/home/abui...RC/cspsv.f(3)

💖 CSPSV 💖

Okay bestie, this is the Library Functions Manual page for /home/abui...RC/cspsv.f(3) — yes, the title is CSPSV, and it's about solving complex symmetric packed linear systems. The vibes are immaculate and the math is doing main character energy. 🦋✨

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🏷 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cspsv.f

That's the file, periodt. 📁

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📜 SYNOPSIS

🧩 Functions/Subroutines

subroutine CSPSV (uplo, n, nrhs, ap, ipiv, b, ldb, info)

CSPSV computes the solution to system of linear equations A * X = B for OTHER matrices ✨.

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🛠 Function/Subroutine Documentation

subroutine CSPSV (character uplo, integer n, integer nrhs, complex,
    dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension(
    ldb, * ) b, integer ldb, integer info)

CSPSV computes the solution to system of linear equations A * X = B for OTHER matrices.

🎯 Purpose

Okay so here's the tea, bestie: CSPSV computes the solution to a complex system of linear equations

A * X = B,

where A is an N-by-N symmetric matrix stored in packed format, and X and B are N-by-NRHS matrices.

The diagonal pivoting method is used to factor A as

A = U * D * U**T,  if UPLO = 'U', or
A = L * D * L**T,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. Slay. 💅

🎀 Parameters

UPLO

UPLO is CHARACTER*1

• = 'U': Upper triangle of A is stored;
• = 'L': Lower triangle of A is stored.

N

N is INTEGER

The number of linear equations, i.e., 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)

On entry, the upper or lower triangle of the symmetric 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)*(2n-j)/2) = A(i,j) for j<=i<=n.

See below for further details. 👀

On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by CSPTRF, stored as a packed triangular matrix in the same storage format as A.

IPIV

IPIV is INTEGER array, dimension (N)

Details of the interchanges and the block structure of D, as determined by CSPTRF.

• If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block.
• If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
• If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

B

B is COMPLEX array, dimension (LDB,NRHS)

On entry, the N-by-NRHS right hand side matrix B.

On exit, if INFO = 0, the N-by-NRHS 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, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

👑 Author

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

🔍 Further Details

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':

Two-dimensional storage of the symmetric matrix A:

   a11 a12 a13 a14
       a22 a23 a24
           a33 a34     (aij = aji)
               a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

📍 Definition at line 161 of file cspsv.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie 🫶. This one's from LAPACK Version 3.12.0, source file /home/abui...RC/cspsv.f(3). Now go solve that system and slay. 💅✨