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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine cgbmv | ( | character | TRANS, |
integer | M, | ||
integer | N, | ||
integer | KL, | ||
integer | KU, | ||
complex | ALPHA, | ||
complex, dimension(lda,*) | A, | ||
integer | LDA, | ||
complex, dimension(*) | X, | ||
integer | INCX, | ||
complex | BETA, | ||
complex, dimension(*) | Y, | ||
integer | INCY | ||
) |
CGBMV
CGBMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or y := alpha*A**H*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals.
[in] | TRANS | TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. |
[in] | M | M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. |
[in] | N | N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. |
[in] | KL | KL is INTEGER On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. |
[in] | KU | KU is INTEGER On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU. |
[in] | ALPHA | ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha. |
[in] | A | A is COMPLEX array of DIMENSION ( LDA, n ). Before entry, the leading ( kl + ku + 1 ) by n part of the array A must contain the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( ku + 1 ) of the array, the first super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer a band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) A( K + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE |
[in] | 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 ( kl + ku + 1 ). |
[in] | X | X is COMPLEX array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
[in] | BETA | BETA is COMPLEX On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. |
[in,out] | Y | Y is COMPLEX array of DIMENSION at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. |
[in] | INCY | INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. |
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- 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.
Definition at line 189 of file cgbmv.f.