Actual source code: bvlapack.c
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
10: /*
11: BV private kernels that use the LAPACK
12: */
14: #include <slepc/private/bvimpl.h>
15: #include <slepcblaslapack.h>
17: /*
18: Reduction operation to compute sqrt(x**2+y**2) when normalizing vectors
19: */
20: SLEPC_EXTERN void MPIAPI SlepcPythag(void *in,void *inout,PetscMPIInt *len,MPI_Datatype *datatype)
21: {
22: PetscBLASInt i,n=*len;
23: PetscReal *x = (PetscReal*)in,*y = (PetscReal*)inout;
25: PetscFunctionBegin;
26: if (PetscUnlikely(*datatype!=MPIU_REAL)) {
27: (void)(*PetscErrorPrintf)("Only implemented for MPIU_REAL data type");
28: MPI_Abort(PETSC_COMM_WORLD,1);
29: }
30: for (i=0;i<n;i++) y[i] = SlepcAbs(x[i],y[i]);
31: PetscFunctionReturnVoid();
32: }
34: /*
35: Compute ||A|| for an mxn matrix
36: */
37: PetscErrorCode BVNorm_LAPACK_Private(BV bv,PetscInt m_,PetscInt n_,const PetscScalar *A,PetscInt lda_,NormType type,PetscReal *nrm,PetscBool mpi)
38: {
39: PetscBLASInt m,n,lda,i,j;
40: PetscMPIInt len;
41: PetscReal lnrm,*rwork=NULL,*rwork2=NULL;
43: PetscFunctionBegin;
44: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
45: PetscCall(PetscBLASIntCast(m_,&m));
46: PetscCall(PetscBLASIntCast(n_,&n));
47: PetscCall(PetscBLASIntCast(lda_,&lda));
48: if (type==NORM_FROBENIUS || type==NORM_2) {
49: lnrm = LAPACKlange_("F",&m,&n,(PetscScalar*)A,&lda,rwork);
50: if (mpi) PetscCallMPI(MPIU_Allreduce(&lnrm,nrm,1,MPIU_REAL,MPIU_LAPY2,PetscObjectComm((PetscObject)bv)));
51: else *nrm = lnrm;
52: PetscCall(PetscLogFlops(2.0*m*n));
53: } else if (type==NORM_1) {
54: if (mpi) {
55: PetscCall(BVAllocateWork_Private(bv,2*n_));
56: rwork = (PetscReal*)bv->work;
57: rwork2 = rwork+n_;
58: PetscCall(PetscArrayzero(rwork,n_));
59: PetscCall(PetscArrayzero(rwork2,n_));
60: for (j=0;j<n_;j++) {
61: for (i=0;i<m_;i++) {
62: rwork[j] += PetscAbsScalar(A[i+j*lda_]);
63: }
64: }
65: PetscCall(PetscMPIIntCast(n_,&len));
66: PetscCallMPI(MPIU_Allreduce(rwork,rwork2,len,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)bv)));
67: *nrm = 0.0;
68: for (j=0;j<n_;j++) if (rwork2[j] > *nrm) *nrm = rwork2[j];
69: } else {
70: *nrm = LAPACKlange_("O",&m,&n,(PetscScalar*)A,&lda,rwork);
71: }
72: PetscCall(PetscLogFlops(1.0*m*n));
73: } else if (type==NORM_INFINITY) {
74: PetscCall(BVAllocateWork_Private(bv,m_));
75: rwork = (PetscReal*)bv->work;
76: lnrm = LAPACKlange_("I",&m,&n,(PetscScalar*)A,&lda,rwork);
77: if (mpi) PetscCallMPI(MPIU_Allreduce(&lnrm,nrm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)bv)));
78: else *nrm = lnrm;
79: PetscCall(PetscLogFlops(1.0*m*n));
80: }
81: PetscCall(PetscFPTrapPop());
82: PetscFunctionReturn(PETSC_SUCCESS);
83: }
85: /*
86: Normalize the columns of an mxn matrix A
87: */
88: PetscErrorCode BVNormalize_LAPACK_Private(BV bv,PetscInt m_,PetscInt n_,const PetscScalar *A,PetscInt lda_,PetscScalar *eigi,PetscBool mpi)
89: {
90: PetscBLASInt m,lda,j,k,zero=0;
91: PetscMPIInt len;
92: PetscReal *norms,*rwork=NULL,*rwork2=NULL,done=1.0;
94: PetscFunctionBegin;
95: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
96: PetscCall(PetscBLASIntCast(m_,&m));
97: PetscCall(PetscBLASIntCast(lda_,&lda));
98: PetscCall(BVAllocateWork_Private(bv,2*n_));
99: rwork = (PetscReal*)bv->work;
100: rwork2 = rwork+n_;
101: /* compute local norms */
102: for (j=0;j<n_;j++) {
103: k = 1;
104: if (!PetscDefined(USE_COMPLEX) && eigi && eigi[j] != 0.0) k = 2;
105: rwork[j] = LAPACKlange_("F",&m,&k,(PetscScalar*)(A+j*lda_),&lda,rwork2);
106: if (k==2) { rwork[j+1] = rwork[j]; j++; }
107: }
108: /* reduction to get global norms */
109: if (mpi) {
110: PetscCall(PetscMPIIntCast(n_,&len));
111: PetscCall(PetscArrayzero(rwork2,n_));
112: PetscCallMPI(MPIU_Allreduce(rwork,rwork2,len,MPIU_REAL,MPIU_LAPY2,PetscObjectComm((PetscObject)bv)));
113: norms = rwork2;
114: } else norms = rwork;
115: /* scale columns */
116: for (j=0;j<n_;j++) {
117: k = 1;
118: #if !PetscDefined(USE_COMPLEX)
119: if (eigi && eigi[j] != 0.0) k = 2;
120: #endif
121: PetscCallLAPACKInfo("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,norms+j,&done,&m,&k,(PetscScalar*)(A+j*lda_),&lda,&info));
122: if (k==2) j++;
123: }
124: PetscCall(PetscLogFlops(3.0*m*n_));
125: PetscCall(PetscFPTrapPop());
126: PetscFunctionReturn(PETSC_SUCCESS);
127: }
129: /*
130: Compute the upper Cholesky factor in R and its inverse in S.
131: If S == R then the inverse overwrites the Cholesky factor.
132: */
133: PetscErrorCode BVMatCholInv_LAPACK_Private(BV bv,Mat R,Mat S)
134: {
135: PetscInt i,k,l,n,m,ld,lds;
136: PetscScalar *pR,*pS;
137: PetscBLASInt info,n_ = 0,m_ = 0,ld_,lds_;
139: PetscFunctionBegin;
140: l = bv->l;
141: k = bv->k;
142: PetscCall(MatGetSize(R,&m,NULL));
143: n = k-l;
144: PetscCall(PetscBLASIntCast(m,&m_));
145: PetscCall(PetscBLASIntCast(n,&n_));
146: ld = m;
147: ld_ = m_;
148: PetscCall(MatDenseGetArray(R,&pR));
150: if (S==R) {
151: PetscCall(BVAllocateWork_Private(bv,m*k));
152: pS = bv->work;
153: lds = ld;
154: lds_ = ld_;
155: } else {
156: PetscCall(MatDenseGetArray(S,&pS));
157: PetscCall(MatGetSize(S,&lds,NULL));
158: PetscCall(PetscBLASIntCast(lds,&lds_));
159: }
161: /* save a copy of matrix in S */
162: for (i=l;i<k;i++) PetscCall(PetscArraycpy(pS+i*lds+l,pR+i*ld+l,n));
164: /* compute upper Cholesky factor in R */
165: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
166: PetscCallBLAS("LAPACKpotrf",LAPACKpotrf_("U",&n_,pR+l*ld+l,&ld_,&info));
167: PetscCall(PetscLogFlops((1.0*n*n*n)/3.0));
169: if (info) { /* LAPACKpotrf failed, retry on diagonally perturbed matrix */
170: for (i=l;i<k;i++) {
171: PetscCall(PetscArraycpy(pR+i*ld+l,pS+i*lds+l,n));
172: pR[i+i*ld] += 50.0*PETSC_MACHINE_EPSILON;
173: }
174: PetscCallLAPACKInfo("LAPACKpotrf",LAPACKpotrf_("U",&n_,pR+l*ld+l,&ld_,&info));
175: PetscCall(PetscLogFlops((1.0*n*n*n)/3.0));
176: }
178: /* compute S = inv(R) */
179: if (S==R) {
180: PetscCallLAPACKInfo("LAPACKtrtri",LAPACKtrtri_("U","N",&n_,pR+l*ld+l,&ld_,&info));
181: } else {
182: PetscCall(PetscArrayzero(pS+l*lds,(k-l)*k));
183: for (i=l;i<k;i++) PetscCall(PetscArraycpy(pS+i*lds+l,pR+i*ld+l,n));
184: PetscCallLAPACKInfo("LAPACKtrtri",LAPACKtrtri_("U","N",&n_,pS+l*lds+l,&lds_,&info));
185: }
186: PetscCall(PetscFPTrapPop());
187: PetscCall(PetscLogFlops(0.33*n*n*n));
189: /* Zero out entries below the diagonal */
190: for (i=l;i<k-1;i++) {
191: PetscCall(PetscArrayzero(pR+i*ld+i+1,(k-i-1)));
192: if (S!=R) PetscCall(PetscArrayzero(pS+i*lds+i+1,(k-i-1)));
193: }
194: PetscCall(MatDenseRestoreArray(R,&pR));
195: if (S!=R) PetscCall(MatDenseRestoreArray(S,&pS));
196: PetscFunctionReturn(PETSC_SUCCESS);
197: }
199: /*
200: Compute the inverse of an upper triangular matrix R, store it in S.
201: If S == R then the inverse overwrites R.
202: */
203: PetscErrorCode BVMatTriInv_LAPACK_Private(BV bv,Mat R,Mat S)
204: {
205: PetscInt i,k,l,n,m,ld,lds;
206: PetscScalar *pR,*pS;
207: PetscBLASInt n_,m_ = 0,ld_,lds_;
209: PetscFunctionBegin;
210: l = bv->l;
211: k = bv->k;
212: PetscCall(MatGetSize(R,&m,NULL));
213: n = k-l;
214: PetscCall(PetscBLASIntCast(m,&m_));
215: PetscCall(PetscBLASIntCast(n,&n_));
216: ld = m;
217: ld_ = m_;
218: PetscCall(MatDenseGetArray(R,&pR));
220: if (S==R) {
221: PetscCall(BVAllocateWork_Private(bv,m*k));
222: pS = bv->work;
223: lds = ld;
224: lds_ = ld_;
225: } else {
226: PetscCall(MatDenseGetArray(S,&pS));
227: PetscCall(MatGetSize(S,&lds,NULL));
228: PetscCall(PetscBLASIntCast(lds,&lds_));
229: }
231: /* compute S = inv(R) */
232: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
233: if (S==R) {
234: PetscCallLAPACKInfo("LAPACKtrtri",LAPACKtrtri_("U","N",&n_,pR+l*ld+l,&ld_,&info));
235: } else {
236: PetscCall(PetscArrayzero(pS+l*lds,(k-l)*k));
237: for (i=l;i<k;i++) PetscCall(PetscArraycpy(pS+i*lds+l,pR+i*ld+l,n));
238: PetscCallLAPACKInfo("LAPACKtrtri",LAPACKtrtri_("U","N",&n_,pS+l*lds+l,&lds_,&info));
239: }
240: PetscCall(PetscFPTrapPop());
241: PetscCall(PetscLogFlops(0.33*n*n*n));
243: PetscCall(MatDenseRestoreArray(R,&pR));
244: if (S!=R) PetscCall(MatDenseRestoreArray(S,&pS));
245: PetscFunctionReturn(PETSC_SUCCESS);
246: }
248: /*
249: Compute the matrix to be used for post-multiplying the basis in the SVQB
250: block orthogonalization method.
251: On input R = V'*V, on output S = D*U*Lambda^{-1/2} where (U,Lambda) is
252: the eigendecomposition of D*R*D with D=diag(R)^{-1/2}.
253: If S == R then the result overwrites R.
254: */
255: PetscErrorCode BVMatSVQB_LAPACK_Private(BV bv,Mat R,Mat S)
256: {
257: PetscInt i,j,k,l,n,m,ld,lds;
258: PetscScalar *pR,*pS,*D,*work,a;
259: PetscReal *eig,dummy;
260: PetscBLASInt lwork,n_,m_ = 0,ld_,lds_;
261: #if PetscDefined(USE_COMPLEX)
262: PetscReal *rwork,rdummy;
263: #endif
265: PetscFunctionBegin;
266: l = bv->l;
267: k = bv->k;
268: PetscCall(MatGetSize(R,&m,NULL));
269: PetscCall(MatDenseGetLDA(R,&ld));
270: n = k-l;
271: PetscCall(PetscBLASIntCast(m,&m_));
272: PetscCall(PetscBLASIntCast(n,&n_));
273: ld_ = m_;
274: PetscCall(MatDenseGetArray(R,&pR));
276: if (S==R) {
277: pS = pR;
278: lds = ld;
279: lds_ = ld_;
280: } else {
281: PetscCall(MatDenseGetArray(S,&pS));
282: PetscCall(MatDenseGetLDA(S,&lds));
283: PetscCall(PetscBLASIntCast(lds,&lds_));
284: }
285: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
287: /* workspace query and memory allocation */
288: lwork = -1;
289: #if PetscDefined(USE_COMPLEX)
290: PetscCallLAPACKInfo("LAPACKsyev",LAPACKsyev_("V","L",&n_,pS,&lds_,&dummy,&a,&lwork,&rdummy,&info));
291: PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork));
292: PetscCall(PetscMalloc4(n,&eig,n,&D,lwork,&work,PetscMax(1,3*n-2),&rwork));
293: #else
294: PetscCallLAPACKInfo("LAPACKsyev",LAPACKsyev_("V","L",&n_,pS,&lds_,&dummy,&a,&lwork,&info));
295: PetscCall(PetscBLASIntCast((PetscInt)a,&lwork));
296: PetscCall(PetscMalloc3(n,&eig,n,&D,lwork,&work));
297: #endif
299: /* copy and scale matrix */
300: for (i=l;i<k;i++) D[i-l] = 1.0/PetscSqrtReal(PetscRealPart(pR[i+i*ld]));
301: for (i=l;i<k;i++) for (j=l;j<k;j++) pS[i+j*lds] = pR[i+j*ld]*D[i-l];
302: for (j=l;j<k;j++) for (i=l;i<k;i++) pS[i+j*lds] *= D[j-l];
304: /* compute eigendecomposition */
305: #if PetscDefined(USE_COMPLEX)
306: PetscCallLAPACKInfo("LAPACKsyev",LAPACKsyev_("V","L",&n_,pS+l*lds+l,&lds_,eig,work,&lwork,rwork,&info));
307: #else
308: PetscCallLAPACKInfo("LAPACKsyev",LAPACKsyev_("V","L",&n_,pS+l*lds+l,&lds_,eig,work,&lwork,&info));
309: #endif
311: if (S!=R) { /* R = U' */
312: for (i=l;i<k;i++) for (j=l;j<k;j++) pR[i+j*ld] = pS[j+i*lds];
313: }
315: /* compute S = D*U*Lambda^{-1/2} */
316: for (i=l;i<k;i++) for (j=l;j<k;j++) pS[i+j*lds] *= D[i-l];
317: for (j=l;j<k;j++) for (i=l;i<k;i++) pS[i+j*lds] /= PetscSqrtReal(eig[j-l]);
319: if (S!=R) { /* compute R = inv(S) = Lambda^{1/2}*U'/D */
320: for (i=l;i<k;i++) for (j=l;j<k;j++) pR[i+j*ld] *= PetscSqrtReal(eig[i-l]);
321: for (j=l;j<k;j++) for (i=l;i<k;i++) pR[i+j*ld] /= D[j-l];
322: }
324: #if PetscDefined(USE_COMPLEX)
325: PetscCall(PetscFree4(eig,D,work,rwork));
326: #else
327: PetscCall(PetscFree3(eig,D,work));
328: #endif
329: PetscCall(PetscLogFlops(9.0*n*n*n));
330: PetscCall(PetscFPTrapPop());
332: PetscCall(MatDenseRestoreArray(R,&pR));
333: if (S!=R) PetscCall(MatDenseRestoreArray(S,&pS));
334: PetscFunctionReturn(PETSC_SUCCESS);
335: }
337: /*
338: QR factorization of an mxn matrix via parallel TSQR
339: */
340: PetscErrorCode BVOrthogonalize_LAPACK_TSQR(BV bv,PetscInt m_,PetscInt n_,PetscScalar *Q,PetscInt ldq_,PetscScalar *R,PetscInt ldr)
341: {
342: PetscInt level,plevel,nlevels,lda,worklen;
343: PetscBLASInt m,n,ldq,i,j,k,l,nb,sz,lwork;
344: PetscScalar *tau,*work,*A=NULL,*QQ=NULL,*Qhalf,*C=NULL,one=1.0,zero=0.0;
345: PetscMPIInt rank,size,count,stride,powtwo,s = 0;
346: MPI_Datatype tmat;
348: PetscFunctionBegin;
349: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
350: PetscCall(PetscBLASIntCast(m_,&m));
351: PetscCall(PetscBLASIntCast(n_,&n));
352: PetscCall(PetscBLASIntCast(ldq_,&ldq));
353: k = PetscMin(m,n);
354: nb = 16;
355: lda = 2*n;
356: PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)bv),&size));
357: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)bv),&rank));
358: nlevels = (PetscInt)PetscCeilReal(PetscLog2Real((PetscReal)size));
359: PetscCall(PetscMPIIntCast(PetscPowInt(2,(PetscInt)PetscFloorReal(PetscLog2Real((PetscReal)size))),&powtwo));
360: worklen = n+n*nb;
361: if (nlevels) worklen += n*lda+n*lda*nlevels+n*lda;
362: PetscCall(BVAllocateWork_Private(bv,worklen));
363: tau = bv->work;
364: work = bv->work+n;
365: PetscCall(PetscBLASIntCast(n*nb,&lwork));
366: if (nlevels) {
367: A = bv->work+n+n*nb;
368: QQ = bv->work+n+n*nb+n*lda;
369: C = bv->work+n+n*nb+n*lda+n*lda*nlevels;
370: }
372: /* Compute QR */
373: PetscCallLAPACKInfo("LAPACKgeqrf",LAPACKgeqrf_(&m,&n,Q,&ldq,tau,work,&lwork,&info));
375: /* Extract R */
376: if (R || nlevels) {
377: for (j=0;j<n;j++) {
378: for (i=0;i<=PetscMin(j,m-1);i++) {
379: if (nlevels) A[i+j*lda] = Q[i+j*ldq];
380: else R[i+j*ldr] = Q[i+j*ldq];
381: }
382: for (i=PetscMin(j,m-1)+1;i<n;i++) {
383: if (nlevels) A[i+j*lda] = 0.0;
384: else R[i+j*ldr] = 0.0;
385: }
386: }
387: }
389: /* Compute orthogonal matrix in Q */
390: PetscCallLAPACKInfo("LAPACKorgqr",LAPACKorgqr_(&m,&k,&k,Q,&ldq,tau,work,&lwork,&info));
392: if (nlevels) {
394: PetscCall(PetscMPIIntCast(n,&count));
395: PetscCall(PetscMPIIntCast(lda,&stride));
396: PetscCall(PetscBLASIntCast(lda,&l));
397: PetscCallMPI(MPI_Type_vector(count,count,stride,MPIU_SCALAR,&tmat));
398: PetscCallMPI(MPI_Type_commit(&tmat));
400: for (level=nlevels;level>=1;level--) {
402: plevel = PetscPowInt(2,level);
403: PetscCall(PetscMPIIntCast(plevel*PetscFloorReal(rank/(PetscReal)plevel)+(rank+PetscPowInt(2,level-1))%plevel,&s));
405: /* Stack triangular matrices */
406: if (rank<s && s<size) { /* send top part, receive bottom part */
407: PetscCallMPI(MPI_Sendrecv(A,1,tmat,s,111,A+n,1,tmat,s,111,PetscObjectComm((PetscObject)bv),MPI_STATUS_IGNORE));
408: } else if (s<size) { /* copy top to bottom, receive top part */
409: PetscCallMPI(MPI_Sendrecv(A,1,tmat,rank,111,A+n,1,tmat,rank,111,PetscObjectComm((PetscObject)bv),MPI_STATUS_IGNORE));
410: PetscCallMPI(MPI_Sendrecv(A+n,1,tmat,s,111,A,1,tmat,s,111,PetscObjectComm((PetscObject)bv),MPI_STATUS_IGNORE));
411: }
412: if (level<nlevels && size!=powtwo) { /* for cases when size is not a power of 2 */
413: if (rank<size-powtwo) { /* send bottom part */
414: PetscCallMPI(MPI_Send(A+n,1,tmat,rank+powtwo,111,PetscObjectComm((PetscObject)bv)));
415: } else if (rank>=powtwo) { /* receive bottom part */
416: PetscCallMPI(MPI_Recv(A+n,1,tmat,rank-powtwo,111,PetscObjectComm((PetscObject)bv),MPI_STATUS_IGNORE));
417: }
418: }
419: /* Compute QR and build orthogonal matrix */
420: if (level<nlevels || (level==nlevels && s<size)) {
421: PetscCallLAPACKInfo("LAPACKgeqrf",LAPACKgeqrf_(&l,&n,A,&l,tau,work,&lwork,&info));
422: PetscCall(PetscArraycpy(QQ+(level-1)*n*lda,A,n*lda));
423: PetscCallLAPACKInfo("LAPACKorgqr",LAPACKorgqr_(&l,&n,&n,QQ+(level-1)*n*lda,&l,tau,work,&lwork,&info));
424: for (j=0;j<n;j++) {
425: for (i=j+1;i<n;i++) A[i+j*lda] = 0.0;
426: }
427: } else if (level==nlevels) { /* only one triangular matrix, set Q=I */
428: PetscCall(PetscArrayzero(QQ+(level-1)*n*lda,n*lda));
429: for (j=0;j<n;j++) QQ[j+j*lda+(level-1)*n*lda] = 1.0;
430: }
431: }
433: /* Extract R */
434: if (R) {
435: for (j=0;j<n;j++) {
436: for (i=0;i<=j;i++) R[i+j*ldr] = A[i+j*lda];
437: for (i=j+1;i<n;i++) R[i+j*ldr] = 0.0;
438: }
439: }
441: /* Accumulate orthogonal matrices */
442: for (level=1;level<=nlevels;level++) {
443: plevel = PetscPowInt(2,level);
444: PetscCall(PetscMPIIntCast(plevel*PetscFloorReal(rank/(PetscReal)plevel)+(rank+PetscPowInt(2,level-1))%plevel,&s));
445: Qhalf = (rank<s)? QQ+(level-1)*n*lda: QQ+(level-1)*n*lda+n;
446: if (level<nlevels) {
447: PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&n,&one,QQ+level*n*lda,&l,Qhalf,&l,&zero,C,&l));
448: PetscCall(PetscArraycpy(QQ+level*n*lda,C,n*lda));
449: } else {
450: for (i=0;i<m/l;i++) {
451: PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&n,&one,Q+i*l,&ldq,Qhalf,&l,&zero,C,&l));
452: for (j=0;j<n;j++) PetscCall(PetscArraycpy(Q+i*l+j*ldq,C+j*l,l));
453: }
454: sz = m%l;
455: if (sz) {
456: PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&sz,&n,&n,&one,Q+(m/l)*l,&ldq,Qhalf,&l,&zero,C,&l));
457: for (j=0;j<n;j++) PetscCall(PetscArraycpy(Q+(m/l)*l+j*ldq,C+j*l,sz));
458: }
459: }
460: }
462: PetscCallMPI(MPI_Type_free(&tmat));
463: }
465: PetscCall(PetscLogFlops(3.0*m*n*n));
466: PetscCall(PetscFPTrapPop());
467: PetscFunctionReturn(PETSC_SUCCESS);
468: }
470: /*
471: Reduction operation to compute [~,Rout]=qr([Rin1;Rin2]) in the TSQR algorithm;
472: all matrices are upper triangular stored in packed format
473: */
474: SLEPC_EXTERN void MPIAPI SlepcGivensPacked(void *in,void *inout,PetscMPIInt *len,MPI_Datatype *datatype)
475: {
476: PetscBLASInt n,i,j,k,one=1;
477: PetscMPIInt tsize;
478: PetscScalar v,s,*R2=(PetscScalar*)in,*R1=(PetscScalar*)inout;
479: PetscReal c;
481: PetscFunctionBegin;
482: PetscCallMPIAbort(PETSC_COMM_SELF,MPI_Type_size(*datatype,&tsize)); /* we assume len=1 */
483: tsize /= sizeof(PetscScalar);
484: n = (-1+(PetscBLASInt)PetscSqrtReal(1+8*tsize))/2;
485: for (j=0;j<n;j++) {
486: for (i=0;i<=j;i++) {
487: LAPACKlartg_(R1+(2*n-j-1)*j/2+j,R2+(2*n-i-1)*i/2+j,&c,&s,&v);
488: R1[(2*n-j-1)*j/2+j] = v;
489: k = n-j-1;
490: if (k) BLASrot_(&k,R1+(2*n-j-1)*j/2+j+1,&one,R2+(2*n-i-1)*i/2+j+1,&one,&c,&s);
491: }
492: }
493: PetscFunctionReturnVoid();
494: }
496: /*
497: Computes the R factor of the QR factorization of an mxn matrix via parallel TSQR
498: */
499: PetscErrorCode BVOrthogonalize_LAPACK_TSQR_OnlyR(BV bv,PetscInt m_,PetscInt n_,PetscScalar *Q,PetscInt ldq_,PetscScalar *R,PetscInt ldr)
500: {
501: PetscInt worklen;
502: PetscBLASInt m,n,ldq,i,j,s,nb,lwork;
503: PetscScalar *tau,*work,*A=NULL,*R1=NULL,*R2=NULL;
504: PetscMPIInt size,count;
505: MPI_Datatype tmat;
507: PetscFunctionBegin;
508: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
509: PetscCall(PetscBLASIntCast(m_,&m));
510: PetscCall(PetscBLASIntCast(n_,&n));
511: PetscCall(PetscBLASIntCast(ldq_,&ldq));
512: nb = 16;
513: s = n+n*(n-1)/2; /* length of packed triangular matrix */
514: PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)bv),&size));
515: worklen = n+n*nb+2*s+ldq*n;
516: PetscCall(BVAllocateWork_Private(bv,worklen));
517: tau = bv->work;
518: work = bv->work+n;
519: R1 = bv->work+n+n*nb;
520: R2 = bv->work+n+n*nb+s;
521: A = bv->work+n+n*nb+2*s;
522: PetscCall(PetscBLASIntCast(n*nb,&lwork));
523: PetscCall(PetscArraycpy(A,Q,ldq*n));
525: /* Compute QR */
526: PetscCallLAPACKInfo("LAPACKgeqrf",LAPACKgeqrf_(&m,&n,A,&ldq,tau,work,&lwork,&info));
528: if (size==1) {
529: /* Extract R */
530: for (j=0;j<n;j++) {
531: for (i=0;i<=PetscMin(j,m-1);i++) R[i+j*ldr] = A[i+j*ldq];
532: for (i=PetscMin(j,m-1)+1;i<n;i++) R[i+j*ldr] = 0.0;
533: }
534: } else {
535: /* Use MPI reduction operation to obtain global R */
536: PetscCall(PetscMPIIntCast(s,&count));
537: PetscCallMPI(MPI_Type_contiguous(count,MPIU_SCALAR,&tmat));
538: PetscCallMPI(MPI_Type_commit(&tmat));
539: for (i=0;i<n;i++) {
540: for (j=i;j<n;j++) R1[(2*n-i-1)*i/2+j] = (i<m)?A[i+j*ldq]:0.0;
541: }
542: PetscCallMPI(MPIU_Allreduce(R1,R2,1,tmat,MPIU_TSQR,PetscObjectComm((PetscObject)bv)));
543: for (i=0;i<n;i++) {
544: for (j=0;j<i;j++) R[i+j*ldr] = 0.0;
545: for (j=i;j<n;j++) R[i+j*ldr] = R2[(2*n-i-1)*i/2+j];
546: }
547: PetscCallMPI(MPI_Type_free(&tmat));
548: }
550: PetscCall(PetscLogFlops(3.0*m*n*n));
551: PetscCall(PetscFPTrapPop());
552: PetscFunctionReturn(PETSC_SUCCESS);
553: }