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Technical Reference: Base Operating System and Extensions , Volume 2
Solves system of
equations.
BLAS Library
(libblas.a)
SUBROUTINE STBSV(UPLO, TRANS, DIAG,
N, K, A, LDA, X, INCX)
INTEGER INCX, K, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
REAL A(LDA,*), X(*)
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(*)
SUBROUTINE CTBSV(UPLO, TRANS, DIAG,
N, K, A, LDA, X, INCX)
INTEGER INCX,K,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
COMPLEX A(LDA,*), X(*)
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(*)
The STBSV,
DTBSV, CTBSV, or ZTBSV subroutine solves one
of the systems of equations:
A * x = b
OR
A' * 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.
UPLO
 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
 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
 On entry, DIAG specifies whether 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
 On entry, N specifies the order of the matrix
A; N must be at least 0; unchanged on
exit.

K
 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; unchanged on exit.

A
 An array of dimension ( LDA, N ). On 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
On 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
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
 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
 A vector of dimension at least (1 + (N1) *
abs(INCX) ); on 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
 On entry, INCX specifies the increment for the elements of
X; INCX must not be 0; unchanged on
exit.

No test for singularity or
nearsingularity is included in this routine. Such tests must be
performed before calling this routine.
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