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Technical Reference: Base Operating System and Extensions, Volume 2
STBMV, DTBMV, CTBMV, or ZTBMV Subroutine
Purpose
Performs matrix-vector operations using a triangular band matrix.
Library
BLAS Library (libblas.a)
FORTRAN Syntax
SUBROUTINE STBMV(UPLO, TRANS, DIAG, N,
K, A, LDA, X, INCX)
INTEGER INCX, K, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
REAL A(LDA,*), X(*)
SUBROUTINE DTBMV(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 CTBMV(UPLO, TRANS, DIAG, N,
K, A, LDA, X, INCX)
INTEGER INCX,K,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
COMPLEX A(LDA,*), X(*)
SUBROUTINE ZTBMV(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 STBMV, DTBMV, CTBMV, or ZTBMV subroutine performs one of the matrix-vector operations:
x := A * x
OR
x := A' * x
where x is an N element vector and A is an N by N unit, or non-unit, upper or lower triangular band matrix, with ( K + 1 ) diagonals.
Parameters
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 operation to be performed as follows:
- TRANS = 'N' or 'n'
- x := A * x
- TRANS = 'T' or 't'
- x := A' * x
- TRANS = 'C' or 'c'
- x := A' * x
Unchanged on exit. |
DIAG |
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 |
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 |
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
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:
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 vector x; on exit, X is overwritten with the transformed vector x. |
INCX |
On entry, INCX specifies the increment for the elements of X; INCX must not be 0; unchanged on exit. |
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