DTBSV - solve one of the systems of equations A*x = b,
or A'*x = b,
SYNOPSIS
SUBROUTINE DTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X,
INCX )
INTEGER INCX, K, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
DOUBLE PRECISION A( LDA, * ), X( * )
PURPOSE
DTBSV solves one of the systems of equations
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 - 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.
Unchanged on exit.
TRANS - 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'*x = b.
TRANS = 'C' or 'c' A'*x = b.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
gular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A. N
must be at least zero. Unchanged on exit.
K - INTEGER.
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 num
ber of sub-diagonals of the matrix A. K must sat
isfy 0 .le. K. Unchanged on exit.
A - DOUBLE PRECISION 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 coeffi
cients, supplied column by column, with the leading
diagonal of the matrix in row ( k + 1 ) of the
array, the first super-diagonal starting at posi
tion 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 CON
TINUE 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 coeffi
cients, 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
to be unity. Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as
declared in the calling (sub) program. LDA must be
at least ( k + 1 ). Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 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 - INTEGER.
On entry, INCX specifies the increment for the ele
ments of X. INCX must not be zero. Unchanged on
exit.
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.
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