gerq2 - gerq2: RQ factor, level 2

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subroutinecgerq2(integerm,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tau,complex,dimension(*)work,integerinfo)CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. Purpose: CGERQ2 computes an RQ factorization of a complex m by n matrix A: A = R * Q. ParametersM M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0. A A is COMPLEX array, dimension (LDA,N) On entry, the m by n matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU TAU is COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK WORK is COMPLEX array, dimension (M) 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. FurtherDetails: The matrix Q is represented as a product of elementary reflectors Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v**H where tau is a complex scalar, and v is a complex vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). subroutinedgerq2(integerm,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)tau,doubleprecision,dimension(*)work,integerinfo)DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. Purpose: DGERQ2 computes an RQ factorization of a real m by n matrix A: A = R * Q. ParametersM M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0. A A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the m by n matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK WORK is DOUBLE PRECISION array, dimension (M) 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. FurtherDetails: The matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(k), where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v**T where tau is a real scalar, and v is a real vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). subroutinesgerq2(integerm,integern,real,dimension(lda,*)a,integerlda,real,dimension(*)tau,real,dimension(*)work,integerinfo)SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. Purpose: SGERQ2 computes an RQ factorization of a real m by n matrix A: A = R * Q. ParametersM M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0. A A is REAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK WORK is REAL array, dimension (M) 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. FurtherDetails: The matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(k), where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v**T where tau is a real scalar, and v is a real vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). subroutinezgerq2(integerm,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tau,complex*16,dimension(*)work,integerinfo)ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. Purpose: ZGERQ2 computes an RQ factorization of a complex m by n matrix A: A = R * Q. ParametersM M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0. A A is COMPLEX*16 array, dimension (LDA,N) On entry, the m by n matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK WORK is COMPLEX*16 array, dimension (M) 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. FurtherDetails: The matrix Q is represented as a product of elementary reflectors Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v**H where tau is a complex scalar, and v is a complex vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

gerq2 - gerq2: RQ factor, level 2

Functions subroutine cgerq2 (m, n, a, lda, tau, work, info) CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. subroutine dgerq2 (m, n, a, lda, tau, work, info) DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. subroutine sgerq2 (m, n, a, lda, tau, work, info) SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. subroutine zgerq2 (m, n, a, lda, tau, work, info) ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.