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- testing 3.12.0-4
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- experimental 3.12.1-1
| ptts2(3) | LAPACK | ptts2(3) |
NAME¶
ptts2 - ptts2: triangular solve using factor, unblocked
SYNOPSIS¶
Functions¶
subroutine cptts2 (iuplo, n, nrhs, d, e, b, ldb)
CPTTS2 solves a tridiagonal system of the form AX=B using the L D LH
factorization computed by spttrf. subroutine dptts2 (n, nrhs, d, e,
b, ldb)
DPTTS2 solves a tridiagonal system of the form AX=B using the L D LH
factorization computed by spttrf. subroutine sptts2 (n, nrhs, d, e,
b, ldb)
SPTTS2 solves a tridiagonal system of the form AX=B using the L D LH
factorization computed by spttrf. subroutine zptts2 (iuplo, n, nrhs,
d, e, b, ldb)
ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH
factorization computed by spttrf.
Detailed Description¶
Function Documentation¶
subroutine cptts2 (integer iuplo, integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb)¶
CPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
Purpose:
CPTTS2 solves a tridiagonal system of the form
A * X = B
using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF.
D is a diagonal matrix specified in the vector D, U (or L) is a unit
bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
the vector E, and X and B are N by NRHS matrices.
Parameters
IUPLO is INTEGER
Specifies the form of the factorization and whether the
vector E is the superdiagonal of the upper bidiagonal factor
U or the subdiagonal of the lower bidiagonal factor L.
= 1: A = U**H *D*U, E is the superdiagonal of U
= 0: A = L*D*L**H, E is the subdiagonal of L
N
N is INTEGER
The order of the tridiagonal 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)
The n diagonal elements of the diagonal matrix D from the
factorization A = U**H *D*U or A = L*D*L**H.
E
E is COMPLEX array, dimension (N-1)
If IUPLO = 1, the (n-1) superdiagonal elements of the unit
bidiagonal factor U from the factorization A = U**H*D*U.
If IUPLO = 0, the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the factorization A = L*D*L**H.
B
B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side vectors B for the system of
linear equations.
On exit, the solution vectors, X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dptts2 (integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldb, * ) b, integer ldb)¶
DPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
Purpose:
DPTTS2 solves a tridiagonal system of the form
A * X = B
using the L*D*L**T factorization of A computed by DPTTRF. D is a
diagonal matrix specified in the vector D, L is a unit bidiagonal
matrix whose subdiagonal is specified in the vector E, and X and B
are N by NRHS matrices.
Parameters
N is INTEGER
The order of the tridiagonal 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)
The n diagonal elements of the diagonal matrix D from the
L*D*L**T factorization of A.
E
E is DOUBLE PRECISION array, dimension (N-1)
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
factorization A = U**T*D*U.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors B for the system of
linear equations.
On exit, the solution vectors, X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine sptts2 (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, * ) b, integer ldb)¶
SPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
Purpose:
SPTTS2 solves a tridiagonal system of the form
A * X = B
using the L*D*L**T factorization of A computed by SPTTRF. D is a
diagonal matrix specified in the vector D, L is a unit bidiagonal
matrix whose subdiagonal is specified in the vector E, and X and B
are N by NRHS matrices.
Parameters
N is INTEGER
The order of the tridiagonal 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)
The n diagonal elements of the diagonal matrix D from the
L*D*L**T factorization of A.
E
E is REAL array, dimension (N-1)
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
factorization A = U**T*D*U.
B
B is REAL array, dimension (LDB,NRHS)
On entry, the right hand side vectors B for the system of
linear equations.
On exit, the solution vectors, X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zptts2 (integer iuplo, integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb)¶
ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
Purpose:
ZPTTS2 solves a tridiagonal system of the form
A * X = B
using the factorization A = U**H *D*U or A = L*D*L**H computed by ZPTTRF.
D is a diagonal matrix specified in the vector D, U (or L) is a unit
bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
the vector E, and X and B are N by NRHS matrices.
Parameters
IUPLO is INTEGER
Specifies the form of the factorization and whether the
vector E is the superdiagonal of the upper bidiagonal factor
U or the subdiagonal of the lower bidiagonal factor L.
= 1: A = U**H *D*U, E is the superdiagonal of U
= 0: A = L*D*L**H, E is the subdiagonal of L
N
N is INTEGER
The order of the tridiagonal 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)
The n diagonal elements of the diagonal matrix D from the
factorization A = U**H *D*U or A = L*D*L**H.
E
E is COMPLEX*16 array, dimension (N-1)
If IUPLO = 1, the (n-1) superdiagonal elements of the unit
bidiagonal factor U from the factorization A = U**H*D*U.
If IUPLO = 0, the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the factorization A = L*D*L**H.
B
B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side vectors B for the system of
linear equations.
On exit, the solution vectors, X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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| Tue Jan 28 2025 00:54:31 | Version 3.12.0 |