diff --git a/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_Core b/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_Core
new file mode 100644
index 000000000000..88ba2296b514
--- /dev/null
+++ b/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_Core
@@ -0,0 +1,11 @@
+--- inst/include/Eigen/Core.orig	2021-08-18 20:41:58 UTC
++++ inst/include/Eigen/Core
+@@ -346,7 +346,7 @@ using std::ptrdiff_t;
+ #include "src/Core/CoreIterators.h"
+ #include "src/Core/ConditionEstimator.h"
+ 
+-#if defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)
++#if defined(EIGEN_VECTORIZE_VSX)
+   #include "src/Core/arch/AltiVec/MatrixProduct.h"
+ #elif defined EIGEN_VECTORIZE_NEON
+   #include "src/Core/arch/NEON/GeneralBlockPanelKernel.h"
diff --git a/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_src_Core_arch_AltiVec_Complex.h b/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_src_Core_arch_AltiVec_Complex.h
new file mode 100644
index 000000000000..ce35095a14a5
--- /dev/null
+++ b/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_src_Core_arch_AltiVec_Complex.h
@@ -0,0 +1,18 @@
+--- inst/include/Eigen/src/Core/arch/AltiVec/Complex.h.orig	2021-08-18 20:41:58 UTC
++++ inst/include/Eigen/src/Core/arch/AltiVec/Complex.h
+@@ -100,6 +100,7 @@ template<> struct packet_traits<std::complex<float> > 
+     HasAbs2   = 0,
+     HasMin    = 0,
+     HasMax    = 0,
++    HasSqrt   = 1,
+ #ifdef __VSX__
+     HasBlend  = 1,
+ #endif
+@@ -320,6 +321,7 @@ template<> struct packet_traits<std::complex<double> >
+     HasAbs2   = 0,
+     HasMin    = 0,
+     HasMax    = 0,
++    HasSqrt   = 1,
+     HasSetLinear = 0
+   };
+ };
diff --git a/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_src_Core_arch_AltiVec_MathFunctions.h b/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_src_Core_arch_AltiVec_MathFunctions.h
new file mode 100644
index 000000000000..ded96d6084c5
--- /dev/null
+++ b/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_src_Core_arch_AltiVec_MathFunctions.h
@@ -0,0 +1,47 @@
+--- inst/include/Eigen/src/Core/arch/AltiVec/MathFunctions.h.orig	2021-08-18 20:41:58 UTC
++++ inst/include/Eigen/src/Core/arch/AltiVec/MathFunctions.h
+@@ -40,16 +40,14 @@ Packet4f pcos<Packet4f>(const Packet4f& _x)
+   return pcos_float(_x);
+ }
+ 
++#ifdef __VSX__
+ #ifndef EIGEN_COMP_CLANG
+ template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+ Packet4f prsqrt<Packet4f>(const Packet4f& x)
+ {
+   return  vec_rsqrt(x);
+ }
+-#endif
+ 
+-#ifdef __VSX__
+-#ifndef EIGEN_COMP_CLANG
+ template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+ Packet2d prsqrt<Packet2d>(const Packet2d& x)
+ {
+@@ -73,6 +71,26 @@ template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEF
+ Packet2d pexp<Packet2d>(const Packet2d& _x)
+ {
+   return pexp_double(_x);
++}
++
++template<> EIGEN_STRONG_INLINE Packet8bf psqrt<Packet8bf> (const Packet8bf& a){
++  BF16_TO_F32_UNARY_OP_WRAPPER(psqrt<Packet4f>, a);
++}
++
++#ifndef EIGEN_COMP_CLANG
++template<> EIGEN_STRONG_INLINE Packet8bf prsqrt<Packet8bf> (const Packet8bf& a){
++  BF16_TO_F32_UNARY_OP_WRAPPER(prsqrt<Packet4f>, a);
++}
++#endif
++#else
++template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
++Packet4f psqrt<Packet4f>(const Packet4f& x)
++{
++  Packet4f a;
++  for (Index i = 0; i < packet_traits<float>::size; i++) {
++    a[i] = numext::sqrt(x[i]);
++  }
++  return a;
+ }
+ #endif
+ 
diff --git a/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_src_Core_arch_AltiVec_PacketMath.h b/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_src_Core_arch_AltiVec_PacketMath.h
new file mode 100644
index 000000000000..ea37c9fe6a2b
--- /dev/null
+++ b/math/R-cran-RcppEigen/files/patch-inst_include_Eigen_src_Core_arch_AltiVec_PacketMath.h
@@ -0,0 +1,117 @@
+--- inst/include/Eigen/src/Core/arch/AltiVec/PacketMath.h.orig	2021-08-18 20:41:58 UTC
++++ inst/include/Eigen/src/Core/arch/AltiVec/PacketMath.h
+@@ -175,16 +175,19 @@ struct packet_traits<float> : default_packet_traits {
+ #else
+     HasRsqrt = 0,
+ #endif
++    HasTanh = EIGEN_FAST_MATH,
++    HasErf = EIGEN_FAST_MATH,
++    HasRint = 1,
+ #else
+     HasSqrt = 0,
+     HasRsqrt = 0,
+-    HasTanh = EIGEN_FAST_MATH,
+-    HasErf = EIGEN_FAST_MATH,
++    HasTanh = 0,
++    HasErf = 0,
++    HasRint = 0,
+ #endif
+     HasRound = 1,
+     HasFloor = 1,
+     HasCeil = 1,
+-    HasRint = 1,
+     HasNegate = 1,
+     HasBlend = 1
+   };
+@@ -217,16 +220,17 @@ struct packet_traits<bfloat16> : default_packet_traits
+ #else
+     HasRsqrt = 0,
+ #endif
++    HasRint = 1,
+ #else
+     HasSqrt = 0,
+     HasRsqrt = 0,
+-    HasTanh = EIGEN_FAST_MATH,
+-    HasErf = EIGEN_FAST_MATH,
++    HasRint = 0,
+ #endif
++    HasTanh = 0,
++    HasErf = 0,
+     HasRound = 1,
+     HasFloor = 1,
+     HasCeil = 1,
+-    HasRint = 1,
+     HasNegate = 1,
+     HasBlend = 1
+   };
+@@ -872,19 +876,29 @@ template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan
+   return vec_nor(c,c);
+ }
+ 
++#ifdef __VSX__
+ template<> EIGEN_STRONG_INLINE Packet4i pcmp_le(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmple(a,b)); }
++#endif
+ template<> EIGEN_STRONG_INLINE Packet4i pcmp_lt(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmplt(a,b)); }
+ template<> EIGEN_STRONG_INLINE Packet4i pcmp_eq(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmpeq(a,b)); }
++#ifdef __VSX__
+ template<> EIGEN_STRONG_INLINE Packet8s pcmp_le(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmple(a,b)); }
++#endif
+ template<> EIGEN_STRONG_INLINE Packet8s pcmp_lt(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmplt(a,b)); }
+ template<> EIGEN_STRONG_INLINE Packet8s pcmp_eq(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmpeq(a,b)); }
++#ifdef __VSX__
+ template<> EIGEN_STRONG_INLINE Packet8us pcmp_le(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmple(a,b)); }
++#endif
+ template<> EIGEN_STRONG_INLINE Packet8us pcmp_lt(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmplt(a,b)); }
+ template<> EIGEN_STRONG_INLINE Packet8us pcmp_eq(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmpeq(a,b)); }
++#ifdef __VSX__
+ template<> EIGEN_STRONG_INLINE Packet16c pcmp_le(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmple(a,b)); }
++#endif
+ template<> EIGEN_STRONG_INLINE Packet16c pcmp_lt(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmplt(a,b)); }
+ template<> EIGEN_STRONG_INLINE Packet16c pcmp_eq(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmpeq(a,b)); }
++#ifdef __VSX__
+ template<> EIGEN_STRONG_INLINE Packet16uc pcmp_le(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmple(a,b)); }
++#endif
+ template<> EIGEN_STRONG_INLINE Packet16uc pcmp_lt(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmplt(a,b)); }
+ template<> EIGEN_STRONG_INLINE Packet16uc pcmp_eq(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmpeq(a,b)); }
+ 
+@@ -937,6 +951,7 @@ template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4
+ }
+ template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const  Packet4f& a) { return vec_ceil(a); }
+ template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return vec_floor(a); }
++#ifdef __VSX__
+ template<> EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a)
+ {
+     Packet4f res;
+@@ -947,6 +962,7 @@ template<> EIGEN_STRONG_INLINE Packet4f print<Packet4f
+ 
+     return res;
+ }
++#endif
+ 
+ template<typename Packet> EIGEN_STRONG_INLINE Packet ploadu_common(const __UNPACK_TYPE__(Packet)* from)
+ {
+@@ -1341,12 +1357,6 @@ template<> EIGEN_STRONG_INLINE Packet8bf psub<Packet8b
+   BF16_TO_F32_BINARY_OP_WRAPPER(psub<Packet4f>, a, b);
+ }
+ 
+-template<> EIGEN_STRONG_INLINE Packet8bf psqrt<Packet8bf> (const Packet8bf& a){
+-  BF16_TO_F32_UNARY_OP_WRAPPER(vec_sqrt, a);
+-}
+-template<> EIGEN_STRONG_INLINE Packet8bf prsqrt<Packet8bf> (const Packet8bf& a){
+-  BF16_TO_F32_UNARY_OP_WRAPPER(prsqrt<Packet4f>, a);
+-}
+ template<> EIGEN_STRONG_INLINE Packet8bf pexp<Packet8bf> (const Packet8bf& a){
+   BF16_TO_F32_UNARY_OP_WRAPPER(pexp_float, a);
+ }
+@@ -1390,9 +1400,11 @@ template<> EIGEN_STRONG_INLINE Packet8bf pceil<Packet8
+ template<> EIGEN_STRONG_INLINE Packet8bf pround<Packet8bf> (const Packet8bf& a){
+   BF16_TO_F32_UNARY_OP_WRAPPER(pround<Packet4f>, a);
+ }
++#ifdef __VSX__
+ template<> EIGEN_STRONG_INLINE Packet8bf print<Packet8bf> (const Packet8bf& a){
+   BF16_TO_F32_UNARY_OP_WRAPPER(print<Packet4f>, a);
+ }
++#endif
+ template<> EIGEN_STRONG_INLINE Packet8bf pmadd(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
+   Packet4f a_even = Bf16ToF32Even(a);
+   Packet4f a_odd = Bf16ToF32Odd(a);