.TH "laqr1" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME laqr1 \- laqr1: step in hseqr .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBclaqr1\fP (n, h, ldh, s1, s2, v)" .br .RI "\fBCLAQR1\fP sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts\&. " .ti -1c .RI "subroutine \fBdlaqr1\fP (n, h, ldh, sr1, si1, sr2, si2, v)" .br .RI "\fBDLAQR1\fP sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts\&. " .ti -1c .RI "subroutine \fBslaqr1\fP (n, h, ldh, sr1, si1, sr2, si2, v)" .br .RI "\fBSLAQR1\fP sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts\&. " .ti -1c .RI "subroutine \fBzlaqr1\fP (n, h, ldh, s1, s2, v)" .br .RI "\fBZLAQR1\fP sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine claqr1 (integer n, complex, dimension( ldh, * ) h, integer ldh, complex s1, complex s2, complex, dimension( * ) v)" .PP \fBCLAQR1\fP sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts\&. .PP \fBPurpose:\fP .RS 4 .PP .nf Given a 2-by-2 or 3-by-3 matrix H, CLAQR1 sets v to a scalar multiple of the first column of the product (*) K = (H - s1*I)*(H - s2*I) scaling to avoid overflows and most underflows\&. This is useful for starting double implicit shift bulges in the QR algorithm\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER Order of the matrix H\&. N must be either 2 or 3\&. .fi .PP .br \fIH\fP .PP .nf H is COMPLEX array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*)\&. .fi .PP .br \fILDH\fP .PP .nf LDH is INTEGER The leading dimension of H as declared in the calling procedure\&. LDH >= N .fi .PP .br \fIS1\fP .PP .nf S1 is COMPLEX .fi .PP .br \fIS2\fP .PP .nf S2 is COMPLEX S1 and S2 are the shifts defining K in (*) above\&. .fi .PP .br \fIV\fP .PP .nf V is COMPLEX array, dimension (N) A scalar multiple of the first column of the matrix K in (*)\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA .RE .PP .SS "subroutine dlaqr1 (integer n, double precision, dimension( ldh, * ) h, integer ldh, double precision sr1, double precision si1, double precision sr2, double precision si2, double precision, dimension( * ) v)" .PP \fBDLAQR1\fP sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts\&. .PP \fBPurpose:\fP .RS 4 .PP .nf Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 sets v to a scalar multiple of the first column of the product (*) 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER Order of the matrix H\&. N must be either 2 or 3\&. .fi .PP .br \fIH\fP .PP .nf H is DOUBLE PRECISION array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*)\&. .fi .PP .br \fILDH\fP .PP .nf LDH is INTEGER The leading dimension of H as declared in the calling procedure\&. LDH >= N .fi .PP .br \fISR1\fP .PP .nf SR1 is DOUBLE PRECISION .fi .PP .br \fISI1\fP .PP .nf SI1 is DOUBLE PRECISION .fi .PP .br \fISR2\fP .PP .nf SR2 is DOUBLE PRECISION .fi .PP .br \fISI2\fP .PP .nf SI2 is DOUBLE PRECISION The shifts in (*)\&. .fi .PP .br \fIV\fP .PP .nf V is DOUBLE PRECISION array, dimension (N) A scalar multiple of the first column of the matrix K in (*)\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA .RE .PP .SS "subroutine slaqr1 (integer n, real, dimension( ldh, * ) h, integer ldh, real sr1, real si1, real sr2, real si2, real, dimension( * ) v)" .PP \fBSLAQR1\fP sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts\&. .PP \fBPurpose:\fP .RS 4 .PP .nf Given a 2-by-2 or 3-by-3 matrix H, SLAQR1 sets v to a scalar multiple of the first column of the product (*) 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER Order of the matrix H\&. N must be either 2 or 3\&. .fi .PP .br \fIH\fP .PP .nf H is REAL array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*)\&. .fi .PP .br \fILDH\fP .PP .nf LDH is INTEGER The leading dimension of H as declared in the calling procedure\&. LDH >= N .fi .PP .br \fISR1\fP .PP .nf SR1 is REAL .fi .PP .br \fISI1\fP .PP .nf SI1 is REAL .fi .PP .br \fISR2\fP .PP .nf SR2 is REAL .fi .PP .br \fISI2\fP .PP .nf SI2 is REAL The shifts in (*)\&. .fi .PP .br \fIV\fP .PP .nf V is REAL array, dimension (N) A scalar multiple of the first column of the matrix K in (*)\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA .RE .PP .SS "subroutine zlaqr1 (integer n, complex*16, dimension( ldh, * ) h, integer ldh, complex*16 s1, complex*16 s2, complex*16, dimension( * ) v)" .PP \fBZLAQR1\fP sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts\&. .PP \fBPurpose:\fP .RS 4 .PP .nf Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a scalar multiple of the first column of the product (*) K = (H - s1*I)*(H - s2*I) scaling to avoid overflows and most underflows\&. This is useful for starting double implicit shift bulges in the QR algorithm\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER Order of the matrix H\&. N must be either 2 or 3\&. .fi .PP .br \fIH\fP .PP .nf H is COMPLEX*16 array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*)\&. .fi .PP .br \fILDH\fP .PP .nf LDH is INTEGER The leading dimension of H as declared in the calling procedure\&. LDH >= N .fi .PP .br \fIS1\fP .PP .nf S1 is COMPLEX*16 .fi .PP .br \fIS2\fP .PP .nf S2 is COMPLEX*16 S1 and S2 are the shifts defining K in (*) above\&. .fi .PP .br \fIV\fP .PP .nf V is COMPLEX*16 array, dimension (N) A scalar multiple of the first column of the matrix K in (*)\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.