| gbtrs(3) | LAPACK | gbtrs(3) |
gbtrs - gbtrs: triangular solve using factor
subroutine cgbtrs (trans, n, kl, ku, nrhs, ab, ldab, ipiv,
b, ldb, info)
CGBTRS subroutine dgbtrs (trans, n, kl, ku, nrhs, ab, ldab,
ipiv, b, ldb, info)
DGBTRS subroutine sgbtrs (trans, n, kl, ku, nrhs, ab, ldab,
ipiv, b, ldb, info)
SGBTRS subroutine zgbtrs (trans, n, kl, ku, nrhs, ab, ldab,
ipiv, b, ldb, info)
ZGBTRS
CGBTRS
Purpose:
CGBTRS solves a system of linear equations
A * X = B, A**T * X = B, or A**H * X = B
with a general band matrix A using the LU factorization computed
by CGBTRF.
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. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AB
AB is COMPLEX array, dimension (LDAB,N)
Details of the LU factorization of the band matrix A, as
computed by CGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
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).
B
B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the 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
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
DGBTRS
Purpose:
DGBTRS solves a system of linear equations
A * X = B or A**T * X = B
with a general band matrix A using the LU factorization computed
by DGBTRF.
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. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AB
AB is DOUBLE PRECISION array, dimension (LDAB,N)
Details of the LU factorization of the band matrix A, as
computed by DGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
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).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the 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
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
SGBTRS
Purpose:
SGBTRS solves a system of linear equations
A * X = B or A**T * X = B
with a general band matrix A using the LU factorization computed
by SGBTRF.
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. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AB
AB is REAL array, dimension (LDAB,N)
Details of the LU factorization of the band matrix A, as
computed by SGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
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).
B
B is REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the 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
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
ZGBTRS
Purpose:
ZGBTRS solves a system of linear equations
A * X = B, A**T * X = B, or A**H * X = B
with a general band matrix A using the LU factorization computed
by ZGBTRF.
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. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AB
AB is COMPLEX*16 array, dimension (LDAB,N)
Details of the LU factorization of the band matrix A, as
computed by ZGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
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).
B
B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the 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
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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| Thu Aug 7 2025 17:26:25 | Version 3.12.0 |