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

🦋 NAME 🦋

okay bestie, this is the zspsv.f(3) page from the Library Functions Manual — page id /home/abui...RC/zspsv.f(3). The actual source path listed here is:

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

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

• subroutine ZSPSV (uplo, n, nrhs, ap, ipiv, b, ldb, info) — ZSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

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💅 Function/Subroutine Documentation 💅

subroutine ZSPSV (character uplo, integer n, integer nrhs, complex*16,
     dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension(
     ldb, * ) b, integer ldb, integer info)

ZSPSV computes the solution to system of linear equations A * X = B for OTHER matrices. yes, OTHER in all caps, that's literally what it says 😭

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🎯 Purpose 🎯

okay so here's the whole vibe, bestie: ZSPSV 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, 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 linear algebra 💅

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🧚 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*16 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 ZSPTRF, 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 ZSPTRF.

• 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*16 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. bestie that's the "it's giving singular 😭" case, no solution for you

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👑 Author 👑

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

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🔍 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 zspsv.f.

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🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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