Visible to Intel only — GUID: GUID-6B7BD4CC-0C4A-44B4-8B98-91543D04F9E6
Visible to Intel only — GUID: GUID-6B7BD4CC-0C4A-44B4-8B98-91543D04F9E6
?laqr1
Sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.
Syntax
call slaqr1( n, h, ldh, sr1, si1, sr2, si2, v )
call dlaqr1( n, h, ldh, sr1, si1, sr2, si2, v )
call claqr1( n, h, ldh, s1, s2, v )
call zlaqr1( n, h, ldh, s1, s2, v )
Include Files
- mkl.fi
Description
Given a 2-by-2 or 3-by-3 matrix H, this routine sets v to a scalar multiple of the first column of the product
K = (H - s1*I)*(H - s2*I), or K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
scaling to avoid overflows and most underflows.
It is assumed that either 1) sr1 = sr2 and si1 = -si2, or 2) si1 = si2 = 0.
This is useful for starting double implicit shift bulges in the QR algorithm.
Input Parameters
- n
-
INTEGER.
The order of the matrix H. n must be equal to 2 or 3.
- sr1, si2, sr2, si2
-
REAL for slaqr1
DOUBLE PRECISION for dlaqr1
Shift values that define K in the formula above.
- s1, s2
-
COMPLEX for claqr1
DOUBLE COMPLEX for zlaqr1.
Shift values that define K in the formula above. - h
-
REAL for slaqr1
DOUBLE PRECISION for dlaqr1
COMPLEX for claqr1
DOUBLE COMPLEX for zlaqr1.
Array, DIMENSION (ldh, n), contains 2-by-2 or 3-by-3 matrix H in the formula above.
- ldh
-
INTEGER.
The leading dimension of the array h just as declared in the calling routine. ldh ≥ n.
Output Parameters
- v
-
REAL for slaqr1
DOUBLE PRECISION for dlaqr1
COMPLEX for claqr1
DOUBLE COMPLEX for zlaqr1.
Array with dimension (n).
A scalar multiple of the first column of the matrix K in the formula above.