STBT02(3)

📦 version 3.12.0, in opensuse-leap 16.0

🎀 STBT02(3) — the triangular-band residual checker bestie 🎀

okay so real talk, this page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/stbt02.f and it's a .f file, so yes it's Fortran, and yes it's iconic 💅 it's part of the LAPACK library functions manual and honestly? it's giving "unsung hero of the testing suite" energy ✨

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine STBT02 (uplo, trans, diag, n, kd, nrhs, ab, ldab, x, ldx, b,
    ldb, work, resid)

STBT02 🫶 that's the whole name, no notes.

💖 Function/Subroutine Documentation 💖

subroutine STBT02 (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer
    ldab, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, *
    ) b, integer ldb, real, dimension( * ) work, real resid)

STBT02 💫 (again, we stan a consistent queen)

🔥 Purpose 🔥

okay so here's the whole vibe:

!>
!> STBT02 computes the residual for the computed solution to a
!> triangular system of linear equations op(A)*X = B, when A is a
!> triangular band matrix. The test ratio is the maximum over
!>    norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
!> where op(A) = A or A**T, b is the column of B, x is the solution
!> vector, and EPS is the machine epsilon.
!> The norm used is the 1-norm.
!>

so basically it computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, when A is a triangular band matrix — and the test ratio is the max over that whole formula up there. op(A) is A or A**T, b is the column of B, x is the solution vector, and EPS is the machine epsilon. and the norm used is the 1-norm. no cap. 📐

🦋 Parameters 🦋

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the matrix A is upper or lower triangular.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>

UPLO is CHARACTER*1 and it says whether matrix A is upper or lower triangular — 'U' means upper triangular, 'L' means lower triangular 💜

TRANS

!>          TRANS is CHARACTER*1
!>          Specifies the operation applied to A.
!>          = 'N':  A    * X = B  (No transpose)
!>          = 'T':  A**T * X = B  (Transpose)
!>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
!>

TRANS is CHARACTER*1, it picks the operation applied to A: 'N' = A * X = B (No transpose), 'T' = A**T * X = B (Transpose), 'C' = A**H * X = B (Conjugate transpose = Transpose). note that last one — conjugate transpose equals transpose here, that's literally in the text bestie 👀

DIAG

!>          DIAG is CHARACTER*1
!>          Specifies whether or not the matrix A is unit triangular.
!>          = 'N':  Non-unit triangular
!>          = 'U':  Unit triangular
!>

DIAG is CHARACTER*1, tells you whether or not matrix A is unit triangular: 'N' = Non-unit triangular, 'U' = Unit triangular 🌟

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

N is INTEGER, the order of matrix A, and N >= 0 fr.

KD

!>          KD is INTEGER
!>          The number of superdiagonals or subdiagonals of the
!>          triangular band matrix A.  KD >= 0.
!>

KD is INTEGER, the number of superdiagonals or subdiagonals of the triangular band matrix A, and KD >= 0 ✨

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrices X and B.  NRHS >= 0.
!>

NRHS is INTEGER, the number of right hand sides — i.e. the number of columns of the matrices X and B. NRHS >= 0 🫶

AB

!>          AB is REAL array, dimension (LDAB,N)
!>          The upper or lower triangular band matrix A, stored in the
!>          first kd+1 rows of the array. The j-th column of A is stored
!>          in the j-th column of the array AB as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>

AB is a REAL array, dimension (LDAB,N) — it's the upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. the j-th column of A lives in the j-th column of AB like this: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). copy those index ranges exactly, they matter 🧚

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+1.
!>

LDAB is INTEGER, the leading dimension of the array AB, and LDAB >= KD+1 ⭐

X

!>          X is REAL array, dimension (LDX,NRHS)
!>          The computed solution vectors for the system of linear
!>          equations.
!>

X is a REAL array, dimension (LDX,NRHS) — the computed solution vectors for the system of linear equations 💖

LDX

!>          LDX is INTEGER
!>          The leading dimension of the array X.  LDX >= max(1,N).
!>

LDX is INTEGER, the leading dimension of the array X, and LDX >= max(1,N) 🌈

B

!>          B is REAL array, dimension (LDB,NRHS)
!>          The right hand side vectors for the system of linear
!>          equations.
!>

B is a REAL array, dimension (LDB,NRHS) — the right hand side vectors for the system of linear equations 🍓

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

LDB is INTEGER, the leading dimension of the array B, and LDB >= max(1,N) 🔥

WORK

!>          WORK is REAL array, dimension (N)
!>

WORK is a REAL array, dimension (N). that's it. it's just vibes and scratch space 💀

RESID

!>          RESID is REAL
!>          The maximum over the number of right hand sides of
!>          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
!>

RESID is REAL — the maximum over the number of right hand sides of norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). this is the output babe, the moment of truth 👑

👑 Author 👑

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

absolute legends, all of them 🫡

Definition at line 152 of file stbt02.f. 📍

🌟 Author (yes, again) 🌟

Generated automatically by Doxygen for LAPACK from the source code. not me being autogenerated by Doxygen and still serving looks 💅

lowkey reminder: every bound up there (N >= 0, KD >= 0, NRHS >= 0, LDAB >= KD+1, LDX >= max(1,N), LDB >= max(1,N)) is a real requirement, not a suggestion — disrespect the leading dimensions and that's on you 🙈

and that's the whole page bestie 🎀 bye from the LAPACK library functions manual, Version 3.12.0 — signed off from /home/abui...IN/stbt02.f(3), mwah 💋✨

📦 where this page comes from