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Rebase on 3.9.0
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Lines changed: 74 additions & 61 deletions

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‎TESTING/EIG/chet21.f‎

Lines changed: 17 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -29,8 +29,9 @@
2929
*>
3030
*> CHET21 generally checks a decomposition of the form
3131
*>
32-
*> A = U S UC>
33-
*> where * means conjugate transpose, A is hermitian, U is unitary, and
32+
*> A = U S U**H
33+
*>
34+
*> where **H means conjugate transpose, A is hermitian, U is unitary, and
3435
*> S is diagonal (if KBAND=0) or (real) symmetric tridiagonal (if
3536
*> KBAND=1).
3637
*>
@@ -42,18 +43,19 @@
4243
*>
4344
*> Specifically, if ITYPE=1, then:
4445
*>
45-
*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp )
46+
*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
47+
*> RESULT(2) = | I - U U**H | / ( n ulp )
4648
*>
4749
*> If ITYPE=2, then:
4850
*>
49-
*> RESULT(1) = | A - V S V* | / ( |A| n ulp )
51+
*> RESULT(1) = | A - V S V**H | / ( |A| n ulp )
5052
*>
5153
*> If ITYPE=3, then:
5254
*>
53-
*> RESULT(1) = | I - UV* | / ( n ulp )
55+
*> RESULT(1) = | I - U V**H | / ( n ulp )
5456
*>
5557
*> For ITYPE > 1, the transformation U is expressed as a product
56-
*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)C> and each
58+
*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)**H and each
5759
*> vector v(j) has its first j elements 0 and the remaining n-j elements
5860
*> stored in V(j+1:n,j).
5961
*> \endverbatim
@@ -66,14 +68,15 @@
6668
*> ITYPE is INTEGER
6769
*> Specifies the type of tests to be performed.
6870
*> 1: U expressed as a dense unitary matrix:
69-
*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp )
71+
*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
72+
*> RESULT(2) = | I - U U**H | / ( n ulp )
7073
*>
7174
*> 2: U expressed as a product V of Housholder transformations:
72-
*> RESULT(1) = | A - V S V* | / ( |A| n ulp )
75+
*> RESULT(1) = | A - V S V**H | / ( |A| n ulp )
7376
*>
7477
*> 3: U expressed both as a dense unitary matrix and
7578
*> as a product of Housholder transformations:
76-
*> RESULT(1) = | I - UV* | / ( n ulp )
79+
*> RESULT(1) = | I - U V**H | / ( n ulp )
7780
*> \endverbatim
7881
*>
7982
*> \param[in] UPLO
@@ -171,7 +174,7 @@
171174
*> \verbatim
172175
*> TAU is COMPLEX array, dimension (N)
173176
*> If ITYPE >= 2, then TAU(j) is the scalar factor of
174-
*> v(j) v(j)* in the Householder transformation H(j) of
177+
*> v(j) v(j)**H in the Householder transformation H(j) of
175178
*> the product U = H(1)...H(n-2)
176179
*> If ITYPE < 2, then TAU is not referenced.
177180
*> \endverbatim
@@ -294,7 +297,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
294297
*
295298
IF( ITYPE.EQ.1 ) THEN
296299
*
297-
* ITYPE=1: error = A - U S U*
300+
* ITYPE=1: error = A - U S U**H
298301
*
299302
CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
300303
CALL CLACPY( CUPLO, N, N, A, LDA, WORK, N )
@@ -304,7 +307,6 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
304307
10 CONTINUE
305308
*
306309
IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
307-
CMK DO 20 J = 1, N - 1
308310
DO 20 J = 2, N - 1
309311
CALL CHER2( CUPLO, N, -CMPLX( E( J ) ), U( 1, J ), 1,
310312
$ U( 1, J-1 ), 1, WORK, N )
@@ -314,7 +316,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
314316
*
315317
ELSE IF( ITYPE.EQ.2 ) THEN
316318
*
317-
* ITYPE=2: error = V S V* - A
319+
* ITYPE=2: error = V S V**H - A
318320
*
319321
CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
320322
*
@@ -371,7 +373,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
371373
*
372374
ELSE IF( ITYPE.EQ.3 ) THEN
373375
*
374-
* ITYPE=3: error = U V* - I
376+
* ITYPE=3: error = U V**H - I
375377
*
376378
IF( N.LT.2 )
377379
$ RETURN
@@ -407,7 +409,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
407409
*
408410
* Do Test 2
409411
*
410-
* Compute UU* - I
412+
* Compute U U**H - I
411413
*
412414
IF( ITYPE.EQ.1 ) THEN
413415
CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,

‎TESTING/EIG/chpt21.f‎

Lines changed: 20 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -29,8 +29,9 @@
2929
*>
3030
*> CHPT21 generally checks a decomposition of the form
3131
*>
32-
*> A = U S UC>
33-
*> where * means conjugate transpose, A is hermitian, U is
32+
*> A = U S U**H
33+
*>
34+
*> where **H means conjugate transpose, A is hermitian, U is
3435
*> unitary, and S is diagonal (if KBAND=0) or (real) symmetric
3536
*> tridiagonal (if KBAND=1). If ITYPE=1, then U is represented as
3637
*> a dense matrix, otherwise the U is expressed as a product of
@@ -41,15 +42,16 @@
4142
*>
4243
*> Specifically, if ITYPE=1, then:
4344
*>
44-
*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp )
45+
*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
46+
*> RESULT(2) = | I - U U**H | / ( n ulp )
4547
*>
4648
*> If ITYPE=2, then:
4749
*>
48-
*> RESULT(1) = | A - V S V* | / ( |A| n ulp )
50+
*> RESULT(1) = | A - V S V**H | / ( |A| n ulp )
4951
*>
5052
*> If ITYPE=3, then:
5153
*>
52-
*> RESULT(1) = | I - UV* | / ( n ulp )
54+
*> RESULT(1) = | I - U V**H | / ( n ulp )
5355
*>
5456
*> Packed storage means that, for example, if UPLO='U', then the columns
5557
*> of the upper triangle of A are stored one after another, so that
@@ -70,14 +72,16 @@
7072
*>
7173
*> If UPLO='U', then V = H(n-1)...H(1), where
7274
*>
73-
*> H(j) = I - tau(j) v(j) v(j)C>
75+
*> H(j) = I - tau(j) v(j) v(j)**H
76+
*>
7477
*> and the first j-1 elements of v(j) are stored in V(1:j-1,j+1),
7578
*> (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ),
7679
*> the j-th element is 1, and the last n-j elements are 0.
7780
*>
7881
*> If UPLO='L', then V = H(1)...H(n-1), where
7982
*>
80-
*> H(j) = I - tau(j) v(j) v(j)C>
83+
*> H(j) = I - tau(j) v(j) v(j)**H
84+
*>
8185
*> and the first j elements of v(j) are 0, the (j+1)-st is 1, and the
8286
*> (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,
8387
*> in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .)
@@ -91,14 +95,15 @@
9195
*> ITYPE is INTEGER
9296
*> Specifies the type of tests to be performed.
9397
*> 1: U expressed as a dense unitary matrix:
94-
*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp )
98+
*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
99+
*> RESULT(2) = | I - U U**H | / ( n ulp )
95100
*>
96101
*> 2: U expressed as a product V of Housholder transformations:
97-
*> RESULT(1) = | A - V S V* | / ( |A| n ulp )
102+
*> RESULT(1) = | A - V S V**H | / ( |A| n ulp )
98103
*>
99104
*> 3: U expressed both as a dense unitary matrix and
100105
*> as a product of Housholder transformations:
101-
*> RESULT(1) = | I - UV* | / ( n ulp )
106+
*> RESULT(1) = | I - U V**H | / ( n ulp )
102107
*> \endverbatim
103108
*>
104109
*> \param[in] UPLO
@@ -181,7 +186,7 @@
181186
*> \verbatim
182187
*> TAU is COMPLEX array, dimension (N)
183188
*> If ITYPE >= 2, then TAU(j) is the scalar factor of
184-
*> v(j) v(j)* in the Householder transformation H(j) of
189+
*> v(j) v(j)**H in the Householder transformation H(j) of
185190
*> the product U = H(1)...H(n-2)
186191
*> If ITYPE < 2, then TAU is not referenced.
187192
*> \endverbatim
@@ -313,7 +318,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP,
313318
*
314319
IF( ITYPE.EQ.1 ) THEN
315320
*
316-
* ITYPE=1: error = A - U S U*
321+
* ITYPE=1: error = A - U S U**H
317322
*
318323
CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
319324
CALL CCOPY( LAP, AP, 1, WORK, 1 )
@@ -332,7 +337,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP,
332337
*
333338
ELSE IF( ITYPE.EQ.2 ) THEN
334339
*
335-
* ITYPE=2: error = V S V* - A
340+
* ITYPE=2: error = V S V**H - A
336341
*
337342
CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
338343
*
@@ -400,7 +405,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP,
400405
*
401406
ELSE IF( ITYPE.EQ.3 ) THEN
402407
*
403-
* ITYPE=3: error = U V* - I
408+
* ITYPE=3: error = U V**H - I
404409
*
405410
IF( N.LT.2 )
406411
$ RETURN
@@ -431,7 +436,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP,
431436
*
432437
* Do Test 2
433438
*
434-
* Compute UU* - I
439+
* Compute U U**H - I
435440
*
436441
IF( ITYPE.EQ.1 ) THEN
437442
CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,

‎TESTING/EIG/zhet21.f‎

Lines changed: 17 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -29,8 +29,9 @@
2929
*>
3030
*> ZHET21 generally checks a decomposition of the form
3131
*>
32-
*> A = U S UC>
33-
*> where * means conjugate transpose, A is hermitian, U is unitary, and
32+
*> A = U S U**H
33+
*>
34+
*> where **H means conjugate transpose, A is hermitian, U is unitary, and
3435
*> S is diagonal (if KBAND=0) or (real) symmetric tridiagonal (if
3536
*> KBAND=1).
3637
*>
@@ -42,18 +43,19 @@
4243
*>
4344
*> Specifically, if ITYPE=1, then:
4445
*>
45-
*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp )
46+
*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
47+
*> RESULT(2) = | I - U U**H | / ( n ulp )
4648
*>
4749
*> If ITYPE=2, then:
4850
*>
49-
*> RESULT(1) = | A - V S V* | / ( |A| n ulp )
51+
*> RESULT(1) = | A - V S V**H | / ( |A| n ulp )
5052
*>
5153
*> If ITYPE=3, then:
5254
*>
53-
*> RESULT(1) = | I - UV* | / ( n ulp )
55+
*> RESULT(1) = | I - U V**H | / ( n ulp )
5456
*>
5557
*> For ITYPE > 1, the transformation U is expressed as a product
56-
*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)C> and each
58+
*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)**H and each
5759
*> vector v(j) has its first j elements 0 and the remaining n-j elements
5860
*> stored in V(j+1:n,j).
5961
*> \endverbatim
@@ -66,14 +68,15 @@
6668
*> ITYPE is INTEGER
6769
*> Specifies the type of tests to be performed.
6870
*> 1: U expressed as a dense unitary matrix:
69-
*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp )
71+
*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
72+
*> RESULT(2) = | I - U U**H | / ( n ulp )
7073
*>
7174
*> 2: U expressed as a product V of Housholder transformations:
72-
*> RESULT(1) = | A - V S V* | / ( |A| n ulp )
75+
*> RESULT(1) = | A - V S V**H | / ( |A| n ulp )
7376
*>
7477
*> 3: U expressed both as a dense unitary matrix and
7578
*> as a product of Housholder transformations:
76-
*> RESULT(1) = | I - UV* | / ( n ulp )
79+
*> RESULT(1) = | I - U V**H | / ( n ulp )
7780
*> \endverbatim
7881
*>
7982
*> \param[in] UPLO
@@ -171,7 +174,7 @@
171174
*> \verbatim
172175
*> TAU is COMPLEX*16 array, dimension (N)
173176
*> If ITYPE >= 2, then TAU(j) is the scalar factor of
174-
*> v(j) v(j)* in the Householder transformation H(j) of
177+
*> v(j) v(j)**H in the Householder transformation H(j) of
175178
*> the product U = H(1)...H(n-2)
176179
*> If ITYPE < 2, then TAU is not referenced.
177180
*> \endverbatim
@@ -294,7 +297,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
294297
*
295298
IF( ITYPE.EQ.1 ) THEN
296299
*
297-
* ITYPE=1: error = A - U S U*
300+
* ITYPE=1: error = A - U S U**H
298301
*
299302
CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
300303
CALL ZLACPY( CUPLO, N, N, A, LDA, WORK, N )
@@ -304,7 +307,6 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
304307
10 CONTINUE
305308
*
306309
IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
307-
CMK DO 20 J = 1, N - 1
308310
DO 20 J = 2, N - 1
309311
CALL ZHER2( CUPLO, N, -DCMPLX( E( J ) ), U( 1, J ), 1,
310312
$ U( 1, J-1 ), 1, WORK, N )
@@ -314,7 +316,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
314316
*
315317
ELSE IF( ITYPE.EQ.2 ) THEN
316318
*
317-
* ITYPE=2: error = V S V* - A
319+
* ITYPE=2: error = V S V**H - A
318320
*
319321
CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
320322
*
@@ -371,7 +373,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
371373
*
372374
ELSE IF( ITYPE.EQ.3 ) THEN
373375
*
374-
* ITYPE=3: error = U V* - I
376+
* ITYPE=3: error = U V**H - I
375377
*
376378
IF( N.LT.2 )
377379
$ RETURN
@@ -407,7 +409,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
407409
*
408410
* Do Test 2
409411
*
410-
* Compute UU* - I
412+
* Compute U U**H - I
411413
*
412414
IF( ITYPE.EQ.1 ) THEN
413415
CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,

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