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

Item Description
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.