ppequ - Man Page

subroutine cppequ (uplo, n, ap, s, scond, amax, info)
CPPEQU
subroutine dppequ (uplo, n, ap, s, scond, amax, info)
DPPEQU
subroutine sppequ (uplo, n, ap, s, scond, amax, info)
SPPEQU
subroutine zppequ (uplo, n, ap, s, scond, amax, info)
ZPPEQU

CPPEQU  

Purpose:

 CPPEQU computes row and column scalings intended to equilibrate a
 Hermitian positive definite matrix A in packed storage and reduce
 its condition number (with respect to the two-norm).  S contains the
 scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix
 B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
 This choice of S puts the condition number of B within a factor N of
 the smallest possible condition number over all possible diagonal
 scalings.

Parameters

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

AP

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

S

          S is REAL array, dimension (N)
          If INFO = 0, S contains the scale factors for A.

SCOND

          SCOND is REAL
          If INFO = 0, S contains the ratio of the smallest S(i) to
          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
          large nor too small, it is not worth scaling by S.

AMAX

          AMAX is REAL
          Absolute value of largest matrix element.  If AMAX is very
          close to overflow or very close to underflow, the matrix
          should be scaled.

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, the i-th diagonal element is nonpositive.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 116 of file cppequ.f.

DPPEQU  

Purpose:

 DPPEQU computes row and column scalings intended to equilibrate a
 symmetric positive definite matrix A in packed storage and reduce
 its condition number (with respect to the two-norm).  S contains the
 scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix
 B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
 This choice of S puts the condition number of B within a factor N of
 the smallest possible condition number over all possible diagonal
 scalings.

Parameters

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

AP

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

S

          S is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, S contains the scale factors for A.

SCOND

          SCOND is DOUBLE PRECISION
          If INFO = 0, S contains the ratio of the smallest S(i) to
          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
          large nor too small, it is not worth scaling by S.

AMAX

          AMAX is DOUBLE PRECISION
          Absolute value of largest matrix element.  If AMAX is very
          close to overflow or very close to underflow, the matrix
          should be scaled.

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, the i-th diagonal element is nonpositive.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 115 of file dppequ.f.

SPPEQU  

Purpose:

 SPPEQU computes row and column scalings intended to equilibrate a
 symmetric positive definite matrix A in packed storage and reduce
 its condition number (with respect to the two-norm).  S contains the
 scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix
 B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
 This choice of S puts the condition number of B within a factor N of
 the smallest possible condition number over all possible diagonal
 scalings.

Parameters

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

AP

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

S

          S is REAL array, dimension (N)
          If INFO = 0, S contains the scale factors for A.

SCOND

          SCOND is REAL
          If INFO = 0, S contains the ratio of the smallest S(i) to
          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
          large nor too small, it is not worth scaling by S.

AMAX

          AMAX is REAL
          Absolute value of largest matrix element.  If AMAX is very
          close to overflow or very close to underflow, the matrix
          should be scaled.

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, the i-th diagonal element is nonpositive.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 115 of file sppequ.f.

ZPPEQU  

Purpose:

 ZPPEQU computes row and column scalings intended to equilibrate a
 Hermitian positive definite matrix A in packed storage and reduce
 its condition number (with respect to the two-norm).  S contains the
 scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix
 B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
 This choice of S puts the condition number of B within a factor N of
 the smallest possible condition number over all possible diagonal
 scalings.

Parameters

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

AP

          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
          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.

S

          S is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, S contains the scale factors for A.

SCOND

          SCOND is DOUBLE PRECISION
          If INFO = 0, S contains the ratio of the smallest S(i) to
          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
          large nor too small, it is not worth scaling by S.

AMAX

          AMAX is DOUBLE PRECISION
          Absolute value of largest matrix element.  If AMAX is very
          close to overflow or very close to underflow, the matrix
          should be scaled.

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, the i-th diagonal element is nonpositive.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 116 of file zppequ.f.