STBSV, DTBSV, CTBSV, or ZTBSV Subroutine

Base Operating System and Extensions Technical Reference, 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

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.

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.

On entry, N specifies the order of the matrix A; N must be at least 0; unchanged on exit.

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.

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.

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.

Implementation Specifics

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