SSPGVD(3)

💅 sspgvd(3) — Library Functions Manual 💅

okay bestie, welcome to the sspgvd(3) page — yes, it's giving very “LAPACK source file walked so you could run” energy, and we're gonna get through every single detail together. 🫶

🌸 NAME 🌸

The NAME here is literally the whole source-file path, no cap:

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

✨ SYNOPSIS ✨

Under Functions/Subroutines, the main character is this subroutine — and yes, it's also named SSPGVD:

   subroutine SSPGVD (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, lwork,
       iwork, liwork, info)
           SSPGVD

🧚 Function/Subroutine Documentation 🧚

Here's the full signature, bestie — all the types and dimensions are right here, exactly as written:

   subroutine SSPGVD (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 lwork, integer, dimension( * ) iwork, integer liwork, integer
       info)
       SSPGVD

🎀 Purpose 🎀

SSPGVD computes all the eigenvalues, and optionally the eigenvectors, of a real generalized symmetric-definite eigenproblem. The forms are 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. If eigenvectors are desired, it uses a divide and conquer algorithm. slay. 🌈

🦋 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. It's the order of the matrices A and B. N >= 0.

🍓 AP

AP is REAL array, dimension (N*(N+1)/2).

On entry, it 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. 💀

🍓 BP

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

On entry, it 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, it 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. math ate. ✨

🍓 W

W is REAL array, dimension (N).

If INFO = 0, the eigenvalues are 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. It's the leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).

🍓 WORK

WORK is REAL array, dimension (MAX(1,LWORK)).

On exit, if INFO = 0, WORK(1) returns the required LWORK.

🍓 LWORK

LWORK is INTEGER. It's the dimension of the array WORK.

• If N <= 1, LWORK >= 1.
• If JOBZ = 'N' and N > 1, LWORK >= 2*N.
• If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the required sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.

🍓 IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK)).

On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

🍓 LIWORK

LIWORK is INTEGER. It's the dimension of the array IWORK.

• If JOBZ = 'N' or N <= 1, LIWORK >= 1.
• If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the routine only calculates the required sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.

🍓 INFO

INFO is INTEGER.

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value
• > 0: SPPTRF or SSPEVD returned an error code:
  • <= N: if INFO = i, SSPEVD 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.

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👑 Author 👑

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

🌈 Contributors 🌈

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 202 of file sspgvd.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie — LAPACK Version 3.12.0, page footer /home/abui...RC/sspgvd.f(3). mwah! 💖🎀🦋