.TH STBSV 1 "November 2008" "BLAS routine" "BLAS routine" .SH NAME STBSV - solves one of the systems of equations A*x = b, or A\(aq*x = b, .SH SYNOPSIS .TP 51 SUBROUTINE STBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) .TP 51 .ti +4 INTEGER INCX,K,LDA,N .TP 51 .ti +4 CHARACTER DIAG,TRANS,UPLO .TP 51 .ti +4 REAL A(LDA,*),X(*) .SH PURPOSE STBSV solves one of the systems of equations 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. .br No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. .SH ARGUMENTS .TP 7 UPLO - CHARACTER*1. On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = \(aqU\(aq or \(aqu\(aq A is an upper triangular matrix. UPLO = \(aqL\(aq or \(aql\(aq A is a lower triangular matrix. Unchanged on exit. .TP 7 TRANS - CHARACTER*1. On entry, TRANS specifies the equations to be solved as follows: TRANS = \(aqN\(aq or \(aqn\(aq A*x = b. TRANS = \(aqT\(aq or \(aqt\(aq A\(aq*x = b. TRANS = \(aqC\(aq or \(aqc\(aq A\(aq*x = b. Unchanged on exit. .TP 7 DIAG - CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = \(aqU\(aq or \(aqu\(aq A is assumed to be unit triangular. DIAG = \(aqN\(aq or \(aqn\(aq A is not assumed to be unit triangular. Unchanged on exit. .TP 7 N - INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. .TP 7 K - INTEGER. On entry with UPLO = \(aqU\(aq or \(aqu\(aq, K specifies the number of super-diagonals of the matrix A. On entry with UPLO = \(aqL\(aq or \(aql\(aq, K specifies the number of sub-diagonals of the matrix A. K must satisfy 0 .le. K. Unchanged on exit. .TP 7 A - REAL array of DIMENSION ( LDA, n ). Before entry with UPLO = \(aqU\(aq or \(aqu\(aq, 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 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 CONTINUE 20 CONTINUE Before entry with UPLO = \(aqL\(aq or \(aql\(aq, 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 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 CONTINUE 20 CONTINUE Note that when DIAG = \(aqU\(aq or \(aqu\(aq 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. .TP 7 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. .TP 7 X - REAL 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 overwritten with the solution vector x. .TP 7 INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. .SH FURTHER DETAILS Level 2 Blas routine. .br -- Written on 22-October-1986. .br Jack Dongarra, Argonne National Lab. .br Jeremy Du Croz, Nag Central Office. .br Sven Hammarling, Nag Central Office. .br Richard Hanson, Sandia National Labs. .br