SRC/ctptrs.f(3)

💅 SRC/ctptrs.f — Library Functions Manual 💅

okay so bestie, welcome to the Library Functions Manual page for SRC/ctptrs.f — this is the one about CTPTRS, and it's lowkey iconic for solving packed triangular systems. ✨

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🎀 NAME 🎀

SRC/ctptrs.f

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🌸 SYNOPSIS 🌸

🧩 Functions/Subroutines 🧩

   subroutine ctptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
       CTPTRS

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🌟 Function/Subroutine Documentation 🌟

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

🎯 Purpose 🎯

CTPTRS 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. 💖

⚠️ caveat time, 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).
• 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 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 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 ctptrs.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, bestie — signing off with LAPACK Version 3.12.0 and SRC/ctptrs.f(3). periodt 💖✨