TESTING/LIN/csbmv.f(3)

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✨ NAME ✨

TESTING/LIN/csbmv.f

🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines

  • subroutine csbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy) — CSBMV

🦋 Function/Subroutine Documentation 🦋

subroutine csbmv (character uplo, integer n, integer k, complex alpha, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integer incx, complex beta, complex, dimension( * ) y, integer incy)

CSBMV

🎯 Purpose 🎯

CSBMV performs the matrix-vector operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric band matrix, with k super-diagonals.

🧡 UPLO — CHARACTER*1

On entry, UPLO specifies whether the upper or lower triangular part of the band matrix A is being supplied as follows:

  • UPLO = 'U' or 'u' — the upper triangular part of A is being supplied.
  • UPLO = 'L' or 'l' — the lower triangular part of A is being supplied.

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, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K.

Unchanged on exit.

💙 ALPHA — COMPLEX

On entry, ALPHA specifies the scalar alpha.

Unchanged on exit.

💜 A — COMPLEX array, 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 symmetric matrix, 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 the upper triangular part of a symmetric 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 symmetric matrix, 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 the lower triangular part of a symmetric 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

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 array, dimension at least ( 1 + ( N - 1 )*abs( INCX ) )

Before entry, the incremented array X must contain the vector x.

Unchanged on exit.

💖 INCX — INTEGER

On entry, INCX specifies the increment for the elements of X. INCX must not be zero.

Unchanged on exit.

💗 BETA — COMPLEX

On entry, BETA specifies the scalar beta.

Unchanged on exit.

💓 Y — COMPLEX array, dimension at least ( 1 + ( N - 1 )*abs( INCY ) )

Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.

💞 INCY — INTEGER

On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.

Unchanged on exit.

💖 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🧚 Definition at line 150 of file csbmv.f.

👑 Author 👑

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