Introduction

It provides a lot of subroutines to manipulate the matrix and implement the linear algebra.

Type

subroutines

Source

src/s_matrix.f90

Usage

(1) Build constants (0) matrix.

subroutine s_zeros_i(n, A)
subroutine s_zeros_d(n, A)
subroutine s_zeros_z(n, A)

To build a matrix with all elements are zero. Here n means size of matrix, A means input/output matrix.

(2) Build constants (1) matrix.

subroutine s_ones_i(n, A)
subroutine s_ones_d(n, A)
subroutine s_ones_z(n, A)

To build a matrix with all elements are zero. Here n means size of matrix, A means input/output matrix.

(3) Build constants (any values) matrix.

subroutine s_any_i(n, i, A)
subroutine s_any_d(n, d, A)
subroutine s_any_z(n, z, A)

To build a matrix with all elements are given by i, d, or z. Here n means size of matrix, A means input/output matrix. i, d, and z are initial values of matrix elements.

(4) Build diagonal matrix.

subroutine s_eye_i(n, k, A)
subroutine s_eye_d(n, k, A)
subroutine s_eye_z(n, k, A)

To build a matrix with ones on the diagonal and zeros elsewhere. Here n means size of matrix, A means input/output matrix, k means index of the diagonal.

(5) Build identity matrix.

subroutine s_identity_i(n, A)
subroutine s_identity_d(n, A)
subroutine s_identity_z(n, A)

To build an identity matrix. Here n means size of matrix, A means input/output matrix.

(6) Build diagonal matrix from vector.

subroutine s_diag_i(n, v, A)
subroutine s_diag_d(n, v, A)
subroutine s_diag_z(n, v, A)

To build a diagonal matrix from a vector. Here n means size of matrix, A means input/output matrix, v means input vector.

(7) Calculate trace for matrix.

subroutine s_trace_d(n, A, tr)
subroutine s_trace_z(n, A, tr)

Return trace for a matrix. Here n means size of matrix, A means input/output matrix, tr means matrix's trace.

(8) Calculate determinant for matrix.

subroutine s_det_d(ndim, dmat, ddet)
subroutine s_det_z(ndim, zmat, zdet)

where ndim means dimension of the matrix, ddet and zdet are the determinants, dmat and zmat are the input matrices.

(9) Calculate matrix inversion.

subroutine s_inv_d(ndim, dmat)
subroutine s_inv_z(ndim, zmat)

where ndim means dimension of the matrix, dmat and zmat are the input/output matrices.

(10) General eigensystem problem.

subroutine s_eig_dg(ldim, ndim, amat, eval, evec)
subroutine s_eig_zg(ldim, ndim, zmat, zeig, zvec)
subroutine s_eigvals_dg(ldim, ndim, amat, eval)
subroutine s_eigvals_zg(ldim, ndim, zmat, zeig)

Here ldim is leading dimension of matrix, ndim is the order of the matrix, amat and zmat are the input matrices, eval and zeig mean eigenvalues, evec and zvec mean eigenvectors.

(11) Symmetric eigensystem problem.

subroutine s_eig_sy(ldim, ndim, amat, eval, evec)
subroutine s_eig_he(ldim, ndim, amat, eval, evec)
subroutine s_eigvals_sy(ldim, ndim, amat, eval)
subroutine s_eigvals_he(ldim, ndim, amat, eval)

Here ldim is leading dimension of matrix, ndim is the order of the matrix, amat is the input matrix, eval means eigenvalues, evec means eigenvectors.

(12) Linear equation solver.

subroutine s_solve_dg(n, nrhs, A, B)
subroutine s_solve_zg(n, nrhs, A, B)
subroutine s_solve_sy(n, nrhs, A, B)
subroutine s_solve_he(n, nrhs, A, B)

Try to solve a linear system $AX = B$. Here, n is the number of linear equations, nrhs is the number of right-hand sides, A and B are input matrices. On exit, B is overwritten by the solution matrix $X$.

(13) General singular value decomposition.

subroutine s_svd_dg(m, n, min_mn, amat, umat, svec, vmat)
subroutine s_svd_zg(m, n, min_mn, amat, umat, svec, vmat)

To perform the singular values decomposition for a general m-by-n matrix $A$, where $A = U \Sigma V'$, return its left vectors, right vectors, and singular values. Here, m is number of rows of $A$ matrix, n is number of columns of $A$ matrix, min_mn is minimal value of m and n, amat means $A$, umat means left vectors $U$, svec means singular values $\Sigma$, vmat means right vectors $V'$.