unmr2 - {un,or}mr2: step in unmrq

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Sun Jul 20 2025 01:40:05 unmr2(3)

subroutinecunmr2(characterside,charactertrans,integerm,integern,integerk,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tau,complex,dimension(ldc,*)c,integerldc,complex,dimension(*)work,integerinfo)CUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm). Purpose: CUNMR2 overwrites the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q**H* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**H if SIDE = 'R' and TRANS = 'C', where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(1)**H H(2)**H . . . H(k)**H as returned by CGERQF. 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': apply Q (No transpose) = 'C': apply Q**H (Conjugate transpose) 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. A A is COMPLEX array, dimension (LDA,M) if SIDE = 'L', (LDA,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 CGERQF in the last k rows of its array argument A. A is modified by the routine but restored on exit. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,K). TAU TAU is COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGERQF. C C is COMPLEX array, dimension (LDC,N) On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q**H*C or 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, dimension (N) if SIDE = 'L', (M) 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. subroutinedormr2(characterside,charactertrans,integerm,integern,integerk,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)tau,doubleprecision,dimension(ldc,*)c,integerldc,doubleprecision,dimension(*)work,integerinfo)DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). Purpose: DORMR2 overwrites the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q**T* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'T', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) . . . H(k) as returned by DGERQF. 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': apply Q (No transpose) = 'T': apply Q' (Transpose) 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. A A is DOUBLE PRECISION array, dimension (LDA,M) if SIDE = 'L', (LDA,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 DGERQF in the last k rows of its array argument A. A is modified by the routine but restored on exit. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,K). TAU TAU is DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGERQF. 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 or Q**T*C or 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, dimension (N) if SIDE = 'L', (M) 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. subroutinesormr2(characterside,charactertrans,integerm,integern,integerk,real,dimension(lda,*)a,integerlda,real,dimension(*)tau,real,dimension(ldc,*)c,integerldc,real,dimension(*)work,integerinfo)SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). Purpose: SORMR2 overwrites the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q**T* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'T', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) . . . H(k) as returned by SGERQF. 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': apply Q (No transpose) = 'T': apply Q' (Transpose) 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. A A is REAL array, dimension (LDA,M) if SIDE = 'L', (LDA,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 SGERQF in the last k rows of its array argument A. A is modified by the routine but restored on exit. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,K). TAU TAU is REAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGERQF. C C is REAL array, dimension (LDC,N) On entry, the m by n matrix C. On exit, C is overwritten by Q*C or Q**T*C or 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, dimension (N) if SIDE = 'L', (M) 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. subroutinezunmr2(characterside,charactertrans,integerm,integern,integerk,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tau,complex*16,dimension(ldc,*)c,integerldc,complex*16,dimension(*)work,integerinfo)ZUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm). Purpose: ZUNMR2 overwrites the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q**H* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**H if SIDE = 'R' and TRANS = 'C', where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(1)**H H(2)**H . . . H(k)**H as returned by ZGERQF. 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': apply Q (No transpose) = 'C': apply Q**H (Conjugate transpose) 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. A A is COMPLEX*16 array, dimension (LDA,M) if SIDE = 'L', (LDA,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 ZGERQF in the last k rows of its array argument A. A is modified by the routine but restored on exit. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,K). TAU TAU is COMPLEX*16 array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGERQF. 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 or Q**H*C or 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, dimension (N) if SIDE = 'L', (M) 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.

unmr2 - {un,or}mr2: step in unmrq

Functions subroutine cunmr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) CUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm). subroutine dormr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). subroutine sormr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). subroutine zunmr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) ZUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm).