STBSV(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 STBSV(3) — or, "how to solve a triangular band system and feel iconic doing it"

okay so real talk, this page lives in the Library Functions Manual, the file is /home/abui...SRC/stbsv.f(3), and bestie… it's a whole BLAS moment. buckle up 🎀

✨ NAME ✨

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

like, yes, the NAME section is literally just the source path. she's mysterious. she's a .f file. we respect her 🫶

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine STBSV (uplo, trans, diag, n, k, a, lda, x, incx) — STBSV 💫

👑 Function/Subroutine Documentation 👑

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

STBSV. that's her name, that's her whole thing 💜

🦋 Purpose 🦋

STBSV solves one of the systems of equations 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. slay 💅

🚨 lowkey important warning bestie: no test for singularity or near-singularity is included in this routine. such tests must be performed before calling this routine. like, she will NOT check for you. she trusts you. do your vibes check first, fr fr.

🍓 Parameters 🍓

  • 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 — 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 — 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 — is INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
  • 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 — is REAL 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. she said "diagonal? never met her." 🙈
  • 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 — is REAL 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. she ate and left no crumbs 💀
  • INCX — is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. like literally do not. 🔥

💖 Author 💖

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

the whole squad, no cap 👑

⭐ 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.

1986!! the vintage of it all. main character energy since before we were born 🧚✨

🌈 Definition 🌈

Definition at line 188 of file stbsv.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code. (not a girlboss, just a doc generator, but she did her best 🫶)

and that's the page!! LAPACK, Version 3.12.0, living at /home/abui...SRC/stbsv.f(3) — mwah, bye bestie, go solve some triangular band systems 💜💅✨

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