BLAS/SRC/stbsv.f(3)

💖 BLAS/SRC/stbsv.f 💖

okay bestie, welcome to the LAPACK corner of the manual — this one is BLAS/SRC/stbsv.f, and it's giving level 2 BLAS energy. it's a whole page about one lil' subroutine and honestly? she ate. 🎀

---

✨ NAME ✨

BLAS/SRC/stbsv.f

---

🌸 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 — say hi to the main character 👑

💅 Purpose:

ok so, STBSV solves one of these systems of equations, no cap:

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. periodt. 💫

not me being the bearer of bad news but… 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 homework first bestie, fr fr. 😭

---

🎀 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 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

heads up bestie: 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 just vibing there unbothered. ✨

• 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 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's a shapeshifter, iconic. 🦋
• INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. (zero is NOT it, okay? 🚫)

---

👑 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 stbsv.f.

---

💜 Author

Generated automatically by Doxygen for LAPACK from the source code.

---

and that's the whole page bestie, we're done here 💅

Version 3.12.0 🌸 Tue Nov 28 2023 12:08:41 🌸 BLAS/SRC/stbsv.f(3) — mwah, tysm for reading, you're the moment, go slay those triangular solves 🫶✨👑