NAME
ZTBSV - solve one of the systems of equations A*x = b, or A’*x = b,
or conjg( A’ )*x = b,
SYNOPSIS
SUBROUTINE ZTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
INTEGER INCX, K, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
COMPLEX*16 A( LDA, * ), X( * )
PURPOSE
ZTBSV 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’ conjg( A’ )*x = b.
Unchanged on exit.
DIAG - 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.
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 number of sub-diagonals of the matrix A. K
must satisfy 0 .le. K. Unchanged on exit.
A - COMPLEX*16 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 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. 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 - COMPLEX*16 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 elements 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.