LAPACK
3.9.1
LAPACK: Linear Algebra PACKage

subroutine sgtsvx  (  character  FACT, 
character  TRANS,  
integer  N,  
integer  NRHS,  
real, dimension( * )  DL,  
real, dimension( * )  D,  
real, dimension( * )  DU,  
real, dimension( * )  DLF,  
real, dimension( * )  DF,  
real, dimension( * )  DUF,  
real, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
real, dimension( ldb, * )  B,  
integer  LDB,  
real, dimension( ldx, * )  X,  
integer  LDX,  
real  RCOND,  
real, dimension( * )  FERR,  
real, dimension( * )  BERR,  
real, dimension( * )  WORK,  
integer, dimension( * )  IWORK,  
integer  INFO  
) 
SGTSVX computes the solution to system of linear equations A * X = B for GT matrices
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SGTSVX uses the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B, where A is a tridiagonal matrix of order N and X and B are NbyNRHS matrices. Error bounds on the solution and a condition estimate are also provided.
The following steps are performed: 1. If FACT = 'N', the LU decomposition is used to factor the matrix A as A = L * U, where L is a product of permutation and unit lower bidiagonal matrices and U is upper triangular with nonzeros in only the main diagonal and first two superdiagonals. 2. If some U(i,i)=0, so that U is exactly singular, 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 A has been supplied on entry. = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not be modified. = 'N': The matrix will be copied to DLF, DF, and DUF and factored. 
[in]  TRANS  TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose = Transpose) 
[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 matrix B. NRHS >= 0. 
[in]  DL  DL is REAL array, dimension (N1) The (n1) subdiagonal elements of A. 
[in]  D  D is REAL array, dimension (N) The n diagonal elements of A. 
[in]  DU  DU is REAL array, dimension (N1) The (n1) superdiagonal elements of A. 
[in,out]  DLF  DLF is REAL array, dimension (N1) If FACT = 'F', then DLF is an input argument and on entry contains the (n1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF. If FACT = 'N', then DLF is an output argument and on exit contains the (n1) multipliers that define the matrix L from the LU factorization of 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 upper triangular matrix U from the LU factorization of A. If FACT = 'N', then DF is an output argument and on exit contains the n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in,out]  DUF  DUF is REAL array, dimension (N1) If FACT = 'F', then DUF is an input argument and on entry contains the (n1) elements of the first superdiagonal of U. If FACT = 'N', then DUF is an output argument and on exit contains the (n1) elements of the first superdiagonal of U. 
[in,out]  DU2  DU2 is REAL array, dimension (N2) If FACT = 'F', then DU2 is an input argument and on entry contains the (n2) elements of the second superdiagonal of U. If FACT = 'N', then DU2 is an output argument and on exit contains the (n2) elements of the second superdiagonal of U. 
[in,out]  IPIV  IPIV is INTEGER array, dimension (N) If FACT = 'F', then IPIV is an input argument and on entry contains the pivot indices from the LU factorization of A as computed by SGTTRF. If FACT = 'N', then IPIV is an output argument and on exit contains the pivot indices from the LU factorization of A; row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required. 
[in]  B  B is REAL array, dimension (LDB,NRHS) The NbyNRHS 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 REAL array, dimension (LDX,NRHS) If INFO = 0 or INFO = N+1, the NbyNRHS 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 estimate of 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 estimated forward error bound for each solution vector X(j) (the jth 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). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error. 
[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 REAL array, dimension (3*N) 
[out]  IWORK  IWORK is INTEGER array, dimension (N) 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, and i is <= N: U(i,i) is exactly zero. The factorization has not been completed unless i = N, but the factor U is exactly singular, so the solution and error bounds could not be 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 290 of file sgtsvx.f.