# REALGTCOMPUTATIONAL(3) - Linux man page online | Library functions

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Chapter

Tue Nov 28 2017

**realGTcomputational(3) LAPACK realGTcomputational(3)**

## NAME

realGTcomputational## SYNOPSIS

Functions 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. Detailed Description This is the group of real computational functions for GT matrices Function Documentation 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 Purpose: 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))). Parameters: NORM NORM 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. N N is INTEGER The order of the matrix A. N >= 0. DL DL is REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF. D D is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU DU is REAL array, dimension (N-1) The (n-1) elements of the first superdiagonal of U. DU2 DU2 is REAL array, dimension (N-2) The (n-2) 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 1-norm of the original matrix A. If NORM = 'I', the infinity-norm 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 1-norm of inv(A) computed in this routine. WORK WORK is REAL array, dimension (2*N) IWORK IWORK is INTEGER array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: December 2016 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 Purpose: 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. 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 = 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 REAL array, dimension (N-1) The (n-1) subdiagonal elements of A. D D is REAL array, dimension (N) The diagonal elements of A. DU DU is REAL array, dimension (N-1) The (n-1) superdiagonal elements of A. DLF DLF is REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF. DF DF is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DUF DUF is REAL array, dimension (N-1) The (n-1) elements of the first superdiagonal of U. DU2 DU2 is REAL array, dimension (N-2) The (n-2) 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 REAL 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 REAL array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by SGTTRS. 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 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. 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 REAL array, dimension (3*N) IWORK IWORK is INTEGER array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th 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. Date: December 2016 subroutine sgttrf (integer N, real, dimension( * ) DL, real, dimension( * ) D, real, dimension( * ) DU, real, dimension( * ) DU2, integer, dimension( * ) IPIV, integer INFO) SGTTRF Purpose: 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. Parameters: N N is INTEGER The order of the matrix A. DL DL is REAL 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. 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. DU DU is REAL 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. DU2 DU2 is REAL array, dimension (N-2) On exit, DU2 is overwritten by the (n-2) elements of the second super-diagonal 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 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 2016 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 Purpose: 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. 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**T* X = B (Conjugate transpose = 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 REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A. D D is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU DU is REAL array, dimension (N-1) The (n-1) elements of the first super-diagonal of U. DU2 DU2 is REAL array, dimension (N-2) The (n-2) elements of the second super-diagonal 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 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. 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 = -i, the i-th argument had an illegal value Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: December 2016 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. Purpose: 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. 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**T* X = B (Conjugate transpose = 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 REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A. D D is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU DU is REAL array, dimension (N-1) The (n-1) elements of the first super-diagonal of U. DU2 DU2 is REAL array, dimension (N-2) The (n-2) elements of the second super-diagonal 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 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. 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. Date: December 2016 Author Generated automatically by Doxygen for LAPACK from the source code.**Version 3.7.1 Tue Nov 28 2017 realGTcomputational(3)**