C Library Functions - stbsv (3)

NAME

stbsv(3f) - [BLAS:SINGLE_BLAS_LEVEL2] SX:=INVERSE(A)*SX, A a triangular band matrix.

Synopsis
Definition
Options
X
Authors
Further Details
See Also

SYNOPSIS

subroutine stbsv(uplo,trans,diag,n,k,a,lda,x,incx)

      .. Scalar Arguments ..
      integer,intent(in)   :: incx,k,lda,n
      character,intent(in) :: diag,trans,uplo
      ..
      .. Array Arguments ..
      real,intent(in)      :: a(lda,*)
      real,intent(inout)   :: x(*)
      ..

DEFINITION

STBSV solves one of the systems of equations
    A*x = b,   or   A**T*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.

OPTIONS

UPLO

UPLO is CHARACTER*1 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.

TRANS

TRANS is CHARACTER*1 On entry, TRANS specifies the equations to be solved as follows:

              TRANS = ’N’ or ’n’   A*x = b.

              TRANS = ’T’ or ’t’   A**T*x = b.

              TRANS = ’C’ or ’c’   A**T*x = b.

DIAG

DIAG is CHARACTER*1 On entry, DIAG specifies whether or not 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.

N

N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero.

K

K is INTEGER On entry with UPLO = ’U’ or ’u’, K specifies the number of super-diagonals of the matrix A. On entry with UPLO = ’L’ or ’l’, K specifies the number of sub-diagonals of the matrix A. K must satisfy 0 .le. K.

A

A is REAL array, dimension ( LDA, N ) Before 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 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 = ’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 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 = ’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.

LDA

LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ).

X

X is REAL array, 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.

INCX

INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.

AUTHORS

o Univ. of Tennessee

o Univ. of California Berkeley

o Univ. of Colorado Denver

o NAG Ltd.
 date:December 2016

FURTHER DETAILS

Level 2 Blas routine.
-- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.