BLAS/SRC/ztbsv.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

Okay bestie, welcome to BLAS/SRC/ztbsv.f(3) from the Library Functions Manual. Buckle up — we’re solving triangular band systems and looking iconic while doing it. 💅

💖 NAME

BLAS/SRC/ztbsv.f — that’s the file name, and also the whole vibe. This is the ZTBSV routine, no cap.

✨ SYNOPSIS

🌸 Functions/Subroutines

  • subroutine ztbsv (uplo, trans, diag, n, k, a, lda, x, incx) — ZTBSV
subroutine ztbsv (uplo, trans, diag, n, k, a, lda, x, incx)
    ZTBSV

🫶 Function/Subroutine Documentation

subroutine ztbsv (character uplo, character trans, character diag, integer
    n, integer k, complex*16, dimension(lda,*) a, integer lda, complex*16,
    dimension(*) x, integer incx)
    ZTBSV

💅 Purpose

Okay so ZTBSV solves one of these systems of equations:

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.

Real talk: there is no test for singularity or near-singularity included in this routine. Such tests must be performed before calling this routine. Do your vibe check first, bestie. 🚨

🎀 Parameters

UPLO

Type: 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

Type: 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**H*x = b.

DIAG

Type: 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

Type: INTEGER

On entry, N specifies the order of the matrix A. N must be at least zero.

K

Type: 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

Type: COMPLEX*16 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.

LDA

Type: 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

Type: COMPLEX*16 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

Type: 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 ztbsv.f.

🎀 Author

Generated automatically by Doxygen for LAPACK from the source code.

Source/version tea: LAPACK Version 3.12.0, page BLAS/SRC/ztbsv.f(3). Date lore on the page: 22-October-1986 — the origin note. Byeee, go solve those triangular band systems and slay. 💖✨🦋

📦 where this page comes from