LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine cptsvx | ( | character | FACT, |
integer | N, | ||
integer | NRHS, | ||
real, dimension( * ) | D, | ||
complex, dimension( * ) | E, | ||
real, dimension( * ) | DF, | ||
complex, dimension( * ) | EF, | ||
complex, dimension( ldb, * ) | B, | ||
integer | LDB, | ||
complex, dimension( ldx, * ) | X, | ||
integer | LDX, | ||
real | RCOND, | ||
real, dimension( * ) | FERR, | ||
real, dimension( * ) | BERR, | ||
complex, dimension( * ) | WORK, | ||
real, dimension( * ) | RWORK, | ||
integer | INFO | ||
) |
CPTSVX computes the solution to system of linear equations A * X = B for PT matrices
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CPTSVX uses the factorization 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 positive definite tridiagonal matrix and X and B are N-by-NRHS matrices. Error bounds on the solution and a condition estimate are also provided.
The following steps are performed: 1. If FACT = 'N', the matrix A is factored as A = L*D*L**H, where L is a unit lower bidiagonal matrix and D is diagonal. The factorization can also be regarded as having the form A = U**H*D*U. 2. If the leading i-by-i principal minor is not positive definite, then the routine returns with INFO = i. Otherwise, the factored form of A is used to estimate the condition number of the matrix A. If the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below. 3. The system of equations is solved for X using the factored form of A. 4. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it.
[in] | FACT | FACT is CHARACTER*1 Specifies whether or not the factored form of the matrix A is supplied on entry. = 'F': On entry, DF and EF contain the factored form of A. D, E, DF, and EF will not be modified. = 'N': The matrix A will be copied to DF and EF and factored. |
[in] | N | N is INTEGER The order of the matrix A. N >= 0. |
[in] | NRHS | NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. |
[in] | D | D is REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix A. |
[in] | E | E is COMPLEX array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A. |
[in,out] | DF | DF is REAL array, dimension (N) If FACT = 'F', then DF is an input argument and on entry contains the n diagonal elements of the diagonal matrix D from the L*D*L**H factorization of A. If FACT = 'N', then DF is an output argument and on exit contains the n diagonal elements of the diagonal matrix D from the L*D*L**H factorization of A. |
[in,out] | EF | EF is COMPLEX array, dimension (N-1) If FACT = 'F', then EF is an input argument and on entry contains the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A. If FACT = 'N', then EF is an output argument and on exit contains the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A. |
[in] | B | B is COMPLEX array, dimension (LDB,NRHS) The N-by-NRHS right hand side matrix B. |
[in] | LDB | LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). |
[out] | X | X is COMPLEX array, dimension (LDX,NRHS) If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. |
[in] | LDX | LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N). |
[out] | RCOND | RCOND is REAL The reciprocal condition number of the matrix A. If RCOND is less than the machine precision (in particular, if RCOND = 0), the matrix is singular to working precision. This condition is indicated by a return code of INFO > 0. |
[out] | FERR | FERR is REAL array, dimension (NRHS) The forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). |
[out] | BERR | BERR is REAL array, dimension (NRHS) The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution). |
[out] | WORK | WORK is COMPLEX array, dimension (N) |
[out] | RWORK | RWORK is REAL array, dimension (N) |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, and i is <= N: the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed. RCOND = 0 is returned. = N+1: U is nonsingular, but RCOND is less than machine precision, meaning that the matrix is singular to working precision. Nevertheless, the solution and error bounds are computed because there are a number of situations where the computed solution can be more accurate than the value of RCOND would suggest. |
Definition at line 236 of file cptsvx.f.