Product of a Triangular Matrix in Banded Storage and a Vector

Calling Sequence

CALL DTBMV	(UPLO, TRANSA, DIAG, N, NDIAG, DA, LDA, DY, INCY)
CALL STBMV	(UPLO, TRANSA, DIAG, N, NDIAG, SA, LDA, SY, INCY)
CALL ZTBMV	(UPLO, TRANSA, DIAG, N, NDIAG, ZA, LDA, ZY, INCY)
CALL CTBMV	(UPLO, TRANSA, DIAG, N, NDIAG, CA, LDA, CY, INCY)
void dtbmv	(char uplo, char trans, char diag, int n, int ndiag, double *da, int lda, double *dx, int incx)
void stbmv	(char uplo, char trans, char diag, int n, int ndiag, float *sa, int lda, float *sx, int incx)
void ztbmv	(char uplo, char trans, char diag, int n, int ndiag, doublecomplex *za, int lda, doublecomplex *zx, int incx)
void ctbmv	(char uplo, char trans, char diag, int n, int ndiag, complex *ca, int lda, complex *cx, int incx)

Arguments

UPLO	Indicates whether the values in a matrix reside in the upper or lower triangle of the array in which the matrix is stored. The legal values for UPLO are listed below. Any value not listed below is illegal.
	'L' or 'l'	Only the lower triangle of the array will be referenced.
	'U' or 'u'	Only the upper triangle of the array will be referenced.
TRANSA	Indicates how to use the matrix stored in the array argument. The legal values for TRANSA are listed below. Any value not listed below is illegal.
	'N' or 'n'	Use the matrix as it is stored in the array.
	'T' or 't'	Use the transpose of the matrix.
	'C' or 'c'	Use the conjugate transpose of the matrix.
DIAG	Indicates whether or not a triangular matrix is unit triangular. If the matrix is unit triangular then none of the diagonal elements of the array will be accessed. The legal values for DIAG are listed below. Any value not listed below is illegal.
	'N' or 'n'	The matrix is not unit triangular.
	'U' or 'u'	The matrix is unit triangular.
N	Size of a matrix with N rows and N columns. N 0.
NDIAG	Bandwidth of a matrix with NDIAG superdiagonals or subdiagonals. N-1 NDIAG 0 but if N = 0 then NDIAG = 0.
xA	Two-dimensional array that contains the input matrix.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA NDIAG + 1.
xY	Y and INCY describe a vector of length N.
	On entry, an input vector.
	On exit, a result vector.
INCY	Scalar that contains the storage spacing between successive elements of the vector Y. INCY 0.
	If INCY is one then elements of the vector are contiguous in memory. INCY may take on values besides 1 to allow the programmer to extract from a matrix a vector that is not stored in contiguous memory locations.
	If Y is a one-dimensional array and INCY = -1 then the array will be accessed in reverse order.
	If Y is a two-dimensional array and INCY = LDA then the vector will be a row of the array.
	If Y is a two-dimensional array and INCY = LDA+1 then the vector will be a diagonal of the array.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, N, NDIAG

PARAMETER (N = 4)

PARAMETER (NDIAG = 2)

PARAMETER (LDA = NDIAG + 1)

C

DOUBLE PRECISION A(LDA,N), X(N)

INTEGER I, J

C

EXTERNAL DTBMV

INTRINSIC DBLE

C

C Initialize the array A to store in triangular banded form

C the matrix A shown below. Initialize the array X to store

C the vector x shown below.

C

C 1 4

C A = 2 4 x = 3

C 3 5 7 2

C 6 8 9 1

C

DATA A /1.0D0, 2.0D0, 3.0D0, 4.0D0, 5.0D0, 6.0D0,

$ 7.0D0, 8.0D0, 8.8D8, 9.0D0, 8.8D8, 8.8D8 /

C

DO 10, I = 1, N

X(I) = DBLE (5 - I)

10 CONTINUE

PRINT 1000

PRINT 1010, A(1,1)

PRINT 1010, A(2,1), A(1,2)

PRINT 1010, A(3,1), A(2,2), A(1,3)

PRINT 1020, A(3,2), A(2,3), A(1,4)

PRINT 1030

DO 20, I = 1, LDA

PRINT 1010, (A(I,J), J = 1, N)

20 CONTINUE

PRINT 1040

PRINT 1050, X

CALL DTBMV ('LOWER TRIANGULAR A', 'NOT TRANSPOSED A',

$ 'NOT UNIT DIAGONAL A', N, NDIAG, A, LDA, X, 1)

PRINT 1060

PRINT 1050, X

C

1000 FORMAT (1X, 'A in full form:')

1010 FORMAT (1X, 4(2X, F5.1))

1020 FORMAT (1X, 7X, 3(2X, F5.1))

1030 FORMAT (/1X, 'A in banded form: (* in unused elements)')

1040 FORMAT (/1X, 'Original x vector:')

1050 FORMAT (1X, 2X, F5.1)

1060 FORMAT (/1X, 'Ax:')

C

END

Sample Output

A in full form:
1.0
2.0 4.0
3.0 5.0 7.0
6.0 8.0 9.0
A in banded form: (* in unused elements)
1.0 4.0 7.0 9.0
2.0 5.0 8.0 *****
3.0 6.0 ***** *****
Original x vector:
4.0
3.0
2.0
1.0
Ax:
4.0
20.0
41.0
43.0