Provided by: liblapack-doc_3.7.1-4ubuntu1_all

**NAME**

complexGTcomputational

**SYNOPSIS**

Functionssubroutinecgtcon(NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO)CGTCONsubroutinecgtrfs(TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)CGTRFSsubroutinecgttrf(N, DL, D, DU, DU2, IPIV, INFO)CGTTRFsubroutinecgttrs(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)CGTTRSsubroutinecgtts2(ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB)CGTTS2solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

**Detailed** **Description**

This is the group of complex computational functions for GT matrices

**Function** **Documentation**

subroutinecgtcon(characterNORM,integerN,complex,dimension(*)DL,complex,dimension(*)D,complex,dimension(*)DU,complex,dimension(*)DU2,integer,dimension(*)IPIV,realANORM,realRCOND,complex,dimension(*)WORK,integerINFO)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:NORMNORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm.NN is INTEGER The order of the matrix A. N >= 0.DLDL is COMPLEX array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF.DD is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.DUDU is COMPLEX array, dimension (N-1) The (n-1) elements of the first superdiagonal of U.DU2DU2 is COMPLEX array, dimension (N-2) The (n-2) elements of the second superdiagonal of U.IPIVIPIV 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.ANORMANORM is REAL If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.RCONDRCOND 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 1-norm of inv(A) computed in this routine.WORKWORK is COMPLEX array, dimension (2*N)INFOINFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal valueAuthor:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:December 2016subroutinecgtrfs(characterTRANS,integerN,integerNRHS,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,integerLDB,complex,dimension(ldx,*)X,integerLDX,real,dimension(*)FERR,real,dimension(*)BERR,complex,dimension(*)WORK,real,dimension(*)RWORK,integerINFO)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:TRANSTRANS 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)NN is INTEGER The order of the matrix A. N >= 0.NRHSNRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.DLDL is COMPLEX array, dimension (N-1) The (n-1) subdiagonal elements of A.DD is COMPLEX array, dimension (N) The diagonal elements of A.DUDU is COMPLEX array, dimension (N-1) The (n-1) superdiagonal elements of A.DLFDLF is COMPLEX array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF.DFDF is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.DUFDUF is COMPLEX array, dimension (N-1) The (n-1) elements of the first superdiagonal of U.DU2DU2 is COMPLEX array, dimension (N-2) The (n-2) elements of the second superdiagonal of U.IPIVIPIV 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.BB is COMPLEX array, dimension (LDB,NRHS) The right hand side matrix B.LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).XX is COMPLEX array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by CGTTRS. On exit, the improved solution matrix X.LDXLDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).FERRFERR is REAL array, dimension (NRHS) The estimated forward error bound for each solution vector X(j) (the j-th 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.BERRBERR 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).WORKWORK is COMPLEX array, dimension (2*N)RWORKRWORK is REAL array, dimension (N)INFOINFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal valueInternalParameters:ITMAX is the maximum number of steps of iterative refinement.Author:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:December 2016subroutinecgttrf(integerN,complex,dimension(*)DL,complex,dimension(*)D,complex,dimension(*)DU,complex,dimension(*)DU2,integer,dimension(*)IPIV,integerINFO)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:NN is INTEGER The order of the matrix A.DLDL is COMPLEX array, dimension (N-1) On entry, DL must contain the (n-1) sub-diagonal elements of A. On exit, DL is overwritten by the (n-1) multipliers that define the matrix L from the LU factorization of A.DD 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.DUDU is COMPLEX array, dimension (N-1) On entry, DU must contain the (n-1) super-diagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first super-diagonal of U.DU2DU2 is COMPLEX array, dimension (N-2) On exit, DU2 is overwritten by the (n-2) elements of the second super-diagonal of U.IPIVIPIV 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.INFOINFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th 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.Date:December 2016subroutinecgttrs(characterTRANS,integerN,integerNRHS,complex,dimension(*)DL,complex,dimension(*)D,complex,dimension(*)DU,complex,dimension(*)DU2,integer,dimension(*)IPIV,complex,dimension(ldb,*)B,integerLDB,integerINFO)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:TRANSTRANS 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)NN is INTEGER The order of the matrix A.NRHSNRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.DLDL is COMPLEX array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A.DD is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.DUDU is COMPLEX array, dimension (N-1) The (n-1) elements of the first super-diagonal of U.DU2DU2 is COMPLEX array, dimension (N-2) The (n-2) elements of the second super-diagonal of U.IPIVIPIV 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.BB 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.LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).INFOINFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal valueAuthor:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:December 2016subroutinecgtts2(integerITRANS,integerN,integerNRHS,complex,dimension(*)DL,complex,dimension(*)D,complex,dimension(*)DU,complex,dimension(*)DU2,integer,dimension(*)IPIV,complex,dimension(ldb,*)B,integerLDB)CGTTS2solves 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:ITRANSITRANS 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)NN is INTEGER The order of the matrix A.NRHSNRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.DLDL is COMPLEX array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A.DD is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.DUDU is COMPLEX array, dimension (N-1) The (n-1) elements of the first super-diagonal of U.DU2DU2 is COMPLEX array, dimension (N-2) The (n-2) elements of the second super-diagonal of U.IPIVIPIV 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.BB 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.LDBLDB 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.Date:December 2016

**Author**

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