| gttrs(3) | LAPACK | gttrs(3) |
gttrs - gttrs: triangular solve using factor
subroutine cgttrs (trans, n, nrhs, dl, d, du, du2, ipiv, b,
ldb, info)
CGTTRS subroutine dgttrs (trans, n, nrhs, dl, d, du, du2, ipiv,
b, ldb, info)
DGTTRS subroutine sgttrs (trans, n, nrhs, dl, d, du, du2, ipiv,
b, ldb, info)
SGTTRS subroutine zgttrs (trans, n, nrhs, dl, d, du, du2, ipiv,
b, ldb, info)
ZGTTRS
CGTTRS
Purpose:
CGTTRS solves one of the systems of equations
A * X = B, A**T * X = B, or A**H * X = B,
with a tridiagonal matrix A using the LU factorization computed
by CGTTRF.
Parameters
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)
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 COMPLEX array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A.
D
D is COMPLEX array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
DU
DU is COMPLEX array, dimension (N-1)
The (n-1) elements of the first super-diagonal of U.
DU2
DU2 is COMPLEX 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 COMPLEX 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 = -k, the k-th argument had an illegal value
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
DGTTRS
Purpose:
DGTTRS 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 DGTTRF.
Parameters
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 DOUBLE PRECISION array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A.
D
D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
DU
DU is DOUBLE PRECISION array, dimension (N-1)
The (n-1) elements of the first super-diagonal of U.
DU2
DU2 is DOUBLE PRECISION 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 DOUBLE PRECISION 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
ZGTTRS
Purpose:
ZGTTRS solves one of the systems of equations
A * X = B, A**T * X = B, or A**H * X = B,
with a tridiagonal matrix A using the LU factorization computed
by ZGTTRF.
Parameters
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)
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 COMPLEX*16 array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A.
D
D is COMPLEX*16 array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
DU
DU is COMPLEX*16 array, dimension (N-1)
The (n-1) elements of the first super-diagonal of U.
DU2
DU2 is COMPLEX*16 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 COMPLEX*16 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 = -k, the k-th argument had an illegal value
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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