gemlqt - gemlqt: multiply by Q from gelqt

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Sun Jul 20 2025 01:40:05 gemlqt(3)

subroutinecgemlqt(characterside,charactertrans,integerm,integern,integerk,integermb,complex,dimension(ldv,*)v,integerldv,complex,dimension(ldt,*)t,integerldt,complex,dimension(ldc,*)c,integerldc,complex,dimension(*)work,integerinfo)CGEMLQTPurpose: CGEMLQT overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'C': Q**H C C Q**H where Q is a complex unitary matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**H generated using the compact WY representation as returned by CGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**H. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. MB MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in CGELQT. V V is COMPLEX array, dimension (LDV,M) if SIDE = 'L', (LDV,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGELQT in the first K rows of its array argument A. LDV LDV is INTEGER The leading dimension of the array V. LDV >= max(1,K). T T is COMPLEX array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by CGELQT, stored as a MB-by-K matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. C C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is COMPLEX array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedgemlqt(characterside,charactertrans,integerm,integern,integerk,integermb,doubleprecision,dimension(ldv,*)v,integerldv,doubleprecision,dimension(ldt,*)t,integerldt,doubleprecision,dimension(ldc,*)c,integerldc,doubleprecision,dimension(*)work,integerinfo)DGEMLQTPurpose: DGEMLQT overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'T': Q**T C C Q**T where Q is a real orthogonal matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**T generated using the compact WY representation as returned by DGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Transpose, apply Q**T. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. MB MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in DGELQT. V V is DOUBLE PRECISION array, dimension (LDV,M) if SIDE = 'L', (LDV,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGELQT in the first K rows of its array argument A. LDV LDV is INTEGER The leading dimension of the array V. LDV >= max(1,K). T T is DOUBLE PRECISION array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by DGELQT, stored as a MB-by-K matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. C C is DOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is DOUBLE PRECISION array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinesgemlqt(characterside,charactertrans,integerm,integern,integerk,integermb,real,dimension(ldv,*)v,integerldv,real,dimension(ldt,*)t,integerldt,real,dimension(ldc,*)c,integerldc,real,dimension(*)work,integerinfo)SGEMLQTPurpose: SGEMLQT overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'T': Q**T C C Q**T where Q is a real orthogonal matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**T generated using the compact WY representation as returned by SGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Transpose, apply Q**T. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. MB MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in SGELQT. V V is REAL array, dimension (LDV,M) if SIDE = 'L', (LDV,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGELQT in the first K rows of its array argument A. LDV LDV is INTEGER The leading dimension of the array V. LDV >= max(1,K). T T is REAL array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by SGELQT, stored as a MB-by-K matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. C C is REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is REAL array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezgemlqt(characterside,charactertrans,integerm,integern,integerk,integermb,complex*16,dimension(ldv,*)v,integerldv,complex*16,dimension(ldt,*)t,integerldt,complex*16,dimension(ldc,*)c,integerldc,complex*16,dimension(*)work,integerinfo)ZGEMLQTPurpose: ZGEMLQT overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'C': Q**H C C Q**H where Q is a complex unitary matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**H generated using the compact WY representation as returned by ZGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**H. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. MB MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in ZGELQT. V V is COMPLEX*16 array, dimension (LDV,M) if SIDE = 'L', (LDV,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGELQT in the first K rows of its array argument A. LDV LDV is INTEGER The leading dimension of the array V. LDV >= max(1,K). T T is COMPLEX*16 array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by ZGELQT, stored as a MB-by-K matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. C C is COMPLEX*16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is COMPLEX*16 array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

gemlqt - gemlqt: multiply by Q from gelqt

Functions subroutine cgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info) CGEMLQT subroutine dgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info) DGEMLQT subroutine sgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info) SGEMLQT subroutine zgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info) ZGEMLQT