LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
subroutine  sgtcon (NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, IWORK, INFO) 
SGTCON  
subroutine  sgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) 
SGTRFS  
subroutine  sgttrf (N, DL, D, DU, DU2, IPIV, INFO) 
SGTTRF  
subroutine  sgttrs (TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO) 
SGTTRS  
subroutine  sgtts2 (ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB) 
SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. 
This is the group of real computational functions for GT matrices
subroutine sgtcon  (  character  NORM, 
integer  N,  
real, dimension( * )  DL,  
real, dimension( * )  D,  
real, dimension( * )  DU,  
real, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
real  ANORM,  
real  RCOND,  
real, dimension( * )  WORK,  
integer, dimension( * )  IWORK,  
integer  INFO  
) 
SGTCON
Download SGTCON + dependencies [TGZ] [ZIP] [TXT]SGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
[in]  NORM  NORM is CHARACTER*1 Specifies whether the 1norm condition number or the infinitynorm condition number is required: = '1' or 'O': 1norm; = 'I': Infinitynorm. 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. 
[in]  DL  DL is REAL array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF. 
[in]  D  D is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DU  DU is REAL array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is REAL array, dimension (N2) The (n2) elements of the second superdiagonal of U. 
[in]  IPIV  IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, 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]  ANORM  ANORM is REAL If NORM = '1' or 'O', the 1norm of the original matrix A. If NORM = 'I', the infinitynorm of the original matrix A. 
[out]  RCOND  RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1norm of inv(A) computed in this routine. 
[out]  WORK  WORK is REAL array, dimension (2*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 
Definition at line 146 of file sgtcon.f.
subroutine sgtrfs  (  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, dimension( * )  FERR,  
real, dimension( * )  BERR,  
real, dimension( * )  WORK,  
integer, dimension( * )  IWORK,  
integer  INFO  
) 
SGTRFS
Download SGTRFS + dependencies [TGZ] [ZIP] [TXT]SGTRFS improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution.
[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 diagonal elements of A. 
[in]  DU  DU is REAL array, dimension (N1) The (n1) superdiagonal elements of A. 
[in]  DLF  DLF is REAL array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF. 
[in]  DF  DF is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DUF  DUF is REAL array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is REAL array, dimension (N2) The (n2) elements of the second superdiagonal of U. 
[in]  IPIV  IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, 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 right hand side matrix B. 
[in]  LDB  LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[in,out]  X  X is REAL array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by SGTTRS. On exit, the improved solution matrix X. 
[in]  LDX  LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N). 
[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 
ITMAX is the maximum number of steps of iterative refinement.
Definition at line 208 of file sgtrfs.f.
subroutine sgttrf  (  integer  N, 
real, dimension( * )  DL,  
real, dimension( * )  D,  
real, dimension( * )  DU,  
real, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
integer  INFO  
) 
SGTTRF
Download SGTTRF + dependencies [TGZ] [ZIP] [TXT]SGTTRF computes an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges. The factorization has the form 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.
[in]  N  N is INTEGER The order of the matrix A. 
[in,out]  DL  DL is REAL array, dimension (N1) On entry, DL must contain the (n1) subdiagonal elements of A. On exit, DL is overwritten by the (n1) multipliers that define the matrix L from the LU factorization of A. 
[in,out]  D  D is REAL array, dimension (N) On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in,out]  DU  DU is REAL array, dimension (N1) On entry, DU must contain the (n1) superdiagonal elements of A. On exit, DU is overwritten by the (n1) elements of the first superdiagonal of U. 
[out]  DU2  DU2 is REAL array, dimension (N2) On exit, DU2 is overwritten by the (n2) elements of the second superdiagonal of U. 
[out]  IPIV  IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, 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. 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = k, the kth argument had an illegal value > 0: if INFO = k, U(k,k) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations. 
Definition at line 125 of file sgttrf.f.
subroutine sgttrs  (  character  TRANS, 
integer  N,  
integer  NRHS,  
real, dimension( * )  DL,  
real, dimension( * )  D,  
real, dimension( * )  DU,  
real, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
real, dimension( ldb, * )  B,  
integer  LDB,  
integer  INFO  
) 
SGTTRS
Download SGTTRS + dependencies [TGZ] [ZIP] [TXT]SGTTRS solves one of the systems of equations A*X = B or A**T*X = B, with a tridiagonal matrix A using the LU factorization computed by SGTTRF.
[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**T* X = B (Conjugate transpose = Transpose) 
[in]  N  N is INTEGER The order of the matrix A. 
[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) multipliers that define the matrix L from the LU factorization of A. 
[in]  D  D is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DU  DU is REAL array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is REAL array, dimension (N2) The (n2) elements of the second superdiagonal of U. 
[in]  IPIV  IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, 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,out]  B  B is REAL array, dimension (LDB,NRHS) On entry, the matrix of right hand side vectors B. On exit, B is overwritten by the solution vectors X. 
[in]  LDB  LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value 
Definition at line 138 of file sgttrs.f.
subroutine sgtts2  (  integer  ITRANS, 
integer  N,  
integer  NRHS,  
real, dimension( * )  DL,  
real, dimension( * )  D,  
real, dimension( * )  DU,  
real, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
real, dimension( ldb, * )  B,  
integer  LDB  
) 
SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
Download SGTTS2 + dependencies [TGZ] [ZIP] [TXT]SGTTS2 solves one of the systems of equations A*X = B or A**T*X = B, with a tridiagonal matrix A using the LU factorization computed by SGTTRF.
[in]  ITRANS  ITRANS is INTEGER Specifies the form of the system of equations. = 0: A * X = B (No transpose) = 1: A**T* X = B (Transpose) = 2: A**T* X = B (Conjugate transpose = Transpose) 
[in]  N  N is INTEGER The order of the matrix A. 
[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) multipliers that define the matrix L from the LU factorization of A. 
[in]  D  D is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DU  DU is REAL array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is REAL array, dimension (N2) The (n2) elements of the second superdiagonal of U. 
[in]  IPIV  IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, 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,out]  B  B is REAL array, dimension (LDB,NRHS) On entry, the matrix of right hand side vectors B. On exit, B is overwritten by the solution vectors X. 
[in]  LDB  LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). 
Definition at line 129 of file sgtts2.f.