DTBMV(3)

✨ NAME ✨

okay so this page is DTBMV(3) from the Library Functions Manual, and the header path is /home/abui...SRC/dtbmv.f(3). The NAME line points at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/BLAS/SRC/dtbmv.f. It’s giving BLAS realness, no cap 💅.

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✨ SYNOPSIS ✨

Functions/Subroutines 🧚

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

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✨ Function/Subroutine Documentation ✨

subroutine DTBMV (character uplo, character trans, character diag, integer
    n, integer k, double precision, dimension(lda,*) a, integer lda, double
    precision, dimension(*) x, integer incx)
    DTBMV

Purpose 🎀

DTBMV performs one of the matrix-vector operations:

x := A*x,   or   x := A**T*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. literally the whole vibe of this routine 🔥.

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**T*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 DOUBLE PRECISION 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 DOUBLE PRECISION 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. bestie do not do it 😭

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 dtbmv.f.

Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

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