
ctbsv.f(3) LAPACK ctbsv.f(3)
NAME
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
nonunit, upper or lower triangular band matrix, with ( k + 1 )
diagonals.
No test for singularity or nearsingularity is included in this
routine. Such tests must be performed before calling this routine.
Parameters:
UPLO
UPLO is CHARACTER*1
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
TRANS is CHARACTER*1
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
DIAG is CHARACTER*1
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
N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
K
K is INTEGER
On entry with UPLO = 'U' or 'u', K specifies the number of
superdiagonals of the matrix A.
On entry with UPLO = 'L' or 'l', K specifies the number of
subdiagonals of the matrix A.
K must satisfy 0 .le. K.
A
A is COMPLEX array of DIMENSION ( LDA, n ).
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 superdiagonal 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 subdiagonal 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
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
( k + 1 ).
X
X is COMPLEX array of dimension at least
( 1 + ( n  1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element righthand side vector b. On exit, X is overwritten
with the solution vector x.
INCX
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 22October1986.
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.
Author
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Version 3.4.2 Tue Sep 25 2012 ctbsv.f(3) 
