BLAS/SRC/ctbmv.f(3)

💖 CTBMV 💖 (that's BLAS/SRC/ctbmv.f, bestie)

okay so like. you're in the LAPACK/BLAS corner of the internet, and you found BLAS/SRC/ctbmv.f — the manual page for one (1) very specific, very iconic Level 2 BLAS routine. sit down, hydrate, let's get into it 🫶

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✨ NAME ✨

BLAS/SRC/ctbmv.f — no cap, that's the whole name, she's just a file path and she owns it 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine ctbmv (uplo, trans, diag, n, k, a, lda, x, incx) — CTBMV

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🦋 Function/Subroutine Documentation 🦋

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

CTBMV. that's her. that's the whole vibe. 🎀

🎯 Purpose:

CTBMV 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. ✨

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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. (so like, zero is fine, negative is a no 🙅‍♀️)

• 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 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

bestie listen: 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. so don't stress about filling them in, she's not even looking 👀

• 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 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. she gets replaced, that's just how it is 😭✨

• INCX

INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. seriously. do not. 💀

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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.

Definition at line 185 of file ctbmv.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole page, you ate that 🍓 she's giving deeply specific numerical linear algebra and honestly? main character energy.

Version 3.12.0 · Tue Nov 28 2023 12:08:41 · BLAS/SRC/ctbmv.f(3)

k bye bestie, go multiply something 💖✨🎀🦋🌸💅🫶👑🌈⭐🧚