LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
subroutine  cgtcon (NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO) 
CGTCON  
subroutine  cgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO) 
CGTRFS  
subroutine  cgttrf (N, DL, D, DU, DU2, IPIV, INFO) 
CGTTRF  
subroutine  cgttrs (TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO) 
CGTTRS  
subroutine  cgtts2 (ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB) 
CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. 
This is the group of complex computational functions for GT matrices
subroutine cgtcon  (  character  NORM, 
integer  N,  
complex, dimension( * )  DL,  
complex, dimension( * )  D,  
complex, dimension( * )  DU,  
complex, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
real  ANORM,  
real  RCOND,  
complex, dimension( * )  WORK,  
integer  INFO  
) 
CGTCON
Download CGTCON + dependencies [TGZ] [ZIP] [TXT]CGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF. 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 COMPLEX array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF. 
[in]  D  D is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DU  DU is COMPLEX array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is COMPLEX 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 COMPLEX array, dimension (2*N) 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value 
Definition at line 141 of file cgtcon.f.
subroutine cgtrfs  (  character  TRANS, 
integer  N,  
integer  NRHS,  
complex, dimension( * )  DL,  
complex, dimension( * )  D,  
complex, dimension( * )  DU,  
complex, dimension( * )  DLF,  
complex, dimension( * )  DF,  
complex, dimension( * )  DUF,  
complex, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
complex, dimension( ldb, * )  B,  
integer  LDB,  
complex, dimension( ldx, * )  X,  
integer  LDX,  
real, dimension( * )  FERR,  
real, dimension( * )  BERR,  
complex, dimension( * )  WORK,  
real, dimension( * )  RWORK,  
integer  INFO  
) 
CGTRFS
Download CGTRFS + dependencies [TGZ] [ZIP] [TXT]CGTRFS 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) 
[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 COMPLEX array, dimension (N1) The (n1) subdiagonal elements of A. 
[in]  D  D is COMPLEX array, dimension (N) The diagonal elements of A. 
[in]  DU  DU is COMPLEX array, dimension (N1) The (n1) superdiagonal elements of A. 
[in]  DLF  DLF is COMPLEX array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF. 
[in]  DF  DF is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DUF  DUF is COMPLEX array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by CGTTRS. 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 COMPLEX array, dimension (2*N) 
[out]  RWORK  RWORK is REAL 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 209 of file cgtrfs.f.
subroutine cgttrf  (  integer  N, 
complex, dimension( * )  DL,  
complex, dimension( * )  D,  
complex, dimension( * )  DU,  
complex, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
integer  INFO  
) 
CGTTRF
Download CGTTRF + dependencies [TGZ] [ZIP] [TXT]CGTTRF computes an LU factorization of a complex 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 cgttrf.f.
subroutine cgttrs  (  character  TRANS, 
integer  N,  
integer  NRHS,  
complex, dimension( * )  DL,  
complex, dimension( * )  D,  
complex, dimension( * )  DU,  
complex, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
complex, dimension( ldb, * )  B,  
integer  LDB,  
integer  INFO  
) 
CGTTRS
Download CGTTRS + dependencies [TGZ] [ZIP] [TXT]CGTTRS solves one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B, with a tridiagonal matrix A using the LU factorization computed by CGTTRF.
[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) 
[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 COMPLEX array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A. 
[in]  D  D is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DU  DU is COMPLEX array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is COMPLEX 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 COMPLEX 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 = k, the kth argument had an illegal value 
Definition at line 138 of file cgttrs.f.
subroutine cgtts2  (  integer  ITRANS, 
integer  N,  
integer  NRHS,  
complex, dimension( * )  DL,  
complex, dimension( * )  D,  
complex, dimension( * )  DU,  
complex, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
complex, dimension( ldb, * )  B,  
integer  LDB  
) 
CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
Download CGTTS2 + dependencies [TGZ] [ZIP] [TXT]CGTTS2 solves one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B, with a tridiagonal matrix A using the LU factorization computed by CGTTRF.
[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**H * X = B (Conjugate 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 COMPLEX array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A. 
[in]  D  D is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DU  DU is COMPLEX array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is COMPLEX 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 COMPLEX 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 cgtts2.f.