/home/abui...IN/zsbmv.f(3)

NAME

Bestie, the name on this one is literally the full path: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zsbmv.f. Also this page is zsbmv.f(3), from the Library Functions Manual, so you know exactly where you are. 💅

SYNOPSIS

Functions/Subroutines

Okay so the subroutine is ZSBMV, and the short version is right here:

   subroutine ZSBMV (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
       ZSBMV

And yes, ZSBMV is the whole name, no cap. ✨

Function/Subroutine Documentation

Here’s the full signature, character-for-character, because we do not play about exact types:

   subroutine ZSBMV (character uplo, integer n, integer k, complex*16 alpha,
       complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( *
       ) x, integer incx, complex*16 beta, complex*16, dimension( * ) y,
       integer incy)
       ZSBMV

Purpose: ✨

Okay so the tea is: ZSBMV 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. The source comment is wrapped in !> Doxygen tags, but the math is giving exactly that. 🫶

Arguments: the whole cast 💖

• 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*16. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. 🎀
• A — COMPLEX*16 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*16 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*16. On entry, BETA specifies the scalar beta. Unchanged on exit. 💜
• Y — COMPLEX*16 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 zsbmv.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that’s the whole glow-up. This page is from LAPACK Version 3.12.0, and the footer path is literally /home/abui...IN/zsbmv.f(3). The footer has no date listed, but the version and path are right there, periodt. 💖✨🎀