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

okay bestie, welcome to /home/abui...RC/dspgv.f(3) — this is a page from the Library Functions Manual. It's giving LAPACK source-file energy, and we're about to read it like the group chat is watching. 💅✨

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dspgv.f — that's the file, bestie. 🫶

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine DSPGV (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, info) — DSPGV

🔥 Function/Subroutine Documentation 🔥

subroutine DSPGV (integer itype, character jobz, character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) bp, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info) — DSPGV

🌸 Purpose 🌸

okay so DSPGV computes all the eigenvalues and, if you ask nicely with JOBZ, the eigenvectors too. It handles a real generalized symmetric-definite eigenproblem, and the forms are:

A*x=(lambda)*B*x
A*Bx=(lambda)*x
B*A*x=(lambda)*x

Here A and B are assumed to be symmetric, stored in packed format, and B is also positive definite. No cap. 💜

💅 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 — chooses what gets computed:
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.

🎀 UPLO

• UPLO is CHARACTER*1 — tells it which triangles are stored:
  • = '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 DOUBLE PRECISION array, dimension (N*(N+1)/2) — on entry, this holds 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.

On exit, the contents of AP are destroyed. Like, gone. Do not expect it back. 💀

🧚 BP

• BP is DOUBLE PRECISION array, dimension (N*(N+1)/2) — on entry, this holds 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, BP holds 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. Slay. ✨

🫶 W

• W is DOUBLE PRECISION array, dimension (N) — if INFO = 0, this contains the eigenvalues in ascending order.

💜 Z

• Z is DOUBLE PRECISION 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. She's off duty. 🙈

🌸 LDZ

• LDZ is INTEGER — the leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).

👑 WORK

• WORK is DOUBLE PRECISION array, dimension (3*N) — that's the workspace, bestie.

🔥 INFO

• INFO is INTEGER — the exit-status tea:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: DPPTRF or DSPEV returned an error code:
    • <= N: if INFO = i, DSPEV 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 dspgv.f.

🎀 Author 🎀

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