| tbtrs(3) | LAPACK | tbtrs(3) |
tbtrs - tbtrs: triangular solve
subroutine ctbtrs (uplo, trans, diag, n, kd, nrhs, ab,
ldab, b, ldb, info)
CTBTRS subroutine dtbtrs (uplo, trans, diag, n, kd, nrhs, ab,
ldab, b, ldb, info)
DTBTRS subroutine stbtrs (uplo, trans, diag, n, kd, nrhs, ab,
ldab, b, ldb, info)
STBTRS subroutine ztbtrs (uplo, trans, diag, n, kd, nrhs, ab,
ldab, b, ldb, info)
ZTBTRS
CTBTRS
Purpose:
CTBTRS solves a triangular system of the form
A * X = B, A**T * X = B, or A**H * X = B,
where A is a triangular band matrix of order N, and B is an
N-by-NRHS matrix. A check is made to verify that A is nonsingular.
Parameters
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS
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)
DIAG
DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N
N is INTEGER
The order of the matrix A. N >= 0.
KD
KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 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)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of AB. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B
B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, 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
> 0: if INFO = i, the i-th diagonal element of A is zero,
indicating that the matrix is singular and the
solutions X have not been computed.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
DTBTRS
Purpose:
DTBTRS solves a triangular system of the form
A * X = B or A**T * X = B,
where A is a triangular band matrix of order N, and B is an
N-by NRHS matrix. A check is made to verify that A is nonsingular.
Parameters
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS
TRANS is CHARACTER*1
Specifies the form the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
DIAG
DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N
N is INTEGER
The order of the matrix A. N >= 0.
KD
KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 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)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of AB. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, 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
> 0: if INFO = i, the i-th diagonal element of A is zero,
indicating that the matrix is singular and the
solutions X have not been computed.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
STBTRS
Purpose:
STBTRS solves a triangular system of the form
A * X = B or A**T * X = B,
where A is a triangular band matrix of order N, and B is an
N-by NRHS matrix. A check is made to verify that A is nonsingular.
Parameters
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS
TRANS is CHARACTER*1
Specifies the form the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
DIAG
DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N
N is INTEGER
The order of the matrix A. N >= 0.
KD
KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 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)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of AB. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B
B is REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, 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
> 0: if INFO = i, the i-th diagonal element of A is zero,
indicating that the matrix is singular and the
solutions X have not been computed.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
ZTBTRS
Purpose:
ZTBTRS solves a triangular system of the form
A * X = B, A**T * X = B, or A**H * X = B,
where A is a triangular band matrix of order N, and B is an
N-by-NRHS matrix. A check is made to verify that A is nonsingular.
Parameters
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS
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)
DIAG
DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N
N is INTEGER
The order of the matrix A. N >= 0.
KD
KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 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)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of AB. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B
B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, 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
> 0: if INFO = i, the i-th diagonal element of A is zero,
indicating that the matrix is singular and the
solutions X have not been computed.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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| Fri Aug 9 2024 02:33:22 | Version 3.12.0 |