CTBMV(3)

💅 CTBMV(3) — the iconic band triangular matvec page 💅

okay bestie, welcome to the CTBMV page from the Library Functions Manual 💖 it lives at /home/abui...SRC/ctbmv.f(3), and we are about to make banded triangular matrix-vector tea together. no cap.

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

Functions/Subroutines

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

📚 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

🦋 Purpose 🦋

okay so 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. periodt.

🌈 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 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 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.
• 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 of file ctbmv.f. 🧭

Definition at line 185 of file ctbmv.f.

🤖 Author 🤖

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k bye bestie 💖 this page is from LAPACK, Version 3.12.0, and it lives at /home/abui...SRC/ctbmv.f(3) ✨🫶