geqrt2 - geqrt2: QR factor, with T, level 2

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subroutinecgeqrt2(integerm,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(ldt,*)t,integerldt,integerinfo)CGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Purpose: CGEQRT2 computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q. ParametersM M is INTEGER The number of rows of the matrix A. M >= N. 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 complex M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is COMPLEX array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details. LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N). 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 V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by H = I - V * T * V**H where V**H is the conjugate transpose of V. subroutinedgeqrt2(integerm,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(ldt,*)t,integerldt,integerinfo)DGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Purpose: DGEQRT2 computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q. ParametersM M is INTEGER The number of rows of the matrix A. M >= N. 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 real M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is DOUBLE PRECISION array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details. LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N). 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 V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by H = I - V * T * V**T where V**T is the transpose of V. subroutinesgeqrt2(integerm,integern,real,dimension(lda,*)a,integerlda,real,dimension(ldt,*)t,integerldt,integerinfo)SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Purpose: SGEQRT2 computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q. ParametersM M is INTEGER The number of rows of the matrix A. M >= N. 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 real M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is REAL array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details. LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N). 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 V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by H = I - V * T * V**T where V**T is the transpose of V. subroutinezgeqrt2(integerm,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldt,*)t,integerldt,integerinfo)ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Purpose: ZGEQRT2 computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q. ParametersM M is INTEGER The number of rows of the matrix A. M >= N. 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 complex M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is COMPLEX*16 array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details. LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N). 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 V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by H = I - V * T * V**H where V**H is the conjugate transpose of V.

geqrt2 - geqrt2: QR factor, with T, level 2

Functions subroutine cgeqrt2 (m, n, a, lda, t, ldt, info) CGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. subroutine dgeqrt2 (m, n, a, lda, t, ldt, info) DGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. subroutine sgeqrt2 (m, n, a, lda, t, ldt, info) SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. subroutine zgeqrt2 (m, n, a, lda, t, ldt, info) ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.