Skip to content

Commit a6c07f6

Browse files
perazzperazz
committed
fix MathJax
1 parent 887f3af commit a6c07f6

File tree

4 files changed

+71
-67
lines changed

4 files changed

+71
-67
lines changed

‎src/stdlib_linalg_blas.fypp

Lines changed: 17 additions & 16 deletions
Original file line numberDiff line numberDiff line change
@@ -1019,16 +1019,16 @@ module stdlib_linalg_blas
10191019

10201020

10211021
interface rotm
1022-
!! ROTM applies the modified Givens transformation, $H$, to the 2-by-N matrix
1023-
!! $\left[ \begin{array}{c}DX^T\\DY^T\\ \end{array} \right]$,
1024-
!! where $^T$ indicates transpose. The elements of $DX$ are in $$
1022+
!! ROTM applies the modified Givens transformation, \(H\), to the 2-by-N matrix
1023+
!! $$ \left[ \begin{array}{c}DX^T\\DY^T\\ \end{array} \right], $$
1024+
!! where \(^T\) indicates transpose. The elements of \(DX\) are in
10251025
!! DX(LX+I*INCX), I = 0:N-1, where LX = 1 if INCX >= 0, else LX = (-INCX)*N,
1026-
!! and similarly for SY using LY and INCY.
1027-
!! With DPARAM(1)=DFLAG, $H$ has one of the following forms:
1028-
!! $H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1029-
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1030-
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1031-
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}.$
1026+
!! and similarly for DY using LY and INCY.
1027+
!! With DPARAM(1)=DFLAG, \(H\) has one of the following forms:
1028+
!! $$ H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1029+
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1030+
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1031+
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}. $$
10321032
!! See ROTMG for a description of data storage in DPARAM.
10331033
#ifdef STDLIB_EXTERNAL_BLAS
10341034
pure subroutine drotm(n,dx,incx,dy,incy,dparam)
@@ -1060,13 +1060,14 @@ module stdlib_linalg_blas
10601060

10611061

10621062
interface rotmg
1063-
!! ROTMG Constructs the modified Givens transformation matrix $H$ which zeros the
1064-
!! second component of the 2-vector $[{\sqrt{DD_1}\cdot DX_1,\sqrt{DD_2}\cdot DY_2}]^T$.
1065-
!! With DPARAM(1)=DFLAG, H has one of the following forms:
1066-
!! $H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1067-
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1068-
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1069-
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}.$
1063+
!! ROTMG Constructs the modified Givens transformation matrix \(H\) which zeros the
1064+
!! second component of the 2-vector
1065+
!! $$ \left[ {\sqrt{DD_1}\cdot DX_1,\sqrt{DD_2}\cdot DY_2} \right]^T. $$
1066+
!! With DPARAM(1)=DFLAG, \(H\) has one of the following forms:
1067+
!! $$ H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1068+
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1069+
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1070+
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}. $$
10701071
!! Locations 2-4 of DPARAM contain DH11, DH21, DH12 and DH22 respectively.
10711072
!! (Values OF 1.0, -1.0, or 0.0 implied by the value of DPARAM(1) are not stored in DPARAM.)
10721073
!! The values of parameters GAMSQ and RGAMSQ may be inexact. This is OK as they are only

‎src/stdlib_linalg_blas_d.fypp

Lines changed: 19 additions & 18 deletions
Original file line numberDiff line numberDiff line change
@@ -1029,17 +1029,17 @@ module stdlib_linalg_blas_d
10291029

10301030

10311031
pure subroutine stdlib_drotm(n,dx,incx,dy,incy,dparam)
1032-
!! DROTM applies the modified Givens transformation, $H$, to the 2-by-N matrix
1033-
!! $\left[ \begin{array}{c}DX^T\\DY^T\\ \end{array} \right]$,
1034-
!! where $^T$ indicates transpose. The elements of $DX$ are in $$
1032+
!! DROTM applies the modified Givens transformation, \(H\), to the 2-by-N matrix
1033+
!! $$ \left[ \begin{array}{c}DX^T\\DY^T\\ \end{array} \right], $$
1034+
!! where \(^T\) indicates transpose. The elements of \(DX\) are in
10351035
!! DX(LX+I*INCX), I = 0:N-1, where LX = 1 if INCX >= 0, else LX = (-INCX)*N,
1036-
!! and similarly for SY using LY and INCY.
1037-
!! With DPARAM(1)=DFLAG, $H$ has one of the following forms:
1038-
!! $H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1039-
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1040-
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1041-
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}.$
1042-
!! See DROTMG for a description of data storage in DPARAM.
1036+
!! and similarly for DY using LY and INCY.
1037+
!! With DPARAM(1)=DFLAG, \(H\) has one of the following forms:
1038+
!! $$ H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1039+
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1040+
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1041+
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}. $$
1042+
!! See DROTMG for a description of data storage in DPARAM.
10431043
! -- reference blas level1 routine --
10441044
! -- reference blas is a software package provided by univ. of tennessee, --
10451045
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
@@ -1136,17 +1136,18 @@ module stdlib_linalg_blas_d
11361136

11371137

11381138
pure subroutine stdlib_drotmg(dd1,dd2,dx1,dy1,dparam)
1139-
!! DROTMG Constructs the modified Givens transformation matrix $H$ which zeros the
1140-
!! second component of the 2-vector $[{\sqrt{DD_1}\cdot DX_1,\sqrt{DD_2}\cdot DY_2}]^T$.
1141-
!! With DPARAM(1)=DFLAG, H has one of the following forms:
1142-
!! $H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1143-
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1144-
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1145-
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=2}.$
1139+
!! DROTMG Constructs the modified Givens transformation matrix \(H\) which zeros the
1140+
!! second component of the 2-vector
1141+
!! $$ \left[ {\sqrt{DD_1}\cdot DX_1,\sqrt{DD_2}\cdot DY_2} \right]^T. $$
1142+
!! With DPARAM(1)=DFLAG, \(H\) has one of the following forms:
1143+
!! $$ H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1144+
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1145+
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1146+
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}. $$
11461147
!! Locations 2-4 of DPARAM contain DH11, DH21, DH12 and DH22 respectively.
11471148
!! (Values OF 1.0, -1.0, or 0.0 implied by the value of DPARAM(1) are not stored in DPARAM.)
11481149
!! The values of parameters GAMSQ and RGAMSQ may be inexact. This is OK as they are only
1149-
!! used for testing the size of DD1 and DD2. All actual scaling of data is done using GAM.
1150+
!! used for testing the size of DD1 and DD2. All actual scaling of data is done using GAM.
11501151
! -- reference blas level1 routine --
11511152
! -- reference blas is a software package provided by univ. of tennessee, --
11521153
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--

‎src/stdlib_linalg_blas_q.fypp

Lines changed: 19 additions & 18 deletions
Original file line numberDiff line numberDiff line change
@@ -1032,17 +1032,17 @@ module stdlib_linalg_blas_q
10321032

10331033

10341034
pure subroutine stdlib_qrotm(n,dx,incx,dy,incy,dparam)
1035-
!! QROTM applies the modified Givens transformation, $H$, to the 2-by-N matrix
1036-
!! $\left[ \begin{array}{c}DX^T\\DY^T\\ \end{array} \right]$,
1037-
!! where $^T$ indicates transpose. The elements of $DX$ are in $$
1035+
!! QROTM applies the modified Givens transformation, \(H\), to the 2-by-N matrix
1036+
!! $$ \left[ \begin{array}{c}DX^T\\DY^T\\ \end{array} \right], $$
1037+
!! where \(^T\) indicates transpose. The elements of \(DX\) are in
10381038
!! DX(LX+I*INCX), I = 0:N-1, where LX = 1 if INCX >= 0, else LX = (-INCX)*N,
1039-
!! and similarly for SY using LY and INCY.
1040-
!! With DPARAM(1)=DFLAG, $H$ has one of the following forms:
1041-
!! $H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1042-
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1043-
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1044-
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}.$
1045-
!! See QROTMG for a description of data storage in DPARAM.
1039+
!! and similarly for DY using LY and INCY.
1040+
!! With DPARAM(1)=DFLAG, \(H\) has one of the following forms:
1041+
!! $$ H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1042+
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1043+
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1044+
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}. $$
1045+
!! See QROTMG for a description of data storage in DPARAM.
10461046
! -- reference blas level1 routine --
10471047
! -- reference blas is a software package provided by univ. of tennessee, --
10481048
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
@@ -1139,17 +1139,18 @@ module stdlib_linalg_blas_q
11391139

11401140

11411141
pure subroutine stdlib_qrotmg(dd1,dd2,dx1,dy1,dparam)
1142-
!! QROTMG Constructs the modified Givens transformation matrix $H$ which zeros the
1143-
!! second component of the 2-vector $[{\sqrt{DD_1}\cdot DX_1,\sqrt{DD_2}\cdot DY_2}]^T$.
1144-
!! With DPARAM(1)=DFLAG, H has one of the following forms:
1145-
!! $H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1146-
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1147-
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1148-
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}.$
1142+
!! QROTMG Constructs the modified Givens transformation matrix \(H\) which zeros the
1143+
!! second component of the 2-vector
1144+
!! $$ \left[ {\sqrt{DD_1}\cdot DX_1,\sqrt{DD_2}\cdot DY_2} \right]^T. $$
1145+
!! With DPARAM(1)=DFLAG, \(H\) has one of the following forms:
1146+
!! $$ H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1},
1147+
!! \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0},
1148+
!! \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1},
1149+
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}. $$
11491150
!! Locations 2-4 of DPARAM contain DH11, DH21, DH12 and DH22 respectively.
11501151
!! (Values OF 1.0, -1.0, or 0.0 implied by the value of DPARAM(1) are not stored in DPARAM.)
11511152
!! The values of parameters GAMSQ and RGAMSQ may be inexact. This is OK as they are only
1152-
!! used for testing the size of DD1 and DD2. All actual scaling of data is done using GAM.
1153+
!! used for testing the size of DD1 and DD2. All actual scaling of data is done using GAM.
11531154
! -- reference blas level1 routine --
11541155
! -- reference blas is a software package provided by univ. of tennessee, --
11551156
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--

‎src/stdlib_linalg_blas_s.fypp

Lines changed: 16 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -1209,16 +1209,16 @@ module stdlib_linalg_blas_s
12091209

12101210

12111211
pure subroutine stdlib_srotm(n,sx,incx,sy,incy,sparam)
1212-
!! SROTM applies the modified Givens transformation, $H$, to the 2-by-N matrix
1213-
!! $\left[ \begin{array}{c}DX^T\\DY^T\\ \end{array} \right]$,
1214-
!! where $^T$ indicates transpose. The elements of $SX$ are in $$
1212+
!! SROTM applies the modified Givens transformation, \(H\), to the 2-by-N matrix
1213+
!! $$ \left[ \begin{array}{c}SX^T\\SY^T\\ \end{array} \right], $$
1214+
!! where \(^T\) indicates transpose. The elements of \(SX\) are in
12151215
!! SX(LX+I*INCX), I = 0:N-1, where LX = 1 if INCX >= 0, else LX = (-INCX)*N,
12161216
!! and similarly for SY using LY and INCY.
1217-
!! With SPARAM(1)=SFLAG, $H$ has one of the following forms:
1218-
!! $H=\underbrace{\begin{bmatrix}SH_{11} & SH_{12}\\SH_{21} & SH_{22}\end{bmatrix}}_{SFLAG=-1},
1219-
!! \underbrace{\begin{bmatrix}1 & SH_{12}\\SH_{21} & 1\end{bmatrix}}_{SFLAG=0},
1220-
!! \underbrace{\begin{bmatrix}SH_{11} & 1\\-1 & SH_{22}\end{bmatrix}}_{SFLAG=1},
1221-
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{SFLAG=-2}.$
1217+
!! With SPARAM(1)=SFLAG, \(H\) has one of the following forms:
1218+
!! $$ H=\underbrace{\begin{bmatrix}SH_{11} & SH_{12}\\SH_{21} & SH_{22}\end{bmatrix}}_{SFLAG=-1},
1219+
!! \underbrace{\begin{bmatrix}1 & SH_{12}\\SH_{21} & 1\end{bmatrix}}_{SFLAG=0},
1220+
!! \underbrace{\begin{bmatrix}SH_{11} & 1\\-1 & SH_{22}\end{bmatrix}}_{SFLAG=1},
1221+
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{SFLAG=-2}. $$
12221222
!! See SROTMG for a description of data storage in SPARAM.
12231223
! -- reference blas level1 routine --
12241224
! -- reference blas is a software package provided by univ. of tennessee, --
@@ -1316,13 +1316,14 @@ module stdlib_linalg_blas_s
13161316

13171317

13181318
pure subroutine stdlib_srotmg(sd1,sd2,sx1,sy1,sparam)
1319-
!! SROTMG Constructs the modified Givens transformation matrix $H$ which zeros the
1320-
!! second component of the 2-vector $[{\sqrt{SD_1}\cdot SX_1,\sqrt{SD_2}\cdot SY_2}]^T$.
1321-
!! With SPARAM(1)=SFLAG, H has one of the following forms:
1322-
!! $H=\underbrace{\begin{bmatrix}SH_{11} & SD_{12}\\SH_{21} & SH_{22}\end{bmatrix}}_{SFLAG=-1},
1323-
!! \underbrace{\begin{bmatrix}1 & SH_{12}\\SH_{21} & 1\end{bmatrix}}_{SFLAG=0},
1324-
!! \underbrace{\begin{bmatrix}SH_{11} & 1\\-1 & SH_{22}\end{bmatrix}}_{SFLAG=1},
1325-
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{SFLAG=2}.$
1319+
!! SROTMG Constructs the modified Givens transformation matrix \(H\) which zeros the
1320+
!! second component of the 2-vector
1321+
!! $$ \left[ {\sqrt{SD_1}\cdot SX_1,\sqrt{SD_2}\cdot SY_2} \right]^T. $$
1322+
!! With SPARAM(1)=SFLAG, \(H\) has one of the following forms:
1323+
!! $$ H=\underbrace{\begin{bmatrix}SH_{11} & SD_{12}\\SH_{21} & SH_{22}\end{bmatrix}}_{SFLAG=-1},
1324+
!! \underbrace{\begin{bmatrix}1 & SH_{12}\\SH_{21} & 1\end{bmatrix}}_{SFLAG=0},
1325+
!! \underbrace{\begin{bmatrix}SH_{11} & 1\\-1 & SH_{22}\end{bmatrix}}_{SFLAG=1},
1326+
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{SFLAG=2}. $$
13261327
!! Locations 2-4 of SPARAM contain SH11, SH21, SH12 and SH22 respectively.
13271328
!! (Values OF 1.0, -1.0, or 0.0 implied by the value of SPARAM(1) are not stored in SPARAM.)
13281329
!! The values of parameters GAMSQ and RGAMSQ may be inexact. This is OK as they are only

0 commit comments

Comments
 (0)