SRC/ztptrs.f(3)

💅 NAME 💅

SRC/ztptrs.f(3) — yes bestie, that's the page — is part of the Library Functions Manual. It covers SRC/ztptrs.f, home of the ztptrs subroutine. Main character energy only, periodt. ✨

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ztptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
    ZTPTRS

🎀 Function/Subroutine Documentation 🎀

👑 ztptrs — ZTPTRS 👑

subroutine ztptrs (character uplo, character trans, character diag, integer n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

💖 Purpose 💖

okay so listen: ZTPTRS solves a triangular system of the form

A * X = B,  A**T * X = B,  or  A**H * X = B,

where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix. No cap, that's the whole vibe. 🦋

🚨 bestie, read this twice: this subroutine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this subroutine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this subroutine.

✨ Parameters ✨

okay, parameter tour, no skipping. 🫶

UPLO

UPLO is CHARACTER*1

• = 'U': A is upper triangular;
• = 'L': A is lower triangular.

TRANS

TRANS is CHARACTER*1. It specifies the form of the system of equations:

• = 'N': A * X = B (No transpose)
• = 'T': A**T * X = B (Transpose)
• = 'C': A**H * X = B (Conjugate transpose)

DIAG

DIAG is CHARACTER*1

• = 'N': A is non-unit triangular;
• = 'U': A is unit triangular.

N

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

NRHS

NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2). The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

B

B is COMPLEX*16 array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, if INFO = 0, the solution matrix X.

LDB

LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). it's giving dimension rules, honestly.

INFO

INFO is INTEGER

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value
• > 0: if INFO = i, the i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed.

🫶 Author 🫶

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

Definition at line 134 of file ztptrs.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie. Signing off with LAPACK Version 3.12.0 and page SRC/ztptrs.f(3) — that's the source/version footer; no separate date is printed on this page. 💖🫶✨