ZTBSV - Online Linux Manual Page

Section : 1
Updated : November 2008
Source : BLAS routine
Note : BLAS routine
NAMEZTBSV - solves one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b,
SYNOPSISSUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)    INTEGER INCX,K,LDA,N  CHARACTER DIAG,TRANS,UPLO  DOUBLE COMPLEX A(LDA,*),X(*)
PURPOSEZTBSV 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.
No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.
ARGUMENTSUPLO - 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' conjg( 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 - COMPLEX*16 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 - COMPLEX*16 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.
FURTHER DETAILSLevel 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.
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