| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /* | ||
| 2 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 3 | SLEPc - Scalable Library for Eigenvalue Problem Computations | ||
| 4 | Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain | ||
| 5 | |||
| 6 | This file is part of SLEPc. | ||
| 7 | SLEPc is distributed under a 2-clause BSD license (see LICENSE). | ||
| 8 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 9 | */ | ||
| 10 | /* | ||
| 11 | Routines for solving dense matrix equations, in some cases calling SLICOT | ||
| 12 | */ | ||
| 13 | |||
| 14 | #include <slepc/private/lmeimpl.h> /*I "slepclme.h" I*/ | ||
| 15 | #include <slepcblaslapack.h> | ||
| 16 | |||
| 17 | /* | ||
| 18 | LMEDenseRankSVD - given a square matrix A, compute its SVD U*S*V', and determine the | ||
| 19 | numerical rank. On exit, U contains U*S and A is overwritten with V' | ||
| 20 | */ | ||
| 21 | 733 | PetscErrorCode LMEDenseRankSVD(LME lme,PetscInt n,PetscScalar *A,PetscInt lda,PetscScalar *U,PetscInt ldu,PetscInt *rank) | |
| 22 | { | ||
| 23 | 733 | PetscInt i,j,rk=0; | |
| 24 | 733 | PetscScalar *work; | |
| 25 | 733 | PetscReal tol,*sg,*rwork; | |
| 26 | 733 | PetscBLASInt n_,lda_,ldu_,lw_; | |
| 27 | |||
| 28 |
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733 | PetscFunctionBegin; |
| 29 |
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733 | PetscCall(PetscCalloc3(n,&sg,10*n,&work,5*n,&rwork)); |
| 30 |
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733 | PetscCall(PetscBLASIntCast(n,&n_)); |
| 31 |
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733 | PetscCall(PetscBLASIntCast(lda,&lda_)); |
| 32 |
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733 | PetscCall(PetscBLASIntCast(ldu,&ldu_)); |
| 33 | 733 | lw_ = 10*n_; | |
| 34 |
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733 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 35 | #if !PetscDefined(USE_COMPLEX) | ||
| 36 |
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446 | PetscCallLAPACKInfo("LAPACKgesvd",LAPACKgesvd_("S","O",&n_,&n_,A,&lda_,sg,U,&ldu_,NULL,&n_,work,&lw_,&info)); |
| 37 | #else | ||
| 38 |
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287 | PetscCallLAPACKInfo("LAPACKgesvd",LAPACKgesvd_("S","O",&n_,&n_,A,&lda_,sg,U,&ldu_,NULL,&n_,work,&lw_,rwork,&info)); |
| 39 | #endif | ||
| 40 |
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733 | PetscCall(PetscFPTrapPop()); |
| 41 | 733 | tol = 10*PETSC_MACHINE_EPSILON*n*sg[0]; | |
| 42 |
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19243 | for (j=0;j<n;j++) { |
| 43 |
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18710 | if (sg[j]>tol) { |
| 44 |
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609954 | for (i=0;i<n;i++) U[i+j*n] *= sg[j]; |
| 45 | 18510 | rk++; | |
| 46 | } else break; | ||
| 47 | } | ||
| 48 | 733 | *rank = rk; | |
| 49 |
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733 | PetscCall(PetscFree3(sg,work,rwork)); |
| 50 |
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118 | PetscFunctionReturn(PETSC_SUCCESS); |
| 51 | } | ||
| 52 | |||
| 53 | #if PetscDefined(USE_INFO) | ||
| 54 | /* | ||
| 55 | LyapunovCholResidual - compute the residual norm ||A*U'*U+U'*U*A'+B*B'|| | ||
| 56 | */ | ||
| 57 | 50 | static PetscErrorCode LyapunovCholResidual(PetscInt m,PetscScalar *A,PetscInt lda,PetscInt k,PetscScalar *B,PetscInt ldb,PetscScalar *U,PetscInt ldu,PetscReal *res) | |
| 58 | { | ||
| 59 | 50 | PetscBLASInt n,kk,la,lb,lu; | |
| 60 | 50 | PetscScalar *M,*R,zero=0.0,done=1.0; | |
| 61 | |||
| 62 |
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50 | PetscFunctionBegin; |
| 63 | 50 | *res = 0; | |
| 64 |
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50 | PetscCall(PetscBLASIntCast(lda,&la)); |
| 65 |
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50 | PetscCall(PetscBLASIntCast(ldb,&lb)); |
| 66 |
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50 | PetscCall(PetscBLASIntCast(ldu,&lu)); |
| 67 |
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50 | PetscCall(PetscBLASIntCast(m,&n)); |
| 68 |
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50 | PetscCall(PetscBLASIntCast(k,&kk)); |
| 69 |
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50 | PetscCall(PetscMalloc2(m*m,&M,m*m,&R)); |
| 70 | |||
| 71 | /* R = B*B' */ | ||
| 72 |
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50 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&kk,&done,B,&lb,B,&lb,&zero,R,&n)); |
| 73 | /* M = A*U' */ | ||
| 74 |
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50 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&n,&done,A,&la,U,&lu,&zero,M,&n)); |
| 75 | /* R = R+M*U */ | ||
| 76 |
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50 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&done,M,&n,U,&lu,&done,R,&n)); |
| 77 | /* R = R+U'*M' */ | ||
| 78 |
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50 | PetscCallBLAS("BLASgemm",BLASgemm_("C","C",&n,&n,&n,&done,U,&lu,M,&n,&done,R,&n)); |
| 79 | |||
| 80 | 50 | *res = LAPACKlange_("F",&n,&n,R,&n,NULL); | |
| 81 |
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50 | PetscCall(PetscFree2(M,R)); |
| 82 |
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10 | PetscFunctionReturn(PETSC_SUCCESS); |
| 83 | } | ||
| 84 | |||
| 85 | /* | ||
| 86 | LyapunovResidual - compute the residual norm ||A*X+X*A'+B|| | ||
| 87 | */ | ||
| 88 | 10 | static PetscErrorCode LyapunovResidual(PetscInt m,PetscScalar *A,PetscInt lda,PetscScalar *B,PetscInt ldb,PetscScalar *X,PetscInt ldx,PetscReal *res) | |
| 89 | { | ||
| 90 | 10 | PetscInt i; | |
| 91 | 10 | PetscBLASInt n,la,lb,lx; | |
| 92 | 10 | PetscScalar *R,done=1.0; | |
| 93 | |||
| 94 |
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10 | PetscFunctionBegin; |
| 95 | 10 | *res = 0; | |
| 96 |
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10 | PetscCall(PetscBLASIntCast(lda,&la)); |
| 97 |
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10 | PetscCall(PetscBLASIntCast(ldb,&lb)); |
| 98 |
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10 | PetscCall(PetscBLASIntCast(ldx,&lx)); |
| 99 |
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10 | PetscCall(PetscBLASIntCast(m,&n)); |
| 100 |
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10 | PetscCall(PetscMalloc1(m*m,&R)); |
| 101 | |||
| 102 | /* R = B+A*X */ | ||
| 103 |
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110 | for (i=0;i<m;i++) PetscCall(PetscArraycpy(R+i*m,B+i*ldb,m)); |
| 104 |
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10 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&done,A,&la,X,&lx,&done,R,&n)); |
| 105 | /* R = R+X*A' */ | ||
| 106 |
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10 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&n,&done,X,&lx,A,&la,&done,R,&n)); |
| 107 | |||
| 108 | 10 | *res = LAPACKlange_("F",&n,&n,R,&n,NULL); | |
| 109 |
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10 | PetscCall(PetscFree(R)); |
| 110 |
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2 | PetscFunctionReturn(PETSC_SUCCESS); |
| 111 | } | ||
| 112 | #endif | ||
| 113 | |||
| 114 | #if defined(SLEPC_HAVE_SLICOT) | ||
| 115 | /* | ||
| 116 | HessLyapunovChol_SLICOT - implementation used when SLICOT is available | ||
| 117 | */ | ||
| 118 | 207 | static PetscErrorCode HessLyapunovChol_SLICOT(PetscInt m,PetscScalar *H,PetscInt ldh,PetscInt k,PetscScalar *B,PetscInt ldb,PetscScalar *U,PetscInt ldu,PetscReal *res) | |
| 119 | { | ||
| 120 | 207 | PetscBLASInt lwork,info,n,kk,lu,ione=1,sdim; | |
| 121 | 207 | PetscInt i,j; | |
| 122 | 207 | PetscReal scal; | |
| 123 | 207 | PetscScalar *Q,*W,*wr,*wi,*work; | |
| 124 | |||
| 125 | 207 | PetscFunctionBegin; | |
| 126 |
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207 | PetscCall(PetscBLASIntCast(ldu,&lu)); |
| 127 |
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207 | PetscCall(PetscBLASIntCast(m,&n)); |
| 128 |
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207 | PetscCall(PetscBLASIntCast(k,&kk)); |
| 129 |
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207 | PetscCall(PetscBLASIntCast(6*m,&lwork)); |
| 130 |
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207 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 131 | |||
| 132 | /* transpose W = H' */ | ||
| 133 |
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207 | PetscCall(PetscMalloc5(m*m,&W,m*m,&Q,m,&wr,m,&wi,lwork,&work)); |
| 134 |
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6415 | for (j=0;j<m;j++) { |
| 135 |
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194138 | for (i=0;i<m;i++) W[i+j*m] = H[j+i*ldh]; |
| 136 | } | ||
| 137 | |||
| 138 | /* compute the real Schur form of W */ | ||
| 139 |
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207 | PetscCallLAPACKInfo("LAPACKgees",LAPACKgees_("V","N",NULL,&n,W,&n,&sdim,wr,wi,Q,&n,work,&lwork,NULL,&info)); |
| 140 | #if PetscDefined(USE_DEBUG) | ||
| 141 | for (i=0;i<m;i++) PetscCheck(PetscRealPart(wr[i])<0.0,PETSC_COMM_SELF,PETSC_ERR_USER_INPUT,"Eigenvalue with non-negative real part, the coefficient matrix is not stable"); | ||
| 142 | #endif | ||
| 143 | |||
| 144 | /* copy B' into first rows of U */ | ||
| 145 |
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415 | for (i=0;i<k;i++) { |
| 146 |
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6426 | for (j=0;j<m;j++) U[i+j*ldu] = B[j+i*ldb]; |
| 147 | } | ||
| 148 | |||
| 149 | /* solve Lyapunov equation (Hammarling) */ | ||
| 150 |
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207 | PetscCallBLAS("SLICOTsb03od",SLICOTsb03od_("C","F","N",&n,&kk,W,&n,Q,&n,U,&lu,&scal,wr,wi,work,&lwork,&info)); |
| 151 |
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207 | PetscCheck(!info,PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SLICOT subroutine SB03OD: info=%" PetscBLASInt_FMT,info); |
| 152 |
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207 | PetscCheck(scal==1.0,PETSC_COMM_SELF,PETSC_ERR_SUP,"Current implementation cannot handle scale factor %g",scal); |
| 153 | |||
| 154 | /* resnorm = norm(H(m+1,:)*U'*U), use Q(:,1) = U'*U(:,m) */ | ||
| 155 |
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207 | if (res) { |
| 156 |
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6404 | for (j=0;j<m;j++) Q[j] = U[j+(m-1)*ldu]; |
| 157 |
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206 | PetscCallBLAS("BLAStrmv",BLAStrmv_("U","C","N",&n,U,&lu,Q,&ione)); |
| 158 |
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206 | PetscCheck(k==1,PETSC_COMM_SELF,PETSC_ERR_LIB,"Residual error is intended for k=1 only, but you set k=%" PetscInt_FMT,k); |
| 159 | 206 | *res *= BLASnrm2_(&n,Q,&ione); | |
| 160 | } | ||
| 161 | |||
| 162 |
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207 | PetscCall(PetscFPTrapPop()); |
| 163 |
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207 | PetscCall(PetscFree5(W,Q,wr,wi,work)); |
| 164 | PetscFunctionReturn(PETSC_SUCCESS); | ||
| 165 | } | ||
| 166 | |||
| 167 | #else | ||
| 168 | |||
| 169 | /* | ||
| 170 | Compute the upper Cholesky factor of A | ||
| 171 | */ | ||
| 172 | 600 | static PetscErrorCode CholeskyFactor(PetscInt m,PetscScalar *A,PetscInt lda) | |
| 173 | { | ||
| 174 | 600 | PetscInt i; | |
| 175 | 600 | PetscScalar *S; | |
| 176 | 600 | PetscBLASInt info,n,ld; | |
| 177 | |||
| 178 |
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600 | PetscFunctionBegin; |
| 179 |
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600 | PetscCall(PetscBLASIntCast(m,&n)); |
| 180 |
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600 | PetscCall(PetscBLASIntCast(lda,&ld)); |
| 181 |
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600 | PetscCall(PetscMalloc1(m*m,&S)); |
| 182 |
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600 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 183 | |||
| 184 | /* save a copy of matrix in S */ | ||
| 185 |
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18702 | for (i=0;i<m;i++) PetscCall(PetscArraycpy(S+i*m,A+i*lda,m)); |
| 186 | |||
| 187 | /* compute upper Cholesky factor in R */ | ||
| 188 |
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600 | PetscCallBLAS("LAPACKpotrf",LAPACKpotrf_("U",&n,A,&ld,&info)); |
| 189 |
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600 | PetscCall(PetscLogFlops((1.0*n*n*n)/3.0)); |
| 190 | |||
| 191 |
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600 | if (info) { |
| 192 |
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18603 | for (i=0;i<m;i++) { |
| 193 |
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18012 | PetscCall(PetscArraycpy(A+i*lda,S+i*m,m)); |
| 194 | 18012 | A[i+i*lda] += 50.0*PETSC_MACHINE_EPSILON; | |
| 195 | } | ||
| 196 |
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591 | PetscCallLAPACKInfo("LAPACKpotrf",LAPACKpotrf_("U",&n,A,&ld,&info)); |
| 197 |
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591 | PetscCall(PetscLogFlops((1.0*n*n*n)/3.0)); |
| 198 | } | ||
| 199 | |||
| 200 | /* Zero out entries below the diagonal */ | ||
| 201 |
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18102 | for (i=0;i<m-1;i++) PetscCall(PetscArrayzero(A+i*lda+i+1,m-i-1)); |
| 202 |
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600 | PetscCall(PetscFPTrapPop()); |
| 203 |
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600 | PetscCall(PetscFree(S)); |
| 204 |
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132 | PetscFunctionReturn(PETSC_SUCCESS); |
| 205 | } | ||
| 206 | |||
| 207 | /* | ||
| 208 | HessLyapunovChol_LAPACK - alternative implementation when SLICOT is not available | ||
| 209 | */ | ||
| 210 | 600 | static PetscErrorCode HessLyapunovChol_LAPACK(PetscInt m,PetscScalar *H,PetscInt ldh,PetscInt k,PetscScalar *B,PetscInt ldb,PetscScalar *U,PetscInt ldu,PetscReal *res) | |
| 211 | { | ||
| 212 | 600 | PetscBLASInt ilo=1,lwork,n,kk,lu,lb,ione=1; | |
| 213 | 600 | PetscInt i,j; | |
| 214 | 600 | PetscReal scal; | |
| 215 | 600 | PetscScalar *Q,*C,*W,*Z,*wr,*work,zero=0.0,done=1.0,dmone=-1.0; | |
| 216 | #if !PetscDefined(USE_COMPLEX) | ||
| 217 | 276 | PetscScalar *wi; | |
| 218 | #endif | ||
| 219 | |||
| 220 |
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600 | PetscFunctionBegin; |
| 221 |
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600 | PetscCall(PetscBLASIntCast(ldb,&lb)); |
| 222 |
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600 | PetscCall(PetscBLASIntCast(ldu,&lu)); |
| 223 |
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600 | PetscCall(PetscBLASIntCast(m,&n)); |
| 224 |
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600 | PetscCall(PetscBLASIntCast(k,&kk)); |
| 225 |
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600 | PetscCall(PetscBLASIntCast(6*m,&lwork)); |
| 226 |
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600 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 227 | 600 | C = U; | |
| 228 | |||
| 229 | #if !PetscDefined(USE_COMPLEX) | ||
| 230 |
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276 | PetscCall(PetscMalloc6(m*m,&Q,m*m,&W,m*k,&Z,m,&wr,m,&wi,lwork,&work)); |
| 231 | #else | ||
| 232 |
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324 | PetscCall(PetscMalloc5(m*m,&Q,m*m,&W,m*k,&Z,m,&wr,lwork,&work)); |
| 233 | #endif | ||
| 234 | |||
| 235 | /* save a copy W = H */ | ||
| 236 |
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18702 | for (j=0;j<m;j++) { |
| 237 |
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583572 | for (i=0;i<m;i++) W[i+j*m] = H[i+j*ldh]; |
| 238 | } | ||
| 239 | |||
| 240 | /* compute the (real) Schur form of W */ | ||
| 241 | #if !PetscDefined(USE_COMPLEX) | ||
| 242 |
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276 | PetscCallLAPACKInfo("LAPACKhseqr",LAPACKhseqr_("S","I",&n,&ilo,&n,W,&n,wr,wi,Q,&n,work,&lwork,&info)); |
| 243 | #else | ||
| 244 |
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324 | PetscCallLAPACKInfo("LAPACKhseqr",LAPACKhseqr_("S","I",&n,&ilo,&n,W,&n,wr,Q,&n,work,&lwork,&info)); |
| 245 | #endif | ||
| 246 | #if PetscDefined(USE_DEBUG) | ||
| 247 |
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4088 | for (i=0;i<m;i++) PetscCheck(PetscRealPart(wr[i])<0.0,PETSC_COMM_SELF,PETSC_ERR_USER_INPUT,"Eigenvalue with non-negative real part %g, the coefficient matrix is not stable",(double)PetscRealPart(wr[i])); |
| 248 | #endif | ||
| 249 | |||
| 250 | /* C = -Z*Z', Z = Q'*B */ | ||
| 251 |
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600 | PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&n,&kk,&n,&done,Q,&n,B,&lb,&zero,Z,&n)); |
| 252 |
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600 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&kk,&dmone,Z,&n,Z,&n,&zero,C,&lu)); |
| 253 | |||
| 254 | /* solve triangular Sylvester equation */ | ||
| 255 |
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600 | PetscCallLAPACKInfo("LAPACKtrsyl",LAPACKtrsyl_("N","C",&ione,&n,&n,W,&n,W,&n,C,&lu,&scal,&info)); |
| 256 |
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600 | PetscCheck(scal==1.0,PETSC_COMM_SELF,PETSC_ERR_SUP,"Current implementation cannot handle scale factor %g",(double)scal); |
| 257 | |||
| 258 | /* back-transform C = Q*C*Q' */ | ||
| 259 |
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600 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&done,Q,&n,C,&n,&zero,W,&n)); |
| 260 |
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600 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&n,&done,W,&n,Q,&n,&zero,C,&lu)); |
| 261 | |||
| 262 | /* resnorm = norm(H(m+1,:)*Y) */ | ||
| 263 |
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600 | if (res) { |
| 264 |
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591 | PetscCheck(k==1,PETSC_COMM_SELF,PETSC_ERR_LIB,"Residual error is intended for k=1 only, but you set k=%" PetscInt_FMT,k); |
| 265 | 591 | *res *= BLASnrm2_(&n,C+m-1,&n); | |
| 266 | } | ||
| 267 | |||
| 268 | /* U = chol(C) */ | ||
| 269 |
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600 | PetscCall(CholeskyFactor(m,C,ldu)); |
| 270 | |||
| 271 |
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600 | PetscCall(PetscFPTrapPop()); |
| 272 | #if !PetscDefined(USE_COMPLEX) | ||
| 273 |
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276 | PetscCall(PetscFree6(Q,W,Z,wr,wi,work)); |
| 274 | #else | ||
| 275 |
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324 | PetscCall(PetscFree5(Q,W,Z,wr,work)); |
| 276 | #endif | ||
| 277 |
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132 | PetscFunctionReturn(PETSC_SUCCESS); |
| 278 | } | ||
| 279 | |||
| 280 | #endif /* SLEPC_HAVE_SLICOT */ | ||
| 281 | |||
| 282 | /*@C | ||
| 283 | LMEDenseHessLyapunovChol - Computes the Cholesky factor of the solution of a | ||
| 284 | dense Lyapunov equation with an upper Hessenberg coefficient matrix. | ||
| 285 | |||
| 286 | Logically Collective | ||
| 287 | |||
| 288 | Input Parameters: | ||
| 289 | + lme - the linear matrix equation solver context | ||
| 290 | . m - number of rows and columns of `H` | ||
| 291 | . H - coefficient matrix | ||
| 292 | . ldh - leading dimension of `H` | ||
| 293 | . k - number of columns of `B` | ||
| 294 | . B - right-hand side matrix | ||
| 295 | . ldb - leading dimension of `B` | ||
| 296 | - ldu - leading dimension of `U` | ||
| 297 | |||
| 298 | Output Parameters: | ||
| 299 | + U - Cholesky factor of the solution | ||
| 300 | - res - (optional) residual norm, on input it should contain $h_{m+1,m}$ | ||
| 301 | |||
| 302 | Note: | ||
| 303 | The Lyapunov equation has the form $HX + XH^* = -BB^*$, where $H$ is an $m\times m$ | ||
| 304 | upper Hessenberg matrix, $B$ is an $m\times k$ matrix and the solution is expressed | ||
| 305 | as $X = U^*U$, where $U$ is upper triangular. $H$ is supposed to be stable. | ||
| 306 | |||
| 307 | When `k=1` and the `res` argument is provided, the last row of `X` is used to | ||
| 308 | compute the residual norm of a Lyapunov equation projected via Arnoldi. | ||
| 309 | |||
| 310 | Level: developer | ||
| 311 | |||
| 312 | .seealso: [](ch:lme), `LMEDenseLyapunov()`, `LMESolve()` | ||
| 313 | @*/ | ||
| 314 | 807 | PetscErrorCode LMEDenseHessLyapunovChol(LME lme,PetscInt m,PetscScalar H[],PetscInt ldh,PetscInt k,PetscScalar B[],PetscInt ldb,PetscScalar U[],PetscInt ldu,PetscReal *res) | |
| 315 | { | ||
| 316 | #if PetscDefined(USE_INFO) | ||
| 317 | 807 | PetscReal error; | |
| 318 | #endif | ||
| 319 | |||
| 320 |
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807 | PetscFunctionBegin; |
| 321 |
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807 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 322 |
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807 | PetscValidLogicalCollectiveInt(lme,m,2); |
| 323 |
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807 | PetscAssertPointer(H,3); |
| 324 |
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807 | PetscValidLogicalCollectiveInt(lme,ldh,4); |
| 325 |
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807 | PetscValidLogicalCollectiveInt(lme,k,5); |
| 326 |
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807 | PetscAssertPointer(B,6); |
| 327 |
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807 | PetscValidLogicalCollectiveInt(lme,ldb,7); |
| 328 |
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807 | PetscAssertPointer(U,8); |
| 329 |
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807 | PetscValidLogicalCollectiveInt(lme,ldu,9); |
| 330 |
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|
807 | if (res) PetscValidLogicalCollectiveReal(lme,*res,10); |
| 331 | |||
| 332 | #if defined(SLEPC_HAVE_SLICOT) | ||
| 333 |
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207 | PetscCall(HessLyapunovChol_SLICOT(m,H,ldh,k,B,ldb,U,ldu,res)); |
| 334 | #else | ||
| 335 |
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600 | PetscCall(HessLyapunovChol_LAPACK(m,H,ldh,k,B,ldb,U,ldu,res)); |
| 336 | #endif | ||
| 337 | |||
| 338 | #if PetscDefined(USE_INFO) | ||
| 339 |
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807 | if (PetscLogPrintInfo) { |
| 340 |
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50 | PetscCall(LyapunovCholResidual(m,H,ldh,k,B,ldb,U,ldu,&error)); |
| 341 |
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50 | PetscCall(PetscInfo(lme,"Residual norm of dense Lyapunov equation = %g\n",(double)error)); |
| 342 | } | ||
| 343 | #endif | ||
| 344 |
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|
132 | PetscFunctionReturn(PETSC_SUCCESS); |
| 345 | } | ||
| 346 | |||
| 347 | #if defined(SLEPC_HAVE_SLICOT) | ||
| 348 | /* | ||
| 349 | Lyapunov_SLICOT - implementation used when SLICOT is available | ||
| 350 | */ | ||
| 351 | 1103 | static PetscErrorCode Lyapunov_SLICOT(PetscInt m,PetscScalar *H,PetscInt ldh,PetscScalar *B,PetscInt ldb,PetscScalar *X,PetscInt ldx) | |
| 352 | { | ||
| 353 | 1103 | PetscBLASInt sdim,lwork,info,n,lx,*iwork; | |
| 354 | 1103 | PetscInt i,j; | |
| 355 | 1103 | PetscReal scal,sep,ferr,*work; | |
| 356 | 1103 | PetscScalar *Q,*W,*wr,*wi; | |
| 357 | |||
| 358 | 1103 | PetscFunctionBegin; | |
| 359 |
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1103 | PetscCall(PetscBLASIntCast(ldx,&lx)); |
| 360 |
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1103 | PetscCall(PetscBLASIntCast(m,&n)); |
| 361 |
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1103 | PetscCall(PetscBLASIntCast(PetscMax(20,m*m),&lwork)); |
| 362 |
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1103 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 363 | |||
| 364 | /* transpose W = H' */ | ||
| 365 |
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1103 | PetscCall(PetscMalloc6(m*m,&W,m*m,&Q,m,&wr,m,&wi,m*m,&iwork,lwork,&work)); |
| 366 |
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8335 | for (j=0;j<m;j++) { |
| 367 |
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65082 | for (i=0;i<m;i++) W[i+j*m] = H[j+i*ldh]; |
| 368 | } | ||
| 369 | |||
| 370 | /* compute the real Schur form of W */ | ||
| 371 |
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1103 | PetscCallLAPACKInfo("LAPACKgees",LAPACKgees_("V","N",NULL,&n,W,&n,&sdim,wr,wi,Q,&n,work,&lwork,NULL,&info)); |
| 372 | |||
| 373 | /* copy -B into X */ | ||
| 374 |
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8335 | for (i=0;i<m;i++) { |
| 375 |
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65082 | for (j=0;j<m;j++) X[i+j*ldx] = -B[i+j*ldb]; |
| 376 | } | ||
| 377 | |||
| 378 | /* solve Lyapunov equation (Hammarling) */ | ||
| 379 |
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1103 | PetscCallBLAS("SLICOTsb03md",SLICOTsb03md_("C","X","F","N",&n,W,&n,Q,&n,X,&lx,&scal,&sep,&ferr,wr,wi,iwork,work,&lwork,&info)); |
| 380 |
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1103 | PetscCheck(!info,PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SLICOT subroutine SB03OD: info=%" PetscBLASInt_FMT,info); |
| 381 |
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1103 | PetscCheck(scal==1.0,PETSC_COMM_SELF,PETSC_ERR_SUP,"Current implementation cannot handle scale factor %g",scal); |
| 382 | |||
| 383 |
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1103 | PetscCall(PetscFPTrapPop()); |
| 384 |
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1103 | PetscCall(PetscFree6(W,Q,wr,wi,iwork,work)); |
| 385 | PetscFunctionReturn(PETSC_SUCCESS); | ||
| 386 | } | ||
| 387 | |||
| 388 | #else | ||
| 389 | |||
| 390 | /* | ||
| 391 | Lyapunov_LAPACK - alternative implementation when SLICOT is not available | ||
| 392 | */ | ||
| 393 | 4189 | static PetscErrorCode Lyapunov_LAPACK(PetscInt m,PetscScalar *A,PetscInt lda,PetscScalar *B,PetscInt ldb,PetscScalar *X,PetscInt ldx) | |
| 394 | { | ||
| 395 | 4189 | PetscBLASInt sdim,lwork,n,lx,lb,ione=1; | |
| 396 | 4189 | PetscInt i,j; | |
| 397 | 4189 | PetscReal scal; | |
| 398 | 4189 | PetscScalar *Q,*W,*Z,*wr,*work,zero=0.0,done=1.0,dmone=-1.0; | |
| 399 | #if PetscDefined(USE_COMPLEX) | ||
| 400 | 5 | PetscReal *rwork; | |
| 401 | #else | ||
| 402 | 4184 | PetscScalar *wi; | |
| 403 | #endif | ||
| 404 | |||
| 405 |
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4189 | PetscFunctionBegin; |
| 406 |
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4189 | PetscCall(PetscBLASIntCast(ldb,&lb)); |
| 407 |
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4189 | PetscCall(PetscBLASIntCast(ldx,&lx)); |
| 408 |
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4189 | PetscCall(PetscBLASIntCast(m,&n)); |
| 409 |
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4189 | PetscCall(PetscBLASIntCast(6*m,&lwork)); |
| 410 |
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4189 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 411 | |||
| 412 | #if !PetscDefined(USE_COMPLEX) | ||
| 413 |
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4184 | PetscCall(PetscMalloc6(m*m,&Q,m*m,&W,m*m,&Z,m,&wr,m,&wi,lwork,&work)); |
| 414 | #else | ||
| 415 |
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5 | PetscCall(PetscMalloc6(m*m,&Q,m*m,&W,m*m,&Z,m,&wr,lwork,&work,m,&rwork)); |
| 416 | #endif | ||
| 417 | |||
| 418 | /* save a copy W = A */ | ||
| 419 |
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43479 | for (j=0;j<m;j++) { |
| 420 |
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411582 | for (i=0;i<m;i++) W[i+j*m] = A[i+j*lda]; |
| 421 | } | ||
| 422 | |||
| 423 | /* compute the (real) Schur form of W */ | ||
| 424 | #if !PetscDefined(USE_COMPLEX) | ||
| 425 |
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4184 | PetscCallLAPACKInfo("LAPACKgees",LAPACKgees_("V","N",NULL,&n,W,&n,&sdim,wr,wi,Q,&n,work,&lwork,NULL,&info)); |
| 426 | #else | ||
| 427 |
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5 | PetscCallLAPACKInfo("LAPACKgees",LAPACKgees_("V","N",NULL,&n,W,&n,&sdim,wr,Q,&n,work,&lwork,rwork,NULL,&info)); |
| 428 | #endif | ||
| 429 | |||
| 430 | /* X = -Q'*B*Q */ | ||
| 431 |
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4189 | PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&n,&n,&n,&done,Q,&n,B,&lb,&zero,Z,&n)); |
| 432 |
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4189 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&dmone,Z,&n,Q,&n,&zero,X,&lx)); |
| 433 | |||
| 434 | /* solve triangular Sylvester equation */ | ||
| 435 |
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4189 | PetscCallLAPACKInfo("LAPACKtrsyl",LAPACKtrsyl_("N","C",&ione,&n,&n,W,&n,W,&n,X,&lx,&scal,&info)); |
| 436 |
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4189 | PetscCheck(scal==1.0,PETSC_COMM_SELF,PETSC_ERR_SUP,"Current implementation cannot handle scale factor %g",(double)scal); |
| 437 | |||
| 438 | /* back-transform X = Q*X*Q' */ | ||
| 439 |
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4189 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&done,Q,&n,X,&n,&zero,W,&n)); |
| 440 |
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4189 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&n,&done,W,&n,Q,&n,&zero,X,&lx)); |
| 441 | |||
| 442 |
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4189 | PetscCall(PetscFPTrapPop()); |
| 443 | #if !PetscDefined(USE_COMPLEX) | ||
| 444 |
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4184 | PetscCall(PetscFree6(Q,W,Z,wr,wi,work)); |
| 445 | #else | ||
| 446 |
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5 | PetscCall(PetscFree6(Q,W,Z,wr,work,rwork)); |
| 447 | #endif | ||
| 448 |
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1051 | PetscFunctionReturn(PETSC_SUCCESS); |
| 449 | } | ||
| 450 | |||
| 451 | #endif /* SLEPC_HAVE_SLICOT */ | ||
| 452 | |||
| 453 | /*@C | ||
| 454 | LMEDenseLyapunov - Computes the solution of a dense continuous-time Lyapunov | ||
| 455 | equation. | ||
| 456 | |||
| 457 | Logically Collective | ||
| 458 | |||
| 459 | Input Parameters: | ||
| 460 | + lme - the linear matrix equation solver context | ||
| 461 | . m - number of rows and columns of `A` | ||
| 462 | . A - coefficient matrix | ||
| 463 | . lda - leading dimension of `A` | ||
| 464 | . B - right-hand side matrix | ||
| 465 | . ldb - leading dimension of `B` | ||
| 466 | - ldx - leading dimension of `X` | ||
| 467 | |||
| 468 | Output Parameter: | ||
| 469 | . X - the solution | ||
| 470 | |||
| 471 | Note: | ||
| 472 | The Lyapunov equation has the form $AX + XA^* = -B$, where all are $m\times m$ | ||
| 473 | matrices, and $B$ is symmetric. | ||
| 474 | |||
| 475 | Level: developer | ||
| 476 | |||
| 477 | .seealso: [](ch:lme), `LMEDenseHessLyapunovChol()`, `LMESolve()` | ||
| 478 | @*/ | ||
| 479 | 5292 | PetscErrorCode LMEDenseLyapunov(LME lme,PetscInt m,PetscScalar A[],PetscInt lda,PetscScalar B[],PetscInt ldb,PetscScalar X[],PetscInt ldx) | |
| 480 | { | ||
| 481 | #if PetscDefined(USE_INFO) | ||
| 482 | 5292 | PetscReal error; | |
| 483 | #endif | ||
| 484 | |||
| 485 |
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5292 | PetscFunctionBegin; |
| 486 |
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5292 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 487 |
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5292 | PetscValidLogicalCollectiveInt(lme,m,2); |
| 488 |
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5292 | PetscAssertPointer(A,3); |
| 489 |
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5292 | PetscValidLogicalCollectiveInt(lme,lda,4); |
| 490 |
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5292 | PetscAssertPointer(B,5); |
| 491 |
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5292 | PetscValidLogicalCollectiveInt(lme,ldb,6); |
| 492 |
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5292 | PetscAssertPointer(X,7); |
| 493 |
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5292 | PetscValidLogicalCollectiveInt(lme,ldx,8); |
| 494 | |||
| 495 | #if defined(SLEPC_HAVE_SLICOT) | ||
| 496 |
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1103 | PetscCall(Lyapunov_SLICOT(m,A,lda,B,ldb,X,ldx)); |
| 497 | #else | ||
| 498 |
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4189 | PetscCall(Lyapunov_LAPACK(m,A,lda,B,ldb,X,ldx)); |
| 499 | #endif | ||
| 500 | |||
| 501 | #if PetscDefined(USE_INFO) | ||
| 502 |
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5292 | if (PetscLogPrintInfo) { |
| 503 |
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10 | PetscCall(LyapunovResidual(m,A,lda,B,ldb,X,ldx,&error)); |
| 504 |
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10 | PetscCall(PetscInfo(lme,"Residual norm of dense Lyapunov equation = %g\n",(double)error)); |
| 505 | } | ||
| 506 | #endif | ||
| 507 |
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1051 | PetscFunctionReturn(PETSC_SUCCESS); |
| 508 | } | ||
| 509 |