laqr1 - laqr1: step in hseqr

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subroutineclaqr1(integern,complex,dimension(ldh,*)h,integerldh,complexs1,complexs2,complex,dimension(*)v)CLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. Purpose: 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. ParametersN N is INTEGER Order of the matrix H. N must be either 2 or 3. H H is COMPLEX array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*). LDH LDH is INTEGER The leading dimension of H as declared in the calling procedure. LDH >= N S1 S1 is COMPLEX S2 S2 is COMPLEX S1 and S2 are the shifts defining K in (*) above. V V is COMPLEX array, dimension (N) A scalar multiple of the first column of the matrix K in (*). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA subroutinedlaqr1(integern,doubleprecision,dimension(ldh,*)h,integerldh,doubleprecisionsr1,doubleprecisionsi1,doubleprecisionsr2,doubleprecisionsi2,doubleprecision,dimension(*)v)DLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. Purpose: 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. ParametersN N is INTEGER Order of the matrix H. N must be either 2 or 3. H H is DOUBLE PRECISION array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*). LDH LDH is INTEGER The leading dimension of H as declared in the calling procedure. LDH >= N SR1 SR1 is DOUBLE PRECISION SI1 SI1 is DOUBLE PRECISION SR2 SR2 is DOUBLE PRECISION SI2 SI2 is DOUBLE PRECISION The shifts in (*). V V is DOUBLE PRECISION array, dimension (N) A scalar multiple of the first column of the matrix K in (*). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA subroutineslaqr1(integern,real,dimension(ldh,*)h,integerldh,realsr1,realsi1,realsr2,realsi2,real,dimension(*)v)SLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. Purpose: 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. ParametersN N is INTEGER Order of the matrix H. N must be either 2 or 3. H H is REAL array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*). LDH LDH is INTEGER The leading dimension of H as declared in the calling procedure. LDH >= N SR1 SR1 is REAL SI1 SI1 is REAL SR2 SR2 is REAL SI2 SI2 is REAL The shifts in (*). V V is REAL array, dimension (N) A scalar multiple of the first column of the matrix K in (*). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA subroutinezlaqr1(integern,complex*16,dimension(ldh,*)h,integerldh,complex*16s1,complex*16s2,complex*16,dimension(*)v)ZLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. Purpose: 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. ParametersN N is INTEGER Order of the matrix H. N must be either 2 or 3. H H is COMPLEX*16 array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*). LDH LDH is INTEGER The leading dimension of H as declared in the calling procedure. LDH >= N S1 S1 is COMPLEX*16 S2 S2 is COMPLEX*16 S1 and S2 are the shifts defining K in (*) above. V V is COMPLEX*16 array, dimension (N) A scalar multiple of the first column of the matrix K in (*). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

laqr1 - laqr1: step in hseqr

Functions subroutine claqr1 (n, h, ldh, s1, s2, v) CLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. subroutine dlaqr1 (n, h, ldh, sr1, si1, sr2, si2, v) DLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. subroutine slaqr1 (n, h, ldh, sr1, si1, sr2, si2, v) SLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. subroutine zlaqr1 (n, h, ldh, s1, s2, v) ZLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.