BLAS/SRC/ctbsv.f(3)

💖 BLAS/SRC/ctbsv.f 💖

okay bestie, this is the ctbsv page from the LAPACK manual (that's the manual name, love that for us) — it lives at BLAS/SRC/ctbsv.f. it's a Level 2 BLAS routine and it's honestly so real for what it does. let's get into it 🫶

---

✨ NAME ✨

BLAS/SRC/ctbsv.f — no cap, that's literally the name, the file is the name, we love a minimalist icon 💅

---

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine ctbsv (uplo, trans, diag, n, k, a, lda, x, incx) — this is CTBSV, the moment, the legend 👑

---

🦋 Function/Subroutine Documentation 🦋

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

CTBSV — say it with me. iconic.

🎀 Purpose 🎀

so CTBSV solves one of these systems of equations, pick your fighter:

A*x = b,   or   A**T*x = b,   or   A**H*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. she's a band matrix, she's triangular, she's booked and busy 💖

⚠️ real talk bestie, this part is important: there is NO test for singularity or near-singularity included in this routine. none. zero. not a vibe check to be found. such tests must be performed before calling this routine. so do your homework first, okay? 🙈

🧚 Parameters 🧚

• UPLO — UPLO is CHARACTER*1. on entry, UPLO specifies whether the matrix is an upper or lower triangular matrix, like this:
  • 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 which equations we're solving, as follows:
  • TRANS = 'N' or 'n' — A*x = b.
  • TRANS = 'T' or 't' — A**T*x = b.
  • TRANS = 'C' or 'c' — A**H*x = b.
• DIAG — DIAG is CHARACTER*1. on entry, DIAG specifies whether or not A is unit triangular, like this:
  • 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. (yes bestie, zero is allowed, we respect the boundary 🫶)
• 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. so like, they're there but we're not looking at them, minding our business 💅

• 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 right-hand side vector b. on exit, X is overwritten with the solution vector x. she gets a glow-up mid-call, obsessed ✨
• INCX — INCX is INTEGER. on entry, INCX specifies the increment for the elements of X. INCX must not be zero. seriously. not zero. 🚫

👑 Author 👑

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

the whole squad showed up, periodt 💜

🌈 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?? they were doing this before most of us were even a thought and it still slaps. main character energy fr fr 🔥

📍 Definition 📍

Definition at line 188 of file ctbsv.f.

---

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code. (not me writing this by hand, the machine did it, but I gave it the sparkle ✨)

---

and that's the whole page bestie, you ate it up 🍓

cute lil sign-off: this was Version 3.12.0, dated Tue Nov 28 2023 12:08:41, from BLAS/SRC/ctbsv.f(3). love you, bye 💖🎀🦋