hpgst(3) Library Functions Manual hpgst(3)

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


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

CHPGST

Purpose:

 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.

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.

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.

ZHPGST

Purpose:

 ZHPGST 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 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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