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complib/zhpevx(3) -- compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
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ZHPEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. Eigenvalues/vectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. |
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complib/zhpgst(3) -- reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage
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ZHPGST reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage. If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. B must have been previously factorized as U**H*U or L*L**H by ZPPTRF.... |
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complib/zhpgv(3) -- a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x
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ZHPGV computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be Hermitian, stored in packed format, and B is also positive definite. |
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complib/zhprfs(3) -- improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefin
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ZHPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution. |
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complib/zhpsv(3) -- X = B,
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ZHPSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices. The diagonal pivoting method is used to factor A as A = U * D * U**H, if UPLO = 'U', or A = L * D * L**H, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used t... |
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complib/zhpsvx(3) -- and X and B are N-by-NRHS matrices
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ZHPSVX uses the diagonal pivoting factorization A = U*D*U**H or A = L*D*L**H to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format 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/zhptrd(3) -- reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary si
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ZHPTRD reduces a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T. |
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complib/zhptrf(3) -- using the Bunch-Kaufman diagonal pivoting method
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ZHPTRF computes the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method: A = U*D*U**H or A = L*D*L**H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. |
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complib/zhptri(3) -- compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U
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ZHPTRI computes the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF. |
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complib/zhptrs(3) -- solve a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the
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ZHPTRS solves a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF. |
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complib/zhsein(3) -- use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H
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ZHSEIN uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H. The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by: H * x = w * x, y**h * H = w * y**h where y**h denotes the conjugate transpose of the vector y. |
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complib/zhseqr(3) -- compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the
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ZHSEQR computes the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors. Optionally Z may be postmultiplied into an input unitary matrix Q, so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the unitary matrix Q: A = Q*H*Q**H = (QZ)*T*(QZ)**H.... |
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complib/zlabrd(3) -- reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal fo
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ZLABRD reduces the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A. If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower bidiagonal form. This is an auxiliary routine called by ZGEBRD |
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complib/zlacgv(3) -- conjugate a complex vector of length N
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ZLACGV conjugates a complex vector of length N. |
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complib/zlacon(3) -- estimate the 1-norm of a square, complex matrix A
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ZLACON estimates the 1-norm of a square, complex matrix A. Reverse communication is used for evaluating matrix-vector products. |
