SRC/dspgv.f(3)

okay bestie, welcome to SRC/dspgv.f(3) from the Library Functions Manual — this is the page for DSPGV, and it is literally giving packed-matrix real generalized symmetric-definite eigenproblem main character energy. 💅✨

🌸 NAME 🌸

SRC/dspgv.f

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✨ SYNOPSIS ✨

💅 Functions/Subroutines

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

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🦋 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 💖

No gatekeeping: DSPGV 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. Periodt. 👑

🍓 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.
• AP — AP is DOUBLE PRECISION 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.

On exit, the contents of AP are destroyed. 💀

• BP — BP is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N). If INFO = 0, 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. 🙈

• 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).
• INFO — INFO is INTEGER
  • = 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.

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🫶 Author 🫶

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