lartg(3) Library Functions Manual lartg(3) NAME lartg - lartg: generate plane rotation, more accurate than BLAS rot SYNOPSIS Functions subroutine clartg (f, g, c, s, r) CLARTG generates a plane rotation with real cosine and complex sine. subroutine dlartg (f, g, c, s, r) DLARTG generates a plane rotation with real cosine and real sine. subroutine slartg (f, g, c, s, r) SLARTG generates a plane rotation with real cosine and real sine. subroutine zlartg (f, g, c, s, r) ZLARTG generates a plane rotation with real cosine and complex sine. Detailed Description Function Documentation subroutine clartg (complex(wp) f, complex(wp) g, real(wp) c, complex(wp) s, complex(wp) r) CLARTG generates a plane rotation with real cosine and complex sine. Purpose: !> !> CLARTG generates a plane rotation so that !> !> [ C S ] . [ F ] = [ R ] !> [ -conjg(S) C ] [ G ] [ 0 ] !> !> where C is real and C**2 + |S|**2 = 1. !> !> The mathematical formulas used for C and S are !> !> sgn(x) = { x / |x|, x != 0 !> { 1, x = 0 !> !> R = sgn(F) * sqrt(|F|**2 + |G|**2) !> !> C = |F| / sqrt(|F|**2 + |G|**2) !> !> S = sgn(F) * conjg(G) / sqrt(|F|**2 + |G|**2) !> !> Special conditions: !> If G=0, then C=1 and S=0. !> If F=0, then C=0 and S is chosen so that R is real. !> !> When F and G are real, the formulas simplify to C = F/R and !> S = G/R, and the returned values of C, S, and R should be !> identical to those returned by SLARTG. !> !> The algorithm used to compute these quantities incorporates scaling !> to avoid overflow or underflow in computing the square root of the !> sum of squares. !> !> This is the same routine CROTG fom BLAS1, except that !> F and G are unchanged on return. !> !> Below, wp=>sp stands for single precision from LA_CONSTANTS module. !> Parameters F !> F is COMPLEX(wp) !> The first component of vector to be rotated. !> G !> G is COMPLEX(wp) !> The second component of vector to be rotated. !> C !> C is REAL(wp) !> The cosine of the rotation. !> S !> S is COMPLEX(wp) !> The sine of the rotation. !> R !> R is COMPLEX(wp) !> The nonzero component of the rotated vector. !> Author Weslley Pereira, University of Colorado Denver, USA Date December 2021 Further Details: !> !> Based on the algorithm from !> !> Anderson E. (2017) !> Algorithm 978: Safe Scaling in the Level 1 BLAS !> ACM Trans Math Softw 44:1--28 !> https://doi.org/10.1145/3061665 !> !> Definition at line 115 of file clartg.f90. subroutine dlartg (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp) r) DLARTG generates a plane rotation with real cosine and real sine. Purpose: !> !> DLARTG generates a plane rotation so that !> !> [ C S ] . [ F ] = [ R ] !> [ -S C ] [ G ] [ 0 ] !> !> where C**2 + S**2 = 1. !> !> The mathematical formulas used for C and S are !> R = sign(F) * sqrt(F**2 + G**2) !> C = F / R !> S = G / R !> Hence C >= 0. The algorithm used to compute these quantities !> incorporates scaling to avoid overflow or underflow in computing the !> square root of the sum of squares. !> !> This version is discontinuous in R at F = 0 but it returns the same !> C and S as ZLARTG for complex inputs (F,0) and (G,0). !> !> This is a more accurate version of the BLAS1 routine DROTG, !> with the following other differences: !> F and G are unchanged on return. !> If G=0, then C=1 and S=0. !> If F=0 and (G .ne. 0), then C=0 and S=sign(1,G) without doing any !> floating point operations (saves work in DBDSQR when !> there are zeros on the diagonal). !> !> Below, wp=>dp stands for double precision from LA_CONSTANTS module. !> Parameters F !> F is REAL(wp) !> The first component of vector to be rotated. !> G !> G is REAL(wp) !> The second component of vector to be rotated. !> C !> C is REAL(wp) !> The cosine of the rotation. !> S !> S is REAL(wp) !> The sine of the rotation. !> R !> R is REAL(wp) !> The nonzero component of the rotated vector. !> Author Edward Anderson, Lockheed Martin Date July 2016 Contributors: Weslley Pereira, University of Colorado Denver, USA Further Details: !> !> Anderson E. (2017) !> Algorithm 978: Safe Scaling in the Level 1 BLAS !> ACM Trans Math Softw 44:1--28 !> https://doi.org/10.1145/3061665 !> !> Definition at line 110 of file dlartg.f90. subroutine slartg (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp) r) SLARTG generates a plane rotation with real cosine and real sine. Purpose: !> !> SLARTG generates a plane rotation so that !> !> [ C S ] . [ F ] = [ R ] !> [ -S C ] [ G ] [ 0 ] !> !> where C**2 + S**2 = 1. !> !> The mathematical formulas used for C and S are !> R = sign(F) * sqrt(F**2 + G**2) !> C = F / R !> S = G / R !> Hence C >= 0. The algorithm used to compute these quantities !> incorporates scaling to avoid overflow or underflow in computing the !> square root of the sum of squares. !> !> This version is discontinuous in R at F = 0 but it returns the same !> C and S as CLARTG for complex inputs (F,0) and (G,0). !> !> This is a more accurate version of the BLAS1 routine SROTG, !> with the following other differences: !> F and G are unchanged on return. !> If G=0, then C=1 and S=0. !> If F=0 and (G .ne. 0), then C=0 and S=sign(1,G) without doing any !> floating point operations (saves work in SBDSQR when !> there are zeros on the diagonal). !> !> Below, wp=>sp stands for single precision from LA_CONSTANTS module. !> Parameters F !> F is REAL(wp) !> The first component of vector to be rotated. !> G !> G is REAL(wp) !> The second component of vector to be rotated. !> C !> C is REAL(wp) !> The cosine of the rotation. !> S !> S is REAL(wp) !> The sine of the rotation. !> R !> R is REAL(wp) !> The nonzero component of the rotated vector. !> Author Edward Anderson, Lockheed Martin Date July 2016 Contributors: Weslley Pereira, University of Colorado Denver, USA Further Details: !> !> Anderson E. (2017) !> Algorithm 978: Safe Scaling in the Level 1 BLAS !> ACM Trans Math Softw 44:1--28 !> https://doi.org/10.1145/3061665 !> !> Definition at line 110 of file slartg.f90. subroutine zlartg (complex(wp) f, complex(wp) g, real(wp) c, complex(wp) s, complex(wp) r) ZLARTG generates a plane rotation with real cosine and complex sine. Purpose: !> !> ZLARTG generates a plane rotation so that !> !> [ C S ] . [ F ] = [ R ] !> [ -conjg(S) C ] [ G ] [ 0 ] !> !> where C is real and C**2 + |S|**2 = 1. !> !> The mathematical formulas used for C and S are !> !> sgn(x) = { x / |x|, x != 0 !> { 1, x = 0 !> !> R = sgn(F) * sqrt(|F|**2 + |G|**2) !> !> C = |F| / sqrt(|F|**2 + |G|**2) !> !> S = sgn(F) * conjg(G) / sqrt(|F|**2 + |G|**2) !> !> Special conditions: !> If G=0, then C=1 and S=0. !> If F=0, then C=0 and S is chosen so that R is real. !> !> When F and G are real, the formulas simplify to C = F/R and !> S = G/R, and the returned values of C, S, and R should be !> identical to those returned by DLARTG. !> !> The algorithm used to compute these quantities incorporates scaling !> to avoid overflow or underflow in computing the square root of the !> sum of squares. !> !> This is the same routine ZROTG fom BLAS1, except that !> F and G are unchanged on return. !> !> Below, wp=>dp stands for double precision from LA_CONSTANTS module. !> Parameters F !> F is COMPLEX(wp) !> The first component of vector to be rotated. !> G !> G is COMPLEX(wp) !> The second component of vector to be rotated. !> C !> C is REAL(wp) !> The cosine of the rotation. !> S !> S is COMPLEX(wp) !> The sine of the rotation. !> R !> R is COMPLEX(wp) !> The nonzero component of the rotated vector. !> Author Weslley Pereira, University of Colorado Denver, USA Date December 2021 Further Details: !> !> Based on the algorithm from !> !> Anderson E. (2017) !> Algorithm 978: Safe Scaling in the Level 1 BLAS !> ACM Trans Math Softw 44:1--28 !> https://doi.org/10.1145/3061665 !> !> Definition at line 115 of file zlartg.f90. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 lartg(3)