Provided by: liblapack-doc_3.11.0-2_all 
NAME
realGTcomputational - real
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.
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.
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.
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.
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.
Author
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