BLAS/SRC/ztbmv.f(3)

📦
version 3.12.1 · 4 versions
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okay bestie, you're reading the BLAS/SRC/ztbmv.f(3) page from the Library Functions Manual — and yes, we're about to make triangular band matrix-vector operations make sense. 💅✨

🌸 NAME 🌸

BLAS/SRC/ztbmv.f

that's the NAME section, short and iconic — it's the BLAS source file for ztbmv. 💖

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

🫶 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 🌟

okay so ZTBMV performs one of these matrix-vector operations, and it's giving math-girlie main character energy:

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. no cap, that's the whole vibe. 🦋

🎀 Parameters 🎀

💜 UPLO

UPLO is CHARACTER*1.

On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix, like this:

  • 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, bestie:

  • 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. periodt. 💅

💜 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. 🔥

💜 INCX

INCX is INTEGER.

On entry, INCX specifies the increment for the elements of X. INCX 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 185 🦋

Definition at line 185 of file ztbmv.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

that's the whole page, bestie — brought to you by LAPACK Version 3.12.0 and the source file BLAS/SRC/ztbmv.f(3). go forth and slay those triangular band operations! 💖✨🎀

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