larz - larz: apply reflector

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Thu Aug 7 2025 17:26:25 larz(3)

subroutineclarz(characterside,integerm,integern,integerl,complex,dimension(*)v,integerincv,complextau,complex,dimension(ldc,*)c,integerldc,complex,dimension(*)work)CLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. Purpose: CLARZ applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**H where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply H**H (the conjugate transpose of H), supply conjg(tau) instead tau. H is a product of k elementary reflectors as returned by CTZRZF. ParametersSIDE SIDE is CHARACTER*1 = 'L': form H * C = 'R': form C * H M M is INTEGER The number of rows of the matrix C. N N is INTEGER The number of columns of the matrix C. L L is INTEGER The number of entries of the vector V containing the meaningful part of the Householder vectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. V V is COMPLEX array, dimension (1+(L-1)*abs(INCV)) The vector v in the representation of H as returned by CTZRZF. V is not used if TAU = 0. INCV INCV is INTEGER The increment between elements of v. INCV <> 0. TAU TAU is COMPLEX The value tau in the representation of H. C C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is COMPLEX array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R' Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA FurtherDetails:subroutinedlarz(characterside,integerm,integern,integerl,doubleprecision,dimension(*)v,integerincv,doubleprecisiontau,doubleprecision,dimension(ldc,*)c,integerldc,doubleprecision,dimension(*)work)DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. Purpose: DLARZ applies a real elementary reflector H to a real M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**T where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix. H is a product of k elementary reflectors as returned by DTZRZF. ParametersSIDE SIDE is CHARACTER*1 = 'L': form H * C = 'R': form C * H M M is INTEGER The number of rows of the matrix C. N N is INTEGER The number of columns of the matrix C. L L is INTEGER The number of entries of the vector V containing the meaningful part of the Householder vectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. V V is DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV)) The vector v in the representation of H as returned by DTZRZF. V is not used if TAU = 0. INCV INCV is INTEGER The increment between elements of v. INCV <> 0. TAU TAU is DOUBLE PRECISION The value tau in the representation of H. C C is DOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is DOUBLE PRECISION array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R' Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA FurtherDetails:subroutineslarz(characterside,integerm,integern,integerl,real,dimension(*)v,integerincv,realtau,real,dimension(ldc,*)c,integerldc,real,dimension(*)work)SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. Purpose: SLARZ applies a real elementary reflector H to a real M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**T where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix. H is a product of k elementary reflectors as returned by STZRZF. ParametersSIDE SIDE is CHARACTER*1 = 'L': form H * C = 'R': form C * H M M is INTEGER The number of rows of the matrix C. N N is INTEGER The number of columns of the matrix C. L L is INTEGER The number of entries of the vector V containing the meaningful part of the Householder vectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. V V is REAL array, dimension (1+(L-1)*abs(INCV)) The vector v in the representation of H as returned by STZRZF. V is not used if TAU = 0. INCV INCV is INTEGER The increment between elements of v. INCV <> 0. TAU TAU is REAL The value tau in the representation of H. C C is REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is REAL array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R' Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA FurtherDetails:subroutinezlarz(characterside,integerm,integern,integerl,complex*16,dimension(*)v,integerincv,complex*16tau,complex*16,dimension(ldc,*)c,integerldc,complex*16,dimension(*)work)ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. Purpose: ZLARZ applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**H where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply H**H (the conjugate transpose of H), supply conjg(tau) instead tau. H is a product of k elementary reflectors as returned by ZTZRZF. ParametersSIDE SIDE is CHARACTER*1 = 'L': form H * C = 'R': form C * H M M is INTEGER The number of rows of the matrix C. N N is INTEGER The number of columns of the matrix C. L L is INTEGER The number of entries of the vector V containing the meaningful part of the Householder vectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. V V is COMPLEX*16 array, dimension (1+(L-1)*abs(INCV)) The vector v in the representation of H as returned by ZTZRZF. V is not used if TAU = 0. INCV INCV is INTEGER The increment between elements of v. INCV <> 0. TAU TAU is COMPLEX*16 The value tau in the representation of H. C C is COMPLEX*16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is COMPLEX*16 array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R' Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA FurtherDetails:

larz - larz: apply reflector

Functions subroutine clarz (side, m, n, l, v, incv, tau, c, ldc, work) CLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. subroutine dlarz (side, m, n, l, v, incv, tau, c, ldc, work) DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. subroutine slarz (side, m, n, l, v, incv, tau, c, ldc, work) SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. subroutine zlarz (side, m, n, l, v, incv, tau, c, ldc, work) ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.