cgbsv.f(3) LAPACK cgbsv.f(3)NAME
subroutine cgbsv (N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
CGBSV computes the solution to system of linear equations A * X =
B for GB matrices (simple driver)
subroutine cgbsv (integerN, integerKL, integerKU, integerNRHS, complex,
dimension( ldab, * )AB, integerLDAB, integer, dimension( * )IPIV,
complex, dimension( ldb, * )B, integerLDB, integerINFO)
CGBSV computes the solution to system of linear equations A * X = B
for GB matrices (simple driver)
CGBSV computes the solution to a complex system of linear equations
A * X = B, where A is a band matrix of order N with KL subdiagonals
and KU superdiagonals, and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as A = L * U, where L is a product of permutation
and unit lower triangular matrices with KL subdiagonals, and U is
upper triangular with KL+KU superdiagonals. The factored form of A
is then used to solve the system of equations A * X = B.
N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AB is COMPLEX array, dimension (LDAB,N)
On entry, the matrix A in band storage, in rows KL+1 to
2*KL+KU+1; rows 1 to KL of the array need not be set.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
On exit, details of the factorization: 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.
See below for further details.
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
IPIV is INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).
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 is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and the solution has not been computed.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
The band storage scheme is illustrated by the following example, when
M = N = 6, KL = 2, KU = 1:
On entry: On exit:
* * * + + + * * * u14 u25 u36
* * + + + + * * u13 u24 u35 u46
* a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
a31 a42 a53 a64 * * m31 m42 m53 m64 * *
Array elements marked * are not used by the routine; elements marked
+ need not be set on entry, but are required by the routine to store
elements of U because of fill-in resulting from the row interchanges.
Definition at line 163 of file cgbsv.f.
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Version 3.4.2 Tue Sep 25 2012 cgbsv.f(3)