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 1norm condition number or the infinitynorm condition number is required: = '1' or 'O': 1norm; = 'I': Infinitynorm.
NN is INTEGER The order of the matrix A. N >= 0.
DLDL is REAL array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.
DD is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUDU is REAL array, dimension (N1) The (n1) elements of the first superdiagonal of U.
DU2DU2 is REAL array, dimension (N2) The (n2) 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 1norm of the original matrix A. If NORM = 'I', the infinitynorm 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 1norm of inv(A) computed in this routine.
WORKWORK is REAL array, dimension (2*N)
IWORKIWORK is INTEGER array, dimension (N)
INFOINFO 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.
Date:
 September 2012
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)
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 REAL array, dimension (N1) The (n1) subdiagonal elements of A.
DD is REAL array, dimension (N) The diagonal elements of A.
DUDU is REAL array, dimension (N1) The (n1) superdiagonal elements of A.
DLFDLF is REAL array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.
DFDF is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUFDUF is REAL array, dimension (N1) The (n1) elements of the first superdiagonal of U.
DU2DU2 is REAL array, dimension (N2) The (n2) 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 REAL 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 REAL array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by SGTTRS. 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 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.
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 REAL array, dimension (3*N)
IWORKIWORK is INTEGER array, dimension (N)
INFOINFO 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.
Date:
 September 2012
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.
DLDL is REAL 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.
DD 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.
DUDU is REAL 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.
DU2DU2 is REAL array, dimension (N2) On exit, DU2 is overwritten by the (n2) 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.
INFOINFO 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.
Date:
 September 2012
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)
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 REAL array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A.
DD is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUDU is REAL array, dimension (N1) The (n1) elements of the first superdiagonal of U.
DU2DU2 is REAL array, dimension (N2) The (n2) 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 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.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
INFOINFO 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.
Date:
 September 2012
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)
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 REAL array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A.
DD is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUDU is REAL array, dimension (N1) The (n1) elements of the first superdiagonal of U.
DU2DU2 is REAL array, dimension (N2) The (n2) 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 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.
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:
 September 2012
Author
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