DTBSV(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 DTBSV(3) — Library Functions Manual 💖

Okay so bestie, this is the Library Functions Manual page for DTBSV(3). The file it’s repping is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/BLAS/SRC/dtbsv.f. That’s the whole NAME vibe. 💅

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

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

🛠️ Function/Subroutine Documentation 🛠️

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

✨ Purpose ✨

DTBSV solves one of these systems of equations, and yes it’s giving main-character linear algebra energy:
A*x = b,   or   A**T*x = b,

where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.

⚠️ No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. So like, do your vibe check first, bestie — this routine is not doing it for you.

🎀 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 equations to be solved as follows:
    • TRANS = 'N' or 'n' → A*x = b.
    • TRANS = 'T' or 't' → A**T*x = b.
    • TRANS = 'C' or 'c' → A**T*x = b.
  • 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. Iconic shortcut behavior, honestly.

  • 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 right-hand side vector b. On exit, X is overwritten with the solution 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.

-- 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 188 of file dtbsv.f.

💜 Author 💜 — Doxygen edition

Generated automatically by Doxygen for LAPACK from the source code.

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