BLAS/SRC/ctpsv.f(3)

💖 NAME 💖

BLAS/SRC/ctpsv.f — bestie, this is from the LAPACK manual (section 3, so it's the file-path-style page), and it's literally the home of ctpsv, your girl for solving triangular systems with complex numbers in packed form ✨

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🎀 SYNOPSIS 🎀

Functions/Subroutines

subroutine ctpsv (uplo, trans, diag, n, ap, x, incx)
    CTPSV

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🌸 Function/Subroutine Documentation 🌸

subroutine ctpsv

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

CTPSV 🫶

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✨ Purpose ✨

Okay so listen: CTPSV solves one of these systems of equations, no cap:

   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 💅

⚠️ Big important heads-up: there is no test for singularity or near-singularity included in this routine. Such tests must be performed before calling this routine. She will not warn you, she will just go. Periodt. 😭

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🌈 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 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 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 replaced, that's the whole gig 💅
• INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.

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👑 Author 👑

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

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💜 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 ctpsv.f.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, you ate it, go solve some triangular systems bestie 🫶✨

Version 3.12.0 — Tue Nov 28 2023 12:08:41 — BLAS/SRC/ctpsv.f(3) 💖🎀🌸