| /aosp_15_r20/external/tensorflow/tensorflow/compiler/xla/stream_executor/cuda/ |
| H A D | cusolver_dense_9_0.inc | 411 float *TAU, float *Workspace,
417 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
422 double *TAU, double *Workspace,
429 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
434 cuComplex *TAU,
442 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
447 int lda, cuDoubleComplex *TAU,
455 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
460 const float *tau, int *lwork) {
466 return func_ptr(handle, m, n, k, A, lda, tau, lwork);
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| H A D | cusolver_dense_10_0.inc | 509 float *TAU, float *Workspace,
515 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
520 double *TAU, double *Workspace,
527 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
532 cuComplex *TAU,
540 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
545 int lda, cuDoubleComplex *TAU,
553 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
558 const float *tau, int *lwork) {
564 return func_ptr(handle, m, n, k, A, lda, tau, lwork);
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| H A D | cusolver_dense_10_1.inc | 791 float *TAU, float *Workspace,
797 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
802 double *TAU, double *Workspace,
809 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
814 cuComplex *TAU,
822 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
827 int lda, cuDoubleComplex *TAU,
835 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
840 const float *tau, int *lwork) {
846 return func_ptr(handle, m, n, k, A, lda, tau, lwork);
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| H A D | cusolver_dense_10_2.inc | 1319 float *TAU, float *Workspace,
1325 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
1330 double *TAU, double *Workspace,
1337 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
1342 cuComplex *TAU,
1350 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
1355 int lda, cuDoubleComplex *TAU,
1363 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
1368 const float *tau, int *lwork) {
1374 return func_ptr(handle, m, n, k, A, lda, tau, lwork);
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| H A D | cusolver_dense_11_0.inc | 2154 float *TAU, float *Workspace,
2160 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
2165 double *TAU, double *Workspace,
2172 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
2177 cuComplex *TAU,
2185 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
2190 int lda, cuDoubleComplex *TAU,
2198 return func_ptr(handle, m, n, A, lda, TAU, Workspace, Lwork, devInfo);
2279 const float *tau, int *lwork) {
2285 return func_ptr(handle, m, n, k, A, lda, tau, lwork);
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| /aosp_15_r20/external/eigen/Eigen/src/Householder/ |
| H A D | Householder.h | 28 * \f$ H = I - tau v v^*\f$
35 * \param tau the scaling factor of the Householder transformation
43 void MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta) in makeHouseholderInPlace() argument
46 makeHouseholder(essentialPart, tau, beta); in makeHouseholderInPlace()
52 * \f$ H = I - tau v v^*\f$
58 * \param tau the scaling factor of the Householder transformation
69 Scalar& tau, in makeHouseholder() argument
84 tau = RealScalar(0); in makeHouseholder()
94 tau = conj((beta - c0) / beta); in makeHouseholder()
99 * \f$ H = I - tau v v^*\f$
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| /aosp_15_r20/external/eigen/lapack/ |
| H A D | dlarft.f | 21 * SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
28 * DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
104 *> \param[in] TAU
106 *> TAU is DOUBLE PRECISION array, dimension (K)
107 *> TAU(i) must contain the scalar factor of the elementary
164 SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) argument
176 DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) local
206 IF( TAU( I ).EQ.ZERO ) THEN
223 T( J, I ) = -TAU( I ) * V( I , J )
227 * T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i)
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| H A D | slarft.f | 21 * SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
28 * REAL T( LDT, * ), TAU( * ), V( LDV, * )
104 *> \param[in] TAU
106 *> TAU is REAL array, dimension (K)
107 *> TAU(i) must contain the scalar factor of the elementary
164 SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) argument
176 REAL T( LDT, * ), TAU( * ), V( LDV, * ) local
206 IF( TAU( I ).EQ.ZERO ) THEN
223 T( J, I ) = -TAU( I ) * V( I , J )
227 * T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i)
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| H A D | zlarft.f | 21 * SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
28 * COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * )
104 *> \param[in] TAU
106 *> TAU is COMPLEX*16 array, dimension (K)
107 *> TAU(i) must contain the scalar factor of the elementary
164 SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) argument
176 COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) local
207 IF( TAU( I ).EQ.ZERO ) THEN
224 T( J, I ) = -TAU( I ) * CONJG( V( I , J ) )
228 * T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i)
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| H A D | clarft.f | 21 * SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
28 * COMPLEX T( LDT, * ), TAU( * ), V( LDV, * )
104 *> \param[in] TAU
106 *> TAU is COMPLEX array, dimension (K)
107 *> TAU(i) must contain the scalar factor of the elementary
164 SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) argument
176 COMPLEX T( LDT, * ), TAU( * ), V( LDV, * ) local
207 IF( TAU( I ).EQ.ZERO ) THEN
224 T( J, I ) = -TAU( I ) * CONJG( V( I , J ) )
228 * T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i)
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| H A D | zlarfg.f | 21 * SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU )
25 * COMPLEX*16 ALPHA, TAU
46 *> H = I - tau * ( 1 ) * ( 1 v**H ) ,
49 *> where tau is a complex scalar and v is a complex (n-1)-element
52 *> If the elements of x are all zero and alpha is real, then tau = 0
55 *> Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 .
88 *> \param[out] TAU
90 *> TAU is COMPLEX*16
91 *> The value tau.
107 SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) argument
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| H A D | clarfg.f | 21 * SUBROUTINE CLARFG( N, ALPHA, X, INCX, TAU )
25 * COMPLEX ALPHA, TAU
46 *> H = I - tau * ( 1 ) * ( 1 v**H ) ,
49 *> where tau is a complex scalar and v is a complex (n-1)-element
52 *> If the elements of x are all zero and alpha is real, then tau = 0
55 *> Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 .
88 *> \param[out] TAU
90 *> TAU is COMPLEX
91 *> The value tau.
107 SUBROUTINE CLARFG( N, ALPHA, X, INCX, TAU ) argument
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| H A D | zlarf.f | 21 * SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
26 * COMPLEX*16 TAU
42 *> H = I - tau * v * v**H
44 *> where tau is a complex scalar and v is a complex vector.
46 *> If tau = 0, then H is taken to be the unit matrix.
48 *> To apply H**H, supply conjg(tau) instead
49 *> tau.
80 *> TAU = 0.
89 *> \param[in] TAU
91 *> TAU is COMPLEX*16
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| H A D | clarf.f | 21 * SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
26 * COMPLEX TAU
42 *> H = I - tau * v * v**H
44 *> where tau is a complex scalar and v is a complex vector.
46 *> If tau = 0, then H is taken to be the unit matrix.
48 *> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
49 *> tau.
80 *> TAU = 0.
89 *> \param[in] TAU
91 *> TAU is COMPLEX
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| H A D | slarfg.f | 21 * SUBROUTINE SLARFG( N, ALPHA, X, INCX, TAU )
25 * REAL ALPHA, TAU
46 *> H = I - tau * ( 1 ) * ( 1 v**T ) ,
49 *> where tau is a real scalar and v is a real (n-1)-element
52 *> If the elements of x are all zero, then tau = 0 and H is taken to be
55 *> Otherwise 1 <= tau <= 2.
88 *> \param[out] TAU
90 *> TAU is REAL
91 *> The value tau.
107 SUBROUTINE SLARFG( N, ALPHA, X, INCX, TAU ) argument
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| H A D | dlarfg.f | 21 * SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
25 * DOUBLE PRECISION ALPHA, TAU
46 *> H = I - tau * ( 1 ) * ( 1 v**T ) ,
49 *> where tau is a real scalar and v is a real (n-1)-element
52 *> If the elements of x are all zero, then tau = 0 and H is taken to be
55 *> Otherwise 1 <= tau <= 2.
88 *> \param[out] TAU
90 *> TAU is DOUBLE PRECISION
91 *> The value tau.
107 SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) argument
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| H A D | dlarf.f | 21 * SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
26 * DOUBLE PRECISION TAU
41 *> H = I - tau * v * v**T
43 *> where tau is a real scalar and v is a real vector.
45 *> If tau = 0, then H is taken to be the unit matrix.
76 *> TAU = 0.
85 *> \param[in] TAU
87 *> TAU is DOUBLE PRECISION
88 *> The value tau in the representation of H.
125 SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) argument
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| H A D | slarf.f | 21 * SUBROUTINE SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
26 * REAL TAU
41 *> H = I - tau * v * v**T
43 *> where tau is a real scalar and v is a real vector.
45 *> If tau = 0, then H is taken to be the unit matrix.
76 *> TAU = 0.
85 *> \param[in] TAU
87 *> TAU is REAL
88 *> The value tau in the representation of H.
125 SUBROUTINE SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) argument
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| /aosp_15_r20/external/bouncycastle/repackaged_platform/bcprov/src/main/java/com/android/internal/org/bouncycastle/math/ec/ |
| H A D | Tnaf.java | 8 * τ-adic nonadjacent form (WTNAF). The algorithms are based on the
77 * <code><b>Z</b>[τ]</code>.
80 * <code><b>Z</b>[τ]</code>.
114 * <code><b>R</b>[τ]</code>, where <code>λ = u + vτ</code>
119 * <code><b>R</b>[τ]</code>.
120 * @param v The <code>τ</code>-adic part of the element
121 * <code>λ</code> of <code><b>R</b>[τ]</code>.
155 * Rounds an element <code>λ</code> of <code><b>R</b>[τ]</code>
156 * to an element of <code><b>Z</b>[τ]</code>, such that their difference
158 * <code>λ = λ<sub>0</sub> + λ<sub>1</sub>τ</code>.
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| /aosp_15_r20/external/bouncycastle/repackaged/bcprov/src/main/java/com/android/org/bouncycastle/math/ec/ |
| H A D | Tnaf.java | 8 * τ-adic nonadjacent form (WTNAF). The algorithms are based on the
77 * <code><b>Z</b>[τ]</code>.
80 * <code><b>Z</b>[τ]</code>.
114 * <code><b>R</b>[τ]</code>, where <code>λ = u + vτ</code>
119 * <code><b>R</b>[τ]</code>.
120 * @param v The <code>τ</code>-adic part of the element
121 * <code>λ</code> of <code><b>R</b>[τ]</code>.
155 * Rounds an element <code>λ</code> of <code><b>R</b>[τ]</code>
156 * to an element of <code><b>Z</b>[τ]</code>, such that their difference
158 * <code>λ = λ<sub>0</sub> + λ<sub>1</sub>τ</code>.
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| /aosp_15_r20/external/bouncycastle/bcprov/src/main/java/org/bouncycastle/math/ec/ |
| H A D | Tnaf.java | 7 * τ-adic nonadjacent form (WTNAF). The algorithms are based on the
76 * <code><b>Z</b>[τ]</code>.
79 * <code><b>Z</b>[τ]</code>.
113 * <code><b>R</b>[τ]</code>, where <code>λ = u + vτ</code>
118 * <code><b>R</b>[τ]</code>.
119 * @param v The <code>τ</code>-adic part of the element
120 * <code>λ</code> of <code><b>R</b>[τ]</code>.
154 * Rounds an element <code>λ</code> of <code><b>R</b>[τ]</code>
155 * to an element of <code><b>Z</b>[τ]</code>, such that their difference
157 * <code>λ = λ<sub>0</sub> + λ<sub>1</sub>τ</code>.
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| /aosp_15_r20/external/pytorch/aten/src/ATen/native/ |
| H A D | BatchLinearAlgebra.cpp | 275 …_(int *m, int *n, std::complex<double> *a, int *lda, std::complex<double> *tau, std::complex<doubl…
276 extern "C" void cgeqrf_(int *m, int *n, std::complex<float> *a, int *lda, std::complex<float> *tau,…
277 extern "C" void dgeqrf_(int *m, int *n, double *a, int *lda, double *tau, double *work, int *lwork,…
278 extern "C" void sgeqrf_(int *m, int *n, float *a, int *lda, float *tau, float *work, int *lwork, in…
281 …, int *n, int *k, std::complex<double> *a, int *lda, std::complex<double> *tau, std::complex<doubl…
282 …*m, int *n, int *k, std::complex<float> *a, int *lda, std::complex<float> *tau, std::complex<float…
283 extern "C" void dorgqr_(int *m, int *n, int *k, double *a, int *lda, double *tau, double *work, int…
284 extern "C" void sorgqr_(int *m, int *n, int *k, float *a, int *lda, float *tau, float *work, int *l…
287 …, int *n, int *k, std::complex<double> *a, int *lda, std::complex<double> *tau, std::complex<doubl…
288 …*m, int *n, int *k, std::complex<float> *a, int *lda, std::complex<float> *tau, std::complex<float…
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| /aosp_15_r20/external/eigen/Eigen/src/misc/ |
| H A D | lapacke.h | 655 float* tau );
658 double* tau );
661 lapack_int lda, lapack_complex_float* tau );
664 lapack_int lda, lapack_complex_double* tau );
678 float* a, lapack_int lda, float* tau );
680 double* a, lapack_int lda, double* tau );
683 lapack_complex_float* tau );
686 lapack_complex_double* tau );
689 float* a, lapack_int lda, float* tau );
691 double* a, lapack_int lda, double* tau );
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| /aosp_15_r20/external/pytorch/aten/src/ATen/native/cuda/linalg/ |
| H A D | CUDASolver.cpp | 743 cusolverDnSgeqrf(handle, m, n, A, lda, tau, work, lwork, devInfo)); in geqrf()
749 cusolverDnDgeqrf(handle, m, n, A, lda, tau, work, lwork, devInfo)); in geqrf()
761 reinterpret_cast<cuComplex*>(tau), in geqrf()
776 reinterpret_cast<cuDoubleComplex*>(tau), in geqrf()
864 const float* tau, int* lwork) { in orgqr_buffersize() argument
866 cusolverDnSorgqr_bufferSize(handle, m, n, k, A, lda, tau, lwork)); in orgqr_buffersize()
874 const double* tau, int* lwork) { in orgqr_buffersize() argument
876 cusolverDnDorgqr_bufferSize(handle, m, n, k, A, lda, tau, lwork)); in orgqr_buffersize()
884 const c10::complex<float>* tau, int* lwork) { in orgqr_buffersize() argument
889 reinterpret_cast<const cuComplex*>(tau), lwork)); in orgqr_buffersize()
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| /aosp_15_r20/external/tensorflow/tensorflow/compiler/xla/service/ |
| H A D | qr_expander.cc | 78 // H = I - tau v v.T.
96 // tau = 0
101 // tau = (beta - alpha) / beta
103 // tau = (beta - np.real(alpha) / beta) + (-np.imag(alpha) / beta) * 1j
106 // return (v, tau, beta)
110 const int64_t m, XlaOp* v, XlaOp* tau, XlaOp* beta) { in House() argument
147 *tau = Complex((*beta - Real(alpha)) / *beta, -Imag(alpha) / *beta); in House()
158 *tau = (*beta - alpha) / *beta; in House()
160 *tau = Select(sigma_is_zero, ZerosLike(*tau), *tau); in House()
190 // v, tau, beta = house(a[:, j], j)
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