BLAS/SRC/ztpsv.f(3)

🌸 BLAS/SRC/ztpsv.f(3) — Library Functions Manual 🌸

okay so this is the glow-up of the BLAS/SRC/ztpsv.f(3) page from the Library Functions Manual, bestie. We're talking ZTPSV: the Level 2 BLAS girlie who solves triangular systems with packed complex*16 matrices. Let's get into it 💅✨

💖 NAME

BLAS/SRC/ztpsv.f

✨ SYNOPSIS

🛠️ Functions/Subroutines

subroutine ztpsv (uplo, trans, diag, n, ap, x, incx)
    ZTPSV

🎀 Function/Subroutine Documentation

🌟 subroutine ztpsv (character uplo, character trans, character diag, integer n, complex*16, dimension() ap, complex16, dimension(*) x, integer incx)

subroutine ztpsv (character uplo, character trans, character diag, integer
    n, complex*16, dimension(*) ap, complex*16, dimension(*) x, integer
    incx)

ZTPSV. That's the name, no cap.

💅 Purpose

okay so ZTPSV solves one of these systems of equations, and yes you need to pick which one with TRANS:

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 matrix, supplied in packed form. iconic packed-storage behavior, honestly.

🚨 real talk: no test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. So do your vibe check first, bestie, because ZTPSV is not doing it for you 😭

🍓 Parameters

• UPLO — 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 — 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 — 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 — INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
• AP — COMPLEX*16 array, dimension at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced, but are assumed to be unity.
• X — 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 — 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 143 of file ztpsv.f.

🌟 Author

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okay that's the whole page, bestie. signing off from LAPACK Version 3.12.0, page BLAS/SRC/ztpsv.f(3) 💖✨🫶