CGBMV(3)

📦 version 3.12.0, in opensuse-leap 16.0

🎀 NAME 🎀

Bestie, this page is literally about this file:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/BLAS/SRC/cgbmv.f

Also, up top vibes: this is the CGBMV(3) page from the Library Functions Manual, and the page path is /home/abui...SRC/cgbmv.f(3). Slay.

✨ SYNOPSIS ✨

💫 Functions/Subroutines 💫

subroutine CGBMV (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y,
    incy)

CGBMV

🦋 Function/Subroutine Documentation 🦋

Here's the whole signature, no cap:

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

🎯 Purpose 🎯

Okay so CGBMV performs one of these 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. Iconic band-matrix behavior, honestly.

💜 Parameters 💜

💖 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.

🌸 M 🌸

M is INTEGER.

On entry, M specifies the number of rows of the matrix A. M must be at least zero.

🦋 N 🦋

N is INTEGER.

On entry, N specifies the number of columns of the matrix A. N must be at least zero.

🎀 KL 🎀

KL is INTEGER.

On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL.

⭐ KU ⭐

KU is INTEGER.

On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU.

🍓 ALPHA 🍓

ALPHA is COMPLEX.

On entry, ALPHA specifies the scalar alpha.

🧚 A 🧚

A is COMPLEX array, 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

🌈 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 ).

🫶 X 🫶

X is COMPLEX array, 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.

💅 INCX 💅

INCX is INTEGER.

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

🔥 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.

👑 Y 👑

Y is COMPLEX array, 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.

If either m or n is zero, then Y not referenced and the function performs a quick return.

🌟 INCY 🌟

INCY is INTEGER.

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

🌸 Author 🌸

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

✨ Further Details ✨

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 188 of file cgbmv.f.

🌸 Author 🌸

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