hpgst(3)

💅 NAME

okay bestie, welcome to hpgst(3) from the Library Functions Manual — and this page is literally:

hpgst - {hp,sp}gst: reduction to standard form, packed

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✨ SYNOPSIS ✨

🫶 Functions

• subroutine chpgst (itype, uplo, n, ap, bp, info) — CHPGST
• subroutine dspgst (itype, uplo, n, ap, bp, info) — DSPGST
• subroutine sspgst (itype, uplo, n, ap, bp, info) — SSPGST
• subroutine zhpgst (itype, uplo, n, ap, bp, info) — ZHPGST

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🌸 Detailed Description 🌸

this section is lowkey empty, bestie — the real detail is in Function Documentation right below. ✨

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👑 Function Documentation 👑

💖 chpgst — the complex Hermitian-definite one, packed

   subroutine chpgst (integer itype, character uplo, integer n, complex,
       dimension( * ) ap, complex, dimension( * ) bp, integer info)
       CHPGST

🌈 Purpose

bestie, CHPGST reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage. 💅

• If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H).
• If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
• B must have been previously factorized as U**H*U or L*L**H by CPPTRF.

Parameters

• ITYPE — ITYPE is INTEGER
  • = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
  • = 2 or 3: compute U*A*U**H or L**H*A*L.
• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored and B is factored as U**H*U;
  • = 'L': Lower triangle of A is stored and B is factored as L*L**H.
• N — N is INTEGER
  • The order of the matrices A and B. N >= 0.
• AP — AP is COMPLEX array, dimension (N*(N+1)/2)
  • On entry, the upper or lower triangle of the Hermitian 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
  • On exit, if INFO = 0, the transformed matrix, stored in the same format as A.
• BP — BP is COMPLEX array, dimension (N*(N+1)/2)
  • The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by CPPTRF.
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

🎀 Author

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

Definition at line 112 of file chpgst.f.

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💜 dspgst — the real symmetric-definite one, packed

   subroutine dspgst (integer itype, character uplo, integer n, double
       precision, dimension( * ) ap, double precision, dimension( * ) bp,
       integer info)
       DSPGST

🌈 Purpose

DSPGST reduces a real symmetric-definite generalized eigenproblem to standard form, using packed storage. 🫶

• If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T).
• If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
• B must have been previously factorized as U**T*U or L*L**T by DPPTRF.

Parameters

• ITYPE — ITYPE is INTEGER
  • = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
  • = 2 or 3: compute U*A*U**T or L**T*A*L.
• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored and B is factored as U**T*U;
  • = 'L': Lower triangle of A is stored and B is factored as L*L**T.
• 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
  • On exit, if INFO = 0, the transformed matrix, stored in the same format as A.
• BP — BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
  • The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by DPPTRF.
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

🎀 Author

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

Definition at line 112 of file dspgst.f.

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🦋 sspgst — the real symmetric-definite one, single precision, packed

   subroutine sspgst (integer itype, character uplo, integer n, real,
       dimension( * ) ap, real, dimension( * ) bp, integer info)
       SSPGST

🌈 Purpose

SSPGST reduces a real symmetric-definite generalized eigenproblem to standard form, using packed storage. ✨

• If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T).
• If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
• B must have been previously factorized as U**T*U or L*L**T by SPPTRF.

Parameters

• ITYPE — ITYPE is INTEGER
  • = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
  • = 2 or 3: compute U*A*U**T or L**T*A*L.
• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored and B is factored as U**T*U;
  • = 'L': Lower triangle of A is stored and B is factored as L*L**T.
• N — N is INTEGER
  • The order of the matrices A and B. N >= 0.
• AP — AP is 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
  • On exit, if INFO = 0, the transformed matrix, stored in the same format as A.
• BP — BP is REAL array, dimension (N*(N+1)/2)
  • The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by SPPTRF.
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

🎀 Author

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

Definition at line 112 of file sspgst.f.

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💖 zhpgst — the complex*16 Hermitian-definite one, packed

   subroutine zhpgst (integer itype, character uplo, integer n, complex*16,
       dimension( * ) ap, complex*16, dimension( * ) bp, integer info)
       ZHPGST

🌈 Purpose

ZHPGST reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage. no cap. 💅

• If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H).
• If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
• B must have been previously factorized as U**H*U or L*L**H by ZPPTRF.

Parameters

• ITYPE — ITYPE is INTEGER
  • = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
  • = 2 or 3: compute U*A*U**H or L**H*A*L.
• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored and B is factored as U**H*U;
  • = 'L': Lower triangle of A is stored and B is factored as L*L**H.
• N — N is INTEGER
  • The order of the matrices A and B. N >= 0.
• AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2)
  • On entry, the upper or lower triangle of the Hermitian 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
  • On exit, if INFO = 0, the transformed matrix, stored in the same format as A.
• BP — BP is COMPLEX*16 array, dimension (N*(N+1)/2)
  • The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by ZPPTRF.
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

🎀 Author

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

Definition at line 112 of file zhpgst.f.

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🦋 Author 🦋

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