BLAS/SRC/ztbmv.f(3)

💖 BLAS/SRC/ztbmv.f(3) — bestie edition 💖

okay so this is a page from the LAPACK manual, and today we're talking about BLAS/SRC/ztbmv.f. it's giving level 2 BLAS, it's giving triangular band matrix realness. buckle up 🎀

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✨ NAME ✨

BLAS/SRC/ztbmv.f — like, that's the whole name, she's lowkey mysterious like that 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine ztbmv (uplo, trans, diag, n, k, a, lda, x, incx) — ZTBMV 🦋

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🫶 Function/Subroutine Documentation 🫶

subroutine ztbmv (character uplo, character trans, character diag, integer n, integer k, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx)

ZTBMV

🎯 Purpose:

no cap, ZTBMV performs one of the matrix-vector operations

x := A*x,   or   x := A**T*x,   or   x := A**H*x,

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals. periodt. 💅

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🧚 Parameters

• UPLO

UPLO is CHARACTER*1. On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows:

• UPLO = 'U' or 'u' → A is an upper triangular matrix. 👑
• UPLO = 'L' or 'l' → A is a lower triangular matrix. 🦋

• TRANS

TRANS is CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows:

• TRANS = 'N' or 'n' → x := A*x.
• TRANS = 'T' or 't' → x := A**T*x.
• TRANS = 'C' or 'c' → x := A**H*x.

• DIAG

DIAG is CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular as follows:

• DIAG = 'U' or 'u' → A is assumed to be unit triangular.
• DIAG = 'N' or 'n' → A is not assumed to be unit triangular.

• N

N is INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.

• K

K is INTEGER. On entry with UPLO = 'U' or 'u', K specifies the number of super-diagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of sub-diagonals of the matrix A. K must satisfy 0 .le. K.

• A

A is 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 matrix of coefficients, 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 an upper triangular 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 matrix of coefficients, 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 a lower triangular 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

Note that when DIAG = 'U' or 'u' the elements of the array A corresponding to the diagonal elements of the matrix are not referenced, but are assumed to be unity. 👀

• 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 ( k + 1 ).

• X

X is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the transformed vector x. slay, she's changed 💅

• INCX

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

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👑 Author

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

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⭐ 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.

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Definition at line 185 of file ztbmv.f. 🦋

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🌈 Author

Generated automatically by Doxygen for LAPACK from the source code. (yes bestie, even the docs are ✨automated✨, iykyk)

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and that's the whole page, no notes 💖

okay so final sign-off, the boring-but-important bits: this is Version 3.12.0, dated Tue Nov 28 2023 12:08:41, and it lives at BLAS/SRC/ztbmv.f(3). mwah, go call ztbmv responsibly 🎀✨💜