Actual source code: slepcbv.h

      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:    User interface for the basis vectors object in SLEPc
     12: */

     14: #pragma once

     16: #include <slepcsys.h>

     18: /* SUBMANSEC = BV */

     20: SLEPC_EXTERN PetscErrorCode BVInitializePackage(void);
     21: SLEPC_EXTERN PetscErrorCode BVFinalizePackage(void);

     23: /*S
     24:     BV - Basis vectors, SLEPc object representing a collection of vectors
     25:     that typically constitute a basis of a subspace.

     27:     Level: beginner

     29: .seealso: [](sec:bv), `BVCreate()`
     30: S*/
     31: typedef struct _p_BV* BV;

     33: /*J
     34:     BVType - String with the name of the type of `BV`. Each type differs in
     35:     the way data is stored internally.

     37:     Level: beginner

     39: .seealso: [](sec:bv), `BVSetType()`, `BV`
     40: J*/
     41: typedef const char *BVType;
     42: #define BVMAT        "mat"
     43: #define BVSVEC       "svec"
     44: #define BVVECS       "vecs"
     45: #define BVCONTIGUOUS "contiguous"
     46: #define BVTENSOR     "tensor"

     48: /* Logging support */
     49: SLEPC_EXTERN PetscClassId BV_CLASSID;

     51: /*E
     52:    BVOrthogType - Determines the method used in the orthogonalization of vectors.

     54:    Values:
     55: +  `BV_ORTHOG_CGS` - Classical Gram-Schmidt
     56: -  `BV_ORTHOG_MGS` - Modified Gram-Schmidt

     58:    Note:
     59:    The default is to use CGS. Both CGS and MGS provide similar numerical accuracy when
     60:    combined with iterative refinement (the default). MGS results in poorer performance,
     61:    both sequential and in parallel, so it is not recommended unless iterative
     62:    refinement is disabled.

     64:    Level: advanced

     66: .seealso: [](sec:bv), `BVSetOrthogonalization()`, `BVGetOrthogonalization()`, `BVOrthogonalizeColumn()`, `BVOrthogRefineType`
     67: E*/
     68: typedef enum { BV_ORTHOG_CGS,
     69:                BV_ORTHOG_MGS } BVOrthogType;
     70: SLEPC_EXTERN const char *BVOrthogTypes[];

     72: /*MC
     73:    BV_ORTHOG_CGS - Use classical Gram-Schmidt for orthogonalization of vectors.

     75:    Level: advanced

     77:    Note:
     78:    Although CGS is not numerically stable, when combined with iterative refinement
     79:    it yields a sufficiently accurate result.

     81: .seealso: [](sec:bv), `BVOrthogType`, `BVSetOrthogonalization()`, `BV_ORTHOG_MGS`
     82: M*/

     84: /*MC
     85:    BV_ORTHOG_MGS - Use modified Gram-Schmidt for orthogonalization of vectors.

     87:    Level: advanced

     89:    Note:
     90:    MGS results in poorer performance, both sequential and in parallel, so it is
     91:    not recommended unless iterative refinement is disabled.

     93: .seealso: [](sec:bv), `BVOrthogType`, `BVSetOrthogonalization()`, `BV_ORTHOG_CGS`
     94: M*/

     96: /*E
     97:    BVOrthogRefineType - Determines what type of iterative refinement to use
     98:    during orthogonalization of vectors.

    100:    Values:
    101: +  `BV_ORTHOG_REFINE_IFNEEDED` - Refine only if a certain criterion is satisfied
    102: .  `BV_ORTHOG_REFINE_NEVER`    - Never refine, do plain CGS or MGS
    103: -  `BV_ORTHOG_REFINE_ALWAYS`   - Always refine, i.e., run CGS2 or MGS2

    105:    Notes:
    106:    The default is to perform one step of iterative refinement if a certain
    107:    numerical criterion holds. In ill-conditioned cases, a third orthogonalization
    108:    can also be done.

    110:    Never refining is not recommended because it will generally make the eigensolver
    111:    numerically unstable.

    113:    Always refining is numerically stable, but it often performs unnecessary
    114:    computation.

    116:    Level: advanced

    118: .seealso: [](sec:bv), `BVSetOrthogonalization()`, `BVGetOrthogonalization()`, `BVOrthogonalizeColumn()`
    119: E*/
    120: typedef enum { BV_ORTHOG_REFINE_IFNEEDED,
    121:                BV_ORTHOG_REFINE_NEVER,
    122:                BV_ORTHOG_REFINE_ALWAYS } BVOrthogRefineType;
    123: SLEPC_EXTERN const char *BVOrthogRefineTypes[];

    125: /*MC
    126:    BV_ORTHOG_REFINE_IFNEEDED - In the orthogonalization of vectors, do iterative
    127:    refinement only if a certain criterion is satisfied.

    129:    Note:
    130:    This is the default. One step of iterative refinement will be done if a certain
    131:    numerical criterion holds. In ill-conditioned cases, a third orthogonalization
    132:    can also be done. The criterion is similar to the one proposed in {cite:p}`Dan76`.
    133:    The parameter $\eta$ for the criterion can be set in `BVSetOrthogonalization()`.

    135:    Level: advanced

    137: .seealso: [](sec:bv), `BVOrthogRefineType`, `BVSetOrthogonalization()`, `BV_ORTHOG_REFINE_NEVER`, `BV_ORTHOG_REFINE_ALWAYS`
    138: M*/

    140: /*MC
    141:    BV_ORTHOG_REFINE_NEVER - In the orthogonalization of vectors, never do an iterative
    142:    refinement step, i.e., do plain CGS or MGS.

    144:    Note:
    145:    Never refining is not recommended because it will generally make the eigensolver
    146:    numerically unstable.

    148:    Level: advanced

    150: .seealso: [](sec:bv), `BVOrthogRefineType`, `BVSetOrthogonalization()`, `BV_ORTHOG_REFINE_IFNEEDED`, `BV_ORTHOG_REFINE_ALWAYS`
    151: M*/

    153: /*MC
    154:    BV_ORTHOG_REFINE_ALWAYS - In the orthogonalization of vectors, always do an iterative
    155:    refinement step, i.e., run CGS2 or MGS2.

    157:    Note:
    158:    Always refining is numerically stable, but it often performs unnecessary
    159:    computation.

    161:    Level: advanced

    163: .seealso: [](sec:bv), `BVOrthogRefineType`, `BVSetOrthogonalization()`, `BV_ORTHOG_REFINE_IFNEEDED`, `BV_ORTHOG_REFINE_NEVER`
    164: M*/

    166: /*E
    167:    BVOrthogBlockType - Determines the method used in block
    168:    orthogonalization (simultaneous orthogonalization of a set of vectors).

    170:    Values:
    171: +  `BV_ORTHOG_BLOCK_GS`       - Gram-Schmidt, column by column
    172: .  `BV_ORTHOG_BLOCK_CHOL`     - Cholesky QR method
    173: .  `BV_ORTHOG_BLOCK_TSQR`     - Tall-Skinny QR method
    174: .  `BV_ORTHOG_BLOCK_TSQRCHOL` - TSQR, but computing the triangular factor only
    175: -  `BV_ORTHOG_BLOCK_SVQB`     - SVQB method

    177:    Level: advanced

    179: .seealso: [](sec:bv), `BVSetOrthogonalization()`, `BVGetOrthogonalization()`, `BVOrthogonalize()`
    180: E*/
    181: typedef enum { BV_ORTHOG_BLOCK_GS,
    182:                BV_ORTHOG_BLOCK_CHOL,
    183:                BV_ORTHOG_BLOCK_TSQR,
    184:                BV_ORTHOG_BLOCK_TSQRCHOL,
    185:                BV_ORTHOG_BLOCK_SVQB     } BVOrthogBlockType;
    186: SLEPC_EXTERN const char *BVOrthogBlockTypes[];

    188: /*E
    189:    BVMatMultType - Different ways of performing the `BVMatMult()` operation.

    191:    Values:
    192:    Allowed values are
    193: +  `BV_MATMULT_VECS`     - perform a matrix-vector multiply per each column
    194: .  `BV_MATMULT_MAT`      - carry out a Mat-Mat product with a dense matrix
    195: -  `BV_MATMULT_MAT_SAVE` - this case is deprecated

    197:    Note:
    198:    The default is `BV_MATMULT_MAT` except in the case of `BVVECS`.

    200:    Level: advanced

    202: .seealso: [](sec:bv), `BVSetMatMultMethod()`, `BVMatMult()`
    203: E*/
    204: typedef enum { BV_MATMULT_VECS,
    205:                BV_MATMULT_MAT,
    206:                BV_MATMULT_MAT_SAVE } BVMatMultType;
    207: SLEPC_EXTERN const char *BVMatMultTypes[];

    209: /*MC
    210:    BV_MATMULT_VECS - Perform a matrix-vector multiply per each column.

    212:    Level: advanced

    214: .seealso: [](sec:bv), `BVMatMultType`, `BVSetMatMultMethod()`, `BVMatMult()`, `BV_MATMULT_MAT`, `BV_MATMULT_MAT_SAVE`
    215: M*/

    217: /*MC
    218:    BV_MATMULT_MAT - Perform a `Mat`-`Mat` product with a dense matrix.

    220:    Level: advanced

    222: .seealso: [](sec:bv), `BVMatMultType`, `BVSetMatMultMethod()`, `BVMatMult()`, `BV_MATMULT_VECS`, `BV_MATMULT_MAT_SAVE`
    223: M*/

    225: /*MC
    226:    BV_MATMULT_MAT_SAVE - This case is deprecated, do not use.

    228:    Level: advanced

    230: .seealso: [](sec:bv), `BVMatMultType`, `BVSetMatMultMethod()`, `BVMatMult()`, `BV_MATMULT_VECS`, `BV_MATMULT_MAT`
    231: M*/

    233: SLEPC_EXTERN PetscErrorCode BVCreate(MPI_Comm,BV*);
    234: SLEPC_EXTERN PetscErrorCode BVDestroy(BV*);
    235: SLEPC_EXTERN PetscErrorCode BVSetType(BV,BVType);
    236: SLEPC_EXTERN PetscErrorCode BVGetType(BV,BVType*);
    237: SLEPC_EXTERN PetscErrorCode BVSetSizes(BV,PetscInt,PetscInt,PetscInt);
    238: SLEPC_EXTERN PetscErrorCode BVSetSizesFromVec(BV,Vec,PetscInt);
    239: SLEPC_EXTERN PetscErrorCode BVSetLeadingDimension(BV,PetscInt);
    240: SLEPC_EXTERN PetscErrorCode BVGetLeadingDimension(BV,PetscInt*);
    241: SLEPC_EXTERN PetscErrorCode BVGetSizes(BV,PetscInt*,PetscInt*,PetscInt*);
    242: SLEPC_EXTERN PetscErrorCode BVResize(BV,PetscInt,PetscBool);
    243: SLEPC_EXTERN PetscErrorCode BVSetFromOptions(BV);
    244: SLEPC_EXTERN PetscErrorCode BVView(BV,PetscViewer);
    245: SLEPC_EXTERN PetscErrorCode BVViewFromOptions(BV,PetscObject,const char[]);

    247: SLEPC_EXTERN PetscErrorCode BVGetColumn(BV,PetscInt,Vec*);
    248: SLEPC_EXTERN PetscErrorCode BVRestoreColumn(BV,PetscInt,Vec*);
    249: SLEPC_EXTERN PetscErrorCode BVGetSplit(BV,BV*,BV*);
    250: SLEPC_EXTERN PetscErrorCode BVRestoreSplit(BV,BV*,BV*);
    251: SLEPC_EXTERN PetscErrorCode BVGetSplitRows(BV,IS,IS,BV*,BV*);
    252: SLEPC_EXTERN PetscErrorCode BVRestoreSplitRows(BV,IS,IS,BV*,BV*);
    253: SLEPC_EXTERN PetscErrorCode BVGetArray(BV,PetscScalar*[]);
    254: SLEPC_EXTERN PetscErrorCode BVRestoreArray(BV,PetscScalar*[]);
    255: SLEPC_EXTERN PetscErrorCode BVGetArrayRead(BV,const PetscScalar*[]);
    256: SLEPC_EXTERN PetscErrorCode BVRestoreArrayRead(BV,const PetscScalar*[]);
    257: SLEPC_EXTERN PetscErrorCode BVCreateVec(BV,Vec*);
    258: SLEPC_EXTERN PetscErrorCode BVCreateVecEmpty(BV,Vec*);
    259: SLEPC_EXTERN PetscErrorCode BVSetVecType(BV,VecType);
    260: SLEPC_EXTERN PetscErrorCode BVGetVecType(BV,VecType*);
    261: SLEPC_EXTERN PetscErrorCode BVSetActiveColumns(BV,PetscInt,PetscInt);
    262: SLEPC_EXTERN PetscErrorCode BVGetActiveColumns(BV,PetscInt*,PetscInt*);
    263: SLEPC_EXTERN PetscErrorCode BVInsertVec(BV,PetscInt,Vec);
    264: SLEPC_EXTERN PetscErrorCode BVInsertVecs(BV,PetscInt,PetscInt*,Vec[],PetscBool);
    265: SLEPC_EXTERN PetscErrorCode BVInsertConstraints(BV,PetscInt*,Vec[]);
    266: SLEPC_EXTERN PetscErrorCode BVSetNumConstraints(BV,PetscInt);
    267: SLEPC_EXTERN PetscErrorCode BVGetNumConstraints(BV,PetscInt*);
    268: SLEPC_EXTERN PetscErrorCode BVSetDefiniteTolerance(BV,PetscReal);
    269: SLEPC_EXTERN PetscErrorCode BVGetDefiniteTolerance(BV,PetscReal*);
    270: SLEPC_EXTERN PetscErrorCode BVDuplicate(BV,BV*);
    271: SLEPC_EXTERN PetscErrorCode BVDuplicateResize(BV,PetscInt,BV*);
    272: SLEPC_EXTERN PetscErrorCode BVCopy(BV,BV);
    273: SLEPC_EXTERN PetscErrorCode BVCopyVec(BV,PetscInt,Vec);
    274: SLEPC_EXTERN PetscErrorCode BVCopyColumn(BV,PetscInt,PetscInt);
    275: SLEPC_EXTERN PetscErrorCode BVSetMatrix(BV,Mat,PetscBool);
    276: SLEPC_EXTERN PetscErrorCode BVGetMatrix(BV,Mat*,PetscBool*);
    277: SLEPC_EXTERN PetscErrorCode BVApplyMatrix(BV,Vec,Vec);
    278: SLEPC_EXTERN PetscErrorCode BVApplyMatrixBV(BV,BV);
    279: SLEPC_EXTERN PetscErrorCode BVGetCachedBV(BV,BV*);
    280: SLEPC_EXTERN PetscErrorCode BVSetSignature(BV,Vec);
    281: SLEPC_EXTERN PetscErrorCode BVGetSignature(BV,Vec);
    282: SLEPC_EXTERN PetscErrorCode BVSetBufferVec(BV,Vec);
    283: SLEPC_EXTERN PetscErrorCode BVGetBufferVec(BV,Vec*);

    285: SLEPC_EXTERN PetscErrorCode BVMult(BV,PetscScalar,PetscScalar,BV,Mat);
    286: SLEPC_EXTERN PetscErrorCode BVMultVec(BV,PetscScalar,PetscScalar,Vec,PetscScalar[]);
    287: SLEPC_EXTERN PetscErrorCode BVMultColumn(BV,PetscScalar,PetscScalar,PetscInt,PetscScalar[]);
    288: SLEPC_EXTERN PetscErrorCode BVMultInPlace(BV,Mat,PetscInt,PetscInt);
    289: SLEPC_EXTERN PetscErrorCode BVMultInPlaceHermitianTranspose(BV,Mat,PetscInt,PetscInt);
    290: PETSC_DEPRECATED_FUNCTION(3, 16, 0, "BVMultInPlaceHermitianTranspose()", ) static inline PetscErrorCode BVMultInPlaceTranspose(BV bv,Mat A,PetscInt s,PetscInt e) {return BVMultInPlaceHermitianTranspose(bv,A,s,e);}
    291: SLEPC_EXTERN PetscErrorCode BVMatMult(BV,Mat,BV);
    292: SLEPC_EXTERN PetscErrorCode BVMatMultTranspose(BV,Mat,BV);
    293: SLEPC_EXTERN PetscErrorCode BVMatMultHermitianTranspose(BV,Mat,BV);
    294: SLEPC_EXTERN PetscErrorCode BVMatMultColumn(BV,Mat,PetscInt);
    295: SLEPC_EXTERN PetscErrorCode BVMatMultTransposeColumn(BV,Mat,PetscInt);
    296: SLEPC_EXTERN PetscErrorCode BVMatMultHermitianTransposeColumn(BV,Mat,PetscInt);
    297: SLEPC_EXTERN PetscErrorCode BVMatProject(BV,Mat,BV,Mat);
    298: SLEPC_EXTERN PetscErrorCode BVMatArnoldi(BV,Mat,Mat,PetscInt,PetscInt*,PetscReal*,PetscBool*);
    299: SLEPC_EXTERN PetscErrorCode BVMatLanczos(BV,Mat,Mat,PetscInt,PetscInt*,PetscReal*,PetscBool*);

    301: SLEPC_EXTERN PetscErrorCode BVDot(BV,BV,Mat);
    302: SLEPC_EXTERN PetscErrorCode BVDotVec(BV,Vec,PetscScalar[]);
    303: SLEPC_EXTERN PetscErrorCode BVDotVecBegin(BV,Vec,PetscScalar[]);
    304: SLEPC_EXTERN PetscErrorCode BVDotVecEnd(BV,Vec,PetscScalar[]);
    305: SLEPC_EXTERN PetscErrorCode BVDotColumn(BV,PetscInt,PetscScalar[]);
    306: SLEPC_EXTERN PetscErrorCode BVDotColumnBegin(BV,PetscInt,PetscScalar[]);
    307: SLEPC_EXTERN PetscErrorCode BVDotColumnEnd(BV,PetscInt,PetscScalar[]);
    308: SLEPC_EXTERN PetscErrorCode BVScale(BV,PetscScalar);
    309: SLEPC_EXTERN PetscErrorCode BVScaleColumn(BV,PetscInt,PetscScalar);
    310: SLEPC_EXTERN PetscErrorCode BVNorm(BV,NormType,PetscReal*);
    311: SLEPC_EXTERN PetscErrorCode BVNormVec(BV,Vec,NormType,PetscReal*);
    312: SLEPC_EXTERN PetscErrorCode BVNormVecBegin(BV,Vec,NormType,PetscReal*);
    313: SLEPC_EXTERN PetscErrorCode BVNormVecEnd(BV,Vec,NormType,PetscReal*);
    314: SLEPC_EXTERN PetscErrorCode BVNormColumn(BV,PetscInt,NormType,PetscReal*);
    315: SLEPC_EXTERN PetscErrorCode BVNormColumnBegin(BV,PetscInt,NormType,PetscReal*);
    316: SLEPC_EXTERN PetscErrorCode BVNormColumnEnd(BV,PetscInt,NormType,PetscReal*);
    317: SLEPC_EXTERN PetscErrorCode BVNormalize(BV,PetscScalar[]);
    318: SLEPC_EXTERN PetscErrorCode BVSetRandom(BV);
    319: SLEPC_EXTERN PetscErrorCode BVSetRandomNormal(BV);
    320: SLEPC_EXTERN PetscErrorCode BVSetRandomSign(BV);
    321: SLEPC_EXTERN PetscErrorCode BVSetRandomColumn(BV,PetscInt);
    322: SLEPC_EXTERN PetscErrorCode BVSetRandomCond(BV,PetscReal);
    323: SLEPC_EXTERN PetscErrorCode BVSetRandomContext(BV,PetscRandom);
    324: SLEPC_EXTERN PetscErrorCode BVGetRandomContext(BV,PetscRandom*);

    326: SLEPC_EXTERN PetscErrorCode BVSetOrthogonalization(BV,BVOrthogType,BVOrthogRefineType,PetscReal,BVOrthogBlockType);
    327: SLEPC_EXTERN PetscErrorCode BVGetOrthogonalization(BV,BVOrthogType*,BVOrthogRefineType*,PetscReal*,BVOrthogBlockType*);
    328: SLEPC_EXTERN PetscErrorCode BVOrthogonalize(BV,Mat);
    329: SLEPC_EXTERN PetscErrorCode BVOrthogonalizeVec(BV,Vec,PetscScalar[],PetscReal*,PetscBool*);
    330: SLEPC_EXTERN PetscErrorCode BVOrthogonalizeColumn(BV,PetscInt,PetscScalar[],PetscReal*,PetscBool*);
    331: SLEPC_EXTERN PetscErrorCode BVOrthonormalizeColumn(BV,PetscInt,PetscBool,PetscReal*,PetscBool*);
    332: SLEPC_EXTERN PetscErrorCode BVOrthogonalizeSomeColumn(BV,PetscInt,PetscBool*,PetscScalar[],PetscReal*,PetscBool*);
    333: SLEPC_EXTERN PetscErrorCode BVBiorthogonalizeColumn(BV,BV,PetscInt);
    334: SLEPC_EXTERN PetscErrorCode BVBiorthonormalizeColumn(BV,BV,PetscInt,PetscReal*);
    335: SLEPC_EXTERN PetscErrorCode BVSetMatMultMethod(BV,BVMatMultType);
    336: SLEPC_EXTERN PetscErrorCode BVGetMatMultMethod(BV,BVMatMultType*);

    338: SLEPC_EXTERN PetscErrorCode BVCreateFromMat(Mat,BV*);
    339: SLEPC_EXTERN PetscErrorCode BVCreateMat(BV,Mat*);
    340: SLEPC_EXTERN PetscErrorCode BVGetMat(BV,Mat*);
    341: SLEPC_EXTERN PetscErrorCode BVRestoreMat(BV,Mat*);

    343: SLEPC_EXTERN PetscErrorCode BVScatter(BV,BV,VecScatter,Vec);
    344: SLEPC_EXTERN PetscErrorCode BVSumQuadrature(BV,BV,PetscInt,PetscInt,PetscInt,PetscScalar[],PetscScalar[],VecScatter,PetscSubcomm,PetscInt,PetscBool);
    345: SLEPC_EXTERN PetscErrorCode BVDotQuadrature(BV,BV,PetscScalar[],PetscInt,PetscInt,PetscInt,PetscScalar[],PetscScalar[],PetscSubcomm,PetscInt,PetscBool);
    346: SLEPC_EXTERN PetscErrorCode BVTraceQuadrature(BV,BV,PetscInt,PetscInt,PetscScalar[],VecScatter,PetscSubcomm,PetscInt,PetscBool,PetscReal*);

    348: /*E
    349:    BVSVDMethod - Different methods for computing the SVD of a `BV`.

    351:    Values:
    352: +  `BV_SVD_METHOD_REFINE` - based on the SVD of the cross product matrix $S^*S$, with refinement
    353: .  `BV_SVD_METHOD_QR`     - based on the SVD of the triangular factor of qr(S)
    354: -  `BV_SVD_METHOD_QR_CAA` - variant of QR intended for use in communication-avoiding Arnoldi

    356:    Level: developer

    358: .seealso: [](sec:bv), `BVSVDAndRank()`
    359: E*/
    360: typedef enum { BV_SVD_METHOD_REFINE,
    361:                BV_SVD_METHOD_QR,
    362:                BV_SVD_METHOD_QR_CAA } BVSVDMethod;
    363: SLEPC_EXTERN const char *BVSVDMethods[];

    365: /*MC
    366:    BV_SVD_METHOD_REFINE - Compute the SVD of the `BV` via the cross product matrix $S^*S$,
    367:    with iterative refinement.

    369:    Level: advanced

    371: .seealso: [](sec:bv), `BVSVDMethod`, `BVSVDAndRank()`, `BV_SVD_METHOD_QR`, `BV_SVD_METHOD_QR_CAA`
    372: M*/

    374: /*MC
    375:    BV_SVD_METHOD_QR - Compute the SVD of the `BV` via the SVD of the triangular factor of
    376:    the QR factorization of $S$.

    378:    Level: advanced

    380: .seealso: [](sec:bv), `BVSVDMethod`, `BVSVDAndRank()`, `BV_SVD_METHOD_REFINE`, `BV_SVD_METHOD_QR_CAA`
    381: M*/

    383: /*MC
    384:    BV_SVD_METHOD_QR_CAA - Compute the SVD of the `BV` employing a variant of
    385:    `BV_SVD_METHOD_QR` intended for use in communication-avoiding Arnoldi.

    387:    Level: advanced

    389: .seealso: [](sec:bv), `BVSVDMethod`, `BVSVDAndRank()`, `BV_SVD_METHOD_REFINE`, `BV_SVD_METHOD_QR`
    390: M*/

    392: SLEPC_EXTERN PetscErrorCode BVSVDAndRank(BV,PetscInt,PetscInt,PetscReal,BVSVDMethod,PetscScalar[],PetscReal[],PetscInt*);
    393: SLEPC_EXTERN PetscErrorCode BVCISSResizeBases(BV,BV,BV,PetscInt,PetscInt,PetscInt,PetscInt);

    395: SLEPC_EXTERN PetscErrorCode BVCreateTensor(BV,PetscInt,BV*);
    396: SLEPC_EXTERN PetscErrorCode BVTensorBuildFirstColumn(BV,PetscInt);
    397: SLEPC_EXTERN PetscErrorCode BVTensorCompress(BV,PetscInt);
    398: SLEPC_EXTERN PetscErrorCode BVTensorGetDegree(BV,PetscInt*);
    399: SLEPC_EXTERN PetscErrorCode BVTensorGetFactors(BV,BV*,Mat*);
    400: SLEPC_EXTERN PetscErrorCode BVTensorRestoreFactors(BV,BV*,Mat*);

    402: SLEPC_EXTERN PetscErrorCode BVSetOptionsPrefix(BV,const char[]);
    403: SLEPC_EXTERN PetscErrorCode BVAppendOptionsPrefix(BV,const char[]);
    404: SLEPC_EXTERN PetscErrorCode BVGetOptionsPrefix(BV,const char*[]);

    406: SLEPC_EXTERN PetscFunctionList BVList;
    407: SLEPC_EXTERN PetscErrorCode BVRegister(const char[],PetscErrorCode(*)(BV));