NAME

stbsv - solve one of the systems of equations A∗x = b, or A’∗x = b

SYNOPSIS

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( ∗ )

#include <sunperf.h>

void stbsv(char uplo, char trans, char diag, int n, int k, float ∗sa, int lda, float ∗sx, int incx) ;

PURPOSE

STBSV  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 - 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.
 
Unchanged on exit.

TRANS - 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’∗x = b.
 
TRANS = ’C’ or ’c’   A’∗x = b.
 
Unchanged on exit.

DIAG - 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.
 
Unchanged on exit.

N - INTEGER. 
On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.

K - 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. Unchanged on exit.

A - REAL             array of 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. Unchanged on exit.

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.

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.

INCX - INTEGER. 
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.

SunOS WorkShop_5.0  —  Last change: 10 Dec 1998