SRC/dtptrs.f(3)

okay so bestie, we're looking at SRC/dtptrs.f(3) from the Library Functions Manual — and it's literally the manual page for the Fortran subroutine dtptrs. This is giving "linear algebra but make it packed triangular" ✨.

💖 NAME 💖

SRC/dtptrs.f

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

• subroutine dtptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info) — DTPTRS

🦋 Function/Subroutine Documentation 🦋

subroutine dtptrs (character uplo, character trans, character diag, integer n, integer nrhs, double precision, dimension( * ) ap, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DTPTRS

🎯 Purpose 🎯

Okay so the whole point: DTPTRS solves a triangular system of the form

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

where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.

Bestie, important caveat: 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. No cap, that's the warning. 🫶

✨ Parameters ✨

💅 UPLO

UPLO is CHARACTER*1

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

🌀 TRANS

TRANS is CHARACTER*1 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 = 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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).

🔥 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 📌

Definition at line 134 of file dtptrs.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole vibe, bestie 💖 — footer check: LAPACK Version 3.12.0, SRC/dtptrs.f(3). Byeee 🫶✨