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(git:31b3539)
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(git:31b3539)
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various cholesky decomposition related routines More...
Functions/Subroutines | |
| subroutine, public | cp_fm_cholesky_decompose (matrix, n, info_out) |
| used to replace a symmetric positive def. matrix M with its cholesky decomposition U: M = U^T * U, with U upper triangular | |
| subroutine, public | cp_fm_cholesky_solve (matrix, matrixb, n, info_out) |
| solves A*X = B for X, given the Cholesky decomposition U of the symmetric positive def. matrix A (A = U^T*U, U upper triangular), as produced by cp_fm_cholesky_decompose | |
| subroutine, public | cp_fm_cholesky_invert (matrix, n, info_out, work) |
| Replace the upper Cholesky factor by the upper triangle of the inverse. When work is provided, expand the upper triangle to a full symmetric matrix. | |
| subroutine, public | cp_fm_cholesky_reduce (matrix, matrixb, itype) |
| reduce a matrix pencil A,B to normal form B has to be cholesky decomposed with cp_fm_cholesky_decompose before calling this routine A,B -> inv(U^T)*A*inv(U),1 (AX=BX -> inv(U^T)*A*inv(U)*U*X=U*X hence evecs U*X) | |
| subroutine, public | cp_fm_cholesky_restore (fm_matrix, neig, fm_matrixb, fm_matrixout, op, pos, transa) |
| apply Cholesky decomposition op can be "SOLVE" (out = U^-1 * in) or "MULTIPLY" (out = U * in) pos can be "LEFT" or "RIGHT" (U at the left or at the right) | |
Variables | |
| integer, save, public | cholesky_type = 0 |
| integer, save, public | dlaf_cholesky_n_min = 0 |
| integer, parameter, public | fm_cholesky_type_scalapack = 101 |
| integer, parameter, public | fm_cholesky_type_dlaf = 104 |
| integer, parameter, public | fm_cholesky_type_default = FM_CHOLESKY_TYPE_SCALAPACK |
various cholesky decomposition related routines
| subroutine, public cp_fm_cholesky::cp_fm_cholesky_decompose | ( | type(cp_fm_type), intent(in) | matrix, |
| integer, intent(in), optional | n, | ||
| integer, intent(out), optional | info_out ) |
used to replace a symmetric positive def. matrix M with its cholesky decomposition U: M = U^T * U, with U upper triangular
| matrix | the matrix to replace with its cholesky decomposition |
| n | the number of row (and columns) of the matrix & (defaults to the min(size(matrix))) |
| info_out | ... |
Definition at line 61 of file cp_fm_cholesky.F.
| subroutine, public cp_fm_cholesky::cp_fm_cholesky_solve | ( | type(cp_fm_type), intent(in) | matrix, |
| type(cp_fm_type), intent(inout) | matrixb, | ||
| integer, intent(in), optional | n, | ||
| integer, intent(out), optional | info_out ) |
solves A*X = B for X, given the Cholesky decomposition U of the symmetric positive def. matrix A (A = U^T*U, U upper triangular), as produced by cp_fm_cholesky_decompose
| matrix | the Cholesky factor U of A, as produced by cp_fm_cholesky_decompose |
| matrixb | on input the right-hand side(s) B, on output the solution(s) X |
| n | the number of rows (and columns) of matrix (defaults to the min(size(matrix))) |
| info_out | ... |
Definition at line 126 of file cp_fm_cholesky.F.
| subroutine, public cp_fm_cholesky::cp_fm_cholesky_invert | ( | type(cp_fm_type), intent(in) | matrix, |
| integer, intent(in), optional | n, | ||
| integer, intent(out), optional | info_out, | ||
| type(cp_fm_type), intent(in), optional | work ) |
Replace the upper Cholesky factor by the upper triangle of the inverse. When work is provided, expand the upper triangle to a full symmetric matrix.
| matrix | the matrix to invert (must be an upper triangular matrix) |
| n | size of the matrix to invert (defaults to the min(size(matrix))) |
| info_out | ... |
| work | optional workspace of the same size and distribution for expanding the upper triangle |
Definition at line 184 of file cp_fm_cholesky.F.
| subroutine, public cp_fm_cholesky::cp_fm_cholesky_reduce | ( | type(cp_fm_type), intent(in) | matrix, |
| type(cp_fm_type), intent(in) | matrixb, | ||
| integer, optional | itype ) |
reduce a matrix pencil A,B to normal form B has to be cholesky decomposed with cp_fm_cholesky_decompose before calling this routine A,B -> inv(U^T)*A*inv(U),1 (AX=BX -> inv(U^T)*A*inv(U)*U*X=U*X hence evecs U*X)
| matrix | the symmetric matrix A |
| matrixb | the cholesky decomposition of matrix B |
| itype | ... |
Definition at line 260 of file cp_fm_cholesky.F.
| subroutine, public cp_fm_cholesky::cp_fm_cholesky_restore | ( | type(cp_fm_type), intent(in) | fm_matrix, |
| integer, intent(in) | neig, | ||
| type(cp_fm_type), intent(in) | fm_matrixb, | ||
| type(cp_fm_type), intent(in) | fm_matrixout, | ||
| character(len=*), intent(in) | op, | ||
| character(len=*), intent(in), optional | pos, | ||
| character(len=*), intent(in), optional | transa ) |
apply Cholesky decomposition op can be "SOLVE" (out = U^-1 * in) or "MULTIPLY" (out = U * in) pos can be "LEFT" or "RIGHT" (U at the left or at the right)
| fm_matrix | ... |
| neig | ... |
| fm_matrixb | ... |
| fm_matrixout | ... |
| op | ... |
| pos | ... |
| transa | ... |
Definition at line 318 of file cp_fm_cholesky.F.
| integer, save, public cp_fm_cholesky::cholesky_type = 0 |
Definition at line 37 of file cp_fm_cholesky.F.
| integer, save, public cp_fm_cholesky::dlaf_cholesky_n_min = 0 |
Definition at line 40 of file cp_fm_cholesky.F.
| integer, parameter, public cp_fm_cholesky::fm_cholesky_type_scalapack = 101 |
Definition at line 42 of file cp_fm_cholesky.F.
| integer, parameter, public cp_fm_cholesky::fm_cholesky_type_dlaf = 104 |
Definition at line 42 of file cp_fm_cholesky.F.
| integer, parameter, public cp_fm_cholesky::fm_cholesky_type_default = FM_CHOLESKY_TYPE_SCALAPACK |
Definition at line 44 of file cp_fm_cholesky.F.
1.15.0