SRC/sspgv.f(3)

💖 SRC/sspgv.f(3) 💖

okay so bestie, this page is from the Library Functions Manual and it's all about SRC/sspgv.f. It's giving “I know linear algebra and I'm not afraid to use it” energy. 🎀

🌸 NAME 🌸

SRC/sspgv.f — that's the file, periodt. 💅

✨ SYNOPSIS ✨

Functions/Subroutines — literally the function/subroutine zone:

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

🦋 Function/Subroutine Documentation 🦋

🎀 subroutine sspgv 🎀

Here's the full signature, copied exactly because we do not play with code:

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 — yes bestie, that's the routine name, all caps and iconic. 👑

💖 Purpose 💖

SSPGV computes all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, in one of these forms: 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. No cap. ✨

🌈 Parameters 🌈

• ITYPE — INTEGER. 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 — CHARACTER*1:
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• UPLO — CHARACTER*1:
  • = 'U': Upper triangles of A and B are stored;
  • = 'L': Lower triangles of A and B are stored.
• N — INTEGER. The order of the matrices A and B. N >= 0.
• AP — 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. Not me warning you — that's literally the page.

• BP — 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 — REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
• Z — 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 — INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — REAL array, dimension (3*N).
• INFO — 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 📍

Definition at line 158 of file sspgv.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie that's the whole page 💖 — it's LAPACK Version 3.12.0, filed as SRC/sspgv.f(3), and it's giving “reference manual but make it cute.” periodt. 🎀✨