
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On Entry A COMPLEX(LDA, N) the output from CGECO or CGEFA. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . IPVT INTEGER(N) the pivot vector from CGECO or CGEFA. WORK COMPLEX(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 COMPLEX(2) determinant of original matrix if requested. Otherwise not referenced. ... |
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complib/cgeequ(3) -- compute row and column scalings intended to equilibrate an Mby-N matrix A and reduce its condition number
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CGEEQU 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/cgees(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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CGEES 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/cgeesx(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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CGEESX 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... |
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complib/cgeev(3) -- compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right ei
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CGEEV 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.... |
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complib/cgeevx(3) -- compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right ei
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CGEEVX 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... |
