SRC/ssygv.f(3)

Okay bestie, welcome to the SRC/ssygv.f(3) page from the Library Functions Manual — LAPACK’s own little corner of the Unix-verse. ✨

🌸 NAME

SRC/ssygv.f

✨ SYNOPSIS

Functions/Subroutines

subroutine ssygv (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork,
    info)

SSYGV

🎀 Function/Subroutine Documentation

🧚 subroutine ssygv

subroutine ssygv (integer itype, character jobz, character uplo, integer n,
    real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,
    integer ldb, real, dimension( * ) w, real, dimension( * ) work, integer
    lwork, integer info)

SSYGV

🎯 Purpose

Okay so SSYGV 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 and B is also positive definite. No cap, that part matters. 💅

💖 Parameters

🧠 ITYPE

• ITYPE is 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

• 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.

💜 A

• A is REAL array, dimension (LDA, N)
• On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A.
• On exit, if JOBZ = 'V', then if INFO = 0, A 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 on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed. 😭

🍓 LDA

• LDA is INTEGER
• The leading dimension of the array A. LDA >= max(1,N).

🧚 B

• B is REAL array, dimension (LDB, N)
• On entry, the symmetric positive definite matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B.
• On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T.

🌈 LDB

• LDB is INTEGER
• The leading dimension of the array B. LDB >= max(1,N).

👑 W

• W is REAL array, dimension (N)
• If INFO = 0, the eigenvalues in ascending order.

🔥 WORK

• WORK is REAL array, dimension (MAX(1,LWORK))
• On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

🫶 LWORK

• LWORK is INTEGER
• The length of the array WORK. LWORK >= max(1,3*N-1).
• For optimal efficiency, LWORK >= (NB+2)*N, where NB is the blocksize for SSYTRD returned by ILAENV.
• If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

💀 INFO

• INFO is INTEGER
• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value
• > 0: SPOTRF or SSYEV returned an error code:
  • <= N: if INFO = i, SSYEV 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 173 of file ssygv.f.

🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.

---

With love from your Unix bestie 💖 — LAPACK Version 3.12.0, SRC/ssygv.f(3). That’s the source/version footer, and the page didn’t hand me a separate date, so no fake date, bestie. 💅🫶