?spcon
?spcon
Estimates the reciprocal of the condition number of a packed symmetric matrix.
Syntax
lapack_int LAPACKE_sspcon
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const float*
ap
,
const lapack_int*
ipiv
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_dspcon
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const double*
ap
,
const lapack_int*
ipiv
,
double
anorm
,
double*
rcond
);
lapack_int LAPACKE_cspcon
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const lapack_complex_float*
ap
,
const lapack_int*
ipiv
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_zspcon
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const lapack_complex_double*
ap
,
const lapack_int*
ipiv
,
double
anorm
,
double*
rcond
);
Include Files
- mkl.h
Description
The routine estimates the reciprocal of the condition number of a packed symmetric matrix
A
:κ
1
(A
) = ||A
||1
||A
-1
||1
A
is symmetric, κ
∞
A
) = κ
1
(A
)An estimate is obtained for .
||
, and the reciprocal of the condition number is computed as A
-1
||rcond
= 1 / (||A
|| ||A
-1
||)Before calling this routine:
- computeanorm(either ||A||1= maxjΣ|ia| or ||ijA||= max∞iΣ|ja|)ij
- call?sptrfto compute the factorization ofA.
Input Parameters
- matrix_layout
- Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
- uplo
- Must be'U'or'L'.Indicates how the input matrixAhas been factored:If, the arrayuplo='U'apstores the packed upper triangular factorUof the factorizationA=.U*D*UTIf, the arrayuplo='L'apstores the packed lower triangular factorLof the factorizationA=.L*D*LT
- n
- The order of matrix.A;n≥0
- ap
- The arrayapcontains the packed factored matrixA, as returned by?sptrf. The dimension ofapmust be at least max(1,n(n+1)/2).
- ipiv
- Array, size at leastmax(1,.n)The arrayipiv, as returned by?sptrf.
- anorm
- The norm of theoriginalmatrixA(see.Description)
Output Parameters
- rcond
- An estimate of the reciprocal of the condition number. The routine setsrcond= 0 if the estimate underflows; in this case the matrix is singular (to working precision). However, anytimercondis small compared to 1.0, for the working precision, the matrix may be poorly conditioned or even singular.
Return Values
This function returns a value
info
.If , the execution is successful.
info
= 0If
info
= -i
, parameter i
had an illegal value.Application Notes
The computed ; the number is usually 4 or 5 and never more than 11. Each solution requires approximately
rcond
is never less than r
(the reciprocal of the true condition number) and in practice is nearly always less than 10r
. A call to this routine involves solving a number of systems of linear equations A
*x
= b
2
floating-point operations for real flavors and n
2
8
for complex flavors.n
2