table of contents
| ptsv(3) | LAPACK | ptsv(3) |
NAME¶
ptsv - ptsv: factor and solve
SYNOPSIS¶
Functions¶
subroutine cptsv (n, nrhs, d, e, b, ldb, info)
CPTSV computes the solution to system of linear equations A * X = B for PT
matrices subroutine dptsv (n, nrhs, d, e, b, ldb, info)
DPTSV computes the solution to system of linear equations A * X = B for PT
matrices subroutine sptsv (n, nrhs, d, e, b, ldb, info)
SPTSV computes the solution to system of linear equations A * X = B for PT
matrices subroutine zptsv (n, nrhs, d, e, b, ldb, info)
ZPTSV computes the solution to system of linear equations A * X = B for PT
matrices
Detailed Description¶
Function Documentation¶
subroutine cptsv (integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, integer info)¶
CPTSV computes the solution to system of linear equations A * X = B for PT matrices
Purpose:
CPTSV computes the solution to a complex system of linear equations
A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
matrix, and X and B are N-by-NRHS matrices.
A is factored as A = L*D*L**H, and the factored form of A is then
used to solve the system of equations.
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.
D
D is REAL array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A. On exit, the n diagonal elements of the diagonal matrix
D from the factorization A = L*D*L**H.
E
E is COMPLEX array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A. On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**H factorization of
A. E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**H*D*U factorization of A.
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, the leading principal minor of order i
is not positive, 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 dptsv (integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldb, * ) b, integer ldb, integer info)¶
DPTSV computes the solution to system of linear equations A * X = B for PT matrices
Purpose:
DPTSV computes the solution to a real system of linear equations
A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
matrix, and X and B are N-by-NRHS matrices.
A is factored as A = L*D*L**T, and the factored form of A is then
used to solve the system of equations.
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.
D
D is DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A. On exit, the n diagonal elements of the diagonal matrix
D from the factorization A = L*D*L**T.
E
E is DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A. On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**T factorization of
A. (E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**T*D*U factorization of A.)
B
B is DOUBLE PRECISION 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, the leading principal minor of order i
is not positive, 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 sptsv (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, integer info)¶
SPTSV computes the solution to system of linear equations A * X = B for PT matrices
Purpose:
SPTSV computes the solution to a real system of linear equations
A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
matrix, and X and B are N-by-NRHS matrices.
A is factored as A = L*D*L**T, and the factored form of A is then
used to solve the system of equations.
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.
D
D is REAL array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A. On exit, the n diagonal elements of the diagonal matrix
D from the factorization A = L*D*L**T.
E
E is REAL array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A. On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**T factorization of
A. (E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**T*D*U factorization of A.)
B
B is REAL 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, the leading principal minor of order i
is not positive, 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 zptsv (integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb, integer info)¶
ZPTSV computes the solution to system of linear equations A * X = B for PT matrices
Purpose:
ZPTSV computes the solution to a complex system of linear equations
A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
matrix, and X and B are N-by-NRHS matrices.
A is factored as A = L*D*L**H, and the factored form of A is then
used to solve the system of equations.
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.
D
D is DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A. On exit, the n diagonal elements of the diagonal matrix
D from the factorization A = L*D*L**H.
E
E is COMPLEX*16 array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A. On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**H factorization of
A. E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**H*D*U factorization of A.
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, the leading principal minor of order i
is not positive, 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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