ctbsv.f (3) Linux Manual Page
ctbsv.f –
Synopsis
Functions/Subroutines
subroutine ctbsv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)CTBSV
Function/Subroutine Documentation
subroutine ctbsv (characterUPLO, characterTRANS, characterDIAG, integerN, integerK, complex, dimension(lda,*)A, integerLDA, complex, dimension(*)X, integerINCX)
CTBSV Purpose:CTBSV solves one of the systems of equations
A*x = b, or A**T*x = b, or A**H*x = b,
where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular band matrix, with ( k + 1 )
diagonals.
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
Parameters:
- UPLO
UPLO is CHARACTER*1
TRANS
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = ‘U’ or ‘u’ A is an upper triangular matrix.
UPLO = ‘L’ or ‘l’ A is a lower triangular matrix.TRANS is CHARACTER*1
DIAG
On entry, TRANS specifies the equations to be solved as
follows:
TRANS = ‘N’ or ‘n’ A*x = b.
TRANS = ‘T’ or ‘t’ A**T*x = b.
TRANS = ‘C’ or ‘c’ A**H*x = b.DIAG is CHARACTER*1
N
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = ‘U’ or ‘u’ A is assumed to be unit triangular.
DIAG = ‘N’ or ‘n’ A is not assumed to be unit
triangular.N is INTEGER
K
On entry, N specifies the order of the matrix A.
N must be at least zero.K is INTEGER
A
On entry with UPLO = ‘U’ or ‘u’, K specifies the number of
super-diagonals of the matrix A.
On entry with UPLO = ‘L’ or ‘l’, K specifies the number of
sub-diagonals of the matrix A.
K must satisfy 0 .le. K.A is COMPLEX array of DIMENSION ( LDA, n ).
LDA
Before entry with UPLO = ‘U’ or ‘u’, the leading ( k + 1 )
by n part of the array A must contain the upper triangular
band part of the matrix of coefficients, supplied column by
column, with the leading diagonal of the matrix in row
( k + 1 ) of the array, the first super-diagonal starting at
position 2 in row k, and so on. The top left k by k triangle
of the array A is not referenced.
The following program segment will transfer an upper
triangular band matrix from conventional full matrix storage
to band storage:
DO 20, J = 1, N
M = K + 1 – J
DO 10, I = MAX( 1, J – K ), J
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
Before entry with UPLO = ‘L’ or ‘l’, the leading ( k + 1 )
by n part of the array A must contain the lower triangular
band part of the matrix of coefficients, supplied column by
column, with the leading diagonal of the matrix in row 1 of
the array, the first sub-diagonal starting at position 1 in
row 2, and so on. The bottom right k by k triangle of the
array A is not referenced.
The following program segment will transfer a lower
triangular band matrix from conventional full matrix storage
to band storage:
DO 20, J = 1, N
M = 1 – J
DO 10, I = J, MIN( N, J + K )
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
Note that when DIAG = ‘U’ or ‘u’ the elements of the array A
corresponding to the diagonal elements of the matrix are not
referenced, but are assumed to be unity.LDA is INTEGER
X
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
( k + 1 ).X is COMPLEX array of dimension at least
INCX
( 1 + ( n – 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element right-hand side vector b. On exit, X is overwritten
with the solution vector x.INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Author:
- Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
- November 2011
Further Details:
Level 2 Blas routine.
— Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Definition at line 190 of file ctbsv.f.