LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
subroutine  zgtcon (NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO) 
ZGTCON  
subroutine  zgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO) 
ZGTRFS  
subroutine  zgttrf (N, DL, D, DU, DU2, IPIV, INFO) 
ZGTTRF  
subroutine  zgttrs (TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO) 
ZGTTRS  
subroutine  zgtts2 (ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB) 
ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. 
This is the group of complex16 computational functions for GT matrices
subroutine zgtcon  (  character  NORM, 
integer  N,  
complex*16, dimension( * )  DL,  
complex*16, dimension( * )  D,  
complex*16, dimension( * )  DU,  
complex*16, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
double precision  ANORM,  
double precision  RCOND,  
complex*16, dimension( * )  WORK,  
integer  INFO  
) 
ZGTCON
Download ZGTCON + dependencies [TGZ] [ZIP] [TXT]ZGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF. 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*16 array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF. 
[in]  D  D is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DU  DU is COMPLEX*16 array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is COMPLEX*16 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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*16 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 zgtcon.f.
subroutine zgtrfs  (  character  TRANS, 
integer  N,  
integer  NRHS,  
complex*16, dimension( * )  DL,  
complex*16, dimension( * )  D,  
complex*16, dimension( * )  DU,  
complex*16, dimension( * )  DLF,  
complex*16, dimension( * )  DF,  
complex*16, dimension( * )  DUF,  
complex*16, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
complex*16, dimension( ldb, * )  B,  
integer  LDB,  
complex*16, dimension( ldx, * )  X,  
integer  LDX,  
double precision, dimension( * )  FERR,  
double precision, dimension( * )  BERR,  
complex*16, dimension( * )  WORK,  
double precision, dimension( * )  RWORK,  
integer  INFO  
) 
ZGTRFS
Download ZGTRFS + dependencies [TGZ] [ZIP] [TXT]ZGTRFS 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*16 array, dimension (N1) The (n1) subdiagonal elements of A. 
[in]  D  D is COMPLEX*16 array, dimension (N) The diagonal elements of A. 
[in]  DU  DU is COMPLEX*16 array, dimension (N1) The (n1) superdiagonal elements of A. 
[in]  DLF  DLF is COMPLEX*16 array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF. 
[in]  DF  DF is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DUF  DUF is COMPLEX*16 array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is COMPLEX*16 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*16 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*16 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by ZGTTRS. 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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*16 array, dimension (2*N) 
[out]  RWORK  RWORK is DOUBLE PRECISION 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 zgtrfs.f.
subroutine zgttrf  (  integer  N, 
complex*16, dimension( * )  DL,  
complex*16, dimension( * )  D,  
complex*16, dimension( * )  DU,  
complex*16, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
integer  INFO  
) 
ZGTTRF
Download ZGTTRF + dependencies [TGZ] [ZIP] [TXT]ZGTTRF 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*16 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*16 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*16 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*16 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 zgttrf.f.
subroutine zgttrs  (  character  TRANS, 
integer  N,  
integer  NRHS,  
complex*16, dimension( * )  DL,  
complex*16, dimension( * )  D,  
complex*16, dimension( * )  DU,  
complex*16, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
complex*16, dimension( ldb, * )  B,  
integer  LDB,  
integer  INFO  
) 
ZGTTRS
Download ZGTTRS + dependencies [TGZ] [ZIP] [TXT]ZGTTRS 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 ZGTTRF.
[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*16 array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A. 
[in]  D  D is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DU  DU is COMPLEX*16 array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is COMPLEX*16 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*16 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 zgttrs.f.
subroutine zgtts2  (  integer  ITRANS, 
integer  N,  
integer  NRHS,  
complex*16, dimension( * )  DL,  
complex*16, dimension( * )  D,  
complex*16, dimension( * )  DU,  
complex*16, dimension( * )  DU2,  
integer, dimension( * )  IPIV,  
complex*16, dimension( ldb, * )  B,  
integer  LDB  
) 
ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
Download ZGTTS2 + dependencies [TGZ] [ZIP] [TXT]ZGTTS2 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 ZGTTRF.
[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*16 array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A. 
[in]  D  D is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 
[in]  DU  DU is COMPLEX*16 array, dimension (N1) The (n1) elements of the first superdiagonal of U. 
[in]  DU2  DU2 is COMPLEX*16 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*16 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 zgtts2.f.