unmr3(3) Library Functions Manual unmr3(3) NAME unmr3 - {un,or}mr3: step in unmrz SYNOPSIS Functions subroutine cunmr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info) CUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm). subroutine dormr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info) DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm). subroutine sormr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info) SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm). subroutine zunmr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info) ZUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm). Detailed Description Function Documentation subroutine cunmr3 (character side, character trans, integer m, integer n, integer k, integer l, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info) CUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm). Purpose: CUNMR3 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(2) . . . H(k) as returned by CTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'. Parameters SIDE 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. L L is INTEGER The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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 CTZRZF 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 CTZRZF. 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. Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA Further Details: Definition at line 176 of file cunmr3.f. subroutine dormr3 (character side, character trans, integer m, integer n, integer k, integer l, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info) DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm). Purpose: DORMR3 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 = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'C', 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 DTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'. Parameters SIDE 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**T (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. L L is INTEGER The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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 DTZRZF 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 DTZRZF. 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. Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA Further Details: Definition at line 176 of file dormr3.f. subroutine sormr3 (character side, character trans, integer m, integer n, integer k, integer l, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info) SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm). Purpose: SORMR3 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 = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'C', 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 STZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'. Parameters SIDE 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**T (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. L L is INTEGER The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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 STZRZF 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 STZRZF. 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. Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA Further Details: Definition at line 176 of file sormr3.f. subroutine zunmr3 (character side, character trans, integer m, integer n, integer k, integer l, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info) ZUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm). Purpose: ZUNMR3 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(2) . . . H(k) as returned by ZTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'. Parameters SIDE 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. L L is INTEGER The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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 ZTZRZF 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 ZTZRZF. 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. Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA Further Details: Definition at line 176 of file zunmr3.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 unmr3(3)