/* Subroutine */ int cunmr3_(char *side, char *trans, integer *m, integer *n, integer *k, integer *l, complex *a, integer *lda, complex *tau, complex *c__, integer *ldc, complex *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3; complex q__1; /* Builtin functions */ void r_cnjg(complex *, complex *); /* Local variables */ integer i__, i1, i2, i3, ja, ic, jc, mi, ni, nq; logical left; complex taui; extern logical lsame_(char *, char *); extern /* Subroutine */ int clarz_(char *, integer *, integer *, integer * , complex *, integer *, complex *, complex *, integer *, complex * ), xerbla_(char *, integer *); logical notran; /* -- LAPACK routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CUNMR3 overwrites the general complex m by n matrix C with */ /* Q * C if SIDE = 'L' and TRANS = 'N', or */ /* Q'* C if SIDE = 'L' and TRANS = 'C', or */ /* C * Q if SIDE = 'R' and TRANS = 'N', or */ /* C * Q' 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'. */ /* Arguments */ /* ========= */ /* SIDE (input) CHARACTER*1 */ /* = 'L': apply Q or Q' from the Left */ /* = 'R': apply Q or Q' from the Right */ /* TRANS (input) CHARACTER*1 */ /* = 'N': apply Q (No transpose) */ /* = 'C': apply Q' (Conjugate transpose) */ /* M (input) INTEGER */ /* The number of rows of the matrix C. M >= 0. */ /* N (input) INTEGER */ /* The number of columns of the matrix C. N >= 0. */ /* K (input) 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 (input) 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 (input) 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 (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,K). */ /* TAU (input) COMPLEX array, dimension (K) */ /* TAU(i) must contain the scalar factor of the elementary */ /* reflector H(i), as returned by CTZRZF. */ /* C (input/output) COMPLEX array, dimension (LDC,N) */ /* On entry, the m-by-n matrix C. */ /* On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q. */ /* LDC (input) INTEGER */ /* The leading dimension of the array C. LDC >= max(1,M). */ /* WORK (workspace) COMPLEX array, dimension */ /* (N) if SIDE = 'L', */ /* (M) if SIDE = 'R' */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* Further Details */ /* =============== */ /* Based on contributions by */ /* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA */ /* ===================================================================== */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input arguments */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; --work; /* Function Body */ *info = 0; left = lsame_(side, "L"); notran = lsame_(trans, "N"); /* NQ is the order of Q */ if (left) { nq = *m; } else { nq = *n; } if (! left && ! lsame_(side, "R")) { *info = -1; } else if (! notran && ! lsame_(trans, "C")) { *info = -2; } else if (*m < 0) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; } else if (*l < 0 || left && *l > *m || ! left && *l > *n) { *info = -6; } else if (*lda < max(1,*k)) { *info = -8; } else if (*ldc < max(1,*m)) { *info = -11; } if (*info != 0) { i__1 = -(*info); xerbla_("CUNMR3", &i__1); return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || *k == 0) { return 0; } if (left && ! notran || ! left && notran) { i1 = 1; i2 = *k; i3 = 1; } else { i1 = *k; i2 = 1; i3 = -1; } if (left) { ni = *n; ja = *m - *l + 1; jc = 1; } else { mi = *m; ja = *n - *l + 1; ic = 1; } i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { if (left) { /* H(i) or H(i)' is applied to C(i:m,1:n) */ mi = *m - i__ + 1; ic = i__; } else { /* H(i) or H(i)' is applied to C(1:m,i:n) */ ni = *n - i__ + 1; jc = i__; } /* Apply H(i) or H(i)' */ if (notran) { i__3 = i__; taui.r = tau[i__3].r, taui.i = tau[i__3].i; } else { r_cnjg(&q__1, &tau[i__]); taui.r = q__1.r, taui.i = q__1.i; } clarz_(side, &mi, &ni, l, &a[i__ + ja * a_dim1], lda, &taui, &c__[ic + jc * c_dim1], ldc, &work[1]); /* L10: */ } return 0; /* End of CUNMR3 */ } /* cunmr3_ */
int clatrz_(int *m, int *n, int *l, complex *a, int *lda, complex *tau, complex *work) { /* System generated locals */ int a_dim1, a_offset, i__1, i__2; complex q__1; /* Builtin functions */ void r_cnjg(complex *, complex *); /* Local variables */ int i__; complex alpha; extern int clarz_(char *, int *, int *, int * , complex *, int *, complex *, complex *, int *, complex * ), clacgv_(int *, complex *, int *), clarfp_( int *, complex *, complex *, int *, complex *); /* -- LAPACK routine (version 3.2) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix */ /* [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means */ /* of unitary transformations, where Z is an (M+L)-by-(M+L) unitary */ /* matrix and, R and A1 are M-by-M upper triangular matrices. */ /* Arguments */ /* ========= */ /* M (input) INTEGER */ /* The number of rows of the matrix A. M >= 0. */ /* N (input) INTEGER */ /* The number of columns of the matrix A. N >= 0. */ /* L (input) INTEGER */ /* The number of columns of the matrix A containing the */ /* meaningful part of the Householder vectors. N-M >= L >= 0. */ /* A (input/output) COMPLEX array, dimension (LDA,N) */ /* On entry, the leading M-by-N upper trapezoidal part of the */ /* array A must contain the matrix to be factorized. */ /* On exit, the leading M-by-M upper triangular part of A */ /* contains the upper triangular matrix R, and elements N-L+1 to */ /* N of the first M rows of A, with the array TAU, represent the */ /* unitary matrix Z as a product of M elementary reflectors. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= MAX(1,M). */ /* TAU (output) COMPLEX array, dimension (M) */ /* The scalar factors of the elementary reflectors. */ /* WORK (workspace) COMPLEX array, dimension (M) */ /* Further Details */ /* =============== */ /* Based on contributions by */ /* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA */ /* The factorization is obtained by Householder's method. The kth */ /* transformation matrix, Z( k ), which is used to introduce zeros into */ /* the ( m - k + 1 )th row of A, is given in the form */ /* Z( k ) = ( I 0 ), */ /* ( 0 T( k ) ) */ /* where */ /* T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ), */ /* ( 0 ) */ /* ( z( k ) ) */ /* tau is a scalar and z( k ) is an l element vector. tau and z( k ) */ /* are chosen to annihilate the elements of the kth row of A2. */ /* The scalar tau is returned in the kth element of TAU and the vector */ /* u( k ) in the kth row of A2, such that the elements of z( k ) are */ /* in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in */ /* the upper triangular part of A1. */ /* Z is given by */ /* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Quick return if possible */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; /* Function Body */ if (*m == 0) { return 0; } else if (*m == *n) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; tau[i__2].r = 0.f, tau[i__2].i = 0.f; /* L10: */ } return 0; } for (i__ = *m; i__ >= 1; --i__) { /* Generate elementary reflector H(i) to annihilate */ /* [ A(i,i) A(i,n-l+1:n) ] */ clacgv_(l, &a[i__ + (*n - *l + 1) * a_dim1], lda); r_cnjg(&q__1, &a[i__ + i__ * a_dim1]); alpha.r = q__1.r, alpha.i = q__1.i; i__1 = *l + 1; clarfp_(&i__1, &alpha, &a[i__ + (*n - *l + 1) * a_dim1], lda, &tau[ i__]); i__1 = i__; r_cnjg(&q__1, &tau[i__]); tau[i__1].r = q__1.r, tau[i__1].i = q__1.i; /* Apply H(i) to A(1:i-1,i:n) from the right */ i__1 = i__ - 1; i__2 = *n - i__ + 1; r_cnjg(&q__1, &tau[i__]); clarz_("Right", &i__1, &i__2, l, &a[i__ + (*n - *l + 1) * a_dim1], lda, &q__1, &a[i__ * a_dim1 + 1], lda, &work[1]); i__1 = i__ + i__ * a_dim1; r_cnjg(&q__1, &alpha); a[i__1].r = q__1.r, a[i__1].i = q__1.i; /* L20: */ } return 0; /* End of CLATRZ */ } /* clatrz_ */
/* Subroutine */ int clatrz_(integer *m, integer *n, integer *l, complex *a, integer *lda, complex *tau, complex *work) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= CLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means of unitary transformations, where Z is an (M+L)-by-(M+L) unitary matrix and, R and A1 are M-by-M upper triangular matrices. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. L (input) INTEGER The number of columns of the matrix A containing the meaningful part of the Householder vectors. N-M >= L >= 0. A (input/output) COMPLEX array, dimension (LDA,N) On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements N-L+1 to N of the first M rows of A, with the array TAU, represent the unitary matrix Z as a product of M elementary reflectors. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU (output) COMPLEX array, dimension (M) The scalar factors of the elementary reflectors. WORK (workspace) COMPLEX array, dimension (M) Further Details =============== Based on contributions by A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA The factorization is obtained by Householder's method. The kth transformation matrix, Z( k ), which is used to introduce zeros into the ( m - k + 1 )th row of A, is given in the form Z( k ) = ( I 0 ), ( 0 T( k ) ) where T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ), ( 0 ) ( z( k ) ) tau is a scalar and z( k ) is an l element vector. tau and z( k ) are chosen to annihilate the elements of the kth row of A2. The scalar tau is returned in the kth element of TAU and the vector u( k ) in the kth row of A2, such that the elements of z( k ) are in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in the upper triangular part of A1. Z is given by Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). ===================================================================== Quick return if possible Parameter adjustments */ /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; complex q__1; /* Builtin functions */ void r_cnjg(complex *, complex *); /* Local variables */ static integer i__; static complex alpha; extern /* Subroutine */ int clarz_(char *, integer *, integer *, integer * , complex *, integer *, complex *, complex *, integer *, complex * ), clarfg_(integer *, complex *, complex *, integer *, complex *), clacgv_(integer *, complex *, integer *); #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --tau; --work; /* Function Body */ if (*m == 0) { return 0; } else if (*m == *n) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; tau[i__2].r = 0.f, tau[i__2].i = 0.f; /* L10: */ } return 0; } for (i__ = *m; i__ >= 1; --i__) { /* Generate elementary reflector H(i) to annihilate [ A(i,i) A(i,n-l+1:n) ] */ clacgv_(l, &a_ref(i__, *n - *l + 1), lda); r_cnjg(&q__1, &a_ref(i__, i__)); alpha.r = q__1.r, alpha.i = q__1.i; i__1 = *l + 1; clarfg_(&i__1, &alpha, &a_ref(i__, *n - *l + 1), lda, &tau[i__]); i__1 = i__; r_cnjg(&q__1, &tau[i__]); tau[i__1].r = q__1.r, tau[i__1].i = q__1.i; /* Apply H(i) to A(1:i-1,i:n) from the right */ i__1 = i__ - 1; i__2 = *n - i__ + 1; r_cnjg(&q__1, &tau[i__]); clarz_("Right", &i__1, &i__2, l, &a_ref(i__, *n - *l + 1), lda, &q__1, &a_ref(1, i__), lda, &work[1]); i__1 = a_subscr(i__, i__); r_cnjg(&q__1, &alpha); a[i__1].r = q__1.r, a[i__1].i = q__1.i; /* L20: */ } return 0; /* End of CLATRZ */ } /* clatrz_ */
/* Subroutine */ int clatrz_(integer *m, integer *n, integer *l, complex *a, integer *lda, complex *tau, complex *work) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; complex q__1; /* Builtin functions */ void r_cnjg(complex *, complex *); /* Local variables */ integer i__; complex alpha; extern /* Subroutine */ int clarz_(char *, integer *, integer *, integer * , complex *, integer *, complex *, complex *, integer *, complex * ), clarfg_(integer *, complex *, complex *, integer *, complex *), clacgv_(integer *, complex *, integer *); /* -- LAPACK computational routine (version 3.4.2) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* September 2012 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Quick return if possible */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; /* Function Body */ if (*m == 0) { return 0; } else if (*m == *n) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; tau[i__2].r = 0.f; tau[i__2].i = 0.f; // , expr subst /* L10: */ } return 0; } for (i__ = *m; i__ >= 1; --i__) { /* Generate elementary reflector H(i) to annihilate */ /* [ A(i,i) A(i,n-l+1:n) ] */ clacgv_(l, &a[i__ + (*n - *l + 1) * a_dim1], lda); r_cnjg(&q__1, &a[i__ + i__ * a_dim1]); alpha.r = q__1.r; alpha.i = q__1.i; // , expr subst i__1 = *l + 1; clarfg_(&i__1, &alpha, &a[i__ + (*n - *l + 1) * a_dim1], lda, &tau[ i__]); i__1 = i__; r_cnjg(&q__1, &tau[i__]); tau[i__1].r = q__1.r; tau[i__1].i = q__1.i; // , expr subst /* Apply H(i) to A(1:i-1,i:n) from the right */ i__1 = i__ - 1; i__2 = *n - i__ + 1; r_cnjg(&q__1, &tau[i__]); clarz_("Right", &i__1, &i__2, l, &a[i__ + (*n - *l + 1) * a_dim1], lda, &q__1, &a[i__ * a_dim1 + 1], lda, &work[1]); i__1 = i__ + i__ * a_dim1; r_cnjg(&q__1, &alpha); a[i__1].r = q__1.r; a[i__1].i = q__1.i; // , expr subst /* L20: */ } return 0; /* End of CLATRZ */ }