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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( * )
#include <sunperf.h>
void ztbsv(char uplo, char trans, char diag, int n, int k,
doublecomplex *za, int lda, doublecomplex *zx, int
incx) ;
PURPOSE
ZTBSV solves one of the systems of equations A*x = b, or
A'*x = b, or conjg( A' )*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 - 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 tri-
angular.
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 coef-
ficients, 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 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 coef-
ficients, 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 CON-
TINUE 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 overwrit-
ten 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.
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