table of contents
| gtsv(3) | LAPACK | gtsv(3) |
NAME¶
gtsv - gtsv: factor and solve
SYNOPSIS¶
Functions¶
subroutine cgtsv (n, nrhs, dl, d, du, b, ldb, info)
CGTSV computes the solution to system of linear equations A * X = B for GT
matrices subroutine dgtsv (n, nrhs, dl, d, du, b, ldb, info)
DGTSV computes the solution to system of linear equations A * X = B for GT
matrices subroutine sgtsv (n, nrhs, dl, d, du, b, ldb, info)
SGTSV computes the solution to system of linear equations A * X = B for GT
matrices subroutine zgtsv (n, nrhs, dl, d, du, b, ldb, info)
ZGTSV computes the solution to system of linear equations A * X = B for GT
matrices
Detailed Description¶
Function Documentation¶
subroutine cgtsv (integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( ldb, * ) b, integer ldb, integer info)¶
CGTSV computes the solution to system of linear equations A * X = B for GT matrices
Purpose:
CGTSV solves the equation
A*X = B,
where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
partial pivoting.
Note that the equation A**T *X = B may be solved by interchanging the
order of the arguments DU and DL.
Parameters
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 (N-1)
On entry, DL must contain the (n-1) subdiagonal elements of
A.
On exit, DL is overwritten by the (n-2) elements of the
second superdiagonal of the upper triangular matrix U from
the LU factorization of A, in DL(1), ..., DL(n-2).
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 U.
DU
DU is COMPLEX array, dimension (N-1)
On entry, DU must contain the (n-1) superdiagonal elements
of A.
On exit, DU is overwritten by the (n-1) elements of the first
superdiagonal of U.
B
B is COMPLEX array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix 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
> 0: if INFO = i, U(i,i) is exactly zero, and the solution
has not been computed. The factorization has not been
completed unless i = N.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dgtsv (integer n, integer nrhs, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( ldb, * ) b, integer ldb, integer info)¶
DGTSV computes the solution to system of linear equations A * X = B for GT matrices
Purpose:
DGTSV solves the equation
A*X = B,
where A is an n by n tridiagonal matrix, by Gaussian elimination with
partial pivoting.
Note that the equation A**T*X = B may be solved by interchanging the
order of the arguments DU and DL.
Parameters
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 DOUBLE PRECISION 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-2) elements of the
second super-diagonal of the upper triangular matrix U from
the LU factorization of A, in DL(1), ..., DL(n-2).
D
D is DOUBLE PRECISION array, dimension (N)
On entry, D must contain the diagonal elements of A.
On exit, D is overwritten by the n diagonal elements of U.
DU
DU is DOUBLE PRECISION 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.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the N by NRHS matrix of right hand side matrix B.
On exit, if INFO = 0, the N by NRHS solution matrix 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
> 0: if INFO = i, U(i,i) is exactly zero, and the solution
has not been computed. The factorization has not been
completed unless i = N.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine sgtsv (integer n, integer nrhs, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( ldb, * ) b, integer ldb, integer info)¶
SGTSV computes the solution to system of linear equations A * X = B for GT matrices
Purpose:
SGTSV solves the equation
A*X = B,
where A is an n by n tridiagonal matrix, by Gaussian elimination with
partial pivoting.
Note that the equation A**T*X = B may be solved by interchanging the
order of the arguments DU and DL.
Parameters
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)
On entry, DL must contain the (n-1) sub-diagonal elements of
A.
On exit, DL is overwritten by the (n-2) elements of the
second super-diagonal of the upper triangular matrix U from
the LU factorization of A, in DL(1), ..., DL(n-2).
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 U.
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.
B
B is REAL array, dimension (LDB,NRHS)
On entry, the N by NRHS matrix of right hand side matrix B.
On exit, if INFO = 0, the N by NRHS solution matrix 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
> 0: if INFO = i, U(i,i) is exactly zero, and the solution
has not been computed. The factorization has not been
completed unless i = N.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zgtsv (integer n, integer nrhs, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( ldb, * ) b, integer ldb, integer info)¶
ZGTSV computes the solution to system of linear equations A * X = B for GT matrices
Purpose:
ZGTSV solves the equation
A*X = B,
where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
partial pivoting.
Note that the equation A**T *X = B may be solved by interchanging the
order of the arguments DU and DL.
Parameters
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*16 array, dimension (N-1)
On entry, DL must contain the (n-1) subdiagonal elements of
A.
On exit, DL is overwritten by the (n-2) elements of the
second superdiagonal of the upper triangular matrix U from
the LU factorization of A, in DL(1), ..., DL(n-2).
D
D is COMPLEX*16 array, dimension (N)
On entry, D must contain the diagonal elements of A.
On exit, D is overwritten by the n diagonal elements of U.
DU
DU is COMPLEX*16 array, dimension (N-1)
On entry, DU must contain the (n-1) superdiagonal elements
of A.
On exit, DU is overwritten by the (n-1) elements of the first
superdiagonal of U.
B
B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix 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
> 0: if INFO = i, U(i,i) is exactly zero, and the solution
has not been computed. The factorization has not been
completed unless i = N.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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