| 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 | 729 | PetscErrorCode LMEDenseRankSVD(LME lme,PetscInt n,PetscScalar *A,PetscInt lda,PetscScalar *U,PetscInt ldu,PetscInt *rank) | |
| 22 | { | ||
| 23 | 729 | PetscInt i,j,rk=0; | |
| 24 | 729 | PetscScalar *work; | |
| 25 | 729 | PetscReal tol,*sg,*rwork; | |
| 26 | 729 | PetscBLASInt n_,lda_,ldu_,info,lw_; | |
| 27 | |||
| 28 |
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729 | PetscFunctionBegin; |
| 29 |
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729 | PetscCall(PetscCalloc3(n,&sg,10*n,&work,5*n,&rwork)); |
| 30 |
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729 | PetscCall(PetscBLASIntCast(n,&n_)); |
| 31 |
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729 | PetscCall(PetscBLASIntCast(lda,&lda_)); |
| 32 |
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729 | PetscCall(PetscBLASIntCast(ldu,&ldu_)); |
| 33 | 729 | lw_ = 10*n_; | |
| 34 |
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729 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 35 | #if !defined (PETSC_USE_COMPLEX) | ||
| 36 |
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446 | PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","O",&n_,&n_,A,&lda_,sg,U,&ldu_,NULL,&n_,work,&lw_,&info)); |
| 37 | #else | ||
| 38 |
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283 | PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","O",&n_,&n_,A,&lda_,sg,U,&ldu_,NULL,&n_,work,&lw_,rwork,&info)); |
| 39 | #endif | ||
| 40 |
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729 | PetscCall(PetscFPTrapPop()); |
| 41 |
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729 | SlepcCheckLapackInfo("gesvd",info); |
| 42 | 729 | tol = 10*PETSC_MACHINE_EPSILON*n*sg[0]; | |
| 43 |
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19071 | for (j=0;j<n;j++) { |
| 44 |
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18542 | if (sg[j]>tol) { |
| 45 |
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602730 | for (i=0;i<n;i++) U[i+j*n] *= sg[j]; |
| 46 | 18342 | rk++; | |
| 47 | } else break; | ||
| 48 | } | ||
| 49 | 729 | *rank = rk; | |
| 50 |
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729 | PetscCall(PetscFree3(sg,work,rwork)); |
| 51 |
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116 | PetscFunctionReturn(PETSC_SUCCESS); |
| 52 | } | ||
| 53 | |||
| 54 | #if defined(PETSC_USE_INFO) | ||
| 55 | /* | ||
| 56 | LyapunovCholResidual - compute the residual norm ||A*U'*U+U'*U*A'+B*B'|| | ||
| 57 | */ | ||
| 58 | 42 | static PetscErrorCode LyapunovCholResidual(PetscInt m,PetscScalar *A,PetscInt lda,PetscInt k,PetscScalar *B,PetscInt ldb,PetscScalar *U,PetscInt ldu,PetscReal *res) | |
| 59 | { | ||
| 60 | 42 | PetscBLASInt n,kk,la,lb,lu; | |
| 61 | 42 | PetscScalar *M,*R,zero=0.0,done=1.0; | |
| 62 | |||
| 63 |
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42 | PetscFunctionBegin; |
| 64 | 42 | *res = 0; | |
| 65 |
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42 | PetscCall(PetscBLASIntCast(lda,&la)); |
| 66 |
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42 | PetscCall(PetscBLASIntCast(ldb,&lb)); |
| 67 |
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42 | PetscCall(PetscBLASIntCast(ldu,&lu)); |
| 68 |
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42 | PetscCall(PetscBLASIntCast(m,&n)); |
| 69 |
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42 | PetscCall(PetscBLASIntCast(k,&kk)); |
| 70 |
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42 | PetscCall(PetscMalloc2(m*m,&M,m*m,&R)); |
| 71 | |||
| 72 | /* R = B*B' */ | ||
| 73 |
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42 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&kk,&done,B,&lb,B,&lb,&zero,R,&n)); |
| 74 | /* M = A*U' */ | ||
| 75 |
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42 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&n,&done,A,&la,U,&lu,&zero,M,&n)); |
| 76 | /* R = R+M*U */ | ||
| 77 |
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42 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&done,M,&n,U,&lu,&done,R,&n)); |
| 78 | /* R = R+U'*M' */ | ||
| 79 |
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42 | PetscCallBLAS("BLASgemm",BLASgemm_("C","C",&n,&n,&n,&done,U,&lu,M,&n,&done,R,&n)); |
| 80 | |||
| 81 | 42 | *res = LAPACKlange_("F",&n,&n,R,&n,NULL); | |
| 82 |
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42 | PetscCall(PetscFree2(M,R)); |
| 83 |
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6 | PetscFunctionReturn(PETSC_SUCCESS); |
| 84 | } | ||
| 85 | |||
| 86 | /* | ||
| 87 | LyapunovResidual - compute the residual norm ||A*X+X*A'+B|| | ||
| 88 | */ | ||
| 89 | 10 | static PetscErrorCode LyapunovResidual(PetscInt m,PetscScalar *A,PetscInt lda,PetscScalar *B,PetscInt ldb,PetscScalar *X,PetscInt ldx,PetscReal *res) | |
| 90 | { | ||
| 91 | 10 | PetscInt i; | |
| 92 | 10 | PetscBLASInt n,la,lb,lx; | |
| 93 | 10 | PetscScalar *R,done=1.0; | |
| 94 | |||
| 95 |
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10 | PetscFunctionBegin; |
| 96 | 10 | *res = 0; | |
| 97 |
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10 | PetscCall(PetscBLASIntCast(lda,&la)); |
| 98 |
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10 | PetscCall(PetscBLASIntCast(ldb,&lb)); |
| 99 |
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10 | PetscCall(PetscBLASIntCast(ldx,&lx)); |
| 100 |
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10 | PetscCall(PetscBLASIntCast(m,&n)); |
| 101 |
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10 | PetscCall(PetscMalloc1(m*m,&R)); |
| 102 | |||
| 103 | /* R = B+A*X */ | ||
| 104 |
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110 | for (i=0;i<m;i++) PetscCall(PetscArraycpy(R+i*m,B+i*ldb,m)); |
| 105 |
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10 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&done,A,&la,X,&lx,&done,R,&n)); |
| 106 | /* R = R+X*A' */ | ||
| 107 |
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10 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&n,&done,X,&lx,A,&la,&done,R,&n)); |
| 108 | |||
| 109 | 10 | *res = LAPACKlange_("F",&n,&n,R,&n,NULL); | |
| 110 |
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10 | PetscCall(PetscFree(R)); |
| 111 |
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2 | PetscFunctionReturn(PETSC_SUCCESS); |
| 112 | } | ||
| 113 | #endif | ||
| 114 | |||
| 115 | #if defined(SLEPC_HAVE_SLICOT) | ||
| 116 | /* | ||
| 117 | HessLyapunovChol_SLICOT - implementation used when SLICOT is available | ||
| 118 | */ | ||
| 119 | 207 | static PetscErrorCode HessLyapunovChol_SLICOT(PetscInt m,PetscScalar *H,PetscInt ldh,PetscInt k,PetscScalar *B,PetscInt ldb,PetscScalar *U,PetscInt ldu,PetscReal *res) | |
| 120 | { | ||
| 121 | 207 | PetscBLASInt lwork,info,n,kk,lu,ione=1,sdim; | |
| 122 | 207 | PetscInt i,j; | |
| 123 | 207 | PetscReal scal; | |
| 124 | 207 | PetscScalar *Q,*W,*wr,*wi,*work; | |
| 125 | |||
| 126 | 207 | PetscFunctionBegin; | |
| 127 |
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207 | PetscCall(PetscBLASIntCast(ldu,&lu)); |
| 128 |
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207 | PetscCall(PetscBLASIntCast(m,&n)); |
| 129 |
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207 | PetscCall(PetscBLASIntCast(k,&kk)); |
| 130 |
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207 | PetscCall(PetscBLASIntCast(6*m,&lwork)); |
| 131 |
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207 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 132 | |||
| 133 | /* transpose W = H' */ | ||
| 134 |
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207 | PetscCall(PetscMalloc5(m*m,&W,m*m,&Q,m,&wr,m,&wi,lwork,&work)); |
| 135 |
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6415 | for (j=0;j<m;j++) { |
| 136 |
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194138 | for (i=0;i<m;i++) W[i+j*m] = H[j+i*ldh]; |
| 137 | } | ||
| 138 | |||
| 139 | /* compute the real Schur form of W */ | ||
| 140 |
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207 | PetscCallBLAS("LAPACKgees",LAPACKgees_("V","N",NULL,&n,W,&n,&sdim,wr,wi,Q,&n,work,&lwork,NULL,&info)); |
| 141 |
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207 | SlepcCheckLapackInfo("gees",info); |
| 142 | #if defined(PETSC_USE_DEBUG) | ||
| 143 | 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"); | ||
| 144 | #endif | ||
| 145 | |||
| 146 | /* copy B' into first rows of U */ | ||
| 147 |
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415 | for (i=0;i<k;i++) { |
| 148 |
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6426 | for (j=0;j<m;j++) U[i+j*ldu] = B[j+i*ldb]; |
| 149 | } | ||
| 150 | |||
| 151 | /* solve Lyapunov equation (Hammarling) */ | ||
| 152 |
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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)); |
| 153 |
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207 | PetscCheck(!info,PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SLICOT subroutine SB03OD: info=%" PetscBLASInt_FMT,info); |
| 154 |
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207 | PetscCheck(scal==1.0,PETSC_COMM_SELF,PETSC_ERR_SUP,"Current implementation cannot handle scale factor %g",scal); |
| 155 | |||
| 156 | /* resnorm = norm(H(m+1,:)*U'*U), use Q(:,1) = U'*U(:,m) */ | ||
| 157 |
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207 | if (res) { |
| 158 |
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6404 | for (j=0;j<m;j++) Q[j] = U[j+(m-1)*ldu]; |
| 159 |
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206 | PetscCallBLAS("BLAStrmv",BLAStrmv_("U","C","N",&n,U,&lu,Q,&ione)); |
| 160 |
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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); |
| 161 | 206 | *res *= BLASnrm2_(&n,Q,&ione); | |
| 162 | } | ||
| 163 | |||
| 164 |
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207 | PetscCall(PetscFPTrapPop()); |
| 165 |
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207 | PetscCall(PetscFree5(W,Q,wr,wi,work)); |
| 166 | PetscFunctionReturn(PETSC_SUCCESS); | ||
| 167 | } | ||
| 168 | |||
| 169 | #else | ||
| 170 | |||
| 171 | /* | ||
| 172 | Compute the upper Cholesky factor of A | ||
| 173 | */ | ||
| 174 | 592 | static PetscErrorCode CholeskyFactor(PetscInt m,PetscScalar *A,PetscInt lda) | |
| 175 | { | ||
| 176 | 592 | PetscInt i; | |
| 177 | 592 | PetscScalar *S; | |
| 178 | 592 | PetscBLASInt info,n,ld; | |
| 179 | |||
| 180 |
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592 | PetscFunctionBegin; |
| 181 |
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592 | PetscCall(PetscBLASIntCast(m,&n)); |
| 182 |
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592 | PetscCall(PetscBLASIntCast(lda,&ld)); |
| 183 |
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592 | PetscCall(PetscMalloc1(m*m,&S)); |
| 184 |
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592 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 185 | |||
| 186 | /* save a copy of matrix in S */ | ||
| 187 |
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18442 | for (i=0;i<m;i++) PetscCall(PetscArraycpy(S+i*m,A+i*lda,m)); |
| 188 | |||
| 189 | /* compute upper Cholesky factor in R */ | ||
| 190 |
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592 | PetscCallBLAS("LAPACKpotrf",LAPACKpotrf_("U",&n,A,&ld,&info)); |
| 191 |
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592 | PetscCall(PetscLogFlops((1.0*n*n*n)/3.0)); |
| 192 | |||
| 193 |
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592 | if (info) { |
| 194 |
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18343 | for (i=0;i<m;i++) { |
| 195 |
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17760 | PetscCall(PetscArraycpy(A+i*lda,S+i*m,m)); |
| 196 | 17760 | A[i+i*lda] += 50.0*PETSC_MACHINE_EPSILON; | |
| 197 | } | ||
| 198 |
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583 | PetscCallBLAS("LAPACKpotrf",LAPACKpotrf_("U",&n,A,&ld,&info)); |
| 199 |
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583 | SlepcCheckLapackInfo("potrf",info); |
| 200 |
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583 | PetscCall(PetscLogFlops((1.0*n*n*n)/3.0)); |
| 201 | } | ||
| 202 | |||
| 203 | /* Zero out entries below the diagonal */ | ||
| 204 |
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17850 | for (i=0;i<m-1;i++) PetscCall(PetscArrayzero(A+i*lda+i+1,m-i-1)); |
| 205 |
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592 | PetscCall(PetscFPTrapPop()); |
| 206 |
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592 | PetscCall(PetscFree(S)); |
| 207 |
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128 | PetscFunctionReturn(PETSC_SUCCESS); |
| 208 | } | ||
| 209 | |||
| 210 | /* | ||
| 211 | HessLyapunovChol_LAPACK - alternative implementation when SLICOT is not available | ||
| 212 | */ | ||
| 213 | 592 | static PetscErrorCode HessLyapunovChol_LAPACK(PetscInt m,PetscScalar *H,PetscInt ldh,PetscInt k,PetscScalar *B,PetscInt ldb,PetscScalar *U,PetscInt ldu,PetscReal *res) | |
| 214 | { | ||
| 215 | 592 | PetscBLASInt ilo=1,lwork,info,n,kk,lu,lb,ione=1; | |
| 216 | 592 | PetscInt i,j; | |
| 217 | 592 | PetscReal scal; | |
| 218 | 592 | PetscScalar *Q,*C,*W,*Z,*wr,*work,zero=0.0,done=1.0,dmone=-1.0; | |
| 219 | #if !defined(PETSC_USE_COMPLEX) | ||
| 220 | 276 | PetscScalar *wi; | |
| 221 | #endif | ||
| 222 | |||
| 223 |
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592 | PetscFunctionBegin; |
| 224 |
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592 | PetscCall(PetscBLASIntCast(ldb,&lb)); |
| 225 |
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592 | PetscCall(PetscBLASIntCast(ldu,&lu)); |
| 226 |
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592 | PetscCall(PetscBLASIntCast(m,&n)); |
| 227 |
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592 | PetscCall(PetscBLASIntCast(k,&kk)); |
| 228 |
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592 | PetscCall(PetscBLASIntCast(6*m,&lwork)); |
| 229 |
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592 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 230 | 592 | C = U; | |
| 231 | |||
| 232 | #if !defined(PETSC_USE_COMPLEX) | ||
| 233 |
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276 | PetscCall(PetscMalloc6(m*m,&Q,m*m,&W,m*k,&Z,m,&wr,m,&wi,lwork,&work)); |
| 234 | #else | ||
| 235 |
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316 | PetscCall(PetscMalloc5(m*m,&Q,m*m,&W,m*k,&Z,m,&wr,lwork,&work)); |
| 236 | #endif | ||
| 237 | |||
| 238 | /* save a copy W = H */ | ||
| 239 |
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18442 | for (j=0;j<m;j++) { |
| 240 |
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574500 | for (i=0;i<m;i++) W[i+j*m] = H[i+j*ldh]; |
| 241 | } | ||
| 242 | |||
| 243 | /* compute the (real) Schur form of W */ | ||
| 244 | #if !defined(PETSC_USE_COMPLEX) | ||
| 245 |
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276 | PetscCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","I",&n,&ilo,&n,W,&n,wr,wi,Q,&n,work,&lwork,&info)); |
| 246 | #else | ||
| 247 |
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316 | PetscCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","I",&n,&ilo,&n,W,&n,wr,Q,&n,work,&lwork,&info)); |
| 248 | #endif | ||
| 249 |
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592 | SlepcCheckLapackInfo("hseqr",info); |
| 250 | #if defined(PETSC_USE_DEBUG) | ||
| 251 |
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3958 | 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])); |
| 252 | #endif | ||
| 253 | |||
| 254 | /* C = -Z*Z', Z = Q'*B */ | ||
| 255 |
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592 | PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&n,&kk,&n,&done,Q,&n,B,&lb,&zero,Z,&n)); |
| 256 |
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592 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&kk,&dmone,Z,&n,Z,&n,&zero,C,&lu)); |
| 257 | |||
| 258 | /* solve triangular Sylvester equation */ | ||
| 259 |
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592 | PetscCallBLAS("LAPACKtrsyl",LAPACKtrsyl_("N","C",&ione,&n,&n,W,&n,W,&n,C,&lu,&scal,&info)); |
| 260 |
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592 | SlepcCheckLapackInfo("trsyl",info); |
| 261 |
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592 | PetscCheck(scal==1.0,PETSC_COMM_SELF,PETSC_ERR_SUP,"Current implementation cannot handle scale factor %g",(double)scal); |
| 262 | |||
| 263 | /* back-transform C = Q*C*Q' */ | ||
| 264 |
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592 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&done,Q,&n,C,&n,&zero,W,&n)); |
| 265 |
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592 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&n,&done,W,&n,Q,&n,&zero,C,&lu)); |
| 266 | |||
| 267 | /* resnorm = norm(H(m+1,:)*Y) */ | ||
| 268 |
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592 | if (res) { |
| 269 |
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583 | PetscCheck(k==1,PETSC_COMM_SELF,PETSC_ERR_LIB,"Residual error is intended for k=1 only, but you set k=%" PetscInt_FMT,k); |
| 270 | 583 | *res *= BLASnrm2_(&n,C+m-1,&n); | |
| 271 | } | ||
| 272 | |||
| 273 | /* U = chol(C) */ | ||
| 274 |
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592 | PetscCall(CholeskyFactor(m,C,ldu)); |
| 275 | |||
| 276 |
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592 | PetscCall(PetscFPTrapPop()); |
| 277 | #if !defined(PETSC_USE_COMPLEX) | ||
| 278 |
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276 | PetscCall(PetscFree6(Q,W,Z,wr,wi,work)); |
| 279 | #else | ||
| 280 |
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316 | PetscCall(PetscFree5(Q,W,Z,wr,work)); |
| 281 | #endif | ||
| 282 |
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128 | PetscFunctionReturn(PETSC_SUCCESS); |
| 283 | } | ||
| 284 | |||
| 285 | #endif /* SLEPC_HAVE_SLICOT */ | ||
| 286 | |||
| 287 | /*@C | ||
| 288 | LMEDenseHessLyapunovChol - Computes the Cholesky factor of the solution of a | ||
| 289 | dense Lyapunov equation with an upper Hessenberg coefficient matrix. | ||
| 290 | |||
| 291 | Logically Collective | ||
| 292 | |||
| 293 | Input Parameters: | ||
| 294 | + lme - linear matrix equation solver context | ||
| 295 | . m - number of rows and columns of H | ||
| 296 | . H - coefficient matrix | ||
| 297 | . ldh - leading dimension of H | ||
| 298 | . k - number of columns of B | ||
| 299 | . B - right-hand side matrix | ||
| 300 | . ldb - leading dimension of B | ||
| 301 | - ldu - leading dimension of U | ||
| 302 | |||
| 303 | Output Parameters: | ||
| 304 | + U - Cholesky factor of the solution | ||
| 305 | - res - (optional) residual norm, on input it should contain H(m+1,m) | ||
| 306 | |||
| 307 | Note: | ||
| 308 | The Lyapunov equation has the form H*X + X*H' = -B*B', where H is an mxm | ||
| 309 | upper Hessenberg matrix, B is an mxk matrix and the solution is expressed | ||
| 310 | as X = U'*U, where U is upper triangular. H is supposed to be stable. | ||
| 311 | |||
| 312 | When k=1 and the res argument is provided, the last row of X is used to | ||
| 313 | compute the residual norm of a Lyapunov equation projected via Arnoldi. | ||
| 314 | |||
| 315 | Level: developer | ||
| 316 | |||
| 317 | .seealso: LMEDenseLyapunov(), LMESolve() | ||
| 318 | @*/ | ||
| 319 | 799 | PetscErrorCode LMEDenseHessLyapunovChol(LME lme,PetscInt m,PetscScalar *H,PetscInt ldh,PetscInt k,PetscScalar *B,PetscInt ldb,PetscScalar *U,PetscInt ldu,PetscReal *res) | |
| 320 | { | ||
| 321 | #if defined(PETSC_USE_INFO) | ||
| 322 | 799 | PetscReal error; | |
| 323 | #endif | ||
| 324 | |||
| 325 |
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799 | PetscFunctionBegin; |
| 326 |
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799 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 327 |
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799 | PetscValidLogicalCollectiveInt(lme,m,2); |
| 328 |
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799 | PetscAssertPointer(H,3); |
| 329 |
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799 | PetscValidLogicalCollectiveInt(lme,ldh,4); |
| 330 |
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799 | PetscValidLogicalCollectiveInt(lme,k,5); |
| 331 |
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799 | PetscAssertPointer(B,6); |
| 332 |
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799 | PetscValidLogicalCollectiveInt(lme,ldb,7); |
| 333 |
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799 | PetscAssertPointer(U,8); |
| 334 |
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799 | PetscValidLogicalCollectiveInt(lme,ldu,9); |
| 335 |
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|
799 | if (res) PetscValidLogicalCollectiveReal(lme,*res,10); |
| 336 | |||
| 337 | #if defined(SLEPC_HAVE_SLICOT) | ||
| 338 |
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207 | PetscCall(HessLyapunovChol_SLICOT(m,H,ldh,k,B,ldb,U,ldu,res)); |
| 339 | #else | ||
| 340 |
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592 | PetscCall(HessLyapunovChol_LAPACK(m,H,ldh,k,B,ldb,U,ldu,res)); |
| 341 | #endif | ||
| 342 | |||
| 343 | #if defined(PETSC_USE_INFO) | ||
| 344 |
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799 | if (PetscLogPrintInfo) { |
| 345 |
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42 | PetscCall(LyapunovCholResidual(m,H,ldh,k,B,ldb,U,ldu,&error)); |
| 346 |
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42 | PetscCall(PetscInfo(lme,"Residual norm of dense Lyapunov equation = %g\n",(double)error)); |
| 347 | } | ||
| 348 | #endif | ||
| 349 |
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|
128 | PetscFunctionReturn(PETSC_SUCCESS); |
| 350 | } | ||
| 351 | |||
| 352 | #if defined(SLEPC_HAVE_SLICOT) | ||
| 353 | /* | ||
| 354 | Lyapunov_SLICOT - implementation used when SLICOT is available | ||
| 355 | */ | ||
| 356 | 1103 | static PetscErrorCode Lyapunov_SLICOT(PetscInt m,PetscScalar *H,PetscInt ldh,PetscScalar *B,PetscInt ldb,PetscScalar *X,PetscInt ldx) | |
| 357 | { | ||
| 358 | 1103 | PetscBLASInt sdim,lwork,info,n,lx,*iwork; | |
| 359 | 1103 | PetscInt i,j; | |
| 360 | 1103 | PetscReal scal,sep,ferr,*work; | |
| 361 | 1103 | PetscScalar *Q,*W,*wr,*wi; | |
| 362 | |||
| 363 | 1103 | PetscFunctionBegin; | |
| 364 |
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1103 | PetscCall(PetscBLASIntCast(ldx,&lx)); |
| 365 |
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1103 | PetscCall(PetscBLASIntCast(m,&n)); |
| 366 |
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1103 | PetscCall(PetscBLASIntCast(PetscMax(20,m*m),&lwork)); |
| 367 |
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1103 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 368 | |||
| 369 | /* transpose W = H' */ | ||
| 370 |
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1103 | PetscCall(PetscMalloc6(m*m,&W,m*m,&Q,m,&wr,m,&wi,m*m,&iwork,lwork,&work)); |
| 371 |
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8335 | for (j=0;j<m;j++) { |
| 372 |
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65082 | for (i=0;i<m;i++) W[i+j*m] = H[j+i*ldh]; |
| 373 | } | ||
| 374 | |||
| 375 | /* compute the real Schur form of W */ | ||
| 376 |
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1103 | PetscCallBLAS("LAPACKgees",LAPACKgees_("V","N",NULL,&n,W,&n,&sdim,wr,wi,Q,&n,work,&lwork,NULL,&info)); |
| 377 |
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1103 | SlepcCheckLapackInfo("gees",info); |
| 378 | |||
| 379 | /* copy -B into X */ | ||
| 380 |
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8335 | for (i=0;i<m;i++) { |
| 381 |
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65082 | for (j=0;j<m;j++) X[i+j*ldx] = -B[i+j*ldb]; |
| 382 | } | ||
| 383 | |||
| 384 | /* solve Lyapunov equation (Hammarling) */ | ||
| 385 |
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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)); |
| 386 |
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1103 | PetscCheck(!info,PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SLICOT subroutine SB03OD: info=%" PetscBLASInt_FMT,info); |
| 387 |
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1103 | PetscCheck(scal==1.0,PETSC_COMM_SELF,PETSC_ERR_SUP,"Current implementation cannot handle scale factor %g",scal); |
| 388 | |||
| 389 |
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1103 | PetscCall(PetscFPTrapPop()); |
| 390 |
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1103 | PetscCall(PetscFree6(W,Q,wr,wi,iwork,work)); |
| 391 | PetscFunctionReturn(PETSC_SUCCESS); | ||
| 392 | } | ||
| 393 | |||
| 394 | #else | ||
| 395 | |||
| 396 | /* | ||
| 397 | Lyapunov_LAPACK - alternative implementation when SLICOT is not available | ||
| 398 | */ | ||
| 399 | 4173 | static PetscErrorCode Lyapunov_LAPACK(PetscInt m,PetscScalar *A,PetscInt lda,PetscScalar *B,PetscInt ldb,PetscScalar *X,PetscInt ldx) | |
| 400 | { | ||
| 401 | 4173 | PetscBLASInt sdim,lwork,info,n,lx,lb,ione=1; | |
| 402 | 4173 | PetscInt i,j; | |
| 403 | 4173 | PetscReal scal; | |
| 404 | 4173 | PetscScalar *Q,*W,*Z,*wr,*work,zero=0.0,done=1.0,dmone=-1.0; | |
| 405 | #if defined(PETSC_USE_COMPLEX) | ||
| 406 | 5 | PetscReal *rwork; | |
| 407 | #else | ||
| 408 | 4168 | PetscScalar *wi; | |
| 409 | #endif | ||
| 410 | |||
| 411 |
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4173 | PetscFunctionBegin; |
| 412 |
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4173 | PetscCall(PetscBLASIntCast(ldb,&lb)); |
| 413 |
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4173 | PetscCall(PetscBLASIntCast(ldx,&lx)); |
| 414 |
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4173 | PetscCall(PetscBLASIntCast(m,&n)); |
| 415 |
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4173 | PetscCall(PetscBLASIntCast(6*m,&lwork)); |
| 416 |
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4173 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 417 | |||
| 418 | #if !defined(PETSC_USE_COMPLEX) | ||
| 419 |
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4168 | PetscCall(PetscMalloc6(m*m,&Q,m*m,&W,m*m,&Z,m,&wr,m,&wi,lwork,&work)); |
| 420 | #else | ||
| 421 |
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5 | PetscCall(PetscMalloc6(m*m,&Q,m*m,&W,m*m,&Z,m,&wr,lwork,&work,m,&rwork)); |
| 422 | #endif | ||
| 423 | |||
| 424 | /* save a copy W = A */ | ||
| 425 |
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43303 | for (j=0;j<m;j++) { |
| 426 |
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409822 | for (i=0;i<m;i++) W[i+j*m] = A[i+j*lda]; |
| 427 | } | ||
| 428 | |||
| 429 | /* compute the (real) Schur form of W */ | ||
| 430 | #if !defined(PETSC_USE_COMPLEX) | ||
| 431 |
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4168 | PetscCallBLAS("LAPACKgees",LAPACKgees_("V","N",NULL,&n,W,&n,&sdim,wr,wi,Q,&n,work,&lwork,NULL,&info)); |
| 432 | #else | ||
| 433 |
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5 | PetscCallBLAS("LAPACKgees",LAPACKgees_("V","N",NULL,&n,W,&n,&sdim,wr,Q,&n,work,&lwork,rwork,NULL,&info)); |
| 434 | #endif | ||
| 435 |
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4173 | SlepcCheckLapackInfo("gees",info); |
| 436 | |||
| 437 | /* X = -Q'*B*Q */ | ||
| 438 |
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4173 | PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&n,&n,&n,&done,Q,&n,B,&lb,&zero,Z,&n)); |
| 439 |
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4173 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&dmone,Z,&n,Q,&n,&zero,X,&lx)); |
| 440 | |||
| 441 | /* solve triangular Sylvester equation */ | ||
| 442 |
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4173 | PetscCallBLAS("LAPACKtrsyl",LAPACKtrsyl_("N","C",&ione,&n,&n,W,&n,W,&n,X,&lx,&scal,&info)); |
| 443 |
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4173 | SlepcCheckLapackInfo("trsyl",info); |
| 444 |
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4173 | PetscCheck(scal==1.0,PETSC_COMM_SELF,PETSC_ERR_SUP,"Current implementation cannot handle scale factor %g",(double)scal); |
| 445 | |||
| 446 | /* back-transform X = Q*X*Q' */ | ||
| 447 |
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4173 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&done,Q,&n,X,&n,&zero,W,&n)); |
| 448 |
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4173 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n,&n,&n,&done,W,&n,Q,&n,&zero,X,&lx)); |
| 449 | |||
| 450 |
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4173 | PetscCall(PetscFPTrapPop()); |
| 451 | #if !defined(PETSC_USE_COMPLEX) | ||
| 452 |
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4168 | PetscCall(PetscFree6(Q,W,Z,wr,wi,work)); |
| 453 | #else | ||
| 454 |
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5 | PetscCall(PetscFree6(Q,W,Z,wr,work,rwork)); |
| 455 | #endif | ||
| 456 |
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1035 | PetscFunctionReturn(PETSC_SUCCESS); |
| 457 | } | ||
| 458 | |||
| 459 | #endif /* SLEPC_HAVE_SLICOT */ | ||
| 460 | |||
| 461 | /*@C | ||
| 462 | LMEDenseLyapunov - Computes the solution of a dense continuous-time Lyapunov | ||
| 463 | equation. | ||
| 464 | |||
| 465 | Logically Collective | ||
| 466 | |||
| 467 | Input Parameters: | ||
| 468 | + lme - linear matrix equation solver context | ||
| 469 | . m - number of rows and columns of A | ||
| 470 | . A - coefficient matrix | ||
| 471 | . lda - leading dimension of A | ||
| 472 | . B - right-hand side matrix | ||
| 473 | . ldb - leading dimension of B | ||
| 474 | - ldx - leading dimension of X | ||
| 475 | |||
| 476 | Output Parameter: | ||
| 477 | . X - the solution | ||
| 478 | |||
| 479 | Note: | ||
| 480 | The Lyapunov equation has the form A*X + X*A' = -B, where all are mxm | ||
| 481 | matrices, and B is symmetric. | ||
| 482 | |||
| 483 | Level: developer | ||
| 484 | |||
| 485 | .seealso: LMEDenseHessLyapunovChol(), LMESolve() | ||
| 486 | @*/ | ||
| 487 | 5276 | PetscErrorCode LMEDenseLyapunov(LME lme,PetscInt m,PetscScalar *A,PetscInt lda,PetscScalar *B,PetscInt ldb,PetscScalar *X,PetscInt ldx) | |
| 488 | { | ||
| 489 | #if defined(PETSC_USE_INFO) | ||
| 490 | 5276 | PetscReal error; | |
| 491 | #endif | ||
| 492 | |||
| 493 |
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5276 | PetscFunctionBegin; |
| 494 |
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5276 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 495 |
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5276 | PetscValidLogicalCollectiveInt(lme,m,2); |
| 496 |
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5276 | PetscAssertPointer(A,3); |
| 497 |
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5276 | PetscValidLogicalCollectiveInt(lme,lda,4); |
| 498 |
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5276 | PetscAssertPointer(B,5); |
| 499 |
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5276 | PetscValidLogicalCollectiveInt(lme,ldb,6); |
| 500 |
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5276 | PetscAssertPointer(X,7); |
| 501 |
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5276 | PetscValidLogicalCollectiveInt(lme,ldx,8); |
| 502 | |||
| 503 | #if defined(SLEPC_HAVE_SLICOT) | ||
| 504 |
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1103 | PetscCall(Lyapunov_SLICOT(m,A,lda,B,ldb,X,ldx)); |
| 505 | #else | ||
| 506 |
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4173 | PetscCall(Lyapunov_LAPACK(m,A,lda,B,ldb,X,ldx)); |
| 507 | #endif | ||
| 508 | |||
| 509 | #if defined(PETSC_USE_INFO) | ||
| 510 |
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5276 | if (PetscLogPrintInfo) { |
| 511 |
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10 | PetscCall(LyapunovResidual(m,A,lda,B,ldb,X,ldx,&error)); |
| 512 |
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10 | PetscCall(PetscInfo(lme,"Residual norm of dense Lyapunov equation = %g\n",(double)error)); |
| 513 | } | ||
| 514 | #endif | ||
| 515 |
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1035 | PetscFunctionReturn(PETSC_SUCCESS); |
| 516 | } | ||
| 517 |