Parallel Engineering and Scientific Subroutine Library for AIX Version 2 Release 3: Guide and Reference

PDTRAN, PZTRANC, and PZTRANU--Matrix Transpose for a General Matrix

PDTRAN and PZTRANU perform the following matrix computation:

C<--betaC+alphaA^T

PZTRANC performs the following matrix computation:

C<--betaC+alphaA^H

where, in the formula above:

A represents the global general submatrix A_{ia:ia+n-1,
ja:ja+m-1}.

C represents the global general submatrix C_{ic:ic+m-1,
jc:jc+n-1}.

alpha and beta are scalars.

Note:: No data should be moved to form A^T or A^H; that is, the matrix A should always be stored in its untransposed form.

In the following three cases, no computation is performed and the subroutine returns after doing some parameter checking:

m = 0
n = 0
alpha is zero and beta is one.

See references [14] and [15].

Table 53. Data Types

alpha, beta, A, C	Subprogram
Long-precision real	PDTRAN
Long-precision complex	PZTRANC and PZTRANU

Syntax

Fortran	CALL PDTRAN \| PZTRANC \| PZTRANU (`m`, `n`, `alpha`, `a`, `ia`, `ja`, `desc_a`, `beta`, `c`, `ic`, `jc`, `desc_c`)
C and C++	pdtran \| pztranc \| pztranu (`m`, `n`, `alpha`, `a`, `ia`, `ja`, `desc_a`, `beta`, `c`, `ic`, `jc`, `desc_c`);

On Entry

m

is the number of rows in submatrix C and the number of columns in submatrix A used in the computation.

Scope: global

Specified as: a fullword integer; m >= 0.

n

is the number of columns in submatrix C and the number of rows in submatrix A used in the computation.

Scope: global

Specified as: a fullword integer; n >= 0.

alpha

is the scalar alpha.

Scope: global

Specified as: a number of the data type indicated in Table 53.

a

is the local part of the global general matrix A. This identifies the first element of the local array A. This subroutine computes the location of the first element of the local subarray used, based on ia, ja, desc_a, p, q, myrow, and mycol; therefore, the leading LOCp(ia+n-1) by LOCq(ja+m-1) part of the local array A must contain the local pieces of the leading ia+n-1 by ja+m-1 part of the global matrix.

Note:: No data should be moved to form A^T or A^H; that is, the matrix A should always be stored in its untransposed form.

Scope: local

Specified as: an LLD_A by (at least) LOCq(N_A) array, containing numbers of the data type indicated in Table 53. Details about the block-cyclic data distribution of global matrix A are stored in desc_a.

ia

is the row index of the global matrix A, identifying the first row of the submatrix A.

Scope: global

Specified as: a fullword integer; 1 <= ia <= M_A and ia+n-1 <= M_A.

ja

is the column index of the global matrix A, identifying the first column of the submatrix A.

Scope: global

Specified as: a fullword integer; 1 <= ja <= N_A and ja+m-1 <= N_A.

desc_a

is the array descriptor for global matrix A, described in the following table:

`desc_a`	Name	Description	Limits	Scope
1	DTYPE_A	Descriptor type	DTYPE_A=1	Global
2	CTXT_A	BLACS context	Valid value, as returned by BLACS_GRIDINIT or BLACS_GRIDMAP	Global
3	M_A	Number of rows in the global matrix	If `m` = 0 or `n` = 0: M_A >= 0 Otherwise: M_A >= 1	Global
4	N_A	Number of columns in the global matrix	If `m` = 0 or `n` = 0: N_A >= 0 Otherwise: N_A >= 1	Global
5	MB_A	Row block size	MB_A >= 1	Global
6	NB_A	Column block size	NB_A >= 1	Global
7	RSRC_A	The process row of the `p` × `q` grid over which the first row of the global matrix is distributed	0 <= RSRC_A < `p`	Global
8	CSRC_A	The process column of the `p` × `q` grid over which the first column of the global matrix is distributed	0 <= CSRC_A < `q`	Global
9	LLD_A	The leading dimension of the local array	LLD_A >= max(1,LOCp(M_A))	Local

Specified as: an array of (at least) length 9, containing fullword integers.

beta

is the scalar beta.

Scope: global

Specified as: a number of the data type indicated in Table 53.

c

is the local part of the global general matrix C. This identifies the first element of the local array C. This subroutine computes the location of the first element of the local subarray used, based on ic, jc, desc_c, p, q, myrow, and mycol; therefore, the leading LOCp(ic+m-1) by LOCq(jc+n-1) part of the local array C must contain the local pieces of the leading ic+m-1 by jc+n-1 part of the global matrix.

When beta is zero, C need not be set on input.

Scope: local

Specified as: an LLD_C by (at least) LOCq(N_C) array, containing numbers of the data type indicated in Table 53. Details about the block-cyclic data distribution of global matrix C are stored in desc_c.

ic

is the row index of the global matrix C, identifying the first row of the submatrix C.

Scope: global

Specified as: a fullword integer; 1 <= ic <= M_C and ic+m-1 <= M_C.

jc

is the column index of the global matrix C, identifying the first column of the submatrix C.

Scope: global

Specified as: a fullword integer; 1 <= jc <= N_C and jc+n-1 <= N_C.

desc_c

is the array descriptor for global matrix C, described in the following table:

`desc_c`	Name	Description	Limits	Scope
1	DTYPE_C	Descriptor type	DTYPE_C=1	Global
2	CTXT_C	BLACS context	Valid value, as returned by BLACS_GRIDINIT or BLACS_GRIDMAP	Global
3	M_C	Number of rows in the global matrix	If `m` = 0 or `n` = 0: M_C >= 0 Otherwise: M_C >= 1	Global
4	N_C	Number of columns in the global matrix	If `m` = 0 or `n` = 0: N_C >= 0 Otherwise: N_C >= 1	Global
5	MB_C	Row block size	MB_C >= 1	Global
6	NB_C	Column block size	NB_C >= 1	Global
7	RSRC_C	The process row of the `p` × `q` grid over which the first row of the global matrix is distributed	0 <= RSRC_C < `p`	Global
8	CSRC_C	The process column of the `p` × `q` grid over which the first column of the global matrix is distributed	0 <= CSRC_C < `q`	Global
9	LLD_C	The leading dimension of the local array	LLD_C >= max(1,LOCp(M_C))	Local

Specified as: an array of (at least) length 9, containing fullword integers.

On Return

c

is the updated local part of the global general matrix C, containing the results of the computation.

Scope: local

Returned as: an LLD_C by (at least) LOCq(N_C) array, containing numbers of the data type indicated in Table 53.

Notes and Coding Rules

The matrices must have no common elements; otherwise, results are unpredictable.
The NUMROC utility subroutine can be used to determine the values of LOCp(M_) and LOCq(N_) used in the argument descriptions above. For details, see Determining the Number of Rows and Columns in Your Local Arrays and NUMROC--Compute the Number of Rows or Columns of a Block-Cyclically Distributed Matrix Contained in a Process.
For suggested block sizes, see Coding Tips for Optimizing Parallel Performance.
The following values must be equal: CTXT_A = CTXT_C.
The coding rules (given in this section) and the error conditions (given in the next section) are written in terms of adist. To determine a value for adist, check the following conditions, in order, and chose the first value having a true condition:
1. If A is a block column matrix, that is:
  
  m+mod(ja-1, NB_A) <= NB_A
  
  then adist = 'C'
2. If A is a block row matrix, that is:
  
  n+mod(ia-1, MB_A) <= MB_A
  
  then adist = 'R'
3. If A is neither a block column or a block row matrix, then:
  - If m <= n, then adist = 'C'.
  - Otherwise, adist = 'R'.
If adist = 'C', then you must follow these coding rules:
- A must be aligned on a block row boundary, that is:
  
  ia-1 must be a multiple of MB_A.
- C must be aligned on a block column boundary, that is:
  
  jc-1 must be a multiple of NB_C.
- MB_A = NB_C
- If looping is required--that is, either of the following is true:
  
  m+mod(ja-1, NB_A) > NB_A
  m+mod(ic-1, MB_C) > MB_C
  
  then:
  - The block column offset of A must be equal to the block row offset of C; that is, mod(ja-1, NB_A) = mod(ic-1, MB_C).
  - NB_A = MB_C
If adist = 'R', then you must follow these coding rules:
- A must be aligned on a block column boundary, that is:
  
  ja-1 must be a multiple of NB_A.
- C must be aligned on a block row boundary, that is:
  
  ic-1 must be a multiple of MB_C.
- NB_A = MB_C
- If looping is required--that is, either of the following is true:
  
  n+mod(ia-1, MB_A) > MB_A
  n+mod(jc-1, NB_C) > NB_C
  
  then:
  - The block row offset of A must be equal to the block column offset of C; that is, mod(ia-1, MB_A) = mod(jc-1, NB_C).
  - MB_A = NB_C

DTYPE_A is invalid.
DTYPE_C is invalid.

Stage 2:

CTXT_A is invalid.

Stage 3:

This subroutine was called from outside the process grid.

Stage 4:

m < 0
n < 0
M_A < 0 and (m = 0 or n = 0); M_A < 1 otherwise
N_A < 0 and (m = 0 or n = 0); N_A < 1 otherwise
MB_A < 1
NB_A < 1
RSRC_A < 0 or RSRC_A >= p
CSRC_A < 0 or CSRC_A >= q
ia < 1
ja < 1
M_C < 0 and (m = 0 or n = 0); M_C < 1 otherwise
N_C < 0 and (m = 0 or n = 0); N_C < 1 otherwise
MB_C < 1
NB_C < 1
RSRC_C < 0 or RSRC_C >= p
CSRC_C < 0 or CSRC_C >= q
ic < 1
jc < 1
CTXT_A <> CTXT_C

Stage 5:

Note:: Some of the following error conditions depend on the value of adist--that is, adist = 'C' or or adist = 'R'. For details on determining the value, see Notes and Coding Rules.

If m <> 0 and n <> 0:

ia > M_A
ja > N_A
ia+n-1 > M_A
ja+m-1 > N_A
ic > M_C
jc > N_C
ic+m-1 > M_C
jc+n-1 > N_C

If adist = 'C':

mod(ia-1, MB_A) <> 0
mod(jc-1, NB_C) <> 0
MB_A <> NB_C
If looping is required--that is, either of the following is true:

m+mod(ja-1, NB_A) > NB_A
m+mod(ic-1, MB_C) > MB_C

then:
1. mod(ja-1, NB_A) <> mod(ic-1, MB_C)
2. NB_A <> MB_C.

If adist = 'R':

mod(ja-1, NB_A) <> 0
mod(ic-1, MB_C) <> 0
NB_A <> MB_C
If looping is required--that is, either of the following is true:

n+mod(ia-1, MB_A) > MB_A
n+mod(jc-1, NB_C) > NB_C

then:
1. mod(ia-1, MB_A) <> mod(jc-1, NB_C)
2. MB_A <> NB_C.

Stage 6:

LLD_A < max(1, LOCp(M_A))
LLD_C < max(1, LOCp(M_C))

Example 1

This example computes C = betaC+alphaA^T using a 2 × 2 process grid.

Call Statements and Input

ORDER = 'R'
NPROW = 2
NPCOL = 2
CALL BLACS_GET (0, 0, ICONTXT)
CALL BLACS_GRIDINIT(ICONTXT, ORDER, NPROW, NPCOL)
CALL BLACS_GRIDINFO(ICONTXT, NPROW, NPCOL, MYROW, MYCOL)
 
              M    N     ALPHA    A  IA  JA    DESC_A    BETA    C  IC  JC   DESC_C
              |    |       |      |   |   |      |         |     |   |   |     |
CALL PDTRAN(  9  , 8  ,  1.0D0  , A , 1 , 1 ,  DESC_A ,  1.0D0 , C , 1 , 1 , DESC_C )

	Desc_A	Desc_C
DTYPE_	1	1
CTXT_	`icontxt`^(IOBG32)	`icontxt`^(IOBG32)
M_	8	9
N_	9	8
MB_	2	4
NB_	4	2
RSRC_	0	0
CSRC_	0	0
LLD_	See below^(EPSSL32)	See below^(EPSSL32)
Notes: `icontxt` is the output of the BLACS_GRIDINIT call. Each process should set the LLD_ as follows: LLD_A = MAX(1,NUMROC(M_A, MB_A, MYROW, RSRC_A, NPROW)) LLD_C = MAX(1,NUMROC(M_C, MB_C, MYROW, RSRC_C, NPROW)) In this example, LLD_A = 4 on all processes, LLD_C = 5 on P₀₀ and P₀₁, and LLD_C = 4 on P₁₀ and P₁₁.

Global general 8 × 9 matrix A with block size 2 × 4:

B,D             0                       1               2
     *                                                      *
 0   |  0.0 -1.0 -1.0  0.0  |   0.0  0.0  0.0  0.0  |   1.0 |
     |  0.0  1.0  0.0  1.0  |   0.0  1.0  0.0  1.0  |   1.0 |
     | ---------------------|-----------------------|------ |
 1   |  0.0  0.0 -1.0 -1.0  |   0.0  0.0  1.0  0.0  |   1.0 |
     |  0.0  1.0  0.0 -1.0  |   1.0  1.0  0.0  1.0  |   1.0 |
     | ---------------------|-----------------------|------ |
 2   |  1.0  0.0  0.0  0.0  |  -1.0  0.0  0.0  0.0  |   1.0 |
     |  1.0  0.0  0.0  0.0  |   1.0  1.0  0.0  0.0  |   1.0 |
     | ---------------------|-----------------------|------ |
 3   |  0.0  0.0 -1.0  0.0  |  -1.0  0.0  0.0  0.0  |   1.0 |
     | -1.0  0.0  0.0  0.0  |   0.0  0.0 -1.0  0.0  |   1.0 |
     *                                                      *

The following is the 2 × 2 process grid:

B,D  |  0 2  | 1 
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁
3    |       |

Local arrays for A:

p,q  |            0              |           1
-----|---------------------------|----------------------
     |  0.0 -1.0 -1.0  0.0  1.0  |   0.0  0.0  0.0  0.0
     |  0.0  1.0  0.0  1.0  1.0  |   0.0  1.0  0.0  1.0
 0   |  1.0  0.0  0.0  0.0  1.0  |  -1.0  0.0  0.0  0.0
     |  1.0  0.0  0.0  0.0  1.0  |   1.0  1.0  0.0  0.0
-----|---------------------------|----------------------
     |  0.0  0.0 -1.0 -1.0  1.0  |   0.0  0.0  1.0  0.0
     |  0.0  1.0  0.0 -1.0  1.0  |   1.0  1.0  0.0  1.0
 1   |  0.0  0.0 -1.0  0.0  1.0  |  -1.0  0.0  0.0  0.0
     | -1.0  0.0  0.0  0.0  1.0  |   0.0  0.0 -1.0  0.0

Global general 9 × 8 matrix C with block size 4 × 2:

B,D        0             1             2             3
     *                                                     *
     |  0.0  1.0  |   1.0  5.0  |   6.0  7.0  |   8.0  9.0 |
     |  0.0 -1.0  |   0.0 -1.0  |   0.0 -1.0  |   0.0  1.0 |
 0   |  0.0  0.0  |   1.0  1.0  |   0.0  0.0  |  -1.0  0.0 |
     |  0.0 -1.0  |   0.0  1.0  |  -1.0 -1.0  |   0.0  1.0 |
     | -----------|-------------|-------------|----------- |
     | -1.0  2.0  |   0.0  0.0  |   1.0  0.0  |   0.0  0.0 |
     | -1.0  3.0  |   0.0  0.0  |  -1.0 -1.0  |   0.0  0.0 |
 1   |  0.0  4.0  |   1.0  0.0  |   1.0  0.0  |   0.0  0.0 |
     |  1.0  5.0  |   0.0  0.0  |   0.0  0.0  |   1.0  0.0 |
     | -----------|-------------|-------------|----------- |
 2   |  1.0  2.0  |   3.0  4.0  |   1.0  1.0  |   1.0  1.0 |
     *                                                     *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁

Local arrays for C:

p,q  |          0           |           1
-----|----------------------|----------------------
     |  0.0  1.0  6.0  7.0  |   1.0  5.0  8.0  9.0
     |  0.0 -1.0  0.0 -1.0  |   0.0 -1.0  0.0  1.0
 0   |  0.0  0.0  0.0  0.0  |   1.0  1.0 -1.0  0.0
     |  0.0 -1.0 -1.0 -1.0  |   0.0  1.0  0.0  1.0
     |  1.0  2.0  1.0  1.0  |   3.0  4.0  1.0  1.0
-----|----------------------|----------------------
     | -1.0  2.0  1.0  0.0  |   0.0  0.0  0.0  0.0
     | -1.0  3.0 -1.0 -1.0  |   0.0  0.0  0.0  0.0
 1   |  0.0  4.0  1.0  0.0  |   1.0  0.0  0.0  0.0
     |  1.0  5.0  0.0  0.0  |   0.0  0.0  1.0  0.0

Output:

Global general 9 × 8 matrix C with block size 4 × 2:

B,D        0             1             2             3
     *                                                     *
     |  0.0  1.0  |   1.0  5.0  |   7.0  8.0  |   8.0  8.0 |
     | -1.0  0.0  |   0.0  0.0  |   0.0 -1.0  |   0.0  1.0 |
 0   | -1.0  0.0  |   0.0  1.0  |   0.0  0.0  |  -2.0  0.0 |
     |  0.0  0.0  |  -1.0  0.0  |  -1.0 -1.0  |   0.0  1.0 |
     | -----------|-------------|-------------|----------- |
     | -1.0  2.0  |   0.0  1.0  |   0.0  1.0  |  -1.0  0.0 |
     | -1.0  4.0  |   0.0  1.0  |  -1.0  0.0  |   0.0  0.0 |
 1   |  0.0  4.0  |   2.0  0.0  |   1.0  0.0  |   0.0 -1.0 |
     |  1.0  6.0  |   0.0  1.0  |   0.0  0.0  |   1.0  0.0 |
     | -----------|-------------|-------------|----------- |
 2   |  2.0  3.0  |   4.0  5.0  |   2.0  2.0  |   2.0  2.0 |
     *                                                     *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁

Local arrays for C:

p,q  |          0           |           1
-----|----------------------|----------------------
     |  0.0  1.0  7.0  8.0  |   1.0  5.0  8.0  8.0
     | -1.0  0.0  0.0 -1.0  |   0.0  0.0  0.0  1.0
 0   | -1.0  0.0  0.0  0.0  |   0.0  1.0 -2.0  0.0
     |  0.0  0.0 -1.0 -1.0  |  -1.0  0.0  0.0  1.0
     |  2.0  3.0  2.0  2.0  |   4.0  5.0  2.0  2.0
-----|----------------------|----------------------
     | -1.0  2.0  0.0  1.0  |   0.0  1.0 -1.0  0.0
     | -1.0  4.0 -1.0  0.0  |   0.0  1.0  0.0  0.0
 1   |  0.0  4.0  1.0  0.0  |   2.0  0.0  0.0 -1.0
     |  1.0  6.0  0.0  0.0  |   0.0  1.0  1.0  0.0

Example 2

This example computes C = betaC+alphaA^H using a 2 × 2 process grid.

Call Statements and Input

ORDER = 'R'
NPROW = 2
NPCOL = 2
CALL BLACS_GET (0, 0, ICONTXT)
CALL BLACS_GRIDINIT(ICONTXT, ORDER, NPROW, NPCOL)
CALL BLACS_GRIDINFO(ICONTXT, NPROW, NPCOL, MYROW, MYCOL)
 
               M    N     ALPHA    A  IA  JA    DESC_A    BETA    C  IC  JC   DESC_C
               |    |       |      |   |   |      |         |     |   |   |     |
CALL PZTRANC(  7  , 8  ,  ALPHA  , A , 1 , 1 ,  DESC_A ,  BETA  , C , 1 , 1 , DESC_C )
 
               ALPHA = (1.0,0.0)
 
               BETA  = (1.0,0.0)

	Desc_A	Desc_C
DTYPE_	1	1
CTXT_	`icontxt`^(IOBG33)	`icontxt`^(IOBG33)
M_	8	7
N_	7	8
MB_	2	3
NB_	3	2
RSRC_	0	0
CSRC_	0	0
LLD_	See below^(EPSSL33)	See below^(EPSSL33)
Notes: `icontxt` is the output of the BLACS_GRIDINIT call. Each process should set the LLD_ as follows: LLD_A = MAX(1,NUMROC(M_A, MB_A, MYROW, RSRC_A, NPROW)) LLD_C = MAX(1,NUMROC(M_C, MB_C, MYROW, RSRC_C, NPROW)) In this example, LLD_A = 4 on all processes, LLD_C = 4 on P₀₀ and P₀₁, and LLD_C = 3 on P₁₀ and P₁₁.

Global general 8 × 7 matrix A with block size 2 × 3:

B,D                     0                                     1                         2
     *                                                                                         *
 0   | ( 0.0, 1.0) (-1.0, 0.0) (-1.0, 0.0) | ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) |
     | ( 0.0, 1.0) ( 1.0, 2.0) ( 0.0, 1.0) | ( 1.0, 2.0) ( 0.0, 1.0) ( 1.0, 2.0) | ( 0.0, 1.0) |
     | ------------------------------------|-------------------------------------|------------ |
 1   | ( 0.0, 1.0) ( 0.0, 1.0) (-1.0, 0.0) | (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 1.0, 2.0) |
     | ( 0.0, 1.0) ( 1.0, 2.0) ( 0.0, 1.0) | (-1.0, 0.0) ( 1.0, 2.0) ( 1.0, 2.0) | ( 0.0, 1.0) |
     | ------------------------------------|-------------------------------------|------------ |
 2   | ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) (-1.0, 0.0) ( 0.0, 1.0) | ( 0.0, 1.0) |
     | ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 1.0, 2.0) ( 1.0, 2.0) | ( 0.0, 1.0) |
     | ------------------------------------|-------------------------------------|------------ |
 3   | ( 0.0, 1.0) ( 0.0, 1.0) (-1.0, 0.0) | ( 0.0, 1.0) (-1.0, 0.0) ( 0.0, 1.0) | ( 0.0, 1.0) |
     | (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0) | (-1.0, 0.0) |
     *                                                                                         *

The following is the 2 × 2 process grid:

B,D  |  0 2  | 1 
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁
3    |       |

Local arrays for A:

p,q  |                        0                        |                  1 
-----|-------------------------------------------------|------------------------------------
     | ( 0.0, 1.0) (-1.0, 0.0) (-1.0, 0.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0)
     | ( 0.0, 1.0) ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 1.0, 2.0) ( 0.0, 1.0) ( 1.0, 2.0)
 0   | ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) (-1.0, 0.0) ( 0.0, 1.0)
     | ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 1.0, 2.0) ( 1.0, 2.0)
-----|-------------------------------------------------|------------------------------------
     | ( 0.0, 1.0) ( 0.0, 1.0) (-1.0, 0.0) ( 1.0, 2.0) | (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0)
     | ( 0.0, 1.0) ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) | (-1.0, 0.0) ( 1.0, 2.0) ( 1.0, 2.0)
 1   | ( 0.0, 1.0) ( 0.0, 1.0) (-1.0, 0.0) ( 0.0, 1.0) | ( 0.0, 1.0) (-1.0, 0.0) ( 0.0, 1.0)
     | (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0) (-1.0, 0.0) | ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0)

Global general 7 × 8 matrix C with block size 3 × 2:

B,D               0                         1                         2                         3
     *                                                                                                       *
     | ( 0.0,-2.0) ( 1.0,-1.0) | ( 1.0,-1.0) ( 5.0, 3.0) | ( 6.0, 4.0) ( 7.0, 5.0) | ( 8.0, 6.0) ( 9.0, 7.0) |
 0   | ( 1.0,-1.0) (-1.0,-3.0) | ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 1.0,-1.0) |
     | ( 2.0, 0.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 1.0,-1.0) | ( 2.0, 0.0) ( 3.0, 1.0) | (-1.0,-3.0) ( 0.0,-2.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | ( 3.0, 1.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 1.0,-1.0) | (-1.0,-3.0) (-1.0,-3.0) | ( 3.0, 1.0) ( 1.0,-1.0) |
 1   | (-1.0,-3.0) ( 2.0, 0.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 1.0,-1.0) | ( 2.0, 0.0) ( 0.0,-2.0) |
     | (-1.0,-3.0) ( 3.0, 1.0) | ( 0.0,-2.0) ( 0.0,-2.0) | (-1.0,-3.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
 2   | ( 5.0, 3.0) ( 4.0, 2.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
     *                                                                                                       *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁

Local arrays for C:

p,q  |                        0                        |                  1 
-----|-------------------------------------------------|------------------------------------------------
     | ( 0.0,-2.0) ( 1.0,-1.0) ( 6.0, 4.0) ( 7.0, 5.0) | ( 1.0,-1.0) ( 5.0, 3.0) ( 8.0, 6.0) ( 9.0, 7.0)
     | ( 1.0,-1.0) (-1.0,-3.0) ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) (-1.0,-3.0) ( 0.0,-2.0) ( 1.0,-1.0)
 0   | ( 2.0, 0.0) ( 0.0,-2.0) ( 2.0, 0.0) ( 3.0, 1.0) | ( 1.0,-1.0) ( 1.0,-1.0) (-1.0,-3.0) ( 0.0,-2.0)
     | ( 5.0, 3.0) ( 4.0, 2.0) ( 1.0,-1.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0)
-----|-------------------------------------------------|------------------------------------------------
     | ( 3.0, 1.0) (-1.0,-3.0) (-1.0,-3.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 1.0,-1.0) ( 3.0, 1.0) ( 1.0,-1.0)
 1   | (-1.0,-3.0) ( 2.0, 0.0) ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 2.0, 0.0) ( 0.0,-2.0)
     | (-1.0,-3.0) ( 3.0, 1.0) (-1.0,-3.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0)

Output:

Global general 7 × 8 matrix C with block size 3 × 2:

B,D               0                         1                         2                         3
     *                                                                                                       *
     | ( 0.0,-3.0) ( 1.0,-2.0) | ( 1.0,-2.0) ( 5.0, 2.0) | ( 7.0, 2.0) ( 8.0, 3.0) | ( 8.0, 5.0) ( 8.0, 7.0) |
 0   | ( 0.0,-1.0) ( 0.0,-5.0) | ( 0.0,-3.0) ( 0.0,-5.0) | ( 0.0,-3.0) (-1.0,-4.0) | ( 0.0,-3.0) ( 1.0,-2.0) |
     | ( 1.0, 0.0) ( 0.0,-3.0) | ( 0.0,-1.0) ( 1.0,-2.0) | ( 2.0,-1.0) ( 3.0, 0.0) | (-2.0,-3.0) ( 0.0,-3.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | ( 3.0, 0.0) ( 0.0,-5.0) | (-1.0,-2.0) ( 0.0,-1.0) | (-1.0,-4.0) (-1.0,-4.0) | ( 3.0, 0.0) ( 1.0,-2.0) |
 1   | (-1.0,-4.0) ( 2.0,-1.0) | ( 0.0,-3.0) ( 1.0,-4.0) | ( 0.0,-1.0) ( 2.0,-3.0) | ( 1.0, 0.0) ( 0.0,-3.0) |
     | (-1.0,-4.0) ( 4.0,-1.0) | ( 0.0,-3.0) ( 1.0,-4.0) | (-1.0,-4.0) ( 0.0,-5.0) | ( 0.0,-3.0) ( 0.0,-3.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
 2   | ( 5.0, 2.0) ( 4.0, 1.0) | ( 2.0,-3.0) ( 0.0,-3.0) | ( 1.0,-2.0) ( 0.0,-3.0) | ( 0.0,-3.0) (-1.0,-2.0) |
     *                                                                                                       *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁

Local arrays for C:

p,q  |                        0                        |                  1 
-----|-------------------------------------------------|------------------------------------------------
     | ( 0.0,-3.0) ( 1.0,-2.0) ( 7.0, 2.0) ( 8.0, 3.0) | ( 1.0,-2.0) ( 5.0, 2.0) ( 8.0, 5.0) ( 8.0, 7.0)
     | ( 0.0,-1.0) ( 0.0,-5.0) ( 0.0,-3.0) (-1.0,-4.0) | ( 0.0,-3.0) ( 0.0,-5.0) ( 0.0,-3.0) ( 1.0,-2.0)
 0   | ( 1.0, 0.0) ( 0.0,-3.0) ( 2.0,-1.0) ( 3.0, 0.0) | ( 0.0,-1.0) ( 1.0,-2.0) (-2.0,-3.0) ( 0.0,-3.0)
     | ( 5.0, 2.0) ( 4.0, 1.0) ( 1.0,-2.0) ( 0.0,-3.0) | ( 2.0,-3.0) ( 0.0,-3.0) ( 0.0,-3.0) (-1.0,-2.0)
-----|-------------------------------------------------|------------------------------------------------
     | ( 3.0, 0.0) ( 0.0,-5.0) (-1.0,-4.0) (-1.0,-4.0) | (-1.0,-2.0) ( 0.0,-1.0) ( 3.0, 0.0) ( 1.0,-2.0)
 1   | (-1.0,-4.0) ( 2.0,-1.0) ( 0.0,-1.0) ( 2.0,-3.0) | ( 0.0,-3.0) ( 1.0,-4.0) ( 1.0, 0.0) ( 0.0,-3.0)
     | (-1.0,-4.0) ( 4.0,-1.0) (-1.0,-4.0) ( 0.0,-5.0) | ( 0.0,-3.0) ( 1.0,-4.0) ( 0.0,-3.0) ( 0.0,-3.0)

Example 3

This example computes C = betaC+alphaA^T using a 2 × 2 process grid.

Call Statements and Input

ORDER = 'R'
NPROW = 2
NPCOL = 2
CALL BLACS_GET (0, 0, ICONTXT)
CALL BLACS_GRIDINIT(ICONTXT, ORDER, NPROW, NPCOL)
CALL BLACS_GRIDINFO(ICONTXT, NPROW, NPCOL, MYROW, MYCOL)
 
               M    N     ALPHA    A  IA  JA    DESC_A    BETA    C  IC  JC   DESC_C
               |    |       |      |   |   |      |         |     |   |   |     |
CALL PZTRANU(  7  , 8  ,  ALPHA  , A , 1 , 1 ,  DESC_A ,  BETA  , C , 1 , 1 , DESC_C )
 
               ALPHA = (1.0,0.0)
 
               BETA  = (1.0,0.0)

	Desc_A	Desc_C
DTYPE_	1	1
CTXT_	`icontxt`^(IOBG34)	`icontxt`^(IOBG34)
M_	8	7
N_	7	8
MB_	2	3
NB_	3	2
RSRC_	0	0
CSRC_	0	0
LLD_	See below^(EPSSL34)	See below^(EPSSL34)
Notes: `icontxt` is the output of the BLACS_GRIDINIT call. Each process should set the LLD_ as follows: LLD_A = MAX(1,NUMROC(M_A, MB_A, MYROW, RSRC_A, NPROW)) LLD_C = MAX(1,NUMROC(M_C, MB_C, MYROW, RSRC_C, NPROW)) In this example, LLD_A = 4 on all processes, LLD_C = 4 on P₀₀ and P₀₁, and LLD_C = 3 on P₁₀ and P₁₁.

Global general 8 × 7 matrix A with block size 2 × 3:

B,D                     0                                     1                         2
     *                                                                                         *
 0   | ( 0.0, 1.0) (-1.0, 0.0) (-1.0, 0.0) | ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) |
     | ( 0.0, 1.0) ( 1.0, 2.0) ( 0.0, 1.0) | ( 1.0, 2.0) ( 0.0, 1.0) ( 1.0, 2.0) | ( 0.0, 1.0) |
     | ------------------------------------|-------------------------------------|------------ |
 1   | ( 0.0, 1.0) ( 0.0, 1.0) (-1.0, 0.0) | (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 1.0, 2.0) |
     | ( 0.0, 1.0) ( 1.0, 2.0) ( 0.0, 1.0) | (-1.0, 0.0) ( 1.0, 2.0) ( 1.0, 2.0) | ( 0.0, 1.0) |
     | ------------------------------------|-------------------------------------|------------ |
 2   | ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) (-1.0, 0.0) ( 0.0, 1.0) | ( 0.0, 1.0) |
     | ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 1.0, 2.0) ( 1.0, 2.0) | ( 0.0, 1.0) |
     | ------------------------------------|-------------------------------------|------------ |
 3   | ( 0.0, 1.0) ( 0.0, 1.0) (-1.0, 0.0) | ( 0.0, 1.0) (-1.0, 0.0) ( 0.0, 1.0) | ( 0.0, 1.0) |
     | (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0) | (-1.0, 0.0) |
     *                                                                                         *

The following is the 2 × 2 process grid:

B,D  |  0 2  | 1 
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁
3    |       |

Local arrays for A:

p,q  |                        0                        |                  1 
-----|-------------------------------------------------|------------------------------------
     | ( 0.0, 1.0) (-1.0, 0.0) (-1.0, 0.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0)
     | ( 0.0, 1.0) ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 1.0, 2.0) ( 0.0, 1.0) ( 1.0, 2.0)
 0   | ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) (-1.0, 0.0) ( 0.0, 1.0)
     | ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 1.0, 2.0) ( 1.0, 2.0)
-----|-------------------------------------------------|------------------------------------
     | ( 0.0, 1.0) ( 0.0, 1.0) (-1.0, 0.0) ( 1.0, 2.0) | (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0)
     | ( 0.0, 1.0) ( 1.0, 2.0) ( 0.0, 1.0) ( 0.0, 1.0) | (-1.0, 0.0) ( 1.0, 2.0) ( 1.0, 2.0)
 1   | ( 0.0, 1.0) ( 0.0, 1.0) (-1.0, 0.0) ( 0.0, 1.0) | ( 0.0, 1.0) (-1.0, 0.0) ( 0.0, 1.0)
     | (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0) (-1.0, 0.0) | ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0)

Global general 7 × 8 matrix C with block size 3 × 2:

B,D               0                         1                         2                         3
     *                                                                                                       *
     | ( 0.0,-2.0) ( 1.0,-1.0) | ( 1.0,-1.0) ( 5.0, 3.0) | ( 6.0, 4.0) ( 7.0, 5.0) | ( 8.0, 6.0) ( 9.0, 7.0) |
 0   | ( 1.0,-1.0) (-1.0,-3.0) | ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 1.0,-1.0) |
     | ( 2.0, 0.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 1.0,-1.0) | ( 2.0, 0.0) ( 3.0, 1.0) | (-1.0,-3.0) ( 0.0,-2.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | ( 3.0, 1.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 1.0,-1.0) | (-1.0,-3.0) (-1.0,-3.0) | ( 3.0, 1.0) ( 1.0,-1.0) |
 1   | (-1.0,-3.0) ( 2.0, 0.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 1.0,-1.0) | ( 2.0, 0.0) ( 0.0,-2.0) |
     | (-1.0,-3.0) ( 3.0, 1.0) | ( 0.0,-2.0) ( 0.0,-2.0) | (-1.0,-3.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
 2   | ( 5.0, 3.0) ( 4.0, 2.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
     *                                                                                                       *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁

Local arrays for C:

p,q  |                        0                        |                  1 
-----|-------------------------------------------------|------------------------------------------------
     | ( 0.0,-2.0) ( 1.0,-1.0) ( 6.0, 4.0) ( 7.0, 5.0) | ( 1.0,-1.0) ( 5.0, 3.0) ( 8.0, 6.0) ( 9.0, 7.0)
     | ( 1.0,-1.0) (-1.0,-3.0) ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) (-1.0,-3.0) ( 0.0,-2.0) ( 1.0,-1.0)
 0   | ( 2.0, 0.0) ( 0.0,-2.0) ( 2.0, 0.0) ( 3.0, 1.0) | ( 1.0,-1.0) ( 1.0,-1.0) (-1.0,-3.0) ( 0.0,-2.0)
     | ( 5.0, 3.0) ( 4.0, 2.0) ( 1.0,-1.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0)
-----|-------------------------------------------------|------------------------------------------------
     | ( 3.0, 1.0) (-1.0,-3.0) (-1.0,-3.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 1.0,-1.0) ( 3.0, 1.0) ( 1.0,-1.0)
 1   | (-1.0,-3.0) ( 2.0, 0.0) ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 2.0, 0.0) ( 0.0,-2.0)
     | (-1.0,-3.0) ( 3.0, 1.0) (-1.0,-3.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0)

Output:

Global general 7 × 8 matrix C with block size 3 × 2:

B,D               0                         1                         2                         3
     *                                                                                                       *
     | ( 0.0,-1.0) ( 1.0, 0.0) | ( 1.0, 0.0) ( 5.0, 4.0) | ( 7.0, 6.0) ( 8.0, 7.0) | ( 8.0, 7.0) ( 8.0, 7.0) |
 0   | ( 0.0,-1.0) ( 0.0,-1.0) | ( 0.0,-1.0) ( 0.0,-1.0) | ( 0.0,-1.0) (-1.0,-2.0) | ( 0.0,-1.0) ( 1.0, 0.0) |
     | ( 1.0, 0.0) ( 0.0,-1.0) | ( 0.0,-1.0) ( 1.0, 0.0) | ( 2.0, 1.0) ( 3.0, 2.0) | (-2.0,-3.0) ( 0.0,-1.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | ( 3.0, 2.0) ( 0.0,-1.0) | (-1.0,-2.0) ( 0.0,-1.0) | (-1.0,-2.0) (-1.0,-2.0) | ( 3.0, 2.0) ( 1.0, 0.0) |
 1   | (-1.0,-2.0) ( 2.0, 1.0) | ( 0.0,-1.0) ( 1.0, 0.0) | ( 0.0,-1.0) ( 2.0, 1.0) | ( 1.0, 0.0) ( 0.0,-1.0) |
     | (-1.0,-2.0) ( 4.0, 3.0) | ( 0.0,-1.0) ( 1.0, 0.0) | (-1.0,-2.0) ( 0.0,-1.0) | ( 0.0,-1.0) ( 0.0,-1.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
 2   | ( 5.0, 4.0) ( 4.0, 3.0) | ( 2.0, 1.0) ( 0.0,-1.0) | ( 1.0, 0.0) ( 0.0,-1.0) | ( 0.0,-1.0) (-1.0,-2.0) |
     *                                                                                                       *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁

Local arrays for C:

p,q  |                        0                        |                  1 
-----|-------------------------------------------------|------------------------------------------------
     | ( 0.0,-1.0) ( 1.0, 0.0) ( 7.0, 6.0) ( 8.0, 7.0) | ( 1.0, 0.0) ( 5.0, 4.0) ( 8.0, 7.0) ( 8.0, 7.0)
     | ( 0.0,-1.0) ( 0.0,-1.0) ( 0.0,-1.0) (-1.0,-2.0) | ( 0.0,-1.0) ( 0.0,-1.0) ( 0.0,-1.0) ( 1.0, 0.0)
 0   | ( 1.0, 0.0) ( 0.0,-1.0) ( 2.0, 1.0) ( 3.0, 2.0) | ( 0.0,-1.0) ( 1.0, 0.0) (-2.0,-3.0) ( 0.0,-1.0)
     | ( 5.0, 4.0) ( 4.0, 3.0) ( 1.0, 0.0) ( 0.0,-1.0) | ( 2.0, 1.0) ( 0.0,-1.0) ( 0.0,-1.0) (-1.0,-2.0)
-----|-------------------------------------------------|------------------------------------------------
     | ( 3.0, 2.0) ( 0.0,-1.0) (-1.0,-2.0) (-1.0,-2.0) | (-1.0,-2.0) ( 0.0,-1.0) ( 3.0, 2.0) ( 1.0, 0.0)
 1   | (-1.0,-2.0) ( 2.0, 1.0) ( 0.0,-1.0) ( 2.0, 1.0) | ( 0.0,-1.0) ( 1.0, 0.0) ( 1.0, 0.0) ( 0.0,-1.0)
     | (-1.0,-2.0) ( 4.0, 3.0) (-1.0,-2.0) ( 0.0,-1.0) | ( 0.0,-1.0) ( 1.0, 0.0) ( 0.0,-1.0) ( 0.0,-1.0)

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Parallel Engineering and Scientific Subroutine Library for AIX Version 2 Release 3: Guide and Reference

PDTRAN, PZTRANC, and PZTRANU--Matrix Transpose for a General Matrix

Syntax

On Entry

On Return

Notes and Coding Rules

Error Conditions

Computational Errors

Resource Errors

Input-Argument and Miscellaneous Errors

Example 1

Call Statements and Input

Example 2

Call Statements and Input

Example 3

Call Statements and Input