SRC/stptrs.f(3)

🌸 NAME 🌸

SRC/stptrs.f — okay bestie, this page is from the Library Functions Manual, and it’s all about the STPTRS routine. 💅

✨ SYNOPSIS ✨

Functions/Subroutines:

subroutine stptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
    STPTRS

🦋 Function/Subroutine Documentation 🦋

stptrs signature

subroutine stptrs (character uplo, character trans, character diag, integer
    n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b,
    integer ldb, integer info)
    STPTRS

Purpose

STPTRS 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.

Real talk, bestie: 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

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 REAL 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 REAL 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 134 of file stptrs.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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bye bestie 💖 — this footer says LAPACK Version 3.12.0, page SRC/stptrs.f(3) — no date on this one, so I’m not inventing one 🙈💅