X-Git-Url: http://git.maemo.org/git/?p=opencv;a=blobdiff_plain;f=3rdparty%2Flapack%2Fslabrd.c;fp=3rdparty%2Flapack%2Fslabrd.c;h=80676413ca1e489d74e33cf265e9a5be185ea666;hp=0000000000000000000000000000000000000000;hb=e4c14cdbdf2fe805e79cd96ded236f57e7b89060;hpb=454138ff8a20f6edb9b65a910101403d8b520643 diff --git a/3rdparty/lapack/slabrd.c b/3rdparty/lapack/slabrd.c new file mode 100644 index 0000000..8067641 --- /dev/null +++ b/3rdparty/lapack/slabrd.c @@ -0,0 +1,419 @@ +#include "clapack.h" + +/* Table of constant values */ + +static real c_b4 = -1.f; +static real c_b5 = 1.f; +static integer c__1 = 1; +static real c_b16 = 0.f; + +/* Subroutine */ int slabrd_(integer *m, integer *n, integer *nb, real *a, + integer *lda, real *d__, real *e, real *tauq, real *taup, real *x, + integer *ldx, real *y, integer *ldy) +{ + /* System generated locals */ + integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2, + i__3; + + /* Local variables */ + integer i__; + extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *), + sgemv_(char *, integer *, integer *, real *, real *, integer *, + real *, integer *, real *, real *, integer *), slarfg_( + integer *, real *, real *, integer *, real *); + + +/* -- LAPACK auxiliary routine (version 3.1) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* SLABRD reduces the first NB rows and columns of a real general */ +/* m by n matrix A to upper or lower bidiagonal form by an orthogonal */ +/* transformation Q' * A * P, and returns the matrices X and Y which */ +/* are needed to apply the transformation to the unreduced part of A. */ + +/* If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower */ +/* bidiagonal form. */ + +/* This is an auxiliary routine called by SGEBRD */ + +/* Arguments */ +/* ========= */ + +/* M (input) INTEGER */ +/* The number of rows in the matrix A. */ + +/* N (input) INTEGER */ +/* The number of columns in the matrix A. */ + +/* NB (input) INTEGER */ +/* The number of leading rows and columns of A to be reduced. */ + +/* A (input/output) REAL array, dimension (LDA,N) */ +/* On entry, the m by n general matrix to be reduced. */ +/* On exit, the first NB rows and columns of the matrix are */ +/* overwritten; the rest of the array is unchanged. */ +/* If m >= n, elements on and below the diagonal in the first NB */ +/* columns, with the array TAUQ, represent the orthogonal */ +/* matrix Q as a product of elementary reflectors; and */ +/* elements above the diagonal in the first NB rows, with the */ +/* array TAUP, represent the orthogonal matrix P as a product */ +/* of elementary reflectors. */ +/* If m < n, elements below the diagonal in the first NB */ +/* columns, with the array TAUQ, represent the orthogonal */ +/* matrix Q as a product of elementary reflectors, and */ +/* elements on and above the diagonal in the first NB rows, */ +/* with the array TAUP, represent the orthogonal matrix P as */ +/* a product of elementary reflectors. */ +/* See Further Details. */ + +/* LDA (input) INTEGER */ +/* The leading dimension of the array A. LDA >= max(1,M). */ + +/* D (output) REAL array, dimension (NB) */ +/* The diagonal elements of the first NB rows and columns of */ +/* the reduced matrix. D(i) = A(i,i). */ + +/* E (output) REAL array, dimension (NB) */ +/* The off-diagonal elements of the first NB rows and columns of */ +/* the reduced matrix. */ + +/* TAUQ (output) REAL array dimension (NB) */ +/* The scalar factors of the elementary reflectors which */ +/* represent the orthogonal matrix Q. See Further Details. */ + +/* TAUP (output) REAL array, dimension (NB) */ +/* The scalar factors of the elementary reflectors which */ +/* represent the orthogonal matrix P. See Further Details. */ + +/* X (output) REAL array, dimension (LDX,NB) */ +/* The m-by-nb matrix X required to update the unreduced part */ +/* of A. */ + +/* LDX (input) INTEGER */ +/* The leading dimension of the array X. LDX >= M. */ + +/* Y (output) REAL array, dimension (LDY,NB) */ +/* The n-by-nb matrix Y required to update the unreduced part */ +/* of A. */ + +/* LDY (input) INTEGER */ +/* The leading dimension of the array Y. LDY >= N. */ + +/* Further Details */ +/* =============== */ + +/* The matrices Q and P are represented as products of elementary */ +/* reflectors: */ + +/* Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) */ + +/* Each H(i) and G(i) has the form: */ + +/* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */ + +/* where tauq and taup are real scalars, and v and u are real vectors. */ + +/* If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in */ +/* A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in */ +/* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */ + +/* If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in */ +/* A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in */ +/* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */ + +/* The elements of the vectors v and u together form the m-by-nb matrix */ +/* V and the nb-by-n matrix U' which are needed, with X and Y, to apply */ +/* the transformation to the unreduced part of the matrix, using a block */ +/* update of the form: A := A - V*Y' - X*U'. */ + +/* The contents of A on exit are illustrated by the following examples */ +/* with nb = 2: */ + +/* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ + +/* ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 ) */ +/* ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 ) */ +/* ( v1 v2 a a a ) ( v1 1 a a a a ) */ +/* ( v1 v2 a a a ) ( v1 v2 a a a a ) */ +/* ( v1 v2 a a a ) ( v1 v2 a a a a ) */ +/* ( v1 v2 a a a ) */ + +/* where a denotes an element of the original matrix which is unchanged, */ +/* vi denotes an element of the vector defining H(i), and ui an element */ +/* of the vector defining G(i). */ + +/* ===================================================================== */ + +/* .. 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; + --d__; + --e; + --tauq; + --taup; + x_dim1 = *ldx; + x_offset = 1 + x_dim1; + x -= x_offset; + y_dim1 = *ldy; + y_offset = 1 + y_dim1; + y -= y_offset; + + /* Function Body */ + if (*m <= 0 || *n <= 0) { + return 0; + } + + if (*m >= *n) { + +/* Reduce to upper bidiagonal form */ + + i__1 = *nb; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Update A(i:m,i) */ + + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda, + &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], & + c__1); + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx, + &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ * + a_dim1], &c__1); + +/* Generate reflection Q(i) to annihilate A(i+1:m,i) */ + + i__2 = *m - i__ + 1; +/* Computing MIN */ + i__3 = i__ + 1; + slarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m)+ i__ * + a_dim1], &c__1, &tauq[i__]); + d__[i__] = a[i__ + i__ * a_dim1]; + if (i__ < *n) { + a[i__ + i__ * a_dim1] = 1.f; + +/* Compute Y(i+1:n,i) */ + + i__2 = *m - i__ + 1; + i__3 = *n - i__; + sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) * + a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, & + y[i__ + 1 + i__ * y_dim1], &c__1); + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], + lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * + y_dim1 + 1], &c__1); + i__2 = *n - i__; + i__3 = i__ - 1; + sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + + y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ + i__ + 1 + i__ * y_dim1], &c__1); + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + sgemv_("Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1], + ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * + y_dim1 + 1], &c__1); + i__2 = i__ - 1; + i__3 = *n - i__; + sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * + a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, + &y[i__ + 1 + i__ * y_dim1], &c__1); + i__2 = *n - i__; + sscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); + +/* Update A(i,i+1:n) */ + + i__2 = *n - i__; + sgemv_("No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 + + y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + ( + i__ + 1) * a_dim1], lda); + i__2 = i__ - 1; + i__3 = *n - i__; + sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * + a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[ + i__ + (i__ + 1) * a_dim1], lda); + +/* Generate reflection P(i) to annihilate A(i,i+2:n) */ + + i__2 = *n - i__; +/* Computing MIN */ + i__3 = i__ + 2; + slarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( + i__3, *n)* a_dim1], lda, &taup[i__]); + e[i__] = a[i__ + (i__ + 1) * a_dim1]; + a[i__ + (i__ + 1) * a_dim1] = 1.f; + +/* Compute X(i+1:m,i) */ + + i__2 = *m - i__; + i__3 = *n - i__; + sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + + 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1], + lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1); + i__2 = *n - i__; + sgemv_("Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1], + ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[ + i__ * x_dim1 + 1], &c__1); + i__2 = *m - i__; + sgemv_("No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 + + a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1); + i__2 = i__ - 1; + i__3 = *n - i__; + sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * + a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, & + c_b16, &x[i__ * x_dim1 + 1], &c__1); + i__2 = *m - i__; + i__3 = i__ - 1; + sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + + x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1); + i__2 = *m - i__; + sscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); + } +/* L10: */ + } + } else { + +/* Reduce to lower bidiagonal form */ + + i__1 = *nb; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Update A(i,i:n) */ + + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy, + &a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1], + lda); + i__2 = i__ - 1; + i__3 = *n - i__ + 1; + sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1], + lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1], + lda); + +/* Generate reflection P(i) to annihilate A(i,i+1:n) */ + + i__2 = *n - i__ + 1; +/* Computing MIN */ + i__3 = i__ + 1; + slarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n)* + a_dim1], lda, &taup[i__]); + d__[i__] = a[i__ + i__ * a_dim1]; + if (i__ < *m) { + a[i__ + i__ * a_dim1] = 1.f; + +/* Compute X(i+1:m,i) */ + + i__2 = *m - i__; + i__3 = *n - i__ + 1; + sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ * + a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, & + x[i__ + 1 + i__ * x_dim1], &c__1); + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + sgemv_("Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1], + ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * + x_dim1 + 1], &c__1); + i__2 = *m - i__; + i__3 = i__ - 1; + sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + + a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1); + i__2 = i__ - 1; + i__3 = *n - i__ + 1; + sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 + + 1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * + x_dim1 + 1], &c__1); + i__2 = *m - i__; + i__3 = i__ - 1; + sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + + x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1); + i__2 = *m - i__; + sscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); + +/* Update A(i+1:m,i) */ + + i__2 = *m - i__; + i__3 = i__ - 1; + sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + + a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + + 1 + i__ * a_dim1], &c__1); + i__2 = *m - i__; + sgemv_("No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 + + x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[ + i__ + 1 + i__ * a_dim1], &c__1); + +/* Generate reflection Q(i) to annihilate A(i+2:m,i) */ + + i__2 = *m - i__; +/* Computing MIN */ + i__3 = i__ + 2; + slarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *m)+ + i__ * a_dim1], &c__1, &tauq[i__]); + e[i__] = a[i__ + 1 + i__ * a_dim1]; + a[i__ + 1 + i__ * a_dim1] = 1.f; + +/* Compute Y(i+1:n,i) */ + + i__2 = *m - i__; + i__3 = *n - i__; + sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + + 1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, + &c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1); + i__2 = *m - i__; + i__3 = i__ - 1; + sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1], + lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ + i__ * y_dim1 + 1], &c__1); + i__2 = *n - i__; + i__3 = i__ - 1; + sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + + y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ + i__ + 1 + i__ * y_dim1], &c__1); + i__2 = *m - i__; + sgemv_("Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1], + ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ + i__ * y_dim1 + 1], &c__1); + i__2 = *n - i__; + sgemv_("Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1 + + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ + + 1 + i__ * y_dim1], &c__1); + i__2 = *n - i__; + sscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); + } +/* L20: */ + } + } + return 0; + +/* End of SLABRD */ + +} /* slabrd_ */