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| real(real64) function | lalg_adv_oct_m::sfmin () |
| | Auxiliary function. More...
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| subroutine | lalg_adv_oct_m::lalg_dgeev (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work, lwork, rwork, info) |
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| subroutine | lalg_adv_oct_m::lalg_zgeev (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work, lwork, rwork, info) |
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| subroutine, public | lalg_adv_oct_m::zlalg_exp (nn, pp, aa, ex, hermitian) |
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| subroutine, public | lalg_adv_oct_m::zlalg_phi (nn, pp, aa, ex, hermitian) |
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| subroutine, public | lalg_adv_oct_m::lalg_zeigenderivatives (n, mat, zeigenvec, zeigenval, zmat) |
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| subroutine | lalg_adv_oct_m::lalg_zpseudoinverse (n, mat, imat) |
| | Computes the Moore-Penrose pseudoinverse of a complex matrix. More...
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| subroutine, public | lalg_adv_oct_m::lalg_check_zeigenderivatives (n, mat) |
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| complex(real64) function, public | lalg_adv_oct_m::lalg_zdni (eigenvec, alpha, beta) |
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| complex(real64) function, public | lalg_adv_oct_m::lalg_zduialpha (eigenvec, mmatrix, alpha, gamma, delta) |
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| complex(real64) function, public | lalg_adv_oct_m::lalg_zd2ni (eigenvec, mmatrix, alpha, beta, gamma, delta) |
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| pure real(real64) function | lalg_adv_oct_m::pseudoinverse_default_tolerance (m, n, sg_values) |
| | Computes the default Moore-Penrose pseudoinverse tolerance for zeroing. More...
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| real(real64) function, dimension(1:n, 1:n), public | lalg_adv_oct_m::lalg_remove_rotation (n, A) |
| | Remove rotation from affine transformation A by computing the polar decomposition and discarding the rotational part. The polar decomposition of A is given by A = U P with P = sqrt(A^T A), where U is a rotation matrix and P is a scaling matrix. This function returns P. More...
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| subroutine | lalg_adv_oct_m::zcholesky (n, a, bof, err_code) |
| | Compute the Cholesky decomposition of real symmetric or complex Hermitian positive definite matrix a, dim(a) = n x n. On return a = u^T u with u upper triangular matrix. More...
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| subroutine | lalg_adv_oct_m::zgeneigensolve (n, a, b, e, preserve_mat, bof, err_code) |
| | Computes all the eigenvalues and the eigenvectors of a real symmetric or complex Hermitian generalized definite eigenproblem, of the form \( Ax=\lambda Bx \). B is also positive definite. More...
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| subroutine | lalg_adv_oct_m::zeigensolve_nonh (n, a, e, err_code, side, sort_eigenvectors) |
| | Computes all the eigenvalues and the right (left) eigenvectors of a real or complex (non-Hermitian) eigenproblem, of the form A*x=(lambda)*x. More...
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| subroutine | lalg_adv_oct_m::zlowest_geneigensolve (k, n, a, b, e, v, preserve_mat, bof, err_code) |
| | Computes the k lowest eigenvalues and the eigenvectors of a real symmetric or complex Hermitian generalized definite eigenproblem, of the form A*x=(lambda)*B*x. B is also positive definite. More...
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| subroutine | lalg_adv_oct_m::zeigensolve (n, a, e, bof, err_code) |
| | Computes all eigenvalues and eigenvectors of a real symmetric or hermitian square matrix A. More...
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| subroutine | lalg_adv_oct_m::zeigensolve_tridiagonal (n, a, e, bof, err_code) |
| | Computes all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. For the Hermitian case, the matrix is assumed to be real symmetric (even if stored in complex) More...
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| subroutine | lalg_adv_oct_m::zlowest_eigensolve (k, n, a, e, v, preserve_mat) |
| | Computes the k lowest eigenvalues and the eigenvectors of a standard symmetric-definite eigenproblem, of the form A*x=(lambda)*x. Here A is assumed to be symmetric. More...
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| complex(real64) function | lalg_adv_oct_m::zdeterminant (n, a, preserve_mat) |
| | Invert a real symmetric or complex Hermitian square matrix a. More...
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| subroutine | lalg_adv_oct_m::zdirect_inverse (n, a, det) |
| | Invert a real symmetric or complex Hermitian square matrix a. More...
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| subroutine | lalg_adv_oct_m::zsym_inverse (uplo, n, a) |
| | Invert a real/complex symmetric square matrix a. More...
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| subroutine | lalg_adv_oct_m::zlinsyssolve (n, nrhs, a, b, x) |
| | compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. More...
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| subroutine | lalg_adv_oct_m::zsingular_value_decomp (m, n, a, u, vt, sg_values, preserve_mat) |
| | Computes the singular value decomposition of a complex MxN matrix a. More...
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| subroutine | lalg_adv_oct_m::zsvd_inverse (m, n, a, threshold) |
| | Computes inverse of a complex MxN matrix, a, using the SVD decomposition. More...
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| subroutine | lalg_adv_oct_m::zlalg_pseudo_inverse (a, threshold) |
| | Invert a matrix with the Moore-Penrose pseudo-inverse. More...
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| integer function | lalg_adv_oct_m::zmatrix_rank_svd (a, preserve_mat, tol) |
| | Compute the rank of the matrix A using SVD. More...
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| subroutine | lalg_adv_oct_m::zupper_triangular_inverse (n, a) |
| | Calculate the inverse of a real/complex upper triangular matrix (in unpacked storage). (lower triangular would be a trivial variant of this) More...
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| subroutine | lalg_adv_oct_m::zleast_squares_vec (nn, aa, bb, xx, preserve_mat) |
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| subroutine | lalg_adv_oct_m::zeigensolve_parallel (n, a, e, bof, err_code) |
| | Computes all the eigenvalues and the eigenvectors of a real symmetric or complex Hermitian eigenproblem in parallel using ScaLAPACK or ELPA on all processors n: dimension of matrix a: input matrix, on exit: contains eigenvectors e: eigenvalues. More...
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| subroutine | lalg_adv_oct_m::zinverse (n, a, method, det, threshold, uplo) |
| | An interface to different method to invert a matrix. More...
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| subroutine, public | lalg_adv_oct_m::zlalg_matrix_function (n, factor, a, fun_a, fun, hermitian, tridiagonal) |
| | This routine calculates a function of a matrix by using an eigenvalue decomposition. More...
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| subroutine | lalg_adv_oct_m::dcholesky (n, a, bof, err_code) |
| | Compute the Cholesky decomposition of real symmetric or complex Hermitian positive definite matrix a, dim(a) = n x n. On return a = u^T u with u upper triangular matrix. More...
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| subroutine | lalg_adv_oct_m::dgeneigensolve (n, a, b, e, preserve_mat, bof, err_code) |
| | Computes all the eigenvalues and the eigenvectors of a real symmetric or complex Hermitian generalized definite eigenproblem, of the form \( Ax=\lambda Bx \). B is also positive definite. More...
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| subroutine | lalg_adv_oct_m::deigensolve_nonh (n, a, e, err_code, side, sort_eigenvectors) |
| | Computes all the eigenvalues and the right (left) eigenvectors of a real or complex (non-Hermitian) eigenproblem, of the form A*x=(lambda)*x. More...
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| subroutine | lalg_adv_oct_m::dlowest_geneigensolve (k, n, a, b, e, v, preserve_mat, bof, err_code) |
| | Computes the k lowest eigenvalues and the eigenvectors of a real symmetric or complex Hermitian generalized definite eigenproblem, of the form A*x=(lambda)*B*x. B is also positive definite. More...
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| subroutine | lalg_adv_oct_m::deigensolve (n, a, e, bof, err_code) |
| | Computes all eigenvalues and eigenvectors of a real symmetric or hermitian square matrix A. More...
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| subroutine | lalg_adv_oct_m::deigensolve_tridiagonal (n, a, e, bof, err_code) |
| | Computes all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. For the Hermitian case, the matrix is assumed to be real symmetric (even if stored in complex) More...
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| subroutine | lalg_adv_oct_m::dlowest_eigensolve (k, n, a, e, v, preserve_mat) |
| | Computes the k lowest eigenvalues and the eigenvectors of a standard symmetric-definite eigenproblem, of the form A*x=(lambda)*x. Here A is assumed to be symmetric. More...
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| real(real64) function | lalg_adv_oct_m::ddeterminant (n, a, preserve_mat) |
| | Invert a real symmetric or complex Hermitian square matrix a. More...
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| subroutine | lalg_adv_oct_m::ddirect_inverse (n, a, det) |
| | Invert a real symmetric or complex Hermitian square matrix a. More...
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| subroutine | lalg_adv_oct_m::dsym_inverse (uplo, n, a) |
| | Invert a real/complex symmetric square matrix a. More...
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| subroutine | lalg_adv_oct_m::dlinsyssolve (n, nrhs, a, b, x) |
| | compute the solution to a real system of linear equations A*X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. More...
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| subroutine | lalg_adv_oct_m::dsingular_value_decomp (m, n, a, u, vt, sg_values, preserve_mat) |
| | Computes the singular value decomposition of a real M x N matrix a. More...
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| subroutine | lalg_adv_oct_m::dsvd_inverse (m, n, a, threshold) |
| | Computes the inverse of a real M x N matrix, a, using the SVD decomposition. More...
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| subroutine | lalg_adv_oct_m::dlalg_pseudo_inverse (a, threshold) |
| | Invert a matrix with the Moore-Penrose pseudo-inverse. More...
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| integer function | lalg_adv_oct_m::dmatrix_rank_svd (a, preserve_mat, tol) |
| | Compute the rank of the matrix A using SVD. More...
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| subroutine | lalg_adv_oct_m::dupper_triangular_inverse (n, a) |
| | Calculate the inverse of a real/complex upper triangular matrix (in unpacked storage). (lower triangular would be a trivial variant of this) More...
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| subroutine | lalg_adv_oct_m::dleast_squares_vec (nn, aa, bb, xx, preserve_mat) |
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| subroutine | lalg_adv_oct_m::deigensolve_parallel (n, a, e, bof, err_code) |
| | Computes all the eigenvalues and the eigenvectors of a real symmetric or complex Hermitian eigenproblem in parallel using ScaLAPACK or ELPA on all processors n: dimension of matrix a: input matrix, on exit: contains eigenvectors e: eigenvalues. More...
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| subroutine | lalg_adv_oct_m::dinverse (n, a, method, det, threshold, uplo) |
| | An interface to different method to invert a matrix. More...
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| subroutine | lalg_adv_oct_m::dlalg_matrix_function (n, factor, a, fun_a, fun, hermitian, tridiagonal) |
| | This routine calculates a function of a matrix by using an eigenvalue decomposition. More...
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1.9.4