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6 Commits

Author SHA1 Message Date
Andrew Kane
0d8cc82908 Added HnswQuery struct [skip ci] 2024-02-04 22:30:59 -08:00
Andrew Kane
2716a223a6 Fixed error with ANALYZE and vectors with different dimensions - fixes #451 2024-02-02 10:47:48 -08:00
Andrew Kane
3697043898 Added note about vacuuming - closes #450 [skip ci] 2024-01-31 14:35:27 -08:00
Andrew Kane
c22740962c Added note for Docker [skip ci] 2024-01-29 15:33:29 -08:00
Andrew Kane
a55ecf3281 Updated changelog [skip ci] 2024-01-29 11:20:33 -08:00
Andrew Kane
fecdd5794e Updated readme [skip ci] 2024-01-29 10:57:54 -08:00
8 changed files with 138 additions and 26 deletions

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@@ -1,10 +1,14 @@
## 0.6.1 (unreleased)
- Fixed error with `ANALYZE` and vectors with different dimensions
## 0.6.0 (2024-01-29) ## 0.6.0 (2024-01-29)
If upgrading with Postgres 12 or Docker, see [these notes](https://github.com/pgvector/pgvector#060). If upgrading with Postgres 12 or Docker, see [these notes](https://github.com/pgvector/pgvector#060).
- Changed storage for vector from `extended` to `external`
- Added support for parallel index builds for HNSW - Added support for parallel index builds for HNSW
- Added validation for GUC parameters - Added validation for GUC parameters
- Changed storage for vector from `extended` to `external`
- Improved performance of HNSW - Improved performance of HNSW
- Reduced memory usage for HNSW index builds - Reduced memory usage for HNSW index builds
- Reduced WAL generation for HNSW index builds - Reduced WAL generation for HNSW index builds

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@@ -16,7 +16,7 @@ Plus [ACID](https://en.wikipedia.org/wiki/ACID) compliance, point-in-time recove
### Linux and Mac ### Linux and Mac
Compile and install the extension (supports Postgres 11+) Compile and install the extension (supports Postgres 12+)
```sh ```sh
cd /tmp cd /tmp
@@ -430,6 +430,15 @@ To speed up queries with an IVFFlat index, increase the number of inverted lists
CREATE INDEX ON items USING ivfflat (embedding vector_l2_ops) WITH (lists = 1000); CREATE INDEX ON items USING ivfflat (embedding vector_l2_ops) WITH (lists = 1000);
``` ```
## Vacuuming
Vacuuming can take a while for HNSW indexes. Speed it up by reindexing first.
```sql
REINDEX INDEX CONCURRENTLY index_name;
VACUUM table_name;
```
## Languages ## Languages
Use pgvector from any language with a Postgres client. You can even generate and store vectors in one language and query them in another. Use pgvector from any language with a Postgres client. You can even generate and store vectors in one language and query them in another.
@@ -657,7 +666,7 @@ Get the [Docker image](https://hub.docker.com/r/pgvector/pgvector) with:
docker pull pgvector/pgvector:pg16 docker pull pgvector/pgvector:pg16
``` ```
This adds pgvector to the [Postgres image](https://hub.docker.com/_/postgres) (run it the same way). This adds pgvector to the [Postgres image](https://hub.docker.com/_/postgres) (replace `16` with your Postgres server version, and run it the same way).
You can also build the image manually: You can also build the image manually:

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@@ -362,6 +362,11 @@ typedef struct HnswVacuumState
MemoryContext tmpCtx; MemoryContext tmpCtx;
} HnswVacuumState; } HnswVacuumState;
typedef struct HnswQuery
{
Datum value;
} HnswQuery;
/* Methods */ /* Methods */
int HnswGetM(Relation index); int HnswGetM(Relation index);
int HnswGetEfConstruction(Relation index); int HnswGetEfConstruction(Relation index);
@@ -370,14 +375,14 @@ bool HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * re
Buffer HnswNewBuffer(Relation index, ForkNumber forkNum); Buffer HnswNewBuffer(Relation index, ForkNumber forkNum);
void HnswInitPage(Buffer buf, Page page); void HnswInitPage(Buffer buf, Page page);
void HnswInit(void); void HnswInit(void);
List *HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement); List *HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement);
HnswElement HnswGetEntryPoint(Relation index); HnswElement HnswGetEntryPoint(Relation index);
void HnswGetMetaPageInfo(Relation index, int *m, HnswElement * entryPoint); void HnswGetMetaPageInfo(Relation index, int *m, HnswElement * entryPoint);
void *HnswAlloc(HnswAllocator * allocator, Size size); void *HnswAlloc(HnswAllocator * allocator, Size size);
HnswElement HnswInitElement(char *base, ItemPointer tid, int m, double ml, int maxLevel, HnswAllocator * alloc); HnswElement HnswInitElement(char *base, ItemPointer tid, int m, double ml, int maxLevel, HnswAllocator * alloc);
HnswElement HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno); HnswElement HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno);
void HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing); void HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing);
HnswCandidate *HnswEntryCandidate(char *base, HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadVec); HnswCandidate *HnswEntryCandidate(char *base, HnswElement em, HnswQuery * q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadVec);
void HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum, bool building); void HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum, bool building);
void HnswSetNeighborTuple(char *base, HnswNeighborTuple ntup, HnswElement e, int m); void HnswSetNeighborTuple(char *base, HnswNeighborTuple ntup, HnswElement e, int m);
void HnswAddHeapTid(HnswElement element, ItemPointer heaptid); void HnswAddHeapTid(HnswElement element, ItemPointer heaptid);
@@ -385,7 +390,7 @@ void HnswInitNeighbors(char *base, HnswElement element, int m, HnswAllocator *
bool HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull, ItemPointer heap_tid, bool building); bool HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull, ItemPointer heap_tid, bool building);
void HnswUpdateNeighborsOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting, bool building); void HnswUpdateNeighborsOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting, bool building);
void HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHeaptids, bool loadVec); void HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHeaptids, bool loadVec);
void HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec); void HnswLoadElement(HnswElement element, float *distance, HnswQuery * q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec);
void HnswSetElementTuple(char *base, HnswElementTuple etup, HnswElement element); void HnswSetElementTuple(char *base, HnswElementTuple etup, HnswElement element);
void HnswUpdateConnection(char *base, HnswElement element, HnswCandidate * hc, int lm, int lc, int *updateIdx, Relation index, FmgrInfo *procinfo, Oid collation); void HnswUpdateConnection(char *base, HnswElement element, HnswCandidate * hc, int lm, int lc, int *updateIdx, Relation index, FmgrInfo *procinfo, Oid collation);
void HnswLoadNeighbors(HnswElement element, Relation index, int m); void HnswLoadNeighbors(HnswElement element, Relation index, int m);

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@@ -11,7 +11,7 @@
* Algorithm 5 from paper * Algorithm 5 from paper
*/ */
static List * static List *
GetScanItems(IndexScanDesc scan, Datum q) GetScanItems(IndexScanDesc scan, Datum value)
{ {
HnswScanOpaque so = (HnswScanOpaque) scan->opaque; HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
Relation index = scan->indexRelation; Relation index = scan->indexRelation;
@@ -22,6 +22,9 @@ GetScanItems(IndexScanDesc scan, Datum q)
int m; int m;
HnswElement entryPoint; HnswElement entryPoint;
char *base = NULL; char *base = NULL;
HnswQuery q;
q.value = value;
/* Get m and entry point */ /* Get m and entry point */
HnswGetMetaPageInfo(index, &m, &entryPoint); HnswGetMetaPageInfo(index, &m, &entryPoint);
@@ -29,15 +32,15 @@ GetScanItems(IndexScanDesc scan, Datum q)
if (entryPoint == NULL) if (entryPoint == NULL)
return NIL; return NIL;
ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, procinfo, collation, false)); ep = list_make1(HnswEntryCandidate(base, entryPoint, &q, index, procinfo, collation, false));
for (int lc = entryPoint->level; lc >= 1; lc--) for (int lc = entryPoint->level; lc >= 1; lc--)
{ {
w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, false, NULL); w = HnswSearchLayer(base, &q, ep, 1, lc, index, procinfo, collation, m, false, NULL);
ep = w; ep = w;
} }
return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL); return HnswSearchLayer(base, &q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL);
} }
/* /*

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@@ -555,7 +555,7 @@ HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHe
* Load an element and optionally get its distance from q * Load an element and optionally get its distance from q
*/ */
void void
HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec) HnswLoadElement(HnswElement element, float *distance, HnswQuery * q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec)
{ {
Buffer buf; Buffer buf;
Page page; Page page;
@@ -575,7 +575,7 @@ HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index,
/* Calculate distance */ /* Calculate distance */
if (distance != NULL) if (distance != NULL)
*distance = (float) DatumGetFloat8(FunctionCall2Coll(procinfo, collation, *q, PointerGetDatum(&etup->data))); *distance = (float) DatumGetFloat8(FunctionCall2Coll(procinfo, collation, q->value, PointerGetDatum(&etup->data)));
UnlockReleaseBuffer(buf); UnlockReleaseBuffer(buf);
} }
@@ -584,19 +584,19 @@ HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index,
* Get the distance for a candidate * Get the distance for a candidate
*/ */
static float static float
GetCandidateDistance(char *base, HnswCandidate * hc, Datum q, FmgrInfo *procinfo, Oid collation) GetCandidateDistance(char *base, HnswCandidate * hc, HnswQuery * q, FmgrInfo *procinfo, Oid collation)
{ {
HnswElement hce = HnswPtrAccess(base, hc->element); HnswElement hce = HnswPtrAccess(base, hc->element);
Datum value = HnswGetValue(base, hce); Datum value = HnswGetValue(base, hce);
return DatumGetFloat8(FunctionCall2Coll(procinfo, collation, q, value)); return DatumGetFloat8(FunctionCall2Coll(procinfo, collation, q->value, value));
} }
/* /*
* Create a candidate for the entry point * Create a candidate for the entry point
*/ */
HnswCandidate * HnswCandidate *
HnswEntryCandidate(char *base, HnswElement entryPoint, Datum q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec) HnswEntryCandidate(char *base, HnswElement entryPoint, HnswQuery * q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec)
{ {
HnswCandidate *hc = palloc(sizeof(HnswCandidate)); HnswCandidate *hc = palloc(sizeof(HnswCandidate));
@@ -604,7 +604,7 @@ HnswEntryCandidate(char *base, HnswElement entryPoint, Datum q, Relation index,
if (index == NULL) if (index == NULL)
hc->distance = GetCandidateDistance(base, hc, q, procinfo, collation); hc->distance = GetCandidateDistance(base, hc, q, procinfo, collation);
else else
HnswLoadElement(entryPoint, &hc->distance, &q, index, procinfo, collation, loadVec); HnswLoadElement(entryPoint, &hc->distance, q, index, procinfo, collation, loadVec);
return hc; return hc;
} }
@@ -722,7 +722,7 @@ CountElement(char *base, HnswElement skipElement, HnswCandidate * hc)
* Algorithm 2 from paper * Algorithm 2 from paper
*/ */
List * List *
HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement) HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement)
{ {
List *w = NIL; List *w = NIL;
pairingheap *C = pairingheap_allocate(CompareNearestCandidates, NULL); pairingheap *C = pairingheap_allocate(CompareNearestCandidates, NULL);
@@ -806,7 +806,7 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
if (index == NULL) if (index == NULL)
eDistance = GetCandidateDistance(base, e, q, procinfo, collation); eDistance = GetCandidateDistance(base, e, q, procinfo, collation);
else else
HnswLoadElement(eElement, &eDistance, &q, index, procinfo, collation, inserting); HnswLoadElement(eElement, &eDistance, q, index, procinfo, collation, inserting);
Assert(!eElement->deleted); Assert(!eElement->deleted);
@@ -1091,7 +1091,9 @@ HnswUpdateConnection(char *base, HnswElement element, HnswCandidate * hc, int lm
/* Load elements on insert */ /* Load elements on insert */
if (index != NULL) if (index != NULL)
{ {
Datum q = HnswGetValue(base, hce); HnswQuery q;
q.value = HnswGetValue(base, hce);
for (int i = 0; i < currentNeighbors->length; i++) for (int i = 0; i < currentNeighbors->length; i++)
{ {
@@ -1101,7 +1103,7 @@ HnswUpdateConnection(char *base, HnswElement element, HnswCandidate * hc, int lm
if (HnswPtrIsNull(base, hc3Element->value)) if (HnswPtrIsNull(base, hc3Element->value))
HnswLoadElement(hc3Element, &hc3->distance, &q, index, procinfo, collation, true); HnswLoadElement(hc3Element, &hc3->distance, &q, index, procinfo, collation, true);
else else
hc3->distance = GetCandidateDistance(base, hc3, q, procinfo, collation); hc3->distance = GetCandidateDistance(base, hc3, &q, procinfo, collation);
/* Prune element if being deleted */ /* Prune element if being deleted */
if (hc3Element->heaptidsLength == 0) if (hc3Element->heaptidsLength == 0)
@@ -1201,9 +1203,11 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
List *w; List *w;
int level = element->level; int level = element->level;
int entryLevel; int entryLevel;
Datum q = HnswGetValue(base, element); HnswQuery q;
HnswElement skipElement = existing ? element : NULL; HnswElement skipElement = existing ? element : NULL;
q.value = HnswGetValue(base, element);
#if PG_VERSION_NUM >= 130000 #if PG_VERSION_NUM >= 130000
/* Precompute hash */ /* Precompute hash */
if (index == NULL) if (index == NULL)
@@ -1215,13 +1219,13 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
return; return;
/* Get entry point and level */ /* Get entry point and level */
ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, procinfo, collation, true)); ep = list_make1(HnswEntryCandidate(base, entryPoint, &q, index, procinfo, collation, true));
entryLevel = entryPoint->level; entryLevel = entryPoint->level;
/* 1st phase: greedy search to insert level */ /* 1st phase: greedy search to insert level */
for (int lc = entryLevel; lc >= level + 1; lc--) for (int lc = entryLevel; lc >= level + 1; lc--)
{ {
w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, true, skipElement); w = HnswSearchLayer(base, &q, ep, 1, lc, index, procinfo, collation, m, true, skipElement);
ep = w; ep = w;
} }
@@ -1239,7 +1243,7 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
List *neighbors; List *neighbors;
List *lw; List *lw;
w = HnswSearchLayer(base, q, ep, efConstruction, lc, index, procinfo, collation, m, true, skipElement); w = HnswSearchLayer(base, &q, ep, efConstruction, lc, index, procinfo, collation, m, true, skipElement);
/* Elements being deleted or skipped can help with search */ /* Elements being deleted or skipped can help with search */
/* but should be removed before selecting neighbors */ /* but should be removed before selecting neighbors */

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@@ -866,9 +866,10 @@ vector_mul(PG_FUNCTION_ARGS)
int int
vector_cmp_internal(Vector * a, Vector * b) vector_cmp_internal(Vector * a, Vector * b)
{ {
CheckDims(a, b); int dim = Min(a->dim, b->dim);
for (int i = 0; i < a->dim; i++) /* Check values before dimensions to be consistent with Postgres arrays */
for (int i = 0; i < dim; i++)
{ {
if (a->x[i] < b->x[i]) if (a->x[i] < b->x[i])
return -1; return -1;
@@ -876,6 +877,13 @@ vector_cmp_internal(Vector * a, Vector * b)
if (a->x[i] > b->x[i]) if (a->x[i] > b->x[i])
return 1; return 1;
} }
if (a->dim < b->dim)
return -1;
if (a->dim > b->dim)
return 1;
return 0; return 0;
} }
@@ -889,6 +897,9 @@ vector_lt(PG_FUNCTION_ARGS)
Vector *a = PG_GETARG_VECTOR_P(0); Vector *a = PG_GETARG_VECTOR_P(0);
Vector *b = PG_GETARG_VECTOR_P(1); Vector *b = PG_GETARG_VECTOR_P(1);
/* TODO Remove in 0.7.0 */
CheckDims(a, b);
PG_RETURN_BOOL(vector_cmp_internal(a, b) < 0); PG_RETURN_BOOL(vector_cmp_internal(a, b) < 0);
} }
@@ -902,6 +913,9 @@ vector_le(PG_FUNCTION_ARGS)
Vector *a = PG_GETARG_VECTOR_P(0); Vector *a = PG_GETARG_VECTOR_P(0);
Vector *b = PG_GETARG_VECTOR_P(1); Vector *b = PG_GETARG_VECTOR_P(1);
/* TODO Remove in 0.7.0 */
CheckDims(a, b);
PG_RETURN_BOOL(vector_cmp_internal(a, b) <= 0); PG_RETURN_BOOL(vector_cmp_internal(a, b) <= 0);
} }
@@ -915,6 +929,9 @@ vector_eq(PG_FUNCTION_ARGS)
Vector *a = PG_GETARG_VECTOR_P(0); Vector *a = PG_GETARG_VECTOR_P(0);
Vector *b = PG_GETARG_VECTOR_P(1); Vector *b = PG_GETARG_VECTOR_P(1);
/* TODO Remove in 0.7.0 */
CheckDims(a, b);
PG_RETURN_BOOL(vector_cmp_internal(a, b) == 0); PG_RETURN_BOOL(vector_cmp_internal(a, b) == 0);
} }
@@ -928,6 +945,9 @@ vector_ne(PG_FUNCTION_ARGS)
Vector *a = PG_GETARG_VECTOR_P(0); Vector *a = PG_GETARG_VECTOR_P(0);
Vector *b = PG_GETARG_VECTOR_P(1); Vector *b = PG_GETARG_VECTOR_P(1);
/* TODO Remove in 0.7.0 */
CheckDims(a, b);
PG_RETURN_BOOL(vector_cmp_internal(a, b) != 0); PG_RETURN_BOOL(vector_cmp_internal(a, b) != 0);
} }
@@ -941,6 +961,9 @@ vector_ge(PG_FUNCTION_ARGS)
Vector *a = PG_GETARG_VECTOR_P(0); Vector *a = PG_GETARG_VECTOR_P(0);
Vector *b = PG_GETARG_VECTOR_P(1); Vector *b = PG_GETARG_VECTOR_P(1);
/* TODO Remove in 0.7.0 */
CheckDims(a, b);
PG_RETURN_BOOL(vector_cmp_internal(a, b) >= 0); PG_RETURN_BOOL(vector_cmp_internal(a, b) >= 0);
} }
@@ -954,6 +977,9 @@ vector_gt(PG_FUNCTION_ARGS)
Vector *a = PG_GETARG_VECTOR_P(0); Vector *a = PG_GETARG_VECTOR_P(0);
Vector *b = PG_GETARG_VECTOR_P(1); Vector *b = PG_GETARG_VECTOR_P(1);
/* TODO Remove in 0.7.0 */
CheckDims(a, b);
PG_RETURN_BOOL(vector_cmp_internal(a, b) > 0); PG_RETURN_BOOL(vector_cmp_internal(a, b) > 0);
} }

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@@ -24,6 +24,56 @@ SELECT '[1e37]'::vector * '[1e37]';
ERROR: value out of range: overflow ERROR: value out of range: overflow
SELECT '[1e-37]'::vector * '[1e-37]'; SELECT '[1e-37]'::vector * '[1e-37]';
ERROR: value out of range: underflow ERROR: value out of range: underflow
SELECT '[1,2,3]'::vector = '[1,2,3]';
?column?
----------
t
(1 row)
SELECT '[1,2,3]'::vector = '[1,2]';
ERROR: different vector dimensions 3 and 2
SELECT vector_cmp('[1,2,3]', '[1,2,3]');
vector_cmp
------------
0
(1 row)
SELECT vector_cmp('[1,2,3]', '[0,0,0]');
vector_cmp
------------
1
(1 row)
SELECT vector_cmp('[0,0,0]', '[1,2,3]');
vector_cmp
------------
-1
(1 row)
SELECT vector_cmp('[1,2]', '[1,2,3]');
vector_cmp
------------
-1
(1 row)
SELECT vector_cmp('[1,2,3]', '[1,2]');
vector_cmp
------------
1
(1 row)
SELECT vector_cmp('[1,2]', '[2,3,4]');
vector_cmp
------------
-1
(1 row)
SELECT vector_cmp('[2,3]', '[1,2,3]');
vector_cmp
------------
1
(1 row)
SELECT vector_dims('[1,2,3]'); SELECT vector_dims('[1,2,3]');
vector_dims vector_dims
------------- -------------

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@@ -6,6 +6,17 @@ SELECT '[1,2,3]'::vector * '[4,5,6]';
SELECT '[1e37]'::vector * '[1e37]'; SELECT '[1e37]'::vector * '[1e37]';
SELECT '[1e-37]'::vector * '[1e-37]'; SELECT '[1e-37]'::vector * '[1e-37]';
SELECT '[1,2,3]'::vector = '[1,2,3]';
SELECT '[1,2,3]'::vector = '[1,2]';
SELECT vector_cmp('[1,2,3]', '[1,2,3]');
SELECT vector_cmp('[1,2,3]', '[0,0,0]');
SELECT vector_cmp('[0,0,0]', '[1,2,3]');
SELECT vector_cmp('[1,2]', '[1,2,3]');
SELECT vector_cmp('[1,2,3]', '[1,2]');
SELECT vector_cmp('[1,2]', '[2,3,4]');
SELECT vector_cmp('[2,3]', '[1,2,3]');
SELECT vector_dims('[1,2,3]'); SELECT vector_dims('[1,2,3]');
SELECT round(vector_norm('[1,1]')::numeric, 5); SELECT round(vector_norm('[1,1]')::numeric, 5);