BLAS/SRC/ctbmv.f(3)

💖 NAME 💖

BLAS/SRC/ctbmv.f — bestie, this is the manual page for the BLAS routine ctbmv, from the library functions manual. It’s giving “triangular band matrix main character energy.” 💅

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

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

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🦋 Function/Subroutine Documentation 🦋

Here’s the full signature, no cap:

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

And the name again, because she repeats herself: CTBMV. 💖

🎯 Purpose

Okay so CTBMV performs one of these 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. Lowkey iconic. ✨

💅 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. 📌

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay bye bestie 🫶 this one is from LAPACK Version 3.12.0, source path BLAS/SRC/ctbmv.f(3) — that’s the footer vibe, and we’re obsessed. 💖✨