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

okay bestie 💖 this is the Library Functions Manual page for sspgv.f(3), and the source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sspgv.f. SSPGV is lowkey iconic: packed-storage generalized symmetric-definite eigenproblem girlie. Let’s get into it. ✨

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sspgv.f — yeah, that’s the file. 💅

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

   subroutine SSPGV (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, info)
           SSPGV

🌈 Function/Subroutine Documentation 🌈

👑 subroutine SSPGV 👑

   subroutine SSPGV (integer itype, character jobz, character uplo, integer n,
       real, dimension( * ) ap, real, dimension( * ) bp, real, dimension( * )
       w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work,
       integer info)
       SSPGV

🍓 Purpose 🍓

okay so here’s the tea ☕: SSPGV computes all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be symmetric, stored in packed format, and B is also positive definite. periodt. 👑

💜 Parameters 💜

• ITYPE — ITYPE is INTEGER; it specifies the problem type to be solved:
  • = 1: A*x = (lambda)*B*x
  • = 2: A*B*x = (lambda)*x
  • = 3: B*A*x = (lambda)*x
• JOBZ — JOBZ is CHARACTER*1;
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• UPLO — UPLO is CHARACTER*1;
  • = 'U': Upper triangles of A and B are stored;
  • = 'L': Lower triangles of A and B are stored.
• N — N is INTEGER; the order of the matrices A and B. N >= 0.
• AP — AP is REAL 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.

💀 heads up: on exit, the contents of AP are destroyed. no cap.

• BP — BP is REAL array, dimension (N*(N+1)/2).

On entry, the upper or lower triangle of the symmetric matrix B, packed columnwise in a linear array. The j-th column of B is stored in the array BP as follows:

• if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
• if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.

On exit, the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T, in the same storage format as B.

• W — W is REAL array, dimension (N).

If INFO = 0, the eigenvalues in ascending order.

• Z — Z is REAL array, dimension (LDZ, N).

If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows:

• if ITYPE = 1 or 2, Z**T*B*Z = I;
• if ITYPE = 3, Z**T*inv(B)*Z = I.

If JOBZ = 'N', then Z is not referenced.

• LDZ — LDZ is INTEGER; the leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — WORK is REAL array, dimension (3*N).
• INFO — INFO is INTEGER;
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: SPPTRF or SSPEV returned an error code:
    • <= N: if INFO = i, SSPEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.
    • > N: if INFO = n + i, for 1 <= i <= n, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

💖 Author 💖

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

Definition at line 158 of file sspgv.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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k bye bestie 🫶 — this page is from LAPACK, Version 3.12.0, and its footer path is /home/abui...RC/sspgv.f(3). mwah 💅✨