
NAMEcomplexGTcomputational  complexSYNOPSISFunctionssubroutine 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. Detailed DescriptionThis is the group of complex computational functions for GT matricesFunction Documentationsubroutine 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)CGTCONPurpose: 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))). Parameters NORM
NORM is CHARACTER*1 Specifies whether the 1norm condition number or the infinitynorm condition number is required: = '1' or 'O': 1norm; = 'I': Infinitynorm. N N is INTEGER The order of the matrix A. N >= 0. 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. D D is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU DU is COMPLEX array, dimension (N1) The (n1) elements of the first superdiagonal of U. DU2 DU2 is COMPLEX array, dimension (N2) The (n2) elements of the second superdiagonal of U. 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. 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. 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. WORK WORK is COMPLEX array, dimension (2*N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value Author Univ. of Tennessee
Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 139 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)CGTRFSPurpose: 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. Parameters 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) N N is INTEGER The order of the matrix A. N >= 0. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. DL DL is COMPLEX array, dimension (N1) The (n1) subdiagonal elements of A. D D is COMPLEX array, dimension (N) The diagonal elements of A. DU DU is COMPLEX array, dimension (N1) The (n1) superdiagonal elements of A. 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. DF DF is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DUF DUF is COMPLEX array, dimension (N1) The (n1) elements of the first superdiagonal of U. DU2 DU2 is COMPLEX array, dimension (N2) The (n2) elements of the second superdiagonal of U. 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. B B is COMPLEX array, dimension (LDB,NRHS) The right hand side matrix B. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). 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. LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N). 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. 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). WORK WORK is COMPLEX array, dimension (2*N) RWORK RWORK is REAL array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value Internal Parameters: ITMAX is the maximum number of steps of iterative refinement. Author Univ. of Tennessee
Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 207 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)CGTTRFPurpose: 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. Parameters N
N is INTEGER The order of the matrix A. 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. 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. 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. DU2 DU2 is COMPLEX array, dimension (N2) On exit, DU2 is overwritten by the (n2) elements of the second superdiagonal of U. 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. 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. Author Univ. of Tennessee
Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 123 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)CGTTRSPurpose: 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. Parameters 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) N N is INTEGER The order of the matrix A. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. DL DL is COMPLEX array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A. D D is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU DU is COMPLEX array, dimension (N1) The (n1) elements of the first superdiagonal of U. DU2 DU2 is COMPLEX array, dimension (N2) The (n2) elements of the second superdiagonal of U. 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. 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. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). INFO INFO is INTEGER = 0: successful exit < 0: if INFO = k, the kth argument had an illegal value Author Univ. of Tennessee
Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 136 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.Purpose: 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. Parameters 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) N N is INTEGER The order of the matrix A. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. DL DL is COMPLEX array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A. D D is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU DU is COMPLEX array, dimension (N1) The (n1) elements of the first superdiagonal of U. DU2 DU2 is COMPLEX array, dimension (N2) The (n2) elements of the second superdiagonal of U. 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. 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. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). Author Univ. of Tennessee
Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 127 of file cgtts2.f. AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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