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Technical Reference: Base Operating System and Extensions, Volume 2
STBSV, DTBSV, CTBSV, or ZTBSV Subroutine
Purpose
Solves system of equations.
Library
BLAS Library (libblas.a)
FORTRAN Syntax
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(*)
Description
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 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 |
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 + (N-1)
* abs(INCX) ); on 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 |
On entry, INCX specifies the increment for
the elements of X; INCX must
not be 0; unchanged on exit. |
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